Environmental Risk Assessment

and Adaptive Management Implementation

in Lake Simcoe, Ontario

by

Alexey Neumann

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Geography University of Toronto

© Copyright by Alexey Neumann (2014)

ii

Environmental Risk Assessment and Adaptive Management

Implementation in Lake Simcoe, Ontario

Doctor of Philosophy Degree, 2014

Alexey Neumann

Department of Geography University of Toronto

Abstract

Addressing the problems of low deep-water oxygen concentrations and impairment of cold-water

fish habitats in Lake Simcoe as a case study of a dimictic mesotrophic lake requires reduction of

external phosphorus (P) loading. However, the efficiency of restoration efforts can be hindered

by persistent internal P loading. This thesis develops a series of ecological and biogeochemical

models, aiming at advancing our understanding of internal P recycling mechanisms in

mesotrophic dimictic lakes. Special emphasis is given to sediment diagenesis processes and their

interplay with the water column, macrophyte-mediated P retention, and the nutrient nearshore

shunt induced by dreissenids. First, a continuous Bayesian network is presented to investigate the

cause-effect relationships among physical conditions, ambient nutrient concentrations, and

plankton dynamics. P sediment internal loading is subsequently quantified with a reactive-

transport simulation model of the transformation of P binding forms. Sediment dynamics are

then assessed under conditions of varying organic matter sedimentation and hypolimnetic oxygen

levels. Finally, an integrated P mass-balance model is used to elucidate the internal P fluxes

stemming from sediments, macrophytes and dreissenids. The model predicts that P diffusive

fluxes from the sediments account for less than 30-35% of the exogenous P loading in Lake

Simcoe. In the post-dreissenid invasion era, the limited decrease of the ice-free TP

iii

concentrations is indicative of the presence of active nutrient recycling pathways, potentially

magnified by the particular morphological features and hydrodynamic patterns of Lake Simcoe,

which counterbalance the direct effects of dreissenid filtration.

iv

Acknowledgments

First of all, I would like to express my profound gratitude to my scientific advisor, Prof. Dr.

George B. Arhonditsis for overwhelming scientific inspiration, guidance and support of my

research.

Secondly, I am deeply thankful to Prof. Dr. Maria Dittrich for scientific guidance in sediment

diagenesis projects as well as Prof. Dr. Miriam Diamond, Prof. Dr. Mathew Wells and Prof.

Dr. Steven Chapra for being members of my dissertation committee.

Thirdly, I would like to thank all my colleagues from Ecological Modelling Lab and

Biogeochemical Lab from Department of Physical and Environmental Sciences whose assistance

was invaluable for the successful completion of my dissertation.

I wish to thank my colleagues: Eavan O’Connor from Lake Simcoe Region Conservation

Authority, Dr. Hamdi Jarjanazi from Ontario Ministry of Environment and Dr. Gertrud Nürnberg

for their cordial support with data.

I would like to acknowledge funding sources of my research: the Natural Sciences and

Engineering Research Council (NSERC), the Ontario Graduate Scholarship Program (OGS) and

a University of Toronto Fellowship.

Finally, I express sincere gratitude to my family: Dmitri and Lana, Leonidas and Riva, Isaac,

Zoey and Nicholas. Thank you for all you did for me. Special gratitude to my wife, Victoria, and

her family who always supported my studies and research.

v

Table of Contents

Contents

Acknowledgments .......................................................................................................................... iv

Table of Contents ............................................................................................................................ v

List of Tables ............................................................................................................................... viii

List of Figures ................................................................................................................................ ix

List of Appendices ....................................................................................................................... xiii

Chapter 1 INTRODUCTION .......................................................................................................... 1

References .................................................................................................................................. 5

Chapter 2 A BAYESIAN NETWORK FOR STUDYING THE CAUSAL LINKS BETWEEN PHOSPHORUS LOADING AND PLANKTON PATTERNS IN LAKE SIMCOE, ONTARIO, CANADA.............................................................................................. 7

2.1. Introduction ......................................................................................................................... 7

2.2. Methods ............................................................................................................................... 9

2.2.1. Study site ................................................................................................................. 9

2.2.2. Model description ................................................................................................. 10

2.3. Results ............................................................................................................................... 14

2.4. Discussion ......................................................................................................................... 17

2.5. References ......................................................................................................................... 23

Chapter 3 DYNAMICS OF P-BINDING FORMS IN SEDIMENTS OF A MESOTROPHIC HARD-WATER LAKE: INSIGHTS FROM NON-STEADY STATE REACTIVE-TRANSPORT MODELLING, SENSITIVITY AND IDENTIFIABILITY ANALYSIS ....... 32

3.1. Introduction ....................................................................................................................... 32

3.2. Material and Methods ....................................................................................................... 34

3.2.1. Study site ............................................................................................................... 34

3.2.2. Model Formulation ............................................................................................... 35

vi

3.2.3. Sensitivity and identifiability analysis .................................................................. 39

3.2.4. Numerical Implementation ................................................................................... 41

3.3. Results ............................................................................................................................... 42

3.3.1. Depth profiles of solids and dissolved substances ................................................ 42

3.3.2. Depth profiles of phosphorus in sediments ........................................................... 43

3.3.3. Seasonal versus long-term dynamics of P binding forms at the sediment surface ................................................................................................................... 44

3.4. Discussion: which processes impact the dynamics of P binding forms in sediments ...... 46

3.4.1. Oxygen and pH at the sediment water interface and composition of settling matter .................................................................................................................... 47

3.4.2. Sedimentation of calcium carbonates and P adsorption and binding to carbonates ............................................................................................................. 47

3.4.3. Parameters of minor sensitivities .......................................................................... 48

3.4.4. Identifiability analysis ........................................................................................... 48

3.5. Conclusions ....................................................................................................................... 52

3.6. References ......................................................................................................................... 55

Chapter 4 THE EFFECTS OF SEDIMENT DIAGENESIS ON HYPOLIMNETIC DISSOLVED OXYGEN DYNAMICS IN MESOTROPHIC LAKE SIMCOE, ONTARIO, CANADA ............................................................................................................. 86

4.1. Introduction ....................................................................................................................... 86

4.2. Methods ............................................................................................................................. 89

4.2.1. Site description ...................................................................................................... 89

4.2.2. Data ....................................................................................................................... 89

4.2.3. Diagenetic model formulation .............................................................................. 90

4.2.4. Sensitivity and uncertainty analysis ...................................................................... 92

4.2.5. Description of scenarios ........................................................................................ 93

4.3. Results ............................................................................................................................... 94

4.3.1. Sensitivity analysis of sediment depth profiles ..................................................... 94

vii

4.3.2. Modelling experiments ......................................................................................... 95

4.3.3. Modelling of SOD ................................................................................................. 96

4.4. Discussion ......................................................................................................................... 97

4.4.1. Effects of boundary conditions on seasonal dynamics of O2 depth profiles ........ 97

4.4.2. Analysis of factors impacting on P dynamics ....................................................... 99

4.4.3. Impact of organic matter sedimentation and hypolimnetic O2 on SOD ............. 101

4.5. Conclusions ..................................................................................................................... 103

4.6. References ....................................................................................................................... 106

Chapter 5 EXAMINATION OF THE ROLE OF DREISSENIDS AND MACROPHYTES IN THE PHOSPHORUS DYNAMICS OF LAKE SIMCOE, ONTARIO, CANADA .............. 129

5.1. Introduction ..................................................................................................................... 129

5.2. Methods ........................................................................................................................... 131

5.2.1. Site description - Dataset .................................................................................... 131

5.2.2. Model description ............................................................................................... 133

5.3. Results ............................................................................................................................. 137

5.4. Discussion ....................................................................................................................... 141

5.5. Acknowledgements ......................................................................................................... 148

5.6. References ....................................................................................................................... 149

Chapter 6 CONCLUSIONS ........................................................................................................ 169

Appendix A ................................................................................................................................. 181

Appendix B ................................................................................................................................. 210

Appendix C ................................................................................................................................. 213

viii

List of Tables

3-1. State variables of the model 62

3-2. Diagenetic reactions in the model 63

3-3a. Process rates of reactions in the model 64

3-3b. Stoichiometric composition of settled organic matter 65

3-4. Parameters used in the sediment model 66

3-5. Ranking of relative sensitivities of model with respect to 37 model parameters 71

3-6. Collinearity indices for selected parameter subsets 72

4-1. Model sediment oxygen consumption pathways 113

4-2a. Limnological characteristics at stations K45, K42 and C9 in Lake Simcoe 114

4-2b. Scenarios Boundary conditions at stations K45, K42 and C9 in Lake Simcoe 114

4-3a. Local sensitivity analysis results for the state variables O2 , Xorg and HPO4- 115

4-3b. Local sensitivity analysis results for the state variables Xorg 116

4-3c. Local sensitivity analysis results for the state variables HPO4 117

4-4. Contribution of the different pathways of sediment oxygen demand in different sediment

layers (site K45) 118

5-1. Forcing functions of exogenous loading, intersegment flow and mass exchanges, model

estimates of settling P fluxes. 157

5-2. Goodness-of-fit statistics for TP predictions based on root-mean-squared error

(RMSE), average error (AE), and relative error (RE). 158

5-3. Model predictions and measured values for aquatic macrophytes, dreissenids and

sediments. 159

5-4. Calibration parameters for Lake Simcoe TP model. 160

5-5. TP fluxes (tonnes P yr-1) from different mechanisms considered by the model under the

characterization of the sediment P release as per Dittrich el al., 2013. 161

5-6. TP fluxes (tonnes P yr-1) from different mechanisms considered by the model under a

characterization of a faster sediment P release. 162

ix

List of Figures

2-1 (A) Basic principle and spatial segmentation of the Continuously-Stirred-Tank Reactor

(CSTR) model, forced with idealized sinusoidal loading, to predict epilimnetic total

phosphorus concentrations in Lake Simcoe, Ontario, Canada. (B) Hierarchical

configuration of the Lake Simcoe Bayesian network. The spatial heterogeneity is

accommodated by viewing the problem of parameter estimation as a hierarchy. At the

bottom of the hierarchy are the parameters for individual segments j; qj ~N(mj, sj). In the

upper level, the segment-specific parameters are specified probabilistically in terms of

lakewide parameters or hyper-parameters; q ~N(m, s). (C) Structural equation model used

to elucidate the interplay among nutrients, ambient light conditions, phytoplankton and

herbivore biomass. 28

2-2 Predicted annual phosphorus mass balance at the different segments of Lake Simcoe

during the study period (1999-2007). 29

2-3 Structural paths underlying plankton patterns in the nine segments of Lake Simcoe. The

direction and colour of the arrows represent the magnitude and sign of the posterior

medians of the standardized path coefficients. The standardized coefficients correspond to

the shift in standard deviation units of the dependent variable that is induced by shifts of

one standard deviation units in the explanatory variables, and thus provide a means to

assess the relative importance of the various model paths. 30

2-4 Predictions of the Bayesian network for the exceedance frequencies of total phosphorus

and chlorophyll a concentrations in Lake Simcoe under the present conditions and two

scenarios of phosphorus loading reduction. 31

3-1. Map of Lake Simcoe with modeled deep water monitoring stations K42, K45 and C9. 75

3-2. Conceptual diagram of the presented phosphorus fractionation model of Lake Simcoe. 76

3-3. Schematic diagram for the breakdown of the incoming flux of settling matter. 77

x

3-4. Boundary conditions for sedimentation flux and initial oxygen concentrations over a

one year time period. Sedimentation flux of total matter (solid gray line) in g/m2/day and

initial O2 concentration (dashed black line) in mg/l, shown for site K45 in the year 2005. 78

3-5. Modeled and measured depth profiles of pH from site C9 (left), O2 from site K42

(center) and porosity from site K45 (right). Measured data is depicted by open squares and

model output is given by a solid black line for each site. 79

3-6. Modeled organic matter sediment profiles for 3 modeled sites K42, K45 and C9.

Measured data is represented by symbols, square for Total OM and circle for Inert OM.

Model is represented by lines, total OM is solid black line, Fast Degradable OM is black

dashed line, and Inert OM is gray dashed line. 80

3-7. Total Phosphorus and P fraction profiles for 3 sites. Measured Data is represented by

symbols, square for total P, circle for organic P, triangle for absorbed P, diamond for redox

sensitive P, and pentagon for apatite P. Model is represented by lines, Total P is solid

black line, apatite P is solid gray line, absorbed P is light gray dashed line, organic P is gray

dashed line and redox sensitive P is dark gray dash dot line. 81

3-8. Modeled dynamics of dissolved phosphorus as HPO4- in three basins of Lake Simcoe

during one year (2011) 82

3-9. Impact of dynamics of sedimentation flux on P Binding forms in surface sediments

for site K45 in the years 2004 and 2005. Values for P Binding forms are an average of the

top 6mm of the sediments. 83

3-10. Impact of long-term dynamics of sedimentation flux on P binding forms in surface

sediments. 84

3-11. Modeled dissolved phosphorus release rates for 3 sites. 85

4-1. Modeled hypolimnetic sites in Lake Simcoe, Ontario, Canada. 121

xi

4-2. Vertical profiles of dissolved oxygen concentrations in the central part of Lake Simcoe

(site K45) in 2008 as per Ontario Ministry of Environment dataset. 122

4-3. Model sensitivity analysis: (a) conceptual schema of the absolute-relative sensitivity

function, ���������,���������.�. ; (b) depth profiles of sensitivity functions ���,��.�. of the

dissolved O2 to model boundary conditions and model parameters: concentration O2SWI,

porosity θsurf, porosity θdeep, rate constant kO2, half-saturation constant KO2, flux of CaCO3,

bioturbation coefficient Db, rate of sediment compaction kθ, concentration NO3SWI

(parameters are defined in per table 4-SI). Mean prediction and uncertainty bounds for (c)

dissolved O2; (d) sediment porosity; (e) degradation rate of organic matter; and (f) total

phosphorus in the sediments; (g) sensitivity function ����,��.�. of SOD to boundary conditions

and model parameters: fraction of total OM in total sediment flux αOrg, refractory OM

fraction in total OM flux αOrg_inert, concentration O2SWI, rate constant kO2 , half-saturation

constant KO2 (as per table 4-SI). 123

4-4. (a-d) Specification of the boundary conditions for the four scenarios examined at the

study site K45: varying organic matter sedimentation fluxes and oxygen levels at the

sediment-water interface (O2SWI). 124

4-5. Modeled transformation rates of organic P in the aerobic and anaerobic zones in the

central area of Lake Simcoe (site 45). 125

4-6. Vertical profiles of dissolved oxygen (a-d), soluble reactive phosphorus (e-h), and total

phosphorus (i-l) in Kempenfelt Bay (site K42), under the four scenarios examined. 126

4-7. SRP release rates (a-h) and sediment oxygen demand (i-p) in Lake Simcoe for March

and September, under the four scenarios examined. 127

xii

4-8. (a) Sediment oxygen demand (SOD) response to changes in organic matter flux and

oxygen concentration at SWI; (b) contribution of sediment oxygen demand and water

column respiration in K42 (Kempenfelt Bay) and K45 (Main Basin) to hypolimnetic DO

depletion; (c) sediment reactivity rates for organic matter degradation against the

Middelburg's (1989) curve for freshly deposited marine sediments; and (d) partitioning of

the relative contribution of the different pathways of SOD. 128

5-1. Flow diagram and spatial segmentation of Lake Simcoe model. 164

5-2. Conceptual diagram of phosphorus pathways of mass-balance model in Lake Simcoe. 165

5-3. Model fit with uncertainty bounds 2.5/97.5% for stochastic P loading and hydraulic

internal exchanges among segments as per coefficient of variations in Table 5-1. 166

5-4. a) Simulated phosphorus fluxes (MT P yr-1) in water column and sediment layer in 4

lake spatial segments; b) comparative phosphorus flow Sankey diagram of exogenous and

internal P sources (MT P yr-1) ; c) comparative diagram of P sink sources at sediment-

water interface (MT P yr-1). 167

5-5. (a) Sankey diagram for comparative description of the phosphorus flows from

exogenous and endogenous P sources (MT P yr-1). Width of the flow pathways is

proportional to annual estimates of relevant fluxes. Dreissenids pathways indicate negative

fluxes associated with the particle rejection/egestion of metabolic excreta minus particle

filtration; (b) comparative diagram of P sinks at sediment-water interface (MT P yr-1). 168

6-1. a) Bubble treemap diagram indicating the relative importance of P fluxes in different

lake segments; b) Bathymetric map of Lake Simcoe with superimposed factors that drive

phosphorus dynamics in the different lake segments. 180

xiii

List of Appendices

Appendix A. Supporting information for Chapter 2. 181

Appendix B. Supporting information for Chapter 4. 210

Appendix C. Supporting information for Chapter 5. 213

1

Chapter 1 INTRODUCTION

Restoration of Lake Simcoe water quality constitutes the main objective of the present research.

A wide range of environmental modelling techniques are used to shed light on nutrient recycling

processes and ultimately address the eutrophication problems in the lake. In aquatic science,

there are simulation models that have been developed for theoretical purposes in order to explore

aspects of system dynamics that are technologically or economically unattainable by other means

(Franks, 1995). These theoretical models also provide a foundation from which one can analyze

chemical or trophic dynamics (Norberg and DeAngelis, 1997), test new ecological theories for

aquatic systems (Jorgensen, 1995), and couple physical processes with biological dynamics

(Kamykowski et al., 1994). The second category, which is not always mutually exclusive with

the previous theoretical class, includes models that have been constructed for management and

forecasting purposes. The performance of these models is constrained by available data, and they

are used as heuristic tools to identify the underlying dynamics of system behavior or as

predictive tools to explore hypothetical conditions that are not described by current observations.

As Franks (1995) pointed out, the first class of models interpolate within the data, while the later

extrapolate beyond the data. In the aquatic ecosystems literature, there are numerous references

to models that have been used for understanding oceanic ecosystems (e.g., bloom dynamics, the

global carbon cycle) and predicting biotic responses to climate change (Kawamiya, 2002), but

this class of models has also been used as management tools for predicting eutrophication or

integrating environmental values with socioeconomic concerns (Hamilton and Schladow, 1997;

Arhonditsis et al., 2002). In this study, I will use a combination of statistical and mathematical

models of varying degrees of complexity to gain insights into the ecosystem functioning, but also

to project the response of Lake Simcoe under alternative management schemes.

Environmental health of Lake Simcoe has experienced a continuous degradation for the last 200

years due to an exponential growth in population and an intensification of agricultural practices

in Lake Simcoe watersheds, shifting the lake trophic status from oligotrophic to eutrophic in the

1970s. Excessive supply of phosphorus (P) has been recognized as the primary regulatory factor,

with the pre-settlement P loading of ~30 MT P/year that has increased up to ~280 MT P/year in

1970s (Wilson, 1986). The Lake Simcoe Protection Plan enforced stringent control measures and

2

successfully reduced P loading to current ~70 MT P/year with an ultimate goal of 44 MT P/year

by 2045 (MOE, 2010). Aside from the typical eutrophication symptoms, such as high total

phosphorus (TP) and chlorophyll-α concentrations, water transparency decrease, occasional

cyanobacteria blooms and E-coli contamination outbreaks, Lake Simcoe has also experienced a

decline in stock of cold water fish species, mainly lake trout (Salvelinus namaycush) and white

fish (Coregonus lavaretus). According to fish metabolism studies, the depletion of hypolimnetic

oxygen (O2) toward the end of summer stratification constrains the reproduction capacity of

salmonid species and ultimately puts them at a risk of extinction (Evans, 2007). The

hypolimnetic O2 deficit is primarily modulated by the aerobic decay of settled organic matter in

both water column and sediments (Hutchinson, 1938; Vollenweider and Janus, 1982). Indeed,

simple regression models in Lake Simcoe demonstrate that chlorophyll-α (proxy of algal

abundance) can explain ~50% of O2 variability in the lake hypolimnion (Nicholls, 1997).

In lakes with a eutrophic past, the sediments normally represent a significant P source, even after

exogenous P reduction measures are implemented (Søndergaard et al., 2003). In the case of Lake

Simcoe, sediments have been previously reported to act as a net P sink with a retention capacity

of ~88% of annual P inputs of 72 MT P/year and outflows of 8±1 MT P/year through Atherley

Narrows. Noting that Lake Simcoe has a history of ~200 year of continuous P accumulation and

that the top 20 cm represent a potential pool for P mobilization (Hiriart-Baer et al., 2011), the

role of sediments can be critical for the success the on-going restoration plans. The previous

paradigm of P release under prevailing anoxic conditions, associated with iron cycling in lake

sediments, has been recently updated with a set of additional biogeochemical mechanisms which

can control long-term P retention (Hupfer and Lewandoswki, 2008). My dissertation aims to

combine the known mechanisms of P transformation in the sediments within a diagenetic

reactive-transport modelling platform, in order to offer a convenient exploratory tool for

studying the role of sediments in the eutrophication patterns in Lake Simcoe.

Climate change is a significant stress factor in Southern Ontario linked to an increase of both air

temperature and precipitation variability. As a result, the beginning of lake stratification has

gradually shifted to early spring thereby prolonging the period of lake thermal stability by ~2

weeks out of ~120 days and further disconnecting the hypolimnetic oxygen from atmospheric

replenishment (Stainsby, 2011). The intensification of precipitation events can increase the

contribution of tributary P loading from adjacent watersheds (LSRCA, 2012). Furthermore, due

3

to warming of surface and ultimately hypolimnetic waters, the volume of trout thermal habitat

(8-12 oC) is expected to decrease by 2 m in depth and 26% in volume in Kempenfelt Bay by

2100 (SIRD, 2012). On-going changes in the food web induced by the invasion of exotic species

represent another major factor which can shape the success of the Lake Simcoe restoration

efforts. Specifically, the integrity of zooplankton community can be altered by the recent

invasion of Bythotrephes longimanus, which is known to prey upon Daphnia (Young, 2011).

This problem may be exacerbated by the cultural introduction of rainbow smelt (Osmerus

mordax), which is a visual feeder with preferential predation for large-bodied Daphnia and

calanoid copepods. Rainbow smelt can also induce collateral damage by controlling the

piscivorous community, since part of its diet consists of eggs and juveniles of higher trophic

level fish. Among the recent invaders, zebra mussels (Dreissena polymorpha) and quagga

mussels (D. rostriformis bugensis) can profoundly modify the ecosystem functioning (Evans et

al., 2011). Dreissenids are efficient filter feeders capable of altering the distribution of energy

and suspended material from pelagic to littoral zones. Further, the increase of water transparency

associated with the dreissenids colonization in near-shore areas can boost the growth of

macrophytes, which in turn can exacerbate hypoxic conditions through decay of senescing

tissues of macrophytes. Phytoplankton abundance can be negatively affected by mussel filtration

and positively by the excretion of bioavailable dissolved P. Generally, there is overwhelming

evidence that a multitude of stressors, characterized by a wide array of feedback mechanisms,

pose significant challenges towards the goal of achieving a sustainable management of Lake

Simcoe.

In this dissertation, my main goal is to shed light on the recycling mechanisms of nutrient

regeneration, mediated by sediment diagenesis, invasive dreissenids and submerged aquatic

macrophytes, and to identify the driving factors of oxygen depletion in Lake Simcoe. In the

second chapter, I introduce a continuous Bayesian network to study the causal linkages between

phosphorus loading and plankton patterns and to estimate the sedimentation fluxes in different

lake segments. In the third chapter, I develop a sediment diagenesis model to investigate the P

transformation processes and to assess the role of sediments as a source of internal nutrient

loading. In the fourth chapter, I use the same diagenetic model to evaluate the spatio temporal

role of sediment oxygen demand on hypolimnetic oxygen depletion. In the fifth chapter, I

combine all sources of P loading to assess the relative contribution of recycling mechanisms to

4

the phosphorus budget and their potential to delay the lake restoration efforts. The final chapter

summarizes the research findings and formulates future perspectives with recommendations to

guide Lake Simcoe modelling research. In general my intent with this research is to advance our

understanding of Lake Simcoe dynamics and to provide guidelines (or testable hypotheses) for

eutrophication management. It is my hope that this dissertation will be a reference point of how

empirical knowledge and rational modelling can be used to alleviate the impact of anthropogenic

and/or natural disturbances on lake ecosystems.

5

References

Arhonditsis, G., Karydis, M., Tsirtsis, G., 2002. Integration of mathematical modelling and

multicriteria methods in assessing environmental change in developing areas: a case

study of a coastal system. J. Coastal. Res. 18, 698–711.

Evans, D.O., 2007. Effects of hypoxia on scope-for-activity and power capacity of lake trout

(Salvelinus namaycush): Canadian Journal of Fisheries and Aquatic Sciences 64, 345-

361.

Evans, D.O., Skinner, A.J., Allen, R., and McMurtry, M.J., 2011. Invasion of zebra mussel,

Dreissena polymorpha, in Lake Simcoe: Journal of Great Lakes Research 37, 36-45.

Franks, P.J.S., 1995. Coupled physical-biological models in oceanography. Rev Geophys. 33:

1177–1187.

Hamilton, D.P., Schladow, S.G., 1997. Prediction of water quality in lakes and reservoirs. 1.

Model description. Ecol. Model. 96, 91–110.

Hiriart-Baer, V.P., Milne, J.E., Marvin, C.H., 2011. Temporal trends in phosphorus and

lacustrine productivity in Lake Simcoe inferred from lake sediment. Journal of Great

Lakes Research 37(4), 764-771.

Hupfer, M., Lewandowski, J., 2008. Oxygen Controls the Phosphorus Release from Lake

Sediments - a Long-Lasting Paradigm in Limnology. International Review of

Hydrobiology 93(4-5), 415-432.

Hutchinson, G.E., 1938. On the relation between the oxygen deficit and the productivity and

typology of lakes: Internationale Revue der gesamten Hydrobiologie und Hydrographie,

36, 336-355.

Jorgensen, S.E., 1995. The growth rate of zooplankton at the edge of chaos: ecological models. J.

Theor. Biol. 175, 13–21.

Kamykowski, D., Yamazaki, H., Janowitz, G.S., 1994. A Lagrangian model of phytoplankton

photosynthetic response in the upper mixed layer. Deep-Sea Res. 16, 059–069.

6

LSRCA, 2012. Annual water balances, total phosphorus budgets and total nitrogen and chloride

loads to Lake Simcoe (2004-2007) Lake Simcoe Region Conservation Authority.

MOE, 2010. Lake Simcoe Water Quality Update. Report to The Minister of the Environment.

Nicholls, K.H., 1997. A limnological basis for a Lake Simcoe phosphorus loading objective:

Lake and Reservoir Management, 13, 189-198.

Norberg, J., DeAngelis, D., 1997. Temperature effects on stocks and stability of a

phytoplankton–zooplankton model and the dependence on light and nutrients. Ecol.

Model. 95, 75–86.

Science and Information Resources Division (SIRD), 2012. Potential Effects of Climate Change

and Adaptive Strategies for Lake Simcoe and the Wetlands and Streams Within the

Watershed - Climate Change Research Report CCRR-21: Ontario Government, Ministry

of Natural Resource, Science and Information Resources Division.

Søndergaard, M., Jensen, J.P., and Jeppesen, E., 2003. Role of sediment and internal loading of

phosphorus in shallow lakes: Hydrobiologia, 506, 135-145.

Stainsby, E.A., Winter, J.G., Jarjanazi, H., Paterson, A.M., Evans, D.O., and Young, J.D., 2011.

Changes in the thermal stability of Lake Simcoe from 1980 to 2008: Journal of Great

Lakes Research 37, 55-62.

Vollenweider R.A., Janus L.L. 1982. Statistical models for predicting hypolimnetic oxygen

depletion rates. Mem. Ist. Ital. Idrobiol. 40, 1-24.

Wilson, J.P., 1986. The use of statistical models to document environmental change in the Lake

Simcoe basin. Ph.D. Thesis. University-of Toronto. 361 pp.

Young, J.D., Winter, J.G., and Molot, L., 2011. A re-evaluation of the empirical relationships

connecting dissolved oxygen and phosphorus loading after dreissenid mussel invasion in

Lake Simcoe: Journal of Great Lakes Research 37, 7-14.

7

Chapter 2 A BAYESIAN NETWORK FOR STUDYING THE CAUSAL LINKS

BETWEEN PHOSPHORUS LOADING AND PLANKTON PATTERNS IN LAKE SIMCOE, ONTARIO, CANADA1

2.1. Introduction

Addressing environmental management problems often involves complex policy decisions that

aim to maintain ecosystem functional integrity, while accommodating social values and

economic concerns. The growing appreciation of the challenges of aquatic ecosystem restoration

and the need to address a wide array of tightly intertwined stressors have triggered a shift from

the historical water quality/fisheries exploitation paradigms to the ecosystem management

paradigm (Minns and Kelso, 2000). Rather than narrowly focusing on water quality problems,

the ecosystem approach simultaneously addresses problems related to fisheries management,

exotic species invasions, biodiversity, habitat conservation and restoration, sustainable economic

development, or even human behaviour and education (Krantzberg, 2004). Although the concept

of holistic ecosystem management makes sense as a pragmatic means to address multifaceted

environmental problems, there is concern that this approach has been accompanied by a shift

from the traditional elucidation of simple cause–effect relationships to a multi-causal way of

thinking to accommodate ecosystem complexity. This shift can be a major impediment to

deriving the straightforward scientific answers required by the regulatory agencies tasked with

implementing environmental protection policies (Zhang and Arhonditsis, 2008).

The ecosystem approach has not only pervaded environmental thinking but also contemporary

modelling practices. Complex ecosystem models have been developed for a number of purposes,

1 Gudimov, A., O’Connor, E., Dittrich, M., Jarjanazi, H., Palmer, M.E., Stainsby, E., Winter, J.G., Young, J.D. and

G.B. Arhonditsis, 2012. Continuous Bayesian network for studying the causal links between phosphorus loading and plankton patterns in Lake Simcoe. Environmental Science & Technology 46(13): 7283-7292. DOI: 10.1021/es300983r

Contributions: AG & GA formulated research objectives and modelling methods. EO and HJ provided datasets. AG carried out the analysis, wrote the paper with input from the co-authors. MD, EO, MP, ES, JW, and JY reviewed the paper and offered comments.

8

including the illumination of causal mechanisms, complex interrelationships, and direct and

indirect ecological paths; the examination of the interplay among a suite of external stressors

(e.g., climate change, urbanization/land-use changes, invasion of exotic organisms); and the

assessment of the potential ramifications of various stressors on ecosystem functioning (e.g.,

food web dynamics, benthic-pelagic coupling, fish communities, see Mills et al., 2003; Leon et

al., 2011). While the development of more holistic modelling constructs is certainly the way

forward, skeptics question the ability to mathematically depict many biotic relationships and

their interactions with the abiotic environment (Arhonditsis and Brett, 2004; Anderson, 2005).

The current generation of mathematical models cannot offer robust predictions in a wide range of

spatiotemporal domains, and our experience is that model performance declines as we move

from physical-chemical to biological components of aquatic ecosystems (Arhonditsis and Brett,

2004). The tendency to invoke complexity as a means for improving the learning capacity of our

models also entails an increase in the disparity between what ideally we want to learn (internal

description of the system and model endpoints) and what can realistically be observed. Thus, our

ability to properly constrain model parameters from observations is reduced, and the resulting

poor identifiability undermines model credibility when used to support environmental

management decisions (Arhonditsis et al., 2007b).

In this study, our thesis is that while the emergence of the holistic environmental management

paradigm reinforces the need for more sophisticated modelling tools, the critical evaluation of

the inference drawn and the impartial differentiation between real knowledge gained and existing

knowledge gaps can be the thrusts for coping with the uncertainty of any modelling exercise. We

also advocate the use of simple models as adequate first-order approximations until simplicity

can be gradually traded for increased explanatory power. In this regard, our primary objective is

to develop a Bayesian hierarchical network of simple ecological models for Lake Simcoe,

Ontario, Canada, that establish a realistic representation of the causal connections among

exogenous nutrient loading, ambient nutrient conditions, and epilimnetic plankton dynamics. We

use a spatially-explicit simple mass-balance model forced with idealized sinusoidal loading to

predict total phosphorus concentrations. A structural equation model is then used to delineate the

interplay among nutrients, ambient light conditions, phytoplankton and herbivorous zooplankton

biomass. Our study also pinpoints directions of future model augmentation, where extra

ecological complexity and finer spatial segmentation will improve our understanding of the

9

system. Finally, we illustrate how our Bayesian network of models can be used to examine the

exceedance frequency of threshold values for total phosphorus (15 µg/L) and chlorophyll a (4

µg/L) concentrations under scenarios of phosphorus loading reduction.

2.2. Methods

2.2.1. Study site

Lake Simcoe is the sixth largest inland lake in the province of Ontario, Canada, with a surface

area of 722 km2, a mean depth of 14 m, and a maximum depth of 42 m (Fig. 1a). It is a dimictic

system that completely freezes over in most winters. Lake Simcoe consists of a large main basin

(mean depth 14 m, maximum depth 33 m) and two large bays: the narrow and deep Kempenfelt

Bay on the west side of the lake (area 34 km2, mean depth 20 m) and the shallow Cook's Bay at

the south end of the lake (area 44 km2, mean depth 13 m) (Palmer et al., 2011). The lake drains

through a single outflow at Atherley Narrows and has a flushing time of approximately 11 years

(MOE Report, 2009). Due to the limestone bedrock underlying its catchment, Lake Simcoe is a

hard-water lake with mean calcium concentration of 41 mg/L, mean alkalinity of 116 mg/L, and

mean sulphate concentration of 20 mg/L (MOE Report, 2009). The lake supports a year-round

sport fish industry (>1 million angler hours per year) as well as recreational activities that

generate over $200 million per year. Lake Simcoe is also a drinking water source for several

communities within its 2,899 km2 watershed (Palmer et al., 2011).

Agriculture and increasing urbanization activities have impacted the ecological health of the

system. In particular, Lake Simcoe currently receives wastewater from fourteen municipal

wastewater treatment plants, which constitute sources of phosphorus loading (6±1 tonnes/yr

between 2004 and 2007) (Palmer et al., 2011). Substantial phosphorus loads are also deposited

from the atmosphere (18±4 tonnes/yr) or stem from other non-point sources, including runoff

from agricultural, urban and natural areas (43±5 tonnes/yr) and rural septic systems (4.4±0.1

tonnes/yr) (Palmer et al., 2011). The exogenous phosphorus inputs modulate the ambient total

phosphorus (TP) levels and subsequently trigger phytoplankton production (Nicholls, 1997),

while the decomposition of the excessive organic material in the sediments likely contributes to

hypolimnetic dissolved oxygen (DO) depletion. Prior to the mid-1990s, end-of-summer

hypolimnetic DO levels reached nearly lethal levels for many coldwater fish species (<3 mg/L)

10

(Evans, 2007). As a result, fish biomass declined for several commercially or recreationally

important fish species, such as lake trout (Salvelinus namaycush), lake whitefish (Coregonus

clupeaformis), and lake herring (Coregonus artedi) (Nicholls, 1997). To alleviate the problem of

hypoxia and thus allow for the restoration of a self-sustaining coldwater fishery, the target for the

end-of-summer minimum volume-weighted hypolimnetic dissolved oxygen (MVWHDO) was

originally established at 5 mg/L and recently revised to 7 mg/L (Evans, 2007, Palmer et al.,

2011). A combination of empirical knowledge and modelling indicates a phosphorus loading rate

of 44 tonnes/yr is needed to meet the 7 mg/L MVWHDO target (Palmer et al., 2011). Between

2004 and 2007, total phosphorus loading into the lake was 74±3 tonnes/yr, a significant

reduction from over 100 tonnes/yr during the 1980s and early 1990s (Palmer et al., 2011).

2.2.2. Model description

2.2.2.1. Spatial Segmentation

Our Bayesian network consists of two models: (i) a spatially-explicit simple mass-balance model

forced with idealized sinusoidal loading to predict epilimnetic total phosphorus; and (ii) a

structural equation model to depict the causal links among nutrients, light availability,

temperature variability, phytoplankton and herbivorous zooplankton biomass in the Lake Simcoe

epilimnion. Data for the model parameterization were obtained from the monitoring program

conducted by the Ontario Ministry of the Environment in partnership with the Lake Simcoe

Region Conservation Authority. Nine stations (C1, C6, C9, K39, K42, K45, S15, E51, and ATH)

have been historically used to monitor the water quality in Lake Simcoe and these stations were

also used to delineate the spatial segmentation of the model (Fig. 2-1a). Loading estimates from

all the major point and non-point sources during the study period (1999-2007) were provided by

the Lake Simcoe Region Conservation Authority (MOE Report, 2009). (More information about

the data used in the present study is provided in the Supporting Information section). Our

modelling analysis used a hierarchical structure (Cheng et al., 2010), which allowed us to obtain

segment–specific estimates of the causal relationships considered to accommodate the spatial

variability in the system (Fig. 2-1b).

11

2.2.2.2. Total Phosphorus Model

Our TP model is founded upon a representation of the Lake Simcoe epilimnion as a feedforward

system of completely mixed reactors (Fig. 2-1a) (Chapra, 1997). A central feature of the

feedforward configuration is the postulation of a net unidirectional flow within the framework of

serial reactors considered. This approach seems conceptually more suitable to model horizontal

mass exchanges in a chain of lakes or a stream (Chapra, 1997), and thus its validity and

limitations to accommodate the spatial heterogeneity of a single lake is critically examined in the

Supporting Information (Section D). The TP balance in each segment is determined by the

exogenous loading sources and three sinks (outflow, reaction, and settling) that deplete the

ambient phosphorus levels in the system:

TPH

vTPkTP

V

Q

V

W

dt

dTP t ⋅−⋅−⋅−= )(

(2-1)

where W(t) denotes the loading entering the segment (tonnes day-1), Q refers to the volumetric

outflow rate for the segment (m3 day-1), V is the volume of the segment (m3), ν represents the

settling velocity (m day-1), H is the mean depth of the segment (m), and k denotes the first-order

reaction coefficient. Under the assumption that the seasonal exogenous TP loading follows a

sinusoidal pattern, the solution of the differential equation that describes the temporal variability

of the epilimnetic TP is:

)](sin[22

ωφθωωλλ

−−+

+= tV

W

V

WTP ampavg

(2-2)

T

πω 2=

)arctan()(λωωφ =

21 κκλ += V

Q=1κ H

vk +=2κ

in which Wavg is the mean loading entering the system (tonnes day-1), Wamp is the amplitude

around the mean loading (tonnes day-1), θ = phase shift of the loading from the standard wave

(radians), φ(ω) is an additional phase shift related to the segment-specific response, and ω

(radians day-1) and T (day) are the angular frequency and period of the loading oscillation. The

12

hierarchical formulation used to accommodate the spatio-temporal variability of the TP

concentrations was specified as follows:

log(TPitj) ~ N (f(κ1tj, κ2tj,Wavgtj, Wamptj, θtj), τ²) (2-3)

1/τ²~G(0.001,0.001)

κ1tj ~ N (κ1j, σκ1j 2)

κ2tj ~ N (κ2, σκ2j2) κ2 ~ N (κ2μ, σκ2

2)

κ2μ ~ N (κ2μlit, σκ2lit2), 1/σκ2

2~ G(a1, a2), 1/σκ2j2 ~ G(a1j, a2j)

Wavgtj ~ N (WavgMLtj, ΣTottj 2)

ΣTottj 2= σWtj

2 + σWavgtj 2

Wamptj ~ N (WampMLtj, σamptj 2)

θtj ~ N (θMLtj, σθtj 2)

i = 1,...,12 j = 1,...,9 t = 1,..., 9

where TPitj corresponds to the average TP concentration at segment j, year t, and month i; τ²

denotes the structural error variance of our TP model; κ1tj is the net outflow rate from segment j

at year t; the κ1j and σκ1j correspondingly denote the segment-specific average flushing rates and

the associated interannual variability, as calculated from the respective water balance budgets;

κ2tj is the net TP loss rate in segment j at year t; κ2 represents the hyperparameter or the lakewide

TP loss rate; σκ2j2 is the segment-specific variance; and κ2μ and σκ2

2 are the mean and variance of

the global parameter distribution, respectively. The normal distribution assigned to the parameter

κ2μ was based on a literature review (κ2μlit, σκ2lit2)14, while the inverse gamma distributions

assigned to the parameters σκ22 and σκ2j

2 were constructed such that their mean was equal to the

variance σκ2lit2. The uncertainty of the same distributions reflected our high level of confidence to

that mean variance estimate (i.e., coefficient of variation < 10%). The mean (Wavgtj), amplitude

(Wamptj), and phase shift (θtj) values of the phosphorus loading at segment j, year t and month i

were drawn from normal distributions in which the mean values (WavgMLtj, WampMLtj, θMLtj) and

13

error variances (σWavgtj 2, σamptj

2, σθtj 2) were the maximum likelihood estimators obtained from

fitting sinusoidal functions to the corresponding monthly loading data. The normal distributions

of the mean annual loading (Wavgtj) also considered the estimates of model error variance (σWtj2)

obtained from the maximum likelihood fitting exercise.

2.2.2.3. Structural Equation Model

We used structural equation modelling (SEM) to elucidate the key causal relationships

underlying the interplay among the physical environment, nutrients, and plankton dynamics in

Lake Simcoe. SEM is a multivariate statistical method that encompasses both factor and path

analysis, which allows decomposing multiple causal pathways and quantifying direct and

indirect relationships among variables16. Another advantage of SEM is that it can explicitly

incorporate uncertainty due to measurement error and/or accommodate the discrepancy between

conceptual ecosystem properties and observed variables that can be directly measured. SEM is

also an a priori statistical method whereby a hypothetical structure of the system studied,

reflecting the best knowledge available, is tested against the observed covariance structure

(Arhonditsis et al., 2006). A Bayesian approach to SEM was also adopted because it offers

several advantages over the classical methods (e.g., maximum likelihood, generalized and

weighted least squares). A Bayesian SEM can incorporate prior knowledge about the parameters

and more effectively treat unidentified models. Moreover, the modelling process does not rely on

asymptotic theory, a feature that is particularly important when the sample size is small and the

classical estimation methods are not robust. Markov Chain Monte Carlo (MCMC) samples are

taken from the posterior distribution, and consequently the procedure works for all sample sizes

and various sources of non-normality (Arhonditsis et al., 2007a,b).

In this study, our starting point is a “conceptual/mental model” that considers the effects of four

latent variables (i.e., phosphorus, nitrogen, water clarity, and herbivorous zooplankton grazing)

on phytoplankton dynamics (Fig A1-SI. in the Appendix A). Each of these conceptual factors (or

latent variables) can be linked with observed data (rectangular boxes in Fig. 2-1c), while

explicitly acknowledging that none of the selected surrogate variables can perfectly represent the

underlying property (measurement errors ε in Fig. 2-1c). Specifically, we established a

connection between the TP mass-balance and structural equation models by considering the

14

causal association between total phosphorus and phytoplankton biomass. We also used the latent

variable nitrogen and two indicator variables: dissolved inorganic nitrogen (DIN) and total

nitrogen concentrations. The role of water clarity was described solely by the existing Secchi

disk depth values, while chlorophyll a concentrations were used to represent the latent variable

“phytoplankton”. The trophic interactions between phytoplankton community and herbivorous

zooplankton were assumed to have a recursive nature, i.e., bottom-up and top-down forcing. The

role of temperature as a regulatory factor of zooplankton biomass was also considered. The

Bayesian hierarchical configuration of the Lake Simcoe SEM is provided in Section SI-D.

2.3. Results

The application of the TP model provided satisfactory fit to the measured TP concentrations in

seven out of the nine segments considered, resulting in root-mean-square-error (RMSE) values

lower than 5 µg TP/L (Fig. A2-SI). The main exceptions were the two inner segments of Cook’s

Bay, C1 (RMSE=26.47 µg TP/L) and C6 (RMSE=10.77 µg TP/L), which are also consistently

characterized by the highest TP levels in the system. In particular, we note that the fairly high

error in segment C1 predominantly stems from a few extreme TP values that occurred distinctly

out of the phase shifts, φ(ωjt), postulated by our model to account for the system response.

Further, one of the fundamental model assumptions is that the segment-specific TP seasonal

patterns are mainly driven by the intra-annual variability of the exogenous loading. In this

regard, our model predicts that the inflowing TP loads alone can induce oscillatory behaviour in

Cook’s Bay, although the agreement between actual and predicted amplitudes cannot be

rigorously verified as the typical sampling intensity (biweekly) and timing (mid-May) may not

always coincide with the observed TP peaks in Lake Simcoe (Fig. A2-SI). On the other hand, the

predicted TP dynamics in larger and/or offshore segments were significantly muted, indicative of

a more complex interplay among exogenous loading, hydrodynamics, and biological

productivity that most likely modulates in-lake TP variability.

In the majority of the modeled sites, the net TP loss rates were well-identified and independent

from the corresponding posterior estimates of the segment-specific flushing (or net exchange)

rates (Fig. A3-SI). They demonstrated low year-to-year variability within each segment,

spanning a range between 0.8-1.0 year-1 or 0.002-0.003 day-1 (Fig. A4-SI & Table A2-SI).

Notable exceptions were the segments C6 and K39, characterized by two- to tenfold increase in

15

their posterior κ2 estimates with considerable interannual variability. Given that both sites are

located in the vicinity of major tributary outlets, there are three plausible explanations for this

substantial discrepancy: (i) the excessive macrophyte growth in the favourable environment of

Cook’s Bay (i.e., shallower depths, elevated nutrient levels, increased water clarity, and fine-

grained sediments) that act as a net sink of the ambient TP (Ginn, 2011); (ii ) the presence of

dreissenids that have the capacity to filter suspended particles from the water column and thus

modulate the TP concentrations (Young et al., 2011); and/or (iii ) the fact that both segments

constitute transitional zones to the deeper parts of the lake. It is conceivable that a substantial

portion of the inflowing TP loads may be directly allotted to the hypolimnion, representing a net

permanent sink for the epilimnetic phosphorus budget (see also following discussion). Generally,

the posterior estimates of the sedimentation and outflow rates suggest that a significant portion

of the annual TP inputs from the Holland River in the southernmost segment (C1) are flushed

into the middle area (C6) of Cook’s Bay, i.e., 1,140 out of 1,201 mg/m2/yr (Fig. 2-2 & Fig. A5-

SI). As previously mentioned, a substantial net amount of phosphorus is lost (976 mg/m2/yr) in

the sediments of this zone or in the hypolimnion of the next segment (C9), while a lower fraction

(311 mg/m2/yr) is transported horizontally to the epilimnion of the outer Bay and subsequently

to the Main Basin (106 mg/m2/yr). In a similar manner, more than half of the TP loads (or 491

mg/m2/yr out of 903 mg/m2/yr) in the innermost segment of Kempenfelt Bay are being subjected

to sedimentation and the remaining amount of phosphorus (415 mg/m2/yr) is being transferred to

the outer segment (K42), ultimately reaching the central area of the lake (113 mg/m2/yr).

Notably, the net areal sedimentation rates in the mouths of the two embayments were

comparable with those predicted in the Main Basin, ranging from 45 to 90 mg/m2/yr. The annual

TP outflows from Atherley Narrows were estimated at an average level of 329 mg/m2/yr (or 9.6

tonnes/yr), and the TP retention fraction varied from 85% to 93%; both values are on par with

existing estimates independently calculated from TP mass balance budgets for Lake Simcoe10,20.

The comparison between measured and predicted chlorophyll a concentrations is presented in

Fig. A6-SI, in which it can be seen that our SEM approach sufficiently describes the observed

chlorophyll a patterns as nearly all the data were included within the 95% credible intervals. The

RMSE values were generally lower than 2 µg chla/L, except in the southernmost segment in

Cook’s Bay (C1 ≈4.8 µg chla/L). In a similar manner, the observed variability of the herbivorous

zooplankton biomass is adequately depicted by our model (RMSE<60 µg C/L). The largest

16

discrepancy was found in the outer part of Cook’s Bay (C6, C9) and the southern Main Basin

(S15), where the error was greater than 70 µg C/L and mainly reflected the influence of several

outlying observations. Our SEM analysis primarily highlights the importance of a positive causal

link between epilimnetic TP and phytoplankton biomass (chlorophyll a); especially, in

Kempenfelt Bay and Eastern Basin (Fig. 2-3 & Table A3-SI). Interestingly, our model predicts a

distinct path from nitrogen to phytoplankton in several segments of the lake (C6, C9, K42, K45),

and the negative nature of this relationship stems from the inclusion of dissolved phase inorganic

nitrogen in the latent variable “nitrogen” (Arhonditsis et al., 2007a,b). The statistically

significant signature though does not imply nitrogen limitation in the system. Ambient dissolved

phase nutrient concentrations partly reflect the residual nutrients from phytoplankton activity,

but there are several other potentially influential factors that are not accounted for in our

approach (e.g., intracellular storage). A strongly negative relationship exists between water

clarity (Secchi disk transparency) and phytoplankton biomass throughout the lake. The capacity

of zooplankton grazing to modulate the algal standing crop (zooplankton→ phytoplankton) is

consistently manifested in the lake, although this trophic linkage was somewhat weaker (and

poorly identified) in the segments associated with the highest predictive error for zooplankton

biomass (C6, S15). On the other hand, the causal path from phytoplankton to zooplankton

(bottom-up forcing) was consistently weak. Water temperature variability appears to be a

significant driver of zooplankton abundance in the system (Fig. 2-3).

The MCMC posterior samples were used to update the two models and subsequently integrate

them into one coherent framework for examining the exceedance frequency of different water

quality standards. Namely, the updated mass-balance model was used to derive the predictive TP

distributions, stemming from both input uncertainty and model error, which were then

propagated through the SEM. To predict the effect of a substantial reduction in phosphorus

inputs, the corresponding marginal TP loading distributions were reduced by 15% and 30%. All

other functions and marginal nodes in the models were left unchanged, and new distributions

were computed for the ecological variables of interest. For illustration purposes, we selected two

threshold levels for TP (15 µg/L) and chlorophyll a (4 µg/L) concentration, representing the

midpoint and the lower bound of the corresponding classification ranges suggested for the

characterization of mesotrophic states (Chapra, 1997). If we consider the present exogenous

loading conditions, we infer that the exceedance frequency of 15 TP µg/L is currently greater

17

than 30-35% during the summer period in nearly all segments modeled (Fig. 2-4, Fig. A7-SI). In

particular, the mean TP levels in Cook’s Bay are higher than 20 µg/L and the corresponding

frequency of violations of 15 TP µg/L is greater than 50%. Similarly, the average chlorophyll a

concentrations exceed the level of 5 µg chla/L in the inner parts of both Cook’s Bay and

Kempenfelt Bay, and the value of 4 µg chla/L is exceeded more than 25% of the time in the

southwestern part of the lake. Our Bayesian network predicts that a 15% phosphorus loading

reduction will result in >25% violations in the inner segments of the two embayments, while the

rest of the lake will result in <20% violations. Interestingly, the chlorophyll a predictions

remained practically unaltered under the scenario of 30% phosphorus loading reduction.

Conversely, the TP levels will decrease in response to the exogenous loading reductions and this

improvement will be primarily manifested in the northcentral segments of the system. Our

integrated model also predicts that the mean TP values will be lower than 20 µg/L in Cook’s

Bay, but the exceedance frequency of the TP level of 15 µg/L will remain >25%, even if the

loading is reduced by 30%.

2.4. Discussion

A major challenge when developing modelling tools aiming to accommodate ecosystem

complexity is the ability to combine quantitative descriptions of ecological processes at multiple

scales and in a variety of forms (intermediate complexity mathematical models, empirical

equations, expert judgments) (Borsuk et al., 2004). Bayesian networks offer an effective means

for integrating various models into one coherent framework, while rigorously assessing how

uncertainties in each component translate to uncertainty in the final predictions. Recent research

has shown that this modelling strategy can effectively alleviate problems of spatiotemporal

resolution mismatch among different submodels of integrated environmental modelling systems;

overcome the conceptual or scale misalignment between processes of interest and supporting

information; exploit disparate sources of data that differ with regards to the measurement error

and resolution; and accommodate tightly intertwined environmental processes operating at

different spatiotemporal scales (Borsuk et al., 2004). Here, we present two models that translate

the processes underlying planktonic patterns into an articulated sequence of conditional

relationships (TP loading→epilimnetic TP→phytoplankton biomass). This work is relevant to

policy and management decisions, because it attempts to quantitatively predict ecological

changes in Lake Simcoe in response to various phosphorus reduction scenarios.

18

Young et al. (2011) recently re-examined the capacity of an empirical equation historically

developed for Lake Simcoe to predict TP concentrations from TP loading rates in the post-

dreissenid period. Counter to the contemporary paradigm on the impact of dreissenid mussels,

the successful application of the model in predicting average, ice-free, whole-lake phosphorus

concentrations was interpreted as evidence that their invasion has not fundamentally altered the

existing relationship between TP loading and TP concentrations. In this study, our hierarchical

spatially-explicit model forced with idealized sinusoidal loading relaxes two features of the

existing empirical modelling work in Lake Simcoe: (i) the system is no longer assumed

thoroughly mixed with uniform concentrations throughout; and (ii ) rather than drawing inference

upon seasonal average TP values, the ambient TP levels are predicted at finer (monthly, daily)

time scales that may be more relevant for addressing the current management issues in Lake

Simcoe. In this regard, the plausibility of our estimates of the TP loss rates and the projected

differences between the two embayments and the main basin are critical for evaluating the

validity of the parameterization obtained. Hiriart-Baier et al. (2011) recently reported post-1970

estimates of the gross TP accumulation rates in Cook’s Bay and Kempenfelt Bay sediments at

the level of 250-750 mg P/m2/yr and 300 mg P/m2/yr, respectively23. Although Hiriart-Baier et

al.’s (2011) gross TP sedimentation rates are proxies that may not be suitable for deterministic

comparisons, our corresponding areal weighted average estimates of the net areal TP loss rates

were approximately 300 mg P/m2/yr (C1, C6, C9) and 150 mg P/m2/yr (K39, K42). Further, the

likelihood of the unidirectional flow patterns postulated by our model to misrepresent the

dilution effects of the water masses from the outer lake suggests that our estimates probably

reflect the upper levels of net sedimentation in the two embayments (see Section D in Supporting

Information). One possible implication of the two-fold difference between gross and net TP

sedimentation rates is that several ecological mechanisms, such as macrophyte growth, transport

to the hypolimnion, sediment resuspension and P release, can significantly modulate TP

dynamics in the two embayments. Another plausible explanation for the substantial discrepancy

between the two studies may simply be the fact that our work spans a shorter time period with

improved water quality and significantly lower TP concentrations (Eimers et al., 2005).

A second regulatory factor of the segment-specific TP budgets is related to our posterior

estimates of the flushing times in the bays, which in turn may influence the quantification of the

net TP export into the main basin. The hydraulic retention times of the bays can vary

19

significantly on a seasonal basis and are regulated by a suite of factors, such as the wind‐induced

momentum, the spring freshet, thermocline development, and water temperature gradients

(Eimers et al., 2005). Hydrodynamic modelling calculations based on acoustic Doppler current

profiles indicated short retention times between one to two weeks in the two embayments (Baird

and Associates, 2006), or flushing rates that correspond to an equivalent of κ1 ≈ 0.06-0.07 days-1.

Although the same values formed the basis for the year-specific κ1 priors used in this analysis

(Eq. 3), the derived posterior estimates (0.009-0.012 days-1) differed significantly suggesting that

they indeed represent the annual net exchange of water in terms of nutrient loadings.

Importantly, the relative mismatch between the reported empirical TP accumulation rates of 80-

300 mg P/m2/yr in the deeper segments of Lake Simcoe (Hiriart-Baer et al., 2011) and our

predicted net epilimnetic TP loss of 45-85 mg P/m2/yr was fairly similar, and thus the

hydrodynamic forcing of the model and consequently our TP mass balance budgets do not seem

to introduce systematic bias among the different segments.

Our SEM reinforces earlier empirical modelling work that showed TP is a reliable predictor of

the phytoplankton biomass in Lake Simcoe (Young et al., 2011; Winter et al., 2011), with the

robustness of the chlorophyll a-TP relationship during the post-dreissenids period being verified

at nearly all sites of the lake (Young et al., 2011). The only exception was at C1, the shallowest

segment in Cook’s Bay, where the historical empirical equation overpredicted the standing algal

biomass possibly due to increased dreissenid filtering activity. Our SEM results appear to differ

somewhat in that this relationship was fairly strong in the C1 segment (0.30± 0.11), but weak

and poorly identified in the middle part of Cook’s Bay (C6: -0.02±0.11). Yet, this discrepancy

should be interpreted with caution as the inclusion of additional covariates in our model along

with the use of contemporaneous measurements from individual samplings for all the water

quality variables (i.e., no temporal-averaging or lagged relationships were considered) largely

determines the relative magnitudes and signs (e.g., negative DIN-phytoplankton) of the various

ecological paths derived (Arhonditsis et al., 2007a,b). In Cook’s Bay, TP concentrations

generally decline moving northward from C1, suggesting that a significant fraction of the TP

load entering Cook’s Bay from the Holland River is retained in sediment, which was predicted

by our model. However, the interesting finding of the present analysis is the substantial

interannual variability of the corresponding estimates in segment C6 (Fig. A4-SI), along with the

weak (i.e., highly uncertain) causal links associated with bottom-up (TP→chla) and top-down

20

(herbivorous grazing→chla) factors (Fig. 2-3). The uncertainty characterizing both our models

in the middle area of Cook’s Bay may be indicative of a dynamic/intermittent environment that

could conceivably mask important cause-effect relationships when analyzing daily snapshots

from the system. Aside from all the structural and functional changes occurring in this shallow

embayment over the last two decades (Palmer et al., 2011), it is plausible that this uncertainty

may also stem from sediment resuspension events, triggered by wind forcing and episodic runoff

events, which in turn can have profound influence on local and lakewide biogeochemistry and

trophic functioning (Johengen et al., 2008).

The daily resolution of our analysis highlights the lakewide strength of the negative linkage

between Secchi disc depth values and chlorophyll a concentrations, although we note that this

path should have the opposite direction in a strict causal sense, i.e., chlorophyll a→Secchi disc

depth. The nature of the water clarity-phytoplankton relationship during the period modeled

(1999-2007) could have been partly shaped by the colonization of dreissenid mussels (Hecky et

al., 2004). Dreissenids can increase water clarity by reducing algae and other suspended solids

through their filtering activity, as well as by reducing whiting events (Evans, 2007). The

improved illumination of the water column has given rise to a dramatic proliferation of

submerged aquatic vegetation in the shallow Cook's Bay, and the mean macrophyte biomass

along with the areal coverage of submerged aquatic vegetation have increased by approximately

260% and 65%, respectively (Ginn, 2011). The increases in macrophyte biomass and abundance

may in turn have induced changes in the local phytoplankton community through a complex

array of direct and indirect effects (e.g., enhanced grazing pressure from pelagic zooplankton,

changes in nutrient cycling, increased sedimentation, shading, and allelopathy), with a notable

example the increase in the abundance of the small flagellate Cryptomonas (Winter et al., 2011).

Another factor that can affect phytoplankton community structure is the control exerted by

herbivorous grazing and our SEM analysis pinpoints the importance of this causal path

throughout the lake (Fig. 2-3). Triggered by the decline of planktivorous fish (smelt and lake

herring), the density of large Daphnia species (e.g., Daphnia longiremis) increased in Lake

Simcoe in the late 1980s and may have temporarily contributed to the decrease of phytoplankton

biomass (Young et al., 2011). Invasion by the zooplanktivore Bythotrephes longimanus may also

be indirectly affecting phytoplankton abundance as Bythotrephes is known to significantly

decrease cladoceran species richness and alter zooplankton behavioral patterns (Winter et al.,

21

2011). Our analysis clearly illustrates that future work on the impact of Bythotrephes and our

understanding of plankton dynamics in Lake Simcoe should be sought in the context of a

combined bottom-up and top-down forcing. While not explicitly considered in our analysis,

climate warming in the region has been suggested to be responsible for recent trends in the Lake

Simcoe thermal structure, such as an increase in the thermal stability of the water column during

the ice-free season, an earlier onset of thermal stratification and delayed fall overturn28. The

impacts of these changes on lake chemistry and biota are currently being investigated and there

is evidence that the multitude of stressors (invasive species, climate change) along with the

contemporary changes in the nutrient loading regime have induced discernible changes in the

phytoplankton biomass and community composition. Namely, the chlorophytes and

cyanobacteria abundance decreased throughout the lake, while the diatom community

composition patterns suggest shifts towards species (e.g., Fragilaria crotonensis) that may gain

competitive advantage in conditions of increased water column stability and reduced mixing

(Winter et al., 2011).

One of the benefits of the probabilistic assessment of Lake Simcoe water quality conditions is

the ability to optimize water quality monitoring programs and to identify specific areas that

require further research efforts. For example, our analysis delineated an area in Cook’s Bay

where the interplay among exogenous nutrient inputs, hydrodynamics, autotrophic and benthic

communities obfuscates the signals of critical relationships between water quality variables of

management interest. Our inability to detect significant causal linkages is also reflected in the

high model uncertainty in these locations, which in turn explains the predicted moderate

response of Cook’s Bay to the nutrient loading reductions examined. In this regard, we believe

that this finding highlights a critical future research question involving the capacity of wind-

driven physical forcing to produce localized “hotspots” of biological productivity in near-shore

regions (Johengen et al., 2008) that could, in turn, conceivably shape the broader impact of

dreissenids in Lake Simcoe (Palmer et al., 2011).

We conclude by reiterating that the present modelling analysis was based on two simple models,

which were used because of their ability to remain within the bounds of empirical parameter

estimation and therefore accommodate complete error analysis. In general, however, model-

based environmental management is preferred to have stronger mechanistic foundation, as this

provides additional assurance that the model will reflect the functional changes in the lake

22

ecosystem induced by the nutrient loading reductions. Yet, adopting a process-based model and

invoking extra complexity raises critical questions in regards to the existence of commensurate

knowledge of the multifaceted aspects of the Lake Simcoe dynamics or even the capacity to

depict them mathematically. Until we can give definitive positive answers to these questions, we

believe that the gradual incorporation of complexity, whenever possible and relevant, is the most

prudent strategy. Any such model development should be tightly coupled with rigorous

assessment of the underlying uncertainty and the Bayesian inference can be an invaluable tool

for assessing model uncertainty.

23

2.5. References

Anderson, T.R., 2005. Plankton functional type modelling: running before we can walk?: Journal

of Plankton Research 27, 1073-1081.

Arhonditsis, G.B., and Brett, M.T., 2004. Evaluation of the current state of mechanistic aquatic

biogeochemical modelling: Marine Ecology-Progress Series 271, 13-26.

Arhonditsis, G.B., Paerl, H.W., Valdes-Weaver, L.M., Stow, C.A., Steinberg, L.J., and Reckhow,

K.H., 2007a. Application of Bayesian structural equation modelling for examining

phytoplankton dynamics in the Neuse River Estuary (North Carolina, USA): Estuarine

Coastal and Shelf Science 72, 63-80.

Arhonditsis, G.B., Qian, S.S., Stow, C.A., Lamon, E.C., and Reckhow, K.H., 2007b.

Eutrophication risk assessment using Bayesian calibration of process-based models:

Application to a mesotrophic lake: Ecological Modelling 208, 215-229.

Arhonditsis, G.B., Stow, C.A., Paerl, H.W., Valdes-Weaver, L.M., Steinberg, L.J., and Reckhow,

K.H., 2007c. Delineation of the role of nutrient dynamics and hydrologic forcing on

phytoplankton patterns along a freshwater-marine continuum: Ecological Modelling

208, 230-246.

Arhonditsis, G.B., Stow, C.A., Steinberg, L.J., Kenney, M.A., Lathrop, R.C., McBride, S.J., and

Reckhow, K.H., 2006. Exploring ecological patterns with structural equation

modelling and Bayesian analysis: Ecological Modelling 192, 385-409.

Borsuk, M.E., Stow, C.A., and Reckhow, K.H., 2004. A Bayesian network of eutrophication

models for synthesis, prediction, and uncertainty analysis: Ecological Modelling 173,

219-239.

Chapra, 1997. Surface Water-Quality Monitoring;: McGraw-Hill Series in Water Resources and

Environmental Engineering.

Cheng, V., Arhonditsis, G.B., and Brett, M.T., 2010. A revaluation of lake-phosphorus loading

models using a Bayesian hierarchical framework: Ecological Research 25, 59-76.

24

Eimers, C.M., Winter, J.G., Scheider, W.A., Watmough, S.A., Nicholls, K.H., Recent changes

and patterns in the water chemistry of Lake Simcoe. J. Great Lakes Res. 2005, 31,

322–332.

Evans, D.O., 2007. Effects of hypoxia on scope-for-activity and power capacity of lake trout

(Salvelinus namaycush): Canadian Journal of Fisheries and Aquatic Sciences 64, 345-

361.

Ginn, B.K.. 2011, Distribution and limnological drivers of submerged aquatic plant communities

in Lake Simcoe (Ontario, Canada): Utility of macrophytes as bioindicators of lake

trophic status: Journal of Great Lakes Research 37, 83-89.

Hecky, R.E., Smith, R.E.H., Barton, D.R., Guildford, S.J., Taylor, W.D., Charlton, M.N., and

Howell, T., 2004. The nearshore phosphorus shunt: a consequence of ecosystem

engineering by dreissenids in the Laurentian Great Lakes: Canadian Journal of

Fisheries and Aquatic Sciences 61, 1285-1293.

Hiriart-Baer, V.P., Milne, J.E., and Marvin, C.H., 2011. Temporal trends in phosphorus and

lacustrine productivity in Lake Simcoe inferred from lake sediment: Journal of Great

Lakes Research 37, 764-771.

Johengen, T.H., Biddanda, B.A., and Cotner, J.B., 2008. Stimulation of Lake Michigan plankton

metabolism by sediment resuspension and river runoff. J. Great Lakes Res 34, 213-

227.

Krantzberg, G., 2004. Science must inform Great Lakes policy: Journal of Great Lakes Research

30, 573-574.

Leon, L.F., Smith, R.E.H., Hipsey, M.R., Bocaniov, S.A., Higgins, S.N., Hecky, R.E.,

Antenucci, J.P., Imberger, J.A., and Guildford, S.J., 2011. Application of a 3D

hydrodynamic-biological model for seasonal and spatial dynamics of water quality and

phytoplankton in Lake Erie: Journal of Great Lakes Research 37, 41-53.

25

Mills, E.L., Casselman, J.M., Dermott, R., Fitzsimons, J.D., Gal, G., Holeck, K.T., Hoyle, J.A.,

Johannsson, O.E., Lantry, B.F., Makarewicz, J.C., Millard, E.S., Munawar, I.F.,

Munawar, M., O'Gorman, R., Owens, R.W., Rudstam, L.G., Schaner, T., and Stewart,

T.J., 2003. Lake Ontario: food web dynamics in a changing ecosystem (1970-2000):

Canadian Journal of Fisheries and Aquatic Sciences 60, 471-490.

Ministry of the Environment, Government of Ontario, Canada and Lake Simcoe Region

Conservation Authority, 2009. Report on the phosphorus loads to Lake Simcoe. 18

pages.

Minns, C.K., and Kelso, J.R.M., 2000. NO! It is time for a Great Lakes Ecosystem Management

Agreement that SUBSUMES the Great Lakes Water Quality Agreement: Journal of

Great Lakes Research 26, 1-2.

Nicholls, K.H., 1997. A limnological basis for a Lake Simcoe phosphorus loading objective:

Lake and Reservoir Management 13, 189-198.

Palmer, M.E., Winter, J.G., Young, J.D., Dillon, P.J., and Guildford, S.J., 2011. Introduction and

summary of research on Lake Simcoe: Research, monitoring, and restoration of a large

lake and its watershed: Journal of Great Lakes Research 37, 1-6.

Stainsby, E.A., Winter, J.G., Jarjanazi, H., Paterson, A.M., Evans, D.O., and Young, J.D., 2011.

Changes in the thermal stability of Lake Simcoe from 1980 to 2008: Journal of Great

Lakes Research 37, 55-62.

W.F. Baird & Associates Coastal Engineers Ltd., 2006. Lake Simcoe hydrodynamic and water

quality model.

Winter, J.G., Young, J.D., Landre, A., Stainsby, E., and Jarjanazi, H., 2011. Changes in

phytoplankton community composition of Lake Simcoe from 1980 to 2007 and

relationships with multiple stressors: Journal of Great Lakes Research 37, 63-71.

26

Young, J.D., Winter, J.G., and Molot, L., 2011. A re-evaluation of the empirical relationships

connecting dissolved oxygen and phosphorus loading after dreissenid mussel invasion

in Lake Simcoe: Journal of Great Lakes Research 37, 7-14.

Zhang, W.T., and Arhonditsis, G.B., 2008. Predicting the Frequency of Water Quality Standard

Violations Using Bayesian Calibration of Eutrophication Models: Journal of Great

Lakes Research 34, 698-720.

27

FIGURES LEGENDS

Figure 2-1: (A) Basic principle and spatial segmentation of the Continuously-Stirred-Tank

Reactor (CSTR) model, forced with idealized sinusoidal loading, to predict epilimnetic total

phosphorus concentrations in Lake Simcoe, Ontario, Canada. (B) Hierarchical configuration of

the Lake Simcoe Bayesian network. The spatial heterogeneity is accommodated by viewing the

problem of parameter estimation as a hierarchy. At the bottom of the hierarchy are the

parameters for individual segments j; qj ~N(mj, sj). In the upper level, the segment-specific

parameters are specified probabilistically in terms of lakewide parameters or hyper-parameters; q

~N(m, s). (C) Structural equation model used to elucidate the interplay among nutrients, ambient

light conditions, phytoplankton and herbivore biomass.

Figure 2-2: Predicted annual phosphorus mass balance at the different segments of Lake Simcoe

during the study period (1999-2007).

Figure 2-3: Structural paths underlying plankton patterns in the nine segments of Lake Simcoe.

The direction and colour of the arrows represent the magnitude and sign of the posterior medians

of the standardized path coefficients. The standardized coefficients correspond to the shift in

standard deviation units of the dependent variable that is induced by shifts of one standard

deviation units in the explanatory variables, and thus provide a means to assess the relative

importance of the various model paths.

Figure 2-4: Predictions of the Bayesian network for the exceedance frequencies of total

phosphorus and chlorophyll α concentrations in Lake Simcoe under the present conditions and

two scenarios of phosphorus loading reduction.

28

Figure 2-1

29

Figure 2-2

30

Figure 2-3

31

Figure 2-4

32

Chapter 3 DYNAMICS OF P-BINDING FORMS IN SEDIMENTS OF A

MESOTROPHIC HARD-WATER LAKE: INSIGHTS FROM NON-STEADY STATE REACTIVE-TRANSPORT MODELLING,

SENSITIVITY AND IDENTIFIABILITY ANALYSIS2

3.1. Introduction

Phosphorus (P) is the typical limiting macronutrient for the growth of primary producers in

freshwater ecosystems and the mechanisms that effect P bioavailability in the water column are

well studied (Carey and Rydin, 2011; Schindler et al., 2008; Wetzel, 2001). In many catchments,

P loads that originate from human activities exceed natural loading by several orders of

magnitude (Falkowski et al., 2000). The anthropogenic P sources can be distinguished into (i)

point sources, especially effluents from waste water treatment plants; and (ii ) diffuse or non-

point sources, usually associated with agricultural activities and urban runoff (Schippers et al.,

2006). The level of exogenous P loading is causally linked with the manifestation of

eutrophication phenomena, such as excessive algal growth, poor water clarity, taste and odour

problems, hypolimnetic oxygen depletion, and subsequently decrease in the recruitment of

coldwater fish in deep stratified lakes (Evans, 2007). Thus, the main focus of lake restoration

projects usually revolves around the control of external point and non-point sources of nutrient

loading.

However, lake sediments act either as sink or source of a large number of organic and inorganic

compounds including phosphorus in the form of readily bioavailable phosphates. When acting as

a P source, lake sediments can considerably increase the P concentration in the water column and

2 McCulloch, J., Gudimov, A., Arhonditsis, G.B., Chesnyuk, A. and M. Dittrich, 2013. Dynamics of P-binding

forms in sediments of a mesotrophic hard-water lake: Insights from non-steady state reactive-transport modelling, sensitivity and identifiability analysis. Chemical Geology 354: 216-232. http://dx.doi.org/10.1016/j.chemgeo.2013.06.011

Contributions: AG & MD formulated research objectives and modelling methods. AG also performed sensitivity and identifiability analysis. JM and AG equally contributed to model development, calibration and validation. AC assisted with the generation of the calibration dataset. AG & JM wrote the paper with extensive inputs from MD & GA.

33

thus modulate the severity of eutrophication regardless of the level of external forcing

(Nürnberg, 2009; Smith et al., 2011). In general, the release of P from lake sediments (or internal

loading) is caused by a suite of physical, chemical, and biological processes such as: desorption,

ligand exchange mechanisms, dissolution of precipitates, mineralization processes, autolysis of

cells (Gao et al., 2005; Hupfer and Lewandowski, 2008; Kleeberg and Kozerski, 1997; Rydin,

2000; Zhou et al., 2005). Other environmental factors related to the release of phosphorus

include the temperature, redox potential (Eh), hydraulic conditions, nitrate and sulfate

concentrations, bioturbation and other biological activities (Gao et al., 2005; Hupfer and

Lewandowski, 2008; Kleeberg and Kozerski, 1997; Rydin, 2000; Zhou et al., 2005).

Consequently, the potential of P in the sediments to become a significant driving force in a

system is related to the conditions under which P can be immobilized or released. Such

information can be provided from the various P binding forms, such as the loosely adsorbed

labile P, redox sensitive FeOOH bound P, P bound to hydrated oxides of Al or Fe, calcium

carbonate bound P (apatite P), and organic P (Psenner and Pusco, 1988), see also the review by

(Lukkari et al., 2007). The predominance of different P binding forms offers insights into the

degree of system susceptibility to internal loading (Boestrom et al., 1988; Kopacek et al., 2005;

Nürnberg, 1988). Yet, despite the substantial efforts to elucidate sediment response to changes in

exogenous P loading, we still do not fully understand the underlying ecological mechanisms that

ultimately mediate the duration and extent of P release (cf. Lewis et al., 2007).

In this regard, dynamic modelling of P binding forms in the sediment can provide critical support

for water quality managers in developing appropriate scenarios regarding the “if", "how", and to

"what extent” internal loading will impact lake P concentrations (see Lewis et al., 2007).

Diagenesis modelling implements non-steady state transport reactive processes based upon

partial differential equations for organic matter decomposition, geochemical transformations

between solid and dissolved components along with biological activities coupled with the

physical processes of diffusion, compaction, and advection (Boudreau, 1997a; Reed et al.,

2011b; Couture et al., 2010; Van Cappellen and Wang, 1996; Dittrich et al., 2009). This family

of models can shed light onto crucial diagenesis processes that are extremely difficult to measure

in-situ. A characteristic example is the recent analysis of the long-term development of hypoxia

in deep waters and its impact on sediment properties, such as sapropel and iron-bounded P in

Mediterranean and Baltic Sea sediments (Reed et al., 2011a). Furthermore, diagenetic modelling

34

has been applied to quantify pathways of organic matter degradation from anoxic lake sediments

(Lopes et al., 2010) or FeS accumulation in deep stratified lake (Dittrich et al., 2009). However,

the application of diagenetic modelling as a tool for dynamic prediction of sediment P release

and immobilization still remains limited, and even rarer is the technical analysis of the most

sensitive parameters/processes that are directly linked with their predictive capacity and

structural uncertainty.

In this study, we calibrate and subsequently validate a dynamic transport-reaction, diagenetic

model which simulates depth profiles of P binding forms, organic carbon, solid iron, calcium and

manganese sediment content as well as the levels of dissolved compounds, such as oxygen,

nitrogen, pH and phosphorus. Our case study is Lake Simcoe, a mesotrophic hard-water system

located in Southern Ontario, Canada. We investigate three basins of the lake with differences in

their land use patterns, urbanization levels, and loading history (Gudimov et al., 2012). We

present results on simulated depth profiles of dissolved P as well as P binding forms, and their

seasonal and long-term dynamics in conjunction with the external loading rates and oxygen

concentrations at the sediment-water interface over the past 400 years. Furthermore, this paper

illustrates a framework for sensitivity and identifiability analysis of the model results on model

parameters. The parameters describe a wide range of biogeochemical processes, such as organic

matter degradation, bioirrigation and bioturbation, precipitation and dissolution of minerals,

adsorption and P transformations. Our analysis aims to address several important research

questions, such as: Can phosphorus retention in lake sediments be predicted based on sediment

mineralogy, sedimentation substance inputs, catchment type, and other characteristics? How

does sediment retention capacity with respect to phosphorus respond to changes caused by

human activities? What are the uncertainties in diagenetic model predictions and how many

parameters are uniquely identifiable?

3.2. Material and Methods

3.2.1. Study site

Lake Simcoe is the 5th largest lake in southern Ontario with some 400,000 people living in its

3,572 km2 watershed. Lake Simcoe has a surface area of 722 km2 with a maximum and mean

depth of 41.5 m and 14.2 m, respectively. The lake has a flushing time of approximately 13

years. Although the ongoing research in Lake Simcoe has provided considerable insights into the

35

interplay between external P loading and ambient water quality conditions (Palmer et al., 2011;

Young et al., 2011), there is a lack of understanding of the role of sediments in the lake P budget,

while the actual mechanisms of P internal loading is a matter of controversy (Hiriart-Baer et al.,

2011). Water quality modelling suggests that there is spatial and temporal variability of TP and

chlorophyll a, but we do not know to what extent this heterogeneity is modulated by the P release

from the sediments (Gudimov et al., 2012).

Three different basins have been investigated in this study: Cook’s Bay (C9), Kempenfelt Bay

(K42) and Main Basin (K45) (Fig. 3-1). These three basins have been chosen because they have

undergone different loading histories (Hiriart-Baer et al., 2011; Landre et al., 2011); Hiriart-Baer

et al., 2011) reports that the sedimentation rates in Cook’s Bay were about twice as high as in the

other basins at the beginning of the 19th century due to an extension of the agricultural and urban

land uses. Loss of wetlands and the channelization of the lower Holland River in the 1930s

caused a substantial increase of the sedimentation rates in Cook’s Bay. In the Kempenfelt Bay,

the urbanization activities associated with the City of Barrie’s population growth after the 1950s

is responsible for the increased sedimentation rates (Hiriart-Baer et al., 2011). The Main Basin

received a larger proportion of terrestrial organic matter, which is likely the result of erosion due

to de-forestation, a main contributor to the sedimentation fluxes. The lake as a whole is

considered to be a hard-water, mesotrophic, dimictic lake (MOE, 2010).

3.2.2. Model Formulation

3.2.2.1. Reactive-Transport Model

An 1-D non-steady state transport reactive model for sediment diagenesis of solid (Xi) and

dissolved (Si) substances was used in this study (Dittrich et al., 2009). The model accounts for

the molecular diffusion of dissolved species (the molecular diffusion coefficient DSi), velocities

of sediment movement (vsed and vwat) due to sedimentation flux (fXi), compaction of porosity θ

with depth (z), bioturbation (DB) and biogeochemical transformation rates (rXi and rSi) in time (t).

Briefly, the following differential equations have been implemented:

(3-1) ∂(θ Si )

∂t= ∂

∂zDB

∂(θSi )

∂z+θDSi

∂Si

∂z

+ rSi

− abioirrig * Θ∗(Si − SiSWI)

36

iXiii r

z

XD

zz

Xv

t

X +

∂∂

∂∂+

∂∂−=

∂∂

Bsed )(

(3-2)

The boundary conditions for sediment water interface, zsurf and the deepest sediment layer zmax:

(3-3)

(3-4)

(3-5)

(3-6)

where is the concentration of dissolved substance i in the water column at the sediment

water interface (SWI), and is a porosity of newly deposited sediment at sediment water

interface surface zSWI. The modeled solid Xi and dissolved Si species considered in the model

along with the associated reaction rates are listed in Tables 3-1,-2 and -3. The organic particles

are represented by degradable and inert fractions with mass composition presented in Table 3-4.

The other modeled solids aside from the P fractions are MnO2, FeOOH, CaCO3, FeCO3, MnCO3

and other inorganic compounds.

3.2.2.2. Reaction kinetics

The primary redox reactions for organic matter bacterial degradation (Table 3-2) are based on

Monod kinetics with inhibition terms to account for gradients in redox potential among oxidants

(Van Cappellen and Gaillard, 1996). The modeled oxidants are oxygen, nitrate, manganese

oxide, iron hydroxides and iron-sulfides (PR1-5), we also take into account ammonium oxidation

as a secondary redox reaction (SR1). The mineralization processes with methane are not modeled

in detail at this stage due to the lack of information on methane concentrations. Furthermore,

mineral precipitation and dissolution for carbonates are included in the model (MR1-4) as well as

equilibrium conditions for carbonic acid and bicarbonate dissociation, ammonium dissociation,

orthophosphate dissociation, and sulfide dissociation (ER1-7).

Si (zSWI) = SSWIi

Xi (zSWI) =fXi

vsed(zSWI)

θ(zSWI) =θSWI

0)( max =∂∂

zz

Si

SSWIi

θSWI

37

The model has been developed to study P retention in the sediments, especially the P binding

forms derived by sequential fractionation. In this study, we used the phosphorus fractionation

method from Psenner and Pusco (1988) as modified by Rydin (2000). The P forms separated

with this sequential fractionation include loosely adsorbed (labile) P (extracted with NH4Cl,

NH4Cl-TP), redox-sensitive bound P (extracted with bicarbonate dithionite, BD-TP), P bound to

hydrated oxides of aluminium or iron oxides (extracted with NaOH, NaOH-SRP), organic bound

P (extracted with NaOH, NaOH-NRP), carbonates bound P (apatite P) (extracted with HCl, HCl-

TP) and refractory P (Refract-P) (Psenner and Pucsko, 1988).

The phosphorus diagenesis model structure, depicted in Fig. 3-2, demonstrates the incorporation

of these P fractions into the model along with the processes and relevant reaction rates

considered. The advancement of the developed dynamic non-steady-state model is the simulation

of the formation of major phosphorus binding forms, i.e., absorbed P (NH4Cl-TP), redox-

sensitive Fe-P (BD-TP), aluminum-bound P Al-P (NaOH-SRP which is a small part (5%) of

NaOH-TP), organic P (NaOH-NRP and refractory P), apatite P (HCl-TP), and dissolved pore

water phosphorus from decomposition of organic matter over time. Organic P is modeled as a

portion of degradable organic matter, based on the Redfield stoichiometric composition. The

modelling of the sorption capacity of phosphorus by sediments was calculated using a modified

Langmuir adsorption isotherm equation (Table 3-2 PBR2, Zhou et al., 2005), given in Table 3-3.

Apatite P formation (Table 3-2, PBR3) is modeled using a precipitation dissociation reaction

based on Stumm and Morgan (1996). The redox sensitive Fe-P fraction is modeled based on an

assumption that Fe-P is formed in the presence of oxygen (Table 3-2, PBR3, Reed et al., 2011a)

and will be reduced in the absence of O2 (Table 3-2, PBR4).

3.2.2.3. Dataset and model parameters

Sediment and pore-water datasets collected from three study sites in the mesotrophic Lake

Simcoe in March and September 2010 have been used to calibrate and validate the model,

respectively (Dittrich et al., 2012). Porewater depth profile data for Ca, Fe, Mn, NO3, HPO4 as

well as data on porosity, organic carbon and P fractions were measured in 2011. pH and O2

profiles were measured with microsensors, while data on CaCO3 were used from Johnson and

Nicholls (1989). Total Fe and Mn in the surface sediment and at the depth of ca. 24 cm have

been measured by Landre et al. (2011). Data on alkalinity and ammonia at the SWI were

38

assumed to be equal to the maximum deep water data measured in the 2004-2008 monitoring

program (MOE, 2008).

The values of all model parameters are listed in Table 3-4 for the site K45. Equilibrium constants

for acid-base equilibria are derived from Stumm and Morgan (1996). The equilibrium processes

including Langmuir isotherms are formulated as dynamic processes with fast rate constants. The

maximum rates of the degradation, dissolution, and precipitation processes were calibrated

through minimization of the sum of squares of the weighted deviations between observed data

and model predictions. A number of specific parameters required for the model were derived

from the literature, such as sedimentation rates, bioturbation and sediment density (Hiriart-Baer

et al., 2011; MOE, 2010; Johnson and Nicholls, 1989).

A previous study by Stantec (2006) provided estimates of benthic invertebrate abundance in the

profundal zones of interest: ~ 2,000 individuals/m2 in station K42, 1,600 individuals/m2 in K45

and 17,200 individuals/m2 in C9. The dominant species are suspension feeding chironomidae

larvae (~50% for K45, ~36% for K42) which are burrow irrigators, deposit feeding oligochaetes

(~43% for K42, 17% for C9) and dreissenid mussels (~16% for K45 and K42, ~46% for C9).

The bivalve populations are represented by Sphaeriidae, which tend to burrow into the sediment

substratum, and fingernail clams. Due to the complexity of bivalve contribution to bioturbation

and bioirrigation, the bivalve activity was lumped together with other species described above

and common lakewide solute transport rates for bioturbation Db =30 cm2/year and bioirrigation α

= 10-7 s-1 were assigned to parameterize their year-round activity, and thus the seasonal

variability in the concentration of bottom dissolved oxygen or ice cover was not considered. In

the absence of experimental measurements and information about the formation and dimensions

of burrows, the 22Na tracer diffusion rates were taken as proxy for major solute variables of

interest. We also introduced an exponential decay function for these rates to delimit the

invertebrate’s activity within the oxygenated zone in the sediments (Reed et al., 2011b). The

bioirrigation term was accommodated with a non-local model (Couture and Van Cappellen,

2011; Boudreau, 1997b).

39

3.2.2.4. Boundary Conditions

3.2.2.4.1. Solid Components

The boundary conditions for the sedimentation fluxes are defined with a piece-wise approach,

postulating that the maximum flux of matter occurs in summer and the minimum in winter (Fig

3-4). The organic and inorganic components of the total flux are shown in Fig 3-3, and the

proportion of each component was determined through the model calibration. The beginning of

the simulations for each sampling station was determined using sedimentation rates taken from

(Landre et al., 2011). The starting dates reflected the sediment depth determined as 1760 AD,

1607 AD and 1432 AD for stations C9, K42 and K45, respectively. The fluxes of FeS and

Fe3PO4 were set equal to zero at the sediment-water interface.

3.2.2.4.2. Dissolved Components

The boundary conditions for the O2 concentrations at the SWI were also defined with a piece-

wise approach, postulating that the maximum O2 concentration occurs in the winter when there is

less consumption from the biota and the minimum concentration in the summer when the lake is

stratified (Fig. 3-4). The boundary conditions are given in Table 3-4. Finally, the temperature in

the sediment was treated as a constant throughout the sediment depth profile according to the

empirical patterns reported in Lake Simcoe.

3.2.3. Sensitivity and identifiability analysis

The technique for sensitivity and identifiability analysis follows the framework originally

introduced by Brun et al. (2001), which is founded upon the derivation of linear sensitivity

functions for each state variable against any parameter θ j:

(3-7)

Where ∆�� represents an apriori uncertainty range of the parameter ��, set equal to 10% and sci

is a scale factor of the state variable yi. The factors sci are used to scale the model outputs and

thus make the results for the various model endpoints comparable. In this study, the scale factors

iy

j

i

i

jji

y

scs

θθ

∂∂∆

=,

40

were set equal to the maximum concentrations of each substance and are listed in Table B1-SI of

Appendix B.

The parameter sensitivity ranking was based on the following sensitivity measure:

. (3-8)

where ���� represents the norm of the vector of sj which depicts the importance of the parameter

θj. A large norm implies that a perturbation in a particular parameter induces significant changes

on the vector of the model endpoints, which in turn makes the parameter identifiable given the

available data, if all other parameters remain fixed.

In a general context though, we can state that a set of model parameters Θ is identifiable from the

calibration data, only if the following criteria are simultaneously met:

1. Model outputs should indicate sensitive dependence on the parameter set Θ . With

increasing number of parameters model sensitivity is expected to decrease.

2. A change in model output caused by a relative change in one parameter should not

be compensated by a change in other parameters of the same set Θ.

The information on the sensitivity of model outputs on parameters can be combined with

information on the degree of linear dependence (or collinearity) of sensitivity functions in order

to find parameter sets that can be estimated from experimental/field data (Omlin et al., 2001).

The analysis of the degree of linear dependence of sensitivity functions is similar to the

technique recommended for collinearity analysis of influence factors in linear regression (Belsley

et al., 1980; Beisley, 1991; Draper and Smith, 1998). If the sensitivity functions sij for a given

parameter set are linearly dependent, changes inmodel outputs induced by a small change in one

parameter can be approximately compensated by appropriate changes in other parameters of the

same parameter set.

j

n

ijij

ns

nsθ

11)(

1

2,

msqr == ∑=

δ

iy

iy jθ

41

In this study, we have applied the identifiability framework proposed by Brun et al. (2001), using

the collinearity index γ to assess the degree of near-linear dependence among k parameters in a

particular subset:

||ˆ||min

1

1|||| βγ

β Sk

=

= (3-9),

where �� = ����� ⋯ ��� … … …��"� ⋯ ��" # represents the matrix of the normalized sensitivities of the k

parameters in the subset, i.e. ��� = �$%‖'(‖ against the n model outputs, and ββββ=(ββββ1,...,ββββk)T represents a

vector of coefficients with the constraint ||ββββ=1||. In essence, theγ index measures linear

dependence among a subset of parameters as the reciprocal of the minimum norm that can be

obtained by the linear combination Ŝββββ, which in turn is known to be equal to the square root of

the smallest eigenvalue of the matrix ŜTŜ (Belsley, 1991).

A γ value equal to 1 suggests absence of collinearity, whereas a value of 20 suggests that a

change in the model outputs caused by a shift in a parameter θj can be compensated to 5% by

appropriate adjustments in the other parameters of the subset. A high value of a collinearity

index thus indicates that the parameter set is poorly identifiable, even if the individual

parameters are very influential to the model output. In particular, any γ value higher than 10

depicts a relatively serious identifiability problem (Brun et al., 2001).

3.2.4. Numerical Implementation

The model equations were implemented in the computer program AQUASIM (Reichert, 1994;

Reichert, 1995; http://www.aquasim.eawag.ch), designed for simulation and data analysis of

aquatic systems. This program first discretizes the spatial derivatives of the partial differential

equations and then integrates the resulting system of ordinary differential equations in time with

the implementation DASSL (Petzold, 1983) of the implicit (backward differencing) variable-

step, variable-order GEAR integration technique (Gear, 1971). The sediment depth profile of 19

cm was discretized with 250 grid space planes. The identifiability analysis was performed with

IDENT package (http://www.aquasim.eawag.ch). The model has been calibrated for the data set

42

collected from three stations (K45, K42 and C9) in March 2010 and validated against the data

collected in September 2010. Sensitivity and identifiability analysis presented below has been

performed for station K45, as a representative site for the whole lake.

3.3. Results

3.3.1. Depth profiles of solids and dissolved substances

The modeled outputs for the porosity and pH of the sediments are shown in Fig. 3-5. Our results

suggest that the model accurately reproduces porosity, and also provides a good representation of

the sediment pH in sites K45 and C9 but slightly underestimates pH in K42. Because pH is a

sensitive integrating indicator for a set of biogeochemical reactions (Jourabchi et al., 2005), the

good agreement between the modeled and measured values of pH for sites K45 and C9 indicates

that the simulated reaction/processes were generally plausible. The model also reproduced the

fact that each site differs in regards to its oxygen profile (Fig. 3-5). Site K42 has a very shallow

penetration depth of 1 cm, while C9 has a deeper penetration depth of 2.5 cm and K45 falls in

the middle around 2 cm. The oxygen penetration depths reflect the oxygen demand for the

mineralization of the settling organic matter, and are closely associated with the boundary

conditions assigned to each site. In Kempenfelt Bay (K42), the sedimentation flux has a very

high portion of organic matter (Fig. 3-4), which underscores the elevated primary production

rates in the water column. Whereas, the sedimentation fluxes in C9 and K45 have much lower

proportions of organic matter and thus higher O2 penetration depths. Furthermore, the model

reproduced the depth profiles of solid matter with good accuracy (Fig. 3-6). Each site shows a

decrease of organic matter from the sediment surface to about 10 cm and remains relatively

constant ever since. The difference between the surface concentration, ~80-90 mg C/g DM for

K45 and K42 and ~60 mg C/g DM for C9, and the stabilized concentration of the deep sediments

(at approximately 10 cm depth) is the amount of organic matter mineralized in the sediment.

The model calibration was carried out with the boundary conditions described above, and aimed

at reproducing the general trends observed in the pore water and solid sediment depth profiles.

Initial values of the reaction parameters were taken from our previous experimental study

(Dittrich et al., 2009) as well as from the literature, and their values were further adjusted to fit

the experimental data while taking into account the parameter ranges reported in the literature

(Table 3-3). We also conducted a model validation exercise which showed good agreement

43

between empirical and simulated depth profiles for solute and solid matter for September 2010,

rendering support to the model parameterization.

3.3.2. Depth profiles of phosphorus in sediments

The model successfully reproduced the P fractionation data, i.e., absorbed P, organic P, apatite P,

Al-P and redox sensitive (Fe-P), as well as the total phosphorus at each site (Fig. 3-7). However,

at site C9, the calculated fraction of adsorbed P is lower than those measured, indicative of the

fact that this site is dominated by sediment erosion from the surrounding intensive agricultural

areas. Most likely other geochemical (e.g. including nitrogen) and transport processes are crucial

for the P-adsorption to the sediments at this basin. The organic P fraction and the total

phosphorus (TP) closely resemble the total organic matter profiles, as they are high at the surface

and then level out in the deeper sediments. The difference between the surface concentration and

the deeper layers represents the P release from the sediments. At sites K45 and C9, the organic P

fraction is responsible for most of the P release. The model predicts that most of the dissolved P

is released into the overlying water column and that only a small fraction of the deposited

reactive Fe is ultimately buried as FeS(s) (Fig. 3-7). Interestingly, site K42 shows a large amount

of redox sensitive P at the surface as well as a large amount of organic P (Fig. 3-7), implying that

a much greater P flux from the sediments to the water column should be expected if conditions at

the sediment-water interface become anoxic. A constant amount of apatite and absorbed P in the

fractionation profiles is indicative of their immobilization in the sediments. For each site, apatite

P is the predominant fraction suggesting a large P retention capacity in Lake Simcoe sediments

(Fig. 3-7).

The modeled dissolved phosphorus profiles provide a reasonable description of the phosphate

concentration gradient at the sediment water interface (Fig. 3-8), despite the challenges posed by

the substantial spatial and temporal variability in Lake Simcoe (Lewandowski et al., 2002). The

latter pattern also suggests significant seasonality of the internal P-release. Based on Fick’s Law,

the estimated benthic fluxes vary seasonally from 0.05 to 0.3 mg P/m2/d, which is similar to the

estimate derived from measured P profiles (Dittrich et al., 2012). According to our model results,

Kempenfelt Bay (K42) exhibits the highest gradient in depth profile of dissolved phosphorus,

primarily driven by the release of the redox sensitive P fraction along with the higher

degradation kinetics that deplete oxygen after the top 3-4 cm of sediments. This finding is also

44

on par with the empirical evidence that Kempenfelt Bay was experiencing hypoxia problems and

internal P loading (Evans, 2007; Nürnberg, 2012).

3.3.3. Seasonal versus long-term dynamics of P binding forms at the sediment surface

The model results demonstrate strong seasonal dynamics of P-binding forms (Fig. 3-9), and their

trends are closely linked to organic matter fluxes and oxygen concentrations at the sediment

water interface (see Table 3-5). In particular, it has been pointed out that P dynamics in Lake

Simcoe, a “marl lake”, may be connected to whiting events or CaCO3 precipitation in the water

column during summer stratification (Nicholls, 1995). In many hard-water lakes, P is supposed

to co-precipitate with calcium carbonates formed in the water column (Koschel et al., 1983;

House, 1990). Our results provide evidence for this hypothesis as both organic P and apatite P

are profoundly located in the surface sediments during the summer stratification (Fig. 3-9). This

pattern has been observed in other hard-water lakes during artificial deep water calcium

carbonate precipitation (Dittrich et al., 2011) or natural calcium carbonate precipitation

(Gonsiorczyk et al., 1998). The whiting phenomenon is an important characteristic for the

ecological health and self-recovering of hard-water lakes (Koschel et al., 1983), and has been

applied as ecological technology for lake restorations (Dittrich et al., 2011). Consequently, the

dynamic simulation of sediment diagenesis can conceivably support decision makers by

providing projections on the long-term responses of sediments when a possible treatment is

implemented (Schauser et al., 2003).

In all basins, the low flux of organic matter in winter coincides with the peak oxygen and low

organic P concentrations. Likewise, diagenesis models for marine systems found a strong link

between hypoxia and P forms in sediments in the Baltic Sea (Reed et al., 2011b). Model

simulations showed that the variability of redox-sensitive P is driven by total sedimentation flux

dynamics and oxygen concentration at the sediment water interface. According to data from

sediment mapping (Landre et al., 2011), iron is enriched in all sediment layers in Kempenfelt

Bay and therefore is readily available as a P binding partner. On the other hand, if conditions at

the sediment surface become anoxic, dissolution of iron hydroxides will be intensified leading to

the release of redox sensitive P.

45

Despite being the smallest fraction in absolute values, the adsorbed P-fraction demonstrated

significant variability, which was captured by the model. This finding is very promising from a

management perspective. The adsorbed-P fraction is in equilibrium with P in the porewater,

thereby determining the diffusive flux into the water column. Thus, our model can provide

decision makers with a reliable prediction of diffusive P flux from the sediments into water

column, the so-called internal loading effect, which is a controversial issue for mesotrophic lakes

as well as lakes in a transitional phase (Katsev et al., 2006; Rydin, 2000; Nürnberg, 1988). Our

model predicts that the Al–P fraction exhibits seasonal variability. Being a redox insensitive

fraction, Al–P is important for P immobilization (Kopacek et al., 2005). Naturally high (or

artificially elevated) concentrations of aluminum hydroxide (Al(OH)3) have been shown to

naturally lower (or artificially reduce) hypolimnetic P release that typically occurs under

reducing conditions. The molar ratios of Al–P to Fe–P can be operationally used as targets for

estimating the potential sediment P release and Al dosing of P-rich sediments to prevent

hypolimnetic P release under anoxic conditions (Kopacek et al., 2005). The presented model

allows estimation of this ratio and subsequent prediction of its broader implications in the system

dynamics. Therefore, it is of wide interest for investigations of both natural and artificially

treated sediments under reducing conditions. However, it is also the second smallest fraction in

absolute values (ca. 1% of TP), and thus cannot determine the extent of P immobilization. The

molar ratio between Al in Al–P fraction to Fe in Fe–P fraction is around 2.7, which is close to

the threshold value for redox sensitive P release from sediments (Kopacek et al., 2005). This

ratio has been used as an operational target for preventing hypolimnetic P release under anoxic

conditions, and when it is greater than 3, P release under reducing conditions practically ceases

(Kopacek et al., 2005).

Quite recently, a detailed paleo-limnological study documented sedimentation rates for three

basins of Lake Simcoe (Hiriart-Baer et al., 2011). Using this data, we simulated the P binding

forms at the sediment surface through a 400-yr period (Fig. 3-9 upper panel). The modeled long-

term patterns of P-fraction reflect a complex interplay between the total sedimentation fluxes and

P transformations (Fig. 3-9, Table 3-2). In Cook’s Bay (C9), the two-fold increase in the total

loading after the 1940s resulted in an accumulation of apatite P in the surface sediments. Apatite

P include phosphorus incorporated in carbonates, formed by both autochthonous (e.g., P co-

precipitated with carbonates during whiting events, Gonsiorzyok, 1998) or allochtonous (e.g.,

46

phosphorus in soil particles flushed from the catchment) material. Thus, the increase of apatite P

may reflect both an increase of CaCO3 precipitation within the lake and/or increased erosion

from the catchment. In the case of Cook’s Bay, the documented history of land use provides

evidence that apatite P accumulation has likely occurred due to an increase of the agricultural

activities and subsequently erosion (Hiriart-Baer et al., 2011).

By contrast, the sediments in Kempenfelt Bay (K42) accumulated organic-P (Fig 3-9, middle

column). This accumulation is particularly pronounced after the 1940s, coinciding with the

expansion of urbanization and other associated anthropogenic activities (LSRCA, 1993). This

finding is also in agreement with a recent 13C isotope analysis asserting that wastewater effluent

might be a dominant driver of P-loading in the Kempenfelt basin (Hiriart-Baer et al., 2011). High

amount of redox sensitive P supports the empirical evidence that this basin has experienced

severe hypoxia events from the 1980s until the mid 1990s. The high Fe amount due to the

geological background of Kempenfelt Bay provides a redox-dependent binding capacity for

phosphorus on iron oxides and hydroxides. However, under reductive conditions induced by

hypoxia, redox-bounded P can be dissolved (Reed et al., 2011b), and this pattern has often been

observed in various stratified freshwater systems (e.g. Ulrich, 1997; Hupfer et al., 1995).

3.4. Discussion: which processes impact the dynamics of P binding forms in sediments

Sensitivity analysis allows us to determine the subset of parameters that are more influential on

the model predictions (Brun et al., 2001; Omlin et al., 2001; Katsev et al., 2006; Arhonditsis and

Brett, 2004). Sensitivity analysis can dictate which parameters need to be constrained with more

information from the field and/or the literature. The ranking of the 34 parameters considered has

been calculated using the sensitivity measure δ (Table 3-5). The central conclusion drawn from

our study is that in order to elucidate the P diagenesis processes and subsequently predict P

efflux to the water column of a hard water mesotrophic lake the concentrations of dissolved

substances such as oxygen (SO2SWI), pH (SH

SWI), alkalinity (SHCO3SWI), nitrate (SNO3

SWI), calcium

(SCaSWI), iron (SFe

SWI), manganese (SMnSWI) and the sedimentation fluxes of organic and inorganic

matter (αOrg, αOrg_inert) should be accurately determined in addition to P species.

47

3.4.1. Oxygen and pH at the sediment water interface and composition of settling matter

Our results primarily highlight the sensitivity of the modeled outputs to the concentrations of

dissolved oxygen (SO2SW1) and pH (SH

SW1) at the sediment water interface. Furthermore, the

model is most sensitive to the composition of settling matter, especially the portions of organic

reactive and refractory carbon (αOrg and αOrg_inert). The second group of parameters in regards to

the sensitivity ranking comprises alkalinity (SHCO3SW1), NO3 sediment surface concentrations

(SNO3SWI), the settling part of redox sensitive phosphorus (αInorg_P_Fe-P), bioturbation (DBioturbation),

the degradation rate of redox sensitive phosphorus (kdegFe-P), equilibrium constant of siderite

(KeqFeCO3num). Interestingly, bioturbation appears to be a critical factor in the model, even though

the effect of benthic invertebrates was only limited to the oxygenated layer. Thus, it is necessary

to have experimental evidence for the functional role of benthic organisms in stratified

mesotrophic lakes, if one wants to understand phosphorus diagenesis over time. It has already

been reported that chironomids can potentially increase the flux of dissolved phosphorus from

the sediments by ingesting large quantities of interstitial pore water, while under anoxic

conditions their combined effect of bioturbation and bioirrigation is insignificant (Graneli, 1999).

The small-scale movements of bivalves aside from their bio-diffusing activity can potentially

induce a bioturbation effect on the sediments, if they are able to bury into the sediment bed, and

thus increase the nutrient flux. Depending on their abundance, bivalves can also become an

additional source of organic matter as well as a sink of dissolved oxygen through their

respiration. In the next iteration of the model, our aim is to explicitly consider the seasonality of

benthic activity, thereby leading to a more realistic simulation of their role in P retention.

3.4.2. Sedimentation of calcium carbonates and P adsorption and binding to carbonates

A lower sensitivity index has been found for the two parameters representing the role of oxygen

with the degradation processes (kO2 and KO2satur), flux of calcium carbonate (fCaCO3), and maximal

phosphorus absorbance capacity of the sediments (Qmax). The sensitivity ranking of the

equilibrium constant of siderite KeqFeCO3num and calcium carbonate flux (fCaCO3) underscores the

importance of the Ca-bounded form of phosphorus in the fate of P in the sediments. Close to the

latter factor were the parameters for calcium carbonate dissolution (keqCaCO3diss), fraction of

settled inorganic iron (αInorg_Fe_Other) and bio-irrigation coefficient (αBioirrig). This finding supports

48

the results that apatite P is a significant fraction of the phosphorus pool in the sediments of Lake

Simcoe (Hiriart-Baer et al., 2011; Dittrich et al., 2009). The impact of calcium carbonate flux

(fCaCO3) on modeled outputs stems from the dominance of the Ca-bound form of phosphorus in

the sediments. A critical question arising though is whether apatite P directly enters the system

from the watershed or it is being formed in water column and subsequently settles down to the

lake bottom.

3.4.3. Parameters of minor sensitivities

Lower sensitivity rankings were assigned to the rate of compaction (kθ), nitrification rate (knitri),

as to the concentration of calcium at the sediment surface interface (SCaSWI). Also, the rate of

secondary reaction (koxiHS), rate constant of OM degradation with manganese oxides (kMnO2)

belong in this category. Likewise, model outputs are less sensitive to dissolved iron

concentration at the sediment water interface (SFeSW1), absorbance of P (KAbsorb), half-saturation

constant of OM degradation with iron hydroxides (KFeOOHsatur), acid base constant for sulphur-

system keqS1, and rate constants of OM degradation with nitrate (kNO3), boundary conditions for

concentrations of dissolved manganese (SMnSW1), HS (SHS) at the sediment water interface, half

saturation constant of OM degradation with nitrate (KNO3satur), rate of OM degradation with iron

hydrooxides (kFeOOH), parameter for formation of apatite P (KeqApatite), sedimentation flux of

manganese oxides (fMnO2), half-saturation constants of OM degradation with manganese oxides

(KMnO2satur), acid base constant for carbonates solubility (keq2) and kinetics of redox sensitive P

(kFe-P). These findings are on par with our calculations of organic carbon mineralization rates,

showing that organic carbon is almost 90% mineralized by oxygen in the sediment depths

considered in this study. Similar observations have been done on the Baltic Sea, where the

majority of re-mineralization also occurs by means of aerobic respiration with the maximum

occurring shortly after the deposition of the spring bloom when both labile organic matter and

oxygen are readily available (Reed et al., 2011b).

3.4.4. Identifiability analysis

In this study, our aim was to elucidate the identifiability problems arising from the compensation

effects among different subsets of parameters. The compensation effects can be deduced from

the collinearity index γ among the investigated parameters. When the index γ lies below a critical

level of 10-20, then the interactions among the parameters do not severely limit their

49

identifiability. Although there is an extremely high number of parameter combinations that can

be formed, the γ index is expected to reach a maximum value after a certain parameter subset

size. Identifiability studies showed that the maximum collinearity index increases very rapidly

with the size of the parameter set. Thus, applications of identifiability analysis can examine

relatively low parameter set sizes without losing much information (Omlin et al., 2001). For

example, Omlin et al. (2001) found that the collinearity index increased up to 9.2 for parameter

subsets of size 2, to 17.0 for parameter subsets of size 3, and to 18.1 for parameter subsets of size

4. This result also implies that despite the large amount of calibration data in that study, there

were already sets of three parameters that led to serious identifiability problems. In our study, we

tested 35 different parameter sets and 22 (the most typical ones) are presented (Table 3-6, 1a-7c).

The parameters have been grouped according to their origin and their sensitivity ranking (Table

3-5). The parameters are divided among those estimated experimentally or supported by

available measurements and those estimated solely through calibration (Brun et al, 2001). A

second criterion to divide the parameters is their sensitivity ranking in Table 3-5. The two groups

of parameters have been cross-examined in different parameter permutations, in which highly

ranked "field measured" parameters, e.g., SO2, and highly ranked "estimated" parameters, e.g.,

kdegFe-P, were grouped together to test their identifiability.

The first five parameter sets, 1a-e, in Table 3-6 with a collinearity index γ below 10-20 suggest

the absence of compensation effects among the process rate constants for the degradation with

oxygen (kO2), degradation rates of redox sensitive P (kdegFe-P), rate of formation of redox sensitive

P (kFe-P) (sets1a,b), as well as the nitrification rates (knitri), rate of OM degradation with nitrate

(kNO3) (sets 1c, d), manganese oxides (kMnO2) and iron hydroxides (kFeOOH) (sets 1e, f). The

results for the sets1a-b demonstrate that the process rates of formation and degradation of redox

sensitive phosphorus (kFe-P and kdeg Fe-P) could be identified simultaneously with the rates of OM

degradation with oxygen (kO2). Although the addition of the nitrification rate (knitri) and the rate

constant of OM degradation with nitrate (kNO3) leads to an increase of the collinearity index to

3.98 or 4.08 (parameter sets 1c, d), the actual value still stays within the range that suggests

minimal compensability problems among the parameters considered. The inclusion of two more

rate constants for OM degradation with manganese oxide (kMnO2) and iron hydroxide (k.FeOOH)

leads to an increase of the collinearity index to 10.04 (parameter set 1e). The subsequent

consideration of the formation rate for redox sensitive P (kFe-P) increases the collinearity index γ

50

to 14.39, which gets close to the upper limit of the acceptable identifiability range (Brun et al.,

2001). Consequently, our study suggests that the available empirical information on phosphorus

binding forms and basic sediment characteristics is adequate for achieving a robust identification

of a substantial number of parameters.

The parameter set 2a clearly demonstrate that that the ratios of degradable and inert organic

matter (αOrg, αOrg_inert) in the sedimentation flux have no compensation problems and can be

identified from our model results. Inclusion of the two rates of OM degradation with oxygen

(kO2) and nitrate (kNO3) increases of γ to 6.88, but all parameters are still identifiable (set 2b).

However, if the parameter set (2c) includes parameters for iron sedimentation flux (αInorg_Fe_Other)

and redox sensitive P sedimentation flux (αInorg_Fe-P), the identification problem arises and the

collinearity index γ (17.63) is beyond the critical value. This means that impact of the ratios of

degradable and inert organic matter components (αOrg, αOrg_inert) and OM degradation rates with

oxygen (kO2) and nitrate (kNO3) may compensate the impact of redox sensitive P and Fe

sedimentation fluxes. This finding points out the importance of having data on Fe and redox

sensitive P flux in addition to OM composition and degradation with O2 and NO3.

Combing the rates of the primary degradation with oxygen (kO2), nitrate (kNO3), manganese

oxides (kMnO2), iron hydrooxides (kFeOOH) and secondary degradation processes of nitrification

(knitri)), the degradation rate for redox sensitive P (kdeg Fe-P) along with the ratios of degradable

and refractory organic matter in the sedimentation flux (αOrg, αOrg_inert) into a parameter set 3b

(set 3a is the same as set 1e) also leads to the collinearity index that is far beyond the critical

values. The results demonstrated that the rate constants for OM primary degradation processes,

rate constant for nitrification and the formation of redox sensitive P can be identified from our

data, but the addition of parameters for the part of organic degradable and refractory matter in

the sedimentation flux leads to compensability problems. However, when we also consider the

part of organic degradable and refractory matter in the sedimentation flux, the distinct

characterization of the parameters included in the set 3b is compromised, leading to the

conclusion that it is crucial to have experimental data on the composition of the sedimentation

flux and the iron and manganese speciation in the sediments.

In agreement with the sensitivity analysis, the boundary conditions for O2 (SO2SWI) and pH

(SHSWI) (parameter set 4a) at the sediment-water interface have no compensability problems

51

(γ=1.65); the addition of a parameter for the P adsorption capacity (Qmax) (parameter set 4b) did

not impact the collinearity index. Inclusions of concentrations for nitrate (SNO3 SWI) and

bicarbonate (SHCO3SWI) at the sediment-water interface (parameter sets 4c, d) increases γ to a

value beyond the critical values, reflecting the fact that the existing empirical information is not

adequate to properly constrain the model. he parameter set 5a with γ=9.18 demonstrates the

absence of compensability problems for the concentration for O2 (SO2SWI ) and pH (SH

SWI) at the

sediment water interface, the rate constants for OM degradation with oxygen (kO2) and nitrate

(kNO3), the ratios of degradable and inert of organic matter (αOrg, αOrg_inert). Inclusions

(parameter set 5b) of the concentration for nitrate (SNO3SWI) and bicarbonate (SHCO3

SWI) at

sediment water interface lead to γ =34.91, stressing the need to study the associated processes in

the field; namely, denitrification and calcium carbonate dissolution.

The parameter sets (6a, b) showed that the rates of OM degradation with oxygen (kO2), nitrate

(kNO3), nitrification rate (knitri) and the degradation of redox sensitive phosphorus (kFe-P) could be

identified (γ=3.98). When the constants for carbonate dissolution (keqCaCO3diss) has been added,

the collinearity index slightly increased to γ=4.73. This finding highlighted the importance of

measurements of calcium-carbonate systems at the sediment water interface.

The parameter set 7a demonstrates that the half-saturation concentrations of OM degradation

with oxygen (KO2satur), nitrate (KNO3

satur), manganese oxides (KMnO2satur), iron hydroxides

(KFeOOHsatur), parameters for adsorption P (KAbsorb) and precipitation constant of siderite (Keq.FeCO3)

can be identified, also when parameter for formation of Apatite P (KeqApatite) has been included

(parameter set 7b). However, the further inclusion of OM degradation rates with oxygen (kO2),

nitrate (kNO3), iron hydroxide (kFeOOH), manganese oxides (kMnO2) and formation rate for redox

sensitive P (kFe-P) leads to an increase of collinearity index, so all 13 parameters cannot be

identified from the available data set.

To put our results into perspective, identifiability studies for biogeochemical lake (Omlin et al.,

2001) and river water quality models (Reichert and Vanrolleghem, 2001) reported approximately

the same number of identifiable parameters. On the other hand, the analysis of a diagenesis

model with significantly more data available showed a greater number of identified parameters

(Dittrich et al., 2009). In a non-steady-state diagenetic modelling study in Lake Zug (Dittrich et

al.,2009), 27 parameters have been found to be identifiable compared to 7 identifiable parameters

52

in the present study (set 1f). A plausible explanation lies in the availability of experimental data

to calibrate the model and therefore to effectively determine model parameters. While in the

Lake Zug study, a four-year seasonal data set on sediment geochemistry was available, the

present study only used two years of field data to build the basics for the model calibration

(Dittrich et al., 2009).

It should be noted that the identifiability of model parameters does not guarantee ecologically

sound values. Biases in the model parameterization can not only stem from parameters that are

not identified from the data, but also from the deficiencies in the model structure and

mathematical foundation. In our study, the most important parameters are the rates for OM

degradation with oxygen (kO2) and nitrate (kNO3), oxygen and pH at SWI, and degradation of

redox sensitive P (kdegFe-P). Our sensitivity and identifiability analysis exercise highlighted the

significance of monitoring the calcium-carbonate system in the sediments for the diagenesis of

phosphorus in hard-water lakes. Furthermore, the data on the dynamics and composition of the

sedimentation fluxes, especially organic carbon, and the portion of redox-sensitive phosphorus,

are of great importance. Measured depth profiles of phosphorus binding forms and organic

matter provide a large amount of information on phosphorus diagenesis. Consequently, the rates

of redox sensitive P degradation (kdegFe-P), sediment P maximum adsorption capacity (Qmax) and

the rates of apatite P formation (KeqApatite) can be estimated accurately. In summary, the

identifiability analysis clearly showed that the majority of our model parameters can be

reasonably identified, supporting the likelihood of achieving robust predictions on phosphorus

fluxes and dynamics of phosphorus binding forms at the sediment surface.

3.5. Conclusions

In the present study, we developed a dynamic reaction-transport model for P transformation and

retention in lake sediments. We also integrated limnological historical data on sedimentation

rates and oxygen in the deep water of the lake as boundary conditions. The model reproduced

depth profiles of phosphorus binding forms, solid-phase, pore-water, and sediment-water

interface concentrations during the mid-spring and early fall period in three basins of the

mesotrophic, hard-water Lake Simcoe.

The non-steady state diagenesis model reveals that apatite-P dominates the P forms in Cook's

Bay, which has been overwhelmingly influenced by agricultural activities in the corresponding

53

watershed during the last 100 years. In contrast, Kempenfelt Bay has been primarily impacted by

urbanization and experienced oxygen depletion in the deep water. Thus, we found that organic P

binding forms dominated over redox sensitive P when urban loading intensified with phosphorus

discharges from waste-water treatment plant which was easily capitalized in phytoplankton

biomass due to its higher bioavailability . Furthermore, we quantified the seasonal dynamics of

benthic P fluxes into the water column in three different basins and tracked the phosphorus

binding forms in the surface sediments over 200 years. The model reasonably quantified the

historical P fluxes to and from the sediments, and thus can be used as a predictive tool to support

the quantification of lake P budgets under different loading and oxygen conditions.

Our findings indicate that Lake Simcoe experiences internal loading that may be causing an

increase of primary production as well as a disconnect between external loading and system

response (Winter et al., 2007; Hiriart-Baer et al., 2011). This result is also in agreement with the

evidence of P accumulation in the deep lake waters (Nürnberg et al., 2012). Our analysis also

demonstrated that the model outputs are sensitive to the concentrations of dissolved oxygen and

pH at the sediment water interface. The sensitivity with respect to these factors overwhelmingly

dominates over all other parameters. Furthermore, the characterization of the sedimentation

fluxes is the second strongest factor that can influence the inference drawn by the model;

namely, the composition of settling organic matter, reflected as the ratio of degradable and inert

organic matter.

Because of the substantial empirical information on P binding forms and associated conditions at

the sediment water interface (O2 and pH), we were able to achieve remarkable identifiability for

a large number of model parameters and P diagenesis processes. For most parameters, we can

expect that the satisfactory identification can lead to mechanistically plausible values and

consequently to predictive statements that are based upon an ecologically robust foundation.

However, we caution that some uncertainty still remains in regards to the sedimentation fluxes of

iron hydro-oxides and manganese oxides, as those compounds were not measured.

Generally, our study demonstrated that the P binding forms in the sediments are indicators of the

prevailing lake redox conditions and the total nutrient inflows from the watershed. Simulations

of phosphorus binding forms in surface sediments offer a quantitative interpretation of recent

paleolimnological data and thus dictate a new perspective into assessing lake P retention and

54

linking land use patterns with sediment P concentrations. In principle, our attempt to recreate the

trajectory from the oligotrophic state 400 years ago to the current mesotrophic conditions, can be

more broadly used to achieve model-based reconstructions of environmental change. From a

water management point of view, the model creates a virtual environment for evaluating organic

matter degradation pathways and oxygen demand regimes, once the boundary conditions and

sediment characteristics are sufficiently described. In this regard, our model provides a process-

based platform for assessing management strategies and making decisions regarding hypoxia

problems in aquatic systems. In a follow-up study, we are investigating the interplay between

changing sedimentation rates and oxygen depletion in the deep waters of the lake.

55

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62

Table 3-1. State variables of the model.

Dissolved Components Solid Components

Oxygen Inert Organic Matter: CαC/12HαHOαO/16NαN/14PαP/31SαS/32

Nitrate Degradable Organic Matter : CαC/12HαHOαO/16NαN/14PαP/31SαS/32

Manganese Manganese Oxide

Iron (II) Anhydrous Iron(III) oxide-hydroxide

Ammonium & Ammonia Manganese Carbonate

Calcium Iron Bound (Redox Sensitive) Phosphorus

Bicarbonate & Carbonate Calcium Carbonate

Dihydrogen Phosphate Calcium Bound Phosphorus

Monohydrogen Phosphate Aluminum Bound Phosphorus

Hydrogen Sulfide Absorbed Phosphorus

Sulfid Siderite

Hydrogen & Hydroxide Organic Phosphorus

Inorganic Matter

63

Table 3-2. Diagenetic reactions in the model. Xorg indicates organic matter with the composition: CαC/12HαHOαO/16NαN/14PαP/31SαS/32. The stoichiometry coefficients of organic components are given in Table 3-4.

Reactants Products Rates

Primary redox reduction

Xorg + O2 +H2O

Xorg + NO3- +H2O

Xorg + XMnO2 +H+

Xorg +X FeOOH +H+

Xorg + SO42- + H2O

NH4 ++HPO4

-+HCO3-+H+ +HS-

NH4+ +HPO4

-+HCO3- +H+ + HS- + N2

NH4+ + HPO4

- +HCO3- +HS-+ H2O + Mn2+

NH4+ +HPO4

- +HCO3- +H+ +HS- +H2O+Fe2+

NH4 ++HPO4

-+HCO3-+H+ +HS-

PR1

PR2

PR3

PR4

PR5

Secondary redox reaction

NH4+ + 2O2 NO3

- +2H+ + H2O SR1

H2S + 2O2

8XFeOOH+H2S+14H+

FeS+2O2

SO42-+2H+

8Fe2+ +SO42- +12H2O

Fe2+ + SO42-

SR2

SR3

SR4

Mineral precipitation-dissolution reactions

Mn2+ + HCO3-

Ca2+ + HCO3-

Fe2+ + CO32-

Fe2++HS-

XMnCO3 + H+

XCaCO3 + H+

2XFeCO3

XFeS + H+

MR1

MR2

MR3

MR4

Acid base

equilibrium conditions

H2O

H2CO3*

HCO3-

NH4+

H2PO42-

H2S

HS-

H+ + OH-

HCO3- + H+

CO32- + H+

NH3 + H+

HPO4- + H+

HS- + H+

S2- + H+

ER1

ER2

ER3

ER4

ER5

ER6

ER7

Phosphorus Binding Forms

Reactions

HPO4-

3Ca2+ + 2HPO42-

4Fe2++4HPO42-+

8HCO3- + O2

XFe_P

HPO4-

XAbsorbed_P

XApatite_P+ 4H+

4XFe_P+ 8CO2 +4XFeOOH

Fe2+ + HPO4-

XAl_P

PBR1

PBR2

PBR3

PBR4

PBR5

Table 3-3a. Process rates of reactions in the model. Sconcentration of the particulate substances i.

Process rates of reactions in the model. Si represents concentrations of a dissolved substance i and Xi indicates the

64

indicates the

65

Table 3-3b. Stoichiometric composition of settled organic matter1) Composition of Organic Components Atoms Mass fraction

αC 106 0.358 gC/gOM

αH 263 0.074 gH/gOM

αO 110 0.496 gO/gOM

αN 16 0.063 gN/gOM

αP 1 0.009 gP/gOM

αS 0 0.000 gS/gOM

Total Redfield composition 3550 1 g Tot/gOM

1) See Dittrich et al., 2009 for more details.

66

Table 3-4. Parameters used in the sediment model. * indicates fitted parameter. DM indicates dry matter and OM indicates organic matter. 1)(Klausmeier et al., 2004), 2)(Stumm and Morgan, 1996), 3)(Clegg and Whitfield, 1995), 4)(Dong et al., 2011), 5)(Reed et al., 2011b). Symbol Description Value Units

Proportional Breakdown of Total Flux

αOrg Fraction of OM 0.42

αInorg Fraction of inorganic matter 1-αOrg

αInorg_P* Fraction of inorganic P 6.2e-6

αInorg_P_Fe-P* Fraction of redox-sensitive P 0.33

αOrg_inert* Fraction of refractory OM 0.52

αdeg Fraction of degradable OM 1- αOrg_inert

αInorg_Total Fe Fraction of total settled iron 1-(αInorg_Other+ αInorg_P)

αInorg_Fe_FeOOH Fraction of settled FeOOH 1-αInorg_Fe_Other

αInorg_Fe_Other* Fraction of settled inorganic Fe,

excluding FeOOH

0.99

αInorg_P_ApatiteP Fraction of settled apatite P 1- αInorg_P_Fe-P

αInorg_Other* Fraction of inorganic matter without

FeOOH and P

0.9999

Primary redox reactions

kO2* Rate constant of OM degradation with

oxygen PR1

0.024 d-1

kNO3* Rate constant of OM degradation with

nitrate PR2

2.09 d-1

kMnO2* Rate constant of OM degradation with

manganese oxides PR3

4.33e-6 d-1

kFeOOH* Rate constant of OM degradation with

iron hydroxides PR4

3.3e-7 d-1

Ksatur*O2 Half-saturation constant for OM

degradation with oxygen

4.18 mmol/l

)*�+,��-�KsaturNO3

* Half-saturation constant for OM

degradation with nitrate

484.7 mmol/l

67

)."��,��-�

KsaturMnO2

*

Half-saturation constant for OM

degradation with manganese oxide

0.09 mmol/g

)/���0,��-�

KsaturFeOOH

*

Half-saturation constant for OM

degradation with iron hydroxide

0.3 mmol/g

Secondary redox reactions

knitri* Rate constant for nitrification SR1 0.37 d-1

KsaturnitriNH4

* Half-saturation constant for

nitrification

1.9 mmol/l

koxiHS* Rate of secondary reaction SR2 0.001 mmol/l/d

)"���� ��,��-�

KsaturoxiH2S

*

Half-saturation constant for sulfide

oxidation

998.39 mmol/l

Mineral dissolution and precipitation

keqMnCO3prec* Rate constant for MnCO3

precipitation, MR1

1.35e-5 mmol/l/d

KeqMnCO32) Equilibrium constant for MnCO3,

MR1

10-10.4 (mmol/l)2

keqMnCO3diss* Rate constant for MnCO3

dissolution, MR1

0 d-1

keqCaCO3prec* Rate constant for CaCO3

precipitation, MR2

0 mmol/l/d

KeqCaCO32) Equilibrium constant for CaCO3,

MR2

10(13.87-

3059/(273.15+T)-

0.04035*(273.15+T))

(mmol/l)2

keqCaCO3diss* Rate constant for CaCO3 dissolution,

MR2

2.5e-7 d-1

keqFeCO3prec* Rate constant for FeCO3

precipitation, MR3

1.35e-5 mol/l/d

KeqFeCO32) Equilibrium constant for FeCO3,

MR3

10KeqFeCO3num (mmol/l)2

KeqFeCO3num2) See above -5

keqFeCO3diss* Rate constant for FeCO3 dissolution, 0 d-1

68

MR3

Acid base equilibrium conditions

keqw* Rate constant ER1 1000 d-1

Keqw2) Water dissociation constant

10(4470.99/(273.15+T)+

12.0875-0.01706*(273.15+T))

(mmol/l)2

keq1* Rate constant ER2 1000 d-1

Keq12) Dissociation constant ER2

10(14.843-

3404.71/(273.15+T)-

0.032786*(273.15+T))

(mmol/l)2

keq2 Rate constant ER3 1000 d-1

Keq22) Dissociation constant ER3 10(6.494-2902.39/(273.15+T)-

0.02379*(273.15+T))

(mmol/l)2

keqN* Equilibrium rate constant ER4 1000 d-1

KeqN3) Dissociation constant ER4 10(-0.09038-

2729/(273.15+T))

(mmol/l)2

keqP* Equilibrium rate constant ER5 4.72 d-1

KeqP2) Dissociation constant ER5 10(-3.46-

219.4/(273.15+T))

(mmol/l)2

keqS1* Equilibrium rate constant ER6 10000 d-1

KeqS12) Dissociation constant ER6 10(-0.14-1158/(273.15+T)) (mmol/l)2

keqS2* Equilibrium rate constant ER7 10000 d-1

KeqS22) Dissociation constant ER7 10(-2.03-2646/(273.15+T)) (mmol/l)2

P Binding Form Reactions

kAbsorb Adsorption rate, PBR1 0.3 d-1

KAbsorb4) Adsorption constant, PBR1 118.8 l/mg

Qmax4) Maximal P absorbance sediment

capacity, PBR1

12.7 mg/g

KeqApatite* Dissociation constant PBR2 1018.4 (mmol/l)2

kFe-P* Rate constant for Fe-P formation,

PBR3

1.5e-4 (mM d)-1

kdegFe-P* Rate constant for Fe-P degradation

PBR4

8.6e-6 d-1

69

Compaction

θsurf Porosity at the SWI 0.91

θdeep Porosity at 19.5 cm (core bottom) 0.8

kθ* Rate of porosity compaction 7e-5 d-1

Boundary conditions

Concentrations at the SWI 1��2342�56

SSWIO2high

Oxygen during mixed period 0.30 mmol/l

1��789�56 SSWIO2low Oxygen during summer stratified period 0.13 mmol/l

SSWINO3 Nitrate, annual average 0.022 mmol/l 1*0:���"�56

SSWINH4mean

Ammonium, annual average 0.05 mmol/l

10�:���"�56

SSWIHPO4mean

Dissolved phosphorus, annual average 7.9e-8 mmol/l

1."�56 SSWIMn Dissolved manganese 0.017 mmol/l

1/��56 SSWIFe Dissolved iron 0.008 mmol/l

1��:�56 SSWISO4 Sulphate 0.03 mmol/l

10��56 SSWICa Dissolved calcium 1.03 mmol/l

1;��56 SSWIH Hydrogen ions 6.76e-5 mmol/l

10�56 SSWIHCO3 Bicarbonate, HCO3 3.63 mmol/l

10;�+�56 SSWIHS Hydrogen sulphide, HS 0.00 mmol/l

1���56 SSWIS2 Sulphide S2- 2.3e-10 mmol/l

Fluxes at the SWI

forg,mean Organic matter, annual average 0.32 gDM/m2/d

forg,amplitude Organic matter, amplitude 0.08 gDM/m2/d

finorg Inorganic matter 0.44 gDM/m2/d

fMnO2mean Manganese oxide, annual average 1.8e-5 mol/m2/d

fFeOOHmean Iron hydroxide, annual average 4.13e-7 mol/m2/d

fCaCO3mean Calcium carbonate, annual average 2.5e-3 mol/m2/d

fApatiteP Apatite P 1.8e-6 mol/m2/d

70

fFe-P Iron-bounded P 9.0e-7 mol/m2/d

Molecular diffusion coefficients (MDC)

mu Dynamic

viscosity

0.01*(1.791-0.06144*T+0.001451*T2-

1.6826*10-5*T 3-0.0001529*p+8.3885*

10-8*p2+0.0024727*S+T*(6.0574*10-6*p-

2.676*10-9*p2)+S*(4.48429*10-5*T-

4.7172*10-6*T 2+7.5986*10-8*T 3))

poise

T Temperature oC

p Water pressure 1.01325+0.0980665*depth bar

S Salinity 0.15 g/kg

DS_Ca MDC for Ca2+ (3.6+0.179*T)*10-6*8.64 m2/d

DS_CO2 MDC for CO2 4.72*10-9*(273.15+T)/(mu*37.30.6)*8.64 m2/d

DS_Fe MDC for Fe2+ (3.31+0.15*T)*10-6*8.64 m2/d

DS_HPO4 MDC for HPO4- (3.26+0.177*T)*10-6*8.64 m2/d

DS_NH4 MDC for NH4+ (9.5+0.413*T)*10-6*8.64 m2/d

DS_O2 MDC for O2 4.72*10-9*(273.15+T)/(mu*27.90.6)*8.64 m2/d

DS_Mn MDC for Mn2+ (3.18+0.155*T)*10-6*8.64 m2/d

DS_SO4 MDC for SO42- (4.88+0.232*T)*10-6*8.64 m2/d

71

Table 3-5. Ranking of relative sensitivities of model with respect to 37 model parameters. The parameters k are process rate constants. Those with index “eq” are equilibrium dissociation, precipitation or dissolution rate constants. The parameters ),��-� are half-saturation or inhibition concentrations of degradation processes. The parameters SSWI are concentrations of dissolved substances at the sediment water interface. The parameters f are mass fluxes of sedimenting particles. Sensitivity rankings based on diagenesis model at Main Basin, K45.

Group Rank Parameter δδδδmsqr Group Rank Parameter δδδδmsqr

Gro

up

1

1 SO2SWI 31.9 3 18 kθ 0.6

2 SHSWI 20.6

Gro

up

4

19 knitri 0.51

3 αOrg 4.9 20 SCaSWI 0.47

4 αOrg_inert 4.8 21 koxiHS 0.32

Gro

up

2

5 SHCO3SWI 4.1 22 kMnO2 0.30

6 SNO3SWI 3.7

Gro

up

5

23 SFeSWI 0.28

7 αInorg_P_Fe-P 3.5 24 KAbsorb 0.26

8 DBioturbation 2.5 25 KFeOOH 0.25

9 kdegFe-P 2.3 26 kNO3 0.20

10 KeqFeCO3num 2.3 27 SMnSWI 0.18

Gro

up

3

11 kO2 1.5 28 SHSSWI 0.17

12 KO2 1.3 29 KNO3 0.16

13 fCaCO3 1.3 30 kFeOOH 0.16

14 Qmax 1.3 31 KeqApatite 0.11

15 αInorg_Fe_Other 1.0 32 fMnO2 0.071

16 keqCaCO3diss 1.0 33 KMnO2 0.064

17 αbioirrig 1.0 34 kFe-P 0.047

72

Table 3-6. Collinearity indices for selected parameter subsets. Set of Parameters

θθθθ (sets) γ(γ(γ(γ(θθθθ))))

1a kO2 kdegFe-P 1.03 1b kO2 kdeg Fe-P kFe-P 1.23 1c kO2 kdegFe-P knitri kNO3 3.98 1d kO2 kdegFe-P kFe-P knitri kNO3 4.08 1e kO2 kdegFe-P knitri kNO3 kMnO2 kFeOOH 10.04 1f kO2 kdegFe-P knitri kNO3 kMnO2 kFeOOH kFe-P 14.39 2a αOrg_inert αOrg 1.99 2b αOrg_inert αOrg kO2 kNO3 6.88 2c αOrg_inert αOrg kO2 kNO3 αInorg_Fe_Other αInorg_Fe-P 17.73 3a kO2 kdeg Fe-P knitri kNO3 kMnO2 kFeOOH 10.04 3b kO2 kdeg Fe-P knitri kNO3 kMnO2 kFeOOH αOrg_inert αOrg 98.30 4a 1���56 SH

SWI 1.65 4b 1���56 SH

SWI Qmax 1.65 4c 1���56 SH

SWI Qmax 1*�+�56 22.52 4d 1���56 SH

SWI Qmax 1*�+�56 10;�+�56 28.23 5a 1���56 SH

SWI kO2 kNO3 αOrg_inert αOrg 9.18 5b 1���56 SH

SWI kO2 kNO3 αOrg_inert αOrg 1*�+�56 10;�+�56 34.91 6a kO2 kNO3 knitri kFe-P 3.98 6b kO2 kNO3 knitri kFe-P keqCaCO3diss 4.73 7a )��,��-� )*�+,��-� )."��,��-�

)/���0,��-� KAbsorb KeqFeCO3 3.11 7b )��,��-� )*�+,��-� )."��,��-� )/���0,��-� KAbsorb KeqFeCO3 KeqApatite 4.74 7c )��,��-� )*�+,��-� )."��,��-� )/���0,��-� KAbsorb KeqFeCO3 KeqApatite kO2 kNO3 kMnO2 kFeOOH knitri kFe-P 98.12

73

FIGURES LEGENDS

Figure 3-1. Map of Lake Simcoe.

Figure 3-2. Conceptual diagram of the presented phosphorus fractionation model of Lake

Simcoe.

Figure 3-3. Schematic diagram for the breakdown of the incoming flux of settling matter.

Figure 3-4. Boundary conditions for sedimentation flux and initial oxygen concentrations over a

one year time period. Sedimentation flux of total matter (solid gray line) in g/m2/day and initial

O2 concentration (dashed black line) in mg/l, shown for site K45 in the year 2005.

Figure 3-5. Modeled and measured depth profiles of pH from site C9 (left), O2 from site K42

(center) and porosity from site K45(right). Measured data is depicted by open squares and model

output is given by a solid black line for each site.

Figure 3-6. Modeled organic matter sediment profiles for 3 sites. Measured data is represented

by symbols, square for Total OM and circle for Inert OM. Model is represented by lines, total

OM is solid black line, Fast Degradable OM is black dashed line, and Inert OM is gray dashed

line.

Figure 3-7. Total Phosphorus and P fraction profiles for 3 sites. Measured Data is represented

by symbols, square for total P, circle for organic P, triangle for absorbed P, diamond for redox

sensitive P, and pentagon for apatite P. Model is represented by lines, Total P is solid black line,

apatite P is solid gray line, absorbed P is light gray dashed line, organic P is gray dashed line and

redox sensitive P is dark gray dash dot line.

Figure 3-8. Modeled dynamics of dissolved phosphorus as HPO4- in three basins of Lake

Simcoe during one year (2011).

Figure 3-9. Impact of dynamics of sedimentation flux on P Binding forms in surface sediments

for site K45 in the years 2004 and 2005. Values for P Binding forms are an average of the top

6mm of the sediments.

74

Figure 3-10. Impact of long-term dynamics of sedimentation flux on P binding forms in surface

sediments

Figure 3-11. Modeled dissolved phosphorus release rates for 3 sites.

Figure 3-1

75

Figure 3-2

76

Figure 3-3

77

Figure 3-4

78

79

Figure 3-5

80

Figure 3-6

81

Figure 3-7

82

Figure 3-8

83

Figure 3-9

84

Figure 3-10

85

Figure 3-11

86

Chapter 4 THE EFFECTS OF SEDIMENT DIAGENESIS ON

HYPOLIMNETIC DISSOLVED OXYGEN DYNAMICS IN MESOTROPHIC LAKE SIMCOE, ONTARIO, CANADA3

4.1. Introduction

A link between lake productivity and hypolimnetic dissolved oxygen (DO) concentration is

well-known for deep stratified lakes (Wetzel, 2003). An increase of productivity and

consequently organic matter loading, leads to a depletion of hypolimnetic DO and consequent

anoxic conditions in deep-water, which often causes both nutrients (phosphate) release from the

sediments and accumulation of metals (manganese and iron) and toxic substances (ammonia,

sulfide) near lake bottom.

The enhancement of phosphorus (P) loading from sediments under low hypolimnetic DO

conditions has been often observed in deep stratified lakes, although DO is not the only

controlling factor for P release (Hupfer and Lewandwski, 2005; Gaechetr and Wehrli, 1998).

Besides the toxic impact of substances released from sediments on benthic organisms (Kalff,

2002), an occurrence and extension of the anoxic deep-water zone limits fish habitat, especially

of coldwater species.

During a turnover period, nutrients, heavy metals and toxic substances are mixed into the pelagic

zone, leading to a further increase of productivity.. Consequently, it is often an aim of lake

management to control and maintain a certain DO concentration in deep water. Various

strategies have been developed to meet this target, including the reduction of external P loading

(Gaechter and Wehrli, 1998), the deep-water oxygenation (Liboriussen et al., 2009), the aeration

or mixing in winter (Mueller and Stadelman, 2004), and the removal of sediments containing

3 Gudimov, A., McCulloch, J., Chen J., Arhonditsis, G.B., Dittrich, M. The effects of sediment diagenesis on

hypolimnetic dissolved oxygen dynamics in mesotrophic Lake Simcoe, Ontario, Canada. Manuscript ready for submission.

Contributions: MD and AG formulated research objectives and methodology. AG performed analysis scenarios and synthesized the results. AG wrote the paper with extensive inputs from MD & GA.

87

high amounts of organic matter (Annadotter et al., 1999). However, in many cases, the

oxygenation has a delayed effect on hypolimnetic DO (see, for example, Liboriussen et al.,

2009; Mueller and Stadelman, 2004). Moreover, an increase of hypolimnetic DO was observed

only after the reduction of external P loading and the decrease of the primary production and

organic carbon sedimentation (e.g., Charlton et al., 1993; Matthews and Effler, 2006). In these

cases, the so-called sediment ‘‘memory effect’’ has been identified to be significant, namely the

sediments remained a major DO sink, even after decades of the hypolimnetic oxygenation and

reduction of P external loading (Matzinger et al., 2010). The reason is that the organic matter

deposition from the past eutrophic periods accumulated in the sediment, degraded slowly and the

degradation products diffused slowly from the sediment into the water column. For example,

Carignan and Lean (1991) found that the degradation of the refractory part of deposited organic

matter to reduced substances could last from decades to centuries. Furthermore, it has been often

shown that hypolimnetic accumulation of reduced substances such as methane, ammonium and

sulfide during summer anoxia originated predominantly from the sediment (Carigan and Lean,

1991; Gelda et al., 1995).

Sediment oxygen demand (SOD) in lakes can be also induced by elevated organic matter loading

and subsequently lead to a decline of DO in the water column (Mueller et al., 2012). The

research on artificial deep-water oxygenation in eutrophic lakes has demonstrated that SOD

impacts significantly the dynamics of hypolimnetic DO depletion (Matzinger et al., 2010; Muller

et al., 2012). Consequently, the sediments can dominate DO demand over decades.

Although the possible sediment memory effect is established by the above examples, the

dynamics of contribution of older sediment layers to the present SOD compared to the present

organic loading and hypolimnetic DO level, as well as a potential decrease in the sediment flux

of reduced substances with time, have not been assessed. Therefore, sediment diagenesis

represents a focal point when attempting to elucidate hypoxia patterns and gain insights into

sediment functioning (Zhang et al., 2008).

In this regard, dynamic reaction-transport models with an explicit consideration of the physical,

chemical and biological processes with fine-scale resolution of vertical sediment layers have

been developed (Wang and Van Cappellen, 1996; Katsev et al., 2007; Dittrich et al., 2009) as an

alternative approach to process-oriented sediment modelling with coarse vertical segments of

88

homogeneous functionality (DiToro and Fitzpatrick, 1993; Schauser et al., 2004). However,

while the mathematical representation and site-specific characterization of the sediment

diagenetic processes is certainly the way forward, what still is rare is their implicit integration

with the exogenous drivers and the prevailing DO conditions in the water column (Gelda et al.,

2012).

In this study, we investigate the role of the sediments in hypolimnetic DO, focusing on the

interplay among hypolimnetic DO dynamics, organic matter loading, SOD and sediment

diagenesis. Several modelling scenarios have been designed to examine the dynamic SOD

response to a wide range of conditions related to the regime of organic matter deposition and

deep-water DO levels in different basins of the mesotrophic Lake Simcoe. The modelling

scenarios of different organic carbon loadings and DO levels are intended to reproduce the lake’s

response to changing nutrient loading conditions and to shed light on the functional role of the

sediment diagenesis processes. We applied a dynamic reaction-transport diagenesis model that

was recently developed in our group to study sediment early diagenesis, with a focus on P

binding forms in sediment, their diagenesis and P release from the sediments in three basins of

Lake Simcoe (McCulloch et al., 2013), based on the field study performed by our group in 2011

in Lake Simcoe (Dittrich et al., 2013).

The Lake Simcoe has experienced varying degrees of eutrophication problems since the first

European settlement was established in 17th century (North et al., 2013). Agriculture,

atmospheric deposition, internal and external P loading and increasing urbanization activities

have impacted the ecological health of the system (Gudimov et al., 2012). The depletion of deep-

water DO triggered by eutrophication processes has been identified as a main reason for recent

collapse in coldwater fishery recruitment, despite reduction of exogenous phosphorus loads

(Young et al., 2011). The target of hypolimnetic DO was established at 7.0 mg/l during summer

stratification to sustain coldwater fishery (Evans et al., 2007)._______________________

89

4.2. Methods

4.2.1. Site description

Lake Simcoe is located 44 km north of Toronto with 11.6 km3 of water volume and a catchment

area of 2,840 km2 (Fig. 4-1). It is a dimictic system that completely freezes over during most

winters. Lake Simcoe currently receives wastewater from fourteen municipal wastewater

treatment plants, which constitute sources of phosphorus (P) loading (6±1 tonnes/yr between

2004 and 2007) while substantial phosphorus loads are also deposited from the atmosphere

(18±4 tonnes/yr) or emanate from other non-point sources, including runoff from agricultural,

urban and natural areas (43±5 tonnes/yr), and rural septic systems (4.4±0.1 tonnes/yr) (Gudimov

et al., 2012). Lake Simcoe consists of a large main basin (mean depth 14 m, maximum depth 33

m) and two large bays: the narrow and deep Kempenfelt Bay on the west side of the lake (area

34 km2, mean depth 20 m) and the shallow Cook's Bay at the south end of the lake (area 44 km2,

mean depth 13 m). Cook’s Bay is connected through dikes and drainage system to Holland

Marsh, an agricultural cluster of artificially reclaimed land rich with organic matter, while the

Kempenfelt Bay subwatershed is the location of the city of Barrie, where a population of about

135,000 resides. Accordingly to McCulloch et al. (2013) the organic matter sedimentation fluxes

in Lake Simcoe ranged from 0.13 to 0.37 gOM/m2/d (Table 4-2a, also see Chapter 3 and

McCulloch et al., 2013). The lake drains through a single outflow at Atherley Narrows and has a

flushing time of approximately 11 years. Lake Simcoe is a hard water marl lake due to the

limestone bedrock underlying the watershed, and whitings from CaCO3 precipitation occur on

occasion. Clays and organic soils are the prevalent soil types in the watershed (Landre et al.,

2011). Cook’s Bay, which has a maximum depth of 15 m, is eutrophic, receiving loads of silt and

P from the agricultural and urban drainage of the Holland River (Evans et al., 1996).

Glaciofluvial ice-contact and outwash deposits (gravel and sand) and glaciolacustrine deposits

(silt and clay, sand) cover bedrock thickly in the western Lake Simcoe area, but form a

relatively thin to discontinuous veneer over bedrock in the eastern Lake Simcoe area (Todd et al.,

2008).

4.2.2. Data

The sediment dataset for model calibration was collected in spring and autumn of 2011 from

three basins of the lake, i.e., sites K42, K45 and C9 (Fig. 4-1, see detailed description in Dittrich

90

et al., 2013). In short, sediment samples were collected using a core sampler Uwitec in a 60 cm

long sampling tube. Microsensor measurements were carried out immediately upon arrival to the

laboratory. One to three cores were used for microsensor analysis for O2 and pH. Two cores were

used for pore water analysis; and two to three cores were used for the fractionation of

phosphorus, and the analysis of porosity, dry weight and total organic matter. Samples from each

layer, from the two to three cores, were combined and centrifuged (11,000 rpm for 10 min),

decanted, and filtered (0.45 µm) for pore water analysis. For each sediment layer at least two

samples were prepared for the pore water analysis and analyzed in replicates. The historical

dissolved oxygen profiles in the water column (Fig. 4-2) were provided by the Ontario's Ministry

of the Environment (pers. comm. Dr. Hamdi Jarjanazi). Historical sedimentation fluxes follow

Hiriart-Baer et al. (2011) dating results. The lake hypolimnetic region during the summer

stratified period refers to layers of the water column below 18 m deep (Young et al., 2011). A

phosphorus sequential extraction analysis (Dittrich et al., 2013) allowed quantifying the

potentially mobile P pools in the sediments, suggesting a distinct heterogeneous pattern of the P-

binding forms in Lake Simcoe. Namely, carbonate-bound P appears to be a major fraction in the

Main Basin, while redox-sensitive P is the dominant form in Kempenfelt Bay (Dittrich et al.,

2013). The data collection in March and September 2011 enhanced understanding of the intra-

annual variability of sediment P efflux. Further details regarding the sampling practices and

analytical protocols can be found in Dittrich et al. (2013).

4.2.3. Diagenetic model formulation

Our process-based reaction-transport model is based upon the following mass-conservation

diagenetic equations for solid and dissolved substances (Berner 1980):

(4-1)

iXiii r

z

XD

zz

Xv

t

X +

∂∂

∂∂+

∂∂−=

∂∂

Bsed )(

(4-2)

where Xi and Si represent solid and dissolved phase species; θ - porosity; z - vertical dimension

of the sediment core; t - time; rSi - and rXi - biogeochemical transformation rates; SiSWI - species

concentration at the sediment water interface.

∂(θ Si )

∂t= ∂

∂zDB

∂(θSi )

∂z+θDSi

∂Si

∂z

+ rSi

− abioirrig * Θ∗(Si − SiSWI)

91

The model structure accounts for deposition fluxes of particulate matter, sediment compaction,

solids bioturbation and solutes bioirrigation, solute molecular diffusion, primary and secondary

redox reactions, mineral precipitation/dissolution, and acid dissociation reactions (Table 4-1-SI).

Settled organic matter (OM) is divided into degradable (Xdeg) and refractory (Xref) fractions. The

chemical composition of degradable OM is assumed to be equal to the Redfield stoichiometric

ratio (Table 3-3b). The degradation rate constants of primary redox reactions for microbial

decomposition of particulate labile OM with major oxidants are characterized by Monod kinetics

with an inhibition term for less favorable electron acceptors (Table 3-3a). For the secondary

reactions, the model considers the amount of O2 necessary to reduce NH4+, which diffuses from

deeper sediment layers towards the sediment surface, as well as O2 associated with the

reoxidation of FeS and H2S (McCulloch et al., 2013; Table 4-1). Mn2+ reoxidation has been

shown to contribute less than 1% in the sediments of lakes comparable with Lake Simcoe

(Adams et al., 1982); thus Mn was omitted from this comparison. The considered sequences of

reaction of organic matter mineralization and re-oxidation of reduced species produced in

anaerobic zone and diffuse into the oxic zone are the major processes that explain the measured

depth-profiles (McCulloch et al., 2013; Dittrich et al., 2013). No doubt that the reduction

reactions of oxidizing compounds are more complex, and the same is true for the oxidation of

dissolved reduced species as many recent studies proposed. For example, nitrate may also be

reduced by Mn2+ and Fe2+, iron oxides and hydroxides are oxidants for sulfide (Luther et al.,

1998; Rickard 1974). However, in this study we include the secondary reactions with O2, H2S

and iron species to understand the interplay between organic matter loading, O2 at the SWI and

SOD. The equilibrium processes are modeled as dynamic reactions with very large relaxation-

time constants to overcome numerical stability issues (Table 3-3a). The model is solved

numerically by integrating the system of partial differential equations in time, which are then

discretized through a vertical grid of 180 layers within the 18 cm simulated core depth (Dittrich

et al., 2009). Model specification was implemented using the open-source AQUASIM platform

(Reichert 1998). Model calibration was performed with the simplex (Nelder and Mead, 1965)

and secant (Ralston and Jennrich, 1978) optimization methods, while the model simulations and

their analysis were originally reported by McCulloch et al. (2013) and are also provided in Fig.

3-5 (see also McCulloch et al., 2013) also presented a detailed identifiability analysis showing

that most of the parameters can be reasonably constrained from the available dataset, despite the

complexity of the RTM structure (McCulloch et al., 2013).

92

SOD comprises both O2 areal fluxes associated with organic matter mineralization,

oxidation of reduced substances in the sediments as well as a flux from sediments to water

column (Maerki et al., 2006; see also Tables 4-1 and 3-2). O2 consumption rates of primary

mineralization reactions were determined through vertical integration of organic matter

transformation rates, expressed in O2 equivalents (Di Toro, 2001). The mineralization half-life

period for degradable OM is estimated as τ=ln(2)/rXdeg, where rXdeg denotes a total degradation

rate (day-1). Soluble reactive phosphorus (SRP) release and NH4+ flux were determined by Fick’s

first law of diffusion (Boudreau, 1997)

(4-3)

(4-4)

where Si is a pore-water concentration of species i; and Ddif is a temperature dependent free-

solution diffusion coefficient (Li and Gregory, 1974; Dittrich et al,. 2009).

The contour maps for SOD and SRP fluxes were estimated for the hypolimnetic areas

below 18m with a Kriging gridding algorithm (Wijsman et al., 1999). The SOD contribution to

hypolimnetic DO depletion was quantified by integrating SOD rates over the summer stratified

period and the hypolimnetic areas around the monitoring stations K42 and K45 (Nicholls, 1997;

see Fig. 1). Relevant water column oxygen demand rates were estimated as the difference

between total hypolimnetic oxygen depletion and SOD.

4.2.4. Sensitivity and uncertainty analysis

Our sensitivity analysis was based upon the estimation of the absolute-relative sensitivity

functions , which eliminates the influence of the units of the explored parameters (Reichert,

1998). The function represents the absolute response of the state variable yi to a 100% change in

a specific parameter pi under the assumption of linear approximation (Fig. 4-3a). ∆pi is equal to

1% of σpi, standard deviation of parameter pi, which in turn was assigned an initial estimate of

10% of the corresponding value:

(4-5), where p- model parameter, y - state variable.

δy,par

93

The model errors associated with predicted sediment depth profiles for porosity, pore-water O2,

total mineralization rate of degradable organic matter, rOMtotal (z) and sediment total phosphorus

(TP) have been assessed for boundary conditions (σ<�-=�56 ,σ���56) and parametric (σpi )

uncertainties that were set equal to ±10% of their mean estimates. A linearized error propagation

approach was also implemented without accounting for parameter correlation (Reichert 1998).

(4-6)

4.2.5. Description of scenarios

Four scenarios were designed to examine different facets of the linkage between sediment

diagenesis, SOD, and hypolimnetic DO. The flux of organic matter (FCorg) has been used as a

proxy variable to represent trophic changes in the lake. The impact of hypolimnetic oxygen

levels on diagenetic redox reactions was examined through variations of the model parameter

oxygen concentration at the sediment-water interface (O2SWI). In this study, we considered two

scenarios with average O2SWI and varying FCorg by ±20% relative to the 2011 annual mean values

(Sc1-O2SWIAvg-CorgHigh and Sc2-O2

SWIAvg-CorgLow, Fig. 4-4a,b) to represent uncertainty

associated with carbon flux estimates; a third scenario mimics the process of re-oligotrophication

with lower FCorg (-20%) and higher O2SWI (Sc3-O2

SWIHigh-CorgLow, Table 4-2b, Fig. 4-4c).

Finally, we examine a scenario of accelerated eutrophication with higher FCorg (+20%) and lower

hypoxic O2SWI (Sc4-O2

SWILow-CorgHigh, Table 4-2b, Fig.4-3d). The boundary conditions of FCorg

and O2SWI were gradually changed from the present state to reach the simulated conditions of the

examined scenarios by 2020 and 2050 (Fig. 4-4). The seasonal variation in the sedimentation

rates and lake stratification were accommodated by considering periodic FCorg and O2SWI within a

year, with minimum O2SWI during the summer and minimum FCorg during the winter months

(Table 4-2b and Fig. 4-4a-d). The latter specification also ensured numerical stability of the

model solution. All other boundary conditions were kept intact from the 2011 sampling year

(McCulloch et al., 2013).

94

4.3. Results

Our simulations demonstrate close agreement with the measured carbon and phosphorus vertical

profiles at all three stations (for detailed analysis see Chapter 3, McCulloch et al. 2013, Fig. 3-5).

The model also captures the pH depth profiles behavior (Fig. 3-5). In our diagenesis model, the

porosity is treated as a dynamic state variable, driven by the transformation processes and

sediment compaction. Our recent work (McCulloch et al. 2013) showed that the model faithfully

reproduces the measured porosity profiles with fairly narrow uncertainty bounds (Fig. 3-5, Fig.

4-3d). Similar conclusions can be drawn for the mean predictions of the O2 depth profiles along

with the uncertainty associated with model parameters and boundary conditions (Fig. 4-3c & Fig.

3-5). At the same time, simulated O2 profiles at stations K45 and C9 showed less sediment O2

consumption relative to what has been measured.

4.3.1. Sensitivity analysis of sediment depth profiles

According to our sensitive analysis, the pore-water O2 depth profiles are particularly dependent

on O2SWI concentration (Fig. 4-3b, Table 4-3). Other influential parameters that modulate O2

depth profiles for a given level of organic matter flux are the surface (θsurf) and core bottom

(θdeep) sediment porosity, and the Monod kinetic parameters of aerobic microbial mineralization

(kO2 and KO2, see definitions provided in Table 3-4). The importance of O2SWI is high at the

sediment-water interface with an exponential decline of its influence with an increase of

sediment depth (see O2 profiles in Fig. 4-3c). The impact of surface porosity gradually replaces

the influence of O2SWI with peak values of sensitivity close to the boundary of the oxic layer at 1

cm, which highlights the importance of molecular diffusion processes in shaping O2 depth

profiles. Interestingly, the sensitivity values of the rate constant of aerobic degradation, kO2, and

the associated Monod half-saturation constant, KO2, are of similar magnitude but opposite sign

( , Table B1-SI), suggesting the high correlation between the two parameters

(McCulloch et al., 2013) and thus their mutual compensability effects in terms of Brun et al.

(1999), namely model results stemming from a change in one of the considered parameters can

be compensated by an appropriate change in the others.

The root mean square (RMS) values of absolute-relative sensitivity functions ( ) for O2

pinpoint the flux of OM sedimentation as another critical boundary condition (Table 4-3a).

rkO2 ,KO2= 0.97

δy,par

95

Calcite precipitation and the bioturbation coefficient are also included within the top ten most

influential parameters of the O2 depth profiles, although their role is clearly less significant

relative to the previously mentioned parameters (Table 4-3a). The RMS of the sensitivity

functions for SRP porewater concentration highlights the importance of boundary conditions,

such as FeOOH flux at SWI, O2SWI, porosity, pHSWI, and OM flux (Table 4-3a). The two-layer

SPIEL box model of Schauser et al. (2006) has identified porosity, bioirrigation, and the

Langmuir sorption coefficient as equally important controlling factors on P release. The

importance of bioirrigation was attributed to the high abundance of benthic invertebrates,

reflecting the previous trophic status of Lake Sempach, while the influential role of sorption was

indicative of the general importance of the absorbed P fraction in the same system (Schauser et

al., 2006).

Finally, the sensitivity analysis confirms that the diffusive boundary layer (DBL) has an impact

on the flux of O2 (Brand et al., 2009; Bryant et al., 2010). As a proxy for the DBL (Brand et al.,

2009), the diffusion coefficient has been proved for an intermediate sensitivity and was ranked

fifth in terms of its sensitivity (Table 4-3).

4.3.2. Modelling experiments

Our modelling experiments demonstrate that the oxygen penetration depth (OPD) in the

sediments can respond to shifts in the boundary conditions depending on the scenario examined;

namely, the OPD varied from 5.5 mm in Sc1-O2Avg-CorgHigh to 54 mm in Sc3-O2High-

CorgLow (see Figs. 4-6a, c). On a seasonal timescale, the OPD is also dynamic, increasing from

5.5 mm in the summer to 7.5 mm after the fall overturn in Sc1-O2Avg-CorgHigh (Fig. 4-6a).

The dissolved inorganic P profiles are characterized by pronounced seasonal variations as

well (Figs. 4-6e-h). The model predicts a dynamic response to seasonally varying boundary

conditions both in recent sediments within the top 5 cm (~ last 25 years of deposition at station

K42), but also in sediments deeper than 10 cm (~70 years of deposition).

The elevated carbon flux FCorg in Sc1-O2Avg-CorgHigh compared to Sc2-O2Avg-CorgLow under

the same O2SWI results in an excessive TP accumulation in the upper sediment layer, manifested

as a deepening of the TP-isopleth of 1.5 mg P/g DW to 3.4 cm compared to 1.2 cm in Sc2-

O2Avg-CorgLow. At the same time, the sediment TP profiles of Sc2-O2Avg-CorgLow and Sc3-

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O2High-CorgLow, postulating similar FCorg but different O2SWI, reveal differences in P burial

within the top sediment layer with more deposited organic P mobilized to soluble phase under

higher O2SWI concentration.

4.3.3. Modelling of SOD

Sensitivity functions that evaluate the impact of parameters associated with aerobic

mineralization on the SOD highlight the importance of O2SWI as well as the total and degradable

fractions of depositing organic matter (Fig. 4-3g). The sensitivity exercise for SOD also

highlights the compensatory effects between the rate constant of aerobic organic matter

mineralization, kO2, and the half-saturation constant, KO2 (85 and -81 mg O2/m2/day). Given that

the same parameters are characterized by low correlation levels with the model boundary

conditions, such as O2SWI ( , Table B1 - SI), flux of organic

matter, defined by αOrg ( , Table B1- SI) and flux of refractory

matter, defined by αOrg_inert ( , Table B1- SI), we have

reason to believe that the derived SOD values are not affected by the pre-specified boundary

conditions.

We registered substantial differences with respect to the SOD among the three stations

C9, K45 and K42, with annual average levels of 55, 168 and 802 mg O2/m2/d, respectively. The

contour maps of SOD and SRP release depict considerable spatial heterogeneity of sediment

response to the examined variations in OM flux and O2SWI (Fig. 4-7). The two scenarios

examining the variability of organic matter deposition under average hypolimnetic oxygen levels

(Sc1-O2Avg-CorgHigh and Sc2-O2Avg-CorgLow) in station K42 reveal pronounced SOD

differences of 800 versus 1200 mg O2/m2/day, prior to the onset of thermal stratification.

However, towards the end of the summer stratification period our model predicts similar SOD

values (~250-300 mg O2/m2/day), for the same two scenarios (Figs. 4-7m,n).

rkO2 ,O2

SWI = −0.002;rKO2 ,O2

SWI = −0.015

rkO2 ,αorg

= −0.00;rKO 2 ,αorg

= −0.106

rkO2 ,αorg _ inert

= −0.064;rKO2 ,αorg _ inert

= −0.231

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4.4. Discussion

4.4.1. Effects of boundary conditions on seasonal dynamics of O2 depth profiles

The simulated and measured O2 profiles at stations K45 and C9 could be matched by applying

spatially variant bioirrigation (abioirrig) and bioturbation (Db) coefficients. However, due to the

high correlation between the bioturbation coefficient and the rate constant for aerobic

mineralization ( Table B1-SI) as well as the absence of site-specific Db estimates,

uniform bioirrigation (abioirrig) and bioturbation (Db) fauna-mediated coefficients were used

across the three study sites.

The seasonal variations of the boundary conditions at SWI strongly impact the pore-water

O2 profiles, as model simulations reveal substantial fluctuations of OPD (> 20 mm) similar to

observations reported by Dittrich et al. (2013). The fluctuations of OPD have been observed in

several recent studies, and can be caused by changes in organic matter sedimentation, e.g.,

phytoplankton blooms (Li et al., 2012). The variations in OPD ultimately affect the predicted

fluxes of redox-sensitive elements from the sediments (Cai and Sayles, 1996; Katsev et al., 2007;

Li et al., 2012). Consequently, our study of the dissolved O2 dynamics casts doubt on the

predictive credibility of simplified sediment box models that are assigned fixed depths for oxic

and anoxic layers (DiToro and Fitzpatrick, 1993). The importance of boundary conditions is

clearly depicted by the wide reactivity uncertainty bounds in the aerobic subsurface layer (Fig. 4-

3e).

Regarding the importance of calcite precipitation and bioturbation for O2 depth profiles, it should

be noted that Lake Simcoe is a hard-water lake due to the limestone bedrock underlying its

catchment, with mean calcium concentration of 41 mg/L, mean alkalinity of 116 mg/L, and mean

sulfate concentration of 20 mg/L, undersaturated in respect with gypsum, the saturation index of

0.65 and oversaturated in respect with calcite, saturation index of 1.6 (Hiriart-Baer et al., 2011).

The model analysis shows that the variability of CaCO3 fluxes does not strongly impact O2 depth

profiles (curve 6 in Fig. 4-3b) compared to O2SWI and porosity (curves 1 and 2, Fig. 4-3b) and

may have limited impact on our simulations of the functioning of the sediments. Likewise,

although the relatively low sensitivity to bioturbation stems from the calibration value assigned

to reflect the low levels of benthic invertebrate metabolism measured in off-shore zones of Lake

rDb ,kO2= 0.61

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Simcoe (Stantec, 2006; McCulloch et al., 2013), their role could be exacerbated by the gradual

proliferation of the invasive quagga mussel to deep hypolimnion which increases flux of

biodeposited organic matter to sediments and elevates benthic invertebrate abundance (North et

al., 2013).

The lack of high resolution data on settling fluxes of degradable and inert organic matter

was adequately compensated by the calibrated (temporally averaged) fractions of organic matter

in total flux (αOrg) and the degradable fraction of the total organic matter flux (αdeg) (Table 3-4).

These OM coefficients have been used as proxies for total and organic matter fluxes in the

present sensitivity analysis, which identified the critical importance of organic matter flux for

reproducing the O2 depth profiles (ranking 3, 4 and 5 in Table 4-3). Similar to our findings, the

sensitivity analysis studies by Katsev et al. (2006) and Schauser et al. (2006) have identified

O2SWI and OM flux among the most influential factors.

The comparison between the results from scenarios Sc2-O2AvgCorgLow (5.5 mm of OPD) and

Sc1-O2AvgCorgHigh (6.5mm of OPD) during the summer stratification showed that the carbon

flux has low impact on OPD. This finding is on par with the results by Kristensen (2000). In

contrast, the comparison between Sc2-O2AvgCorgLow and Sc3-O2High-CorgLow reveals that the

increase of O2 SWI from 3.7 to 7.0 mg O2/L is accompanied by a tenfold increase in the OPD,

from 5.5 to 53 mm. The decrease of O2SWI under the same organic carbon loading (Sc4-O2Low-

CorgHigh) leads to a limited O2 supply (~1 mg O2/L) and associated decrease of OPD from 5.5 to

3.5 mm at the end-of-summer low O2 conditions. Similar OPD levels were observed under

conditions of low organic carbon flux and low O2SWI=3.5 mg/L, during ice cover period in Lake

Simcoe (Dittrich et al., 2013). Organic matter content of the Lake Simcoe sediments varied

between 7.5 % at the surface and 4.5 % in the deeper layers, and therefore, the portion of the

degradable organic matter is ca. 40%, which can cause an OPD decline even under low organic

matter sedimentation flux. Our model predictions regarding the considerable seasonal OPD

variability are consistent with the conclusions drawn from a number of sediment modelling and

field studies (Katsev et al., 2007; Revsbech, 1989; Li et al., 2012), and calls into question the

typical practice of assigning fixed values (DiToro and Fitzpatrick, 1993; US EPA WASP7

models). Thus, the predicted temporal variability of the aerobic zone should be an essential

feature in sediment submodels in order to (i) effectively integrate diagenetic and water-column

99

processes and (2) realistically depict fluxes of O2 into sediments and/or fluxes of reduced

substances from the sediments into water column (Muller et al., 2012).

Similar to the findings from the oligotrophic Lake Aplnach (Brand et al., 2009; Bryant et al.,

2013; Scalo and Boegman, 2013), our study highlights the importance of the DBL in the shallow

sloping lakebed Lake Simcoe (Table 4-3). The two lakes differ strongly with respect to their

hydrodynamics: while Lake Alpnach is a seiche-driven alpine lake (Bryant et al., 2013), Lake

Simcoe’s mixing processes are governed both by geostrophics and internal waves (Bouffard and

Boegman, 2012). Recent observations of benthic turbulence in Lake Simcoe showed that

turbulent diffusivities in the benthic boundary layer are only intermittently high, following

excursions of the thermocline in response to strong wind events (Cossu and Wells, 2013). The

authors proposed that shear-driven convection is a more important process for benthic turbulence

levels than the breaking of nonlinear internal waves at the level of thermocline. However, more

field data on soluble components and DBL are needed to estimate the impact of DBL in Lake

Simcoe.

Interestingly, the sensitivity analysis of organic matter and O2 profiles clearly demonstrated

(Table 4-3) that DBL does not strongly impact the re-oxidation of Fe2+ and Mn2+. This result

deviates from the findings by Brand et al. (2009), who reported that the DBL governs the re-

oxidation of Fe2+ and Mn2+ compounds. The reason for the discrepancy may be caused by the

differences in the two models structures. While the Brand’s model takes into account only

dissolved compounds such as O2, nitrate, nitrious oxides, ferrous iron, manganese and methane,

our model includes both solid (organic matter, binding forms of solid P, FeOOH and FeS) and

dissolved compounds (Table 3-1).

4.4.2. Analysis of factors impacting on P dynamics

The simulated seasonal variability of SRP in deep anaerobic sediment layers (~10 cm) suggests

the existence of an "intermediate" P memory in the sediments, which extends beyond the recent

sediment time scale of 10-20 years (Fig. 4-6e-h). The anaerobic layer is considered a long-term

P sink in lakes (Hupfer and Lewandowski, 2008; Gächter and Müller, 2003), converse to the

aerobic layer which is usually responsible for short-term P release (Katsev and Dittrich, 2013).

Our simulated TP depth profiles have less seasonal variability as compared to SRP and O2,

which supports previously reported observations in Lake Simcoe (Dittrich et al., 2013) as well as

100

other studies of seasonal behavior of lake sediment profiles (Koretsky et al., 2006). The lack of

sensitivity of TP in anaerobic zones with respect to boundary conditions and parameters used in

the model (Fig. 4-3f) provides an argument that long-term sediment P retention in lakes is

controlled by P burial in anaerobic sediments layers (Katsev and Dittrich, 2013).

The comparison between two scenarios with the similar organic deposition and different O2SWI

showed more TP under lower O2SWI (Fig. 4-6j), and higher SRP under higher O2

SWI (Fig. 4-6g).

Thus, P in the top aerobic sediment layer can be easily modulated by bottom-water

characteristics. The Lake Simcoe sediments content relatively low redox-sensitive bound P,

which is often related to P bound with FeOOH. Furthermore, it has been shown that Al-P

phosphorus is the dominant P binding (Dittrich et al., 2013; McCulloch et al., 2014), and thus P

retention will be primarily controlled by O2 dynamics instead of Fe-S-P interaction. In this

regard, our model also supports the findings of Carey and Rydin (2011) that the TP

concentrations in the upper sediment layers of mesotrophic lakes do not necessarily correlate

with water column P, as relevant sediment burial capacity is typically undersaturated and the

sediment may accumulate rather than release deposited P. The latter pattern also implies that the

results of short-term incubation experiments should not be extrapolated to long-term predictions

(Katsev et al., 2007). In incubation experimental settings, sampled sediments become

disconnected from continuous organic matter sedimentation and the relatively small volumed

sampling tubes are prone to profoundly overinflating concentration gradients between the water

column and the sediment relative to the more stable conditions experienced in-situ (Loh et al.,

2013). The dominance of redox-insensitive P-bindings forms, such as carbonates bound P and

organic P forms in the sediments of Lake Simcoe supports these results (Dittrich et al., 2013).

Furthermore, it has been also shown that O2 influence on P retention in sediments depends on

geochemical sediment composition, and maybe negligible, in case of intensive Fe and S

interactions in the sediments (Gaechter and Mueller, 2003). The simulated phosphorus transfer

associated with organic matter mineralization suggests that the contribution of aerobic

degradation accounts for 367 mg P/m2/year (reaction PR1 in Table 3-2), which is tenfold higher

than the contribution of the anaerobic mineralization pathways (29 mg P/m2/year, PR2-5) in

Lake Simcoe (Fig. 4-5). The predicted net organic P accumulation rate of 104 mg P/m2/year is on

par with the estimate of ~100 mg P /m2/year by Hiriart-Baer et al. (2011). Our diffusive P efflux

101

estimate of ~30 mg P/m2/year (Dittrich et al., 2013) represents less than 10% of annual P

sedimentation fluxes (500 mg P/m2/year).

4.4.3. Impact of organic matter sedimentation and hypolimnetic O2 on SOD

High sensitivity of model parameters is a necessary condition for their identifiability during

model calibration, in that parameters demonstrating limited sensitivity response against model

endpoints are the least identifiable from the provided dataset (McCulloch et al., 2013). In a

recent study by McCulloch et al. (2013), we showed that the consideration of P-binding forms

along with additional information typically collected from sediment cores (e.g. depth profiles of

organic carbon, pH, porosity, etc) act as an additional constraint during model calibration, and

thus improves the identification level of the parameter vector (McCulloch et al., 2013). In

particular, the parameters associated with the aerobic mineralization were characterized by a

collinearity index γ = 10 suggesting low compensability problems among the calibrated process

rates and thus subsequently the SOD levels in Lake Simcoe with satisfactory degree of

confidence (see parameters set 1e in Table 4-6 and discussion in McCulloch et al. (2013)).

The predicted SOD values are within the range typically reported for mesotrophic lakes in North

America (Veenstra and Nolen, 1991; Smith and Matisoff, 2008) and correspond well with

historical records in Lake Simcoe. For example, if the station K45 is taken as a proxy for the

lake-wide hypolimnetic SOD during the summer stratified period, then the corresponding mean

estimate of 109 mg O2/m2/d is on par with the SOD of 112±226 mg O2/m

2/d for the 1971-1985

period (Snodgrass and Holubeshen, 1992). The latter values though should be treated with

caution, as other empirical measurements made by MOE (1975) were indicative of SOD levels

greater than 650 mg O2/m2/day during the eutrophic era of Lake Simcoe (MOE, 1975).

On the other hand, the SOD heterogeneity can be driven by differences in primary production

rates, sedimentation fluxes, and the quality of the settling organic matter between the two

embayments and the offshore area in Lake Simcoe (Hiriart-Baer et al., 2012; see also Table 4-

2a). Our scenario analysis predicts also significant seasonal SOD fluctuations in Kempenfelt

Bay, station K42 ranging from 200 to 2000 mg O2/m2/day, with the O2

SWI acting as a prevailing

controlling factor compared to organic matter flux (Fig. 4-7). The steep shore slopes and deep

morphology of Kempenfelt Bay likely leads to enhanced hypolimnetic O2 consumption (Blais

and Kalff, 1995). Additionally, the deep hypolimnetic water seems to be transported out of

102

Kempenfelt Bay to the main basin (Baird & Associates, 2010). In laboratory experiments, the

addition of O2 to overlying water was found to cause similar SOD increases from 90 to 800 mg

O2/m2/day (Murrell and Lehrter, 2011). The SOD dependence on O2

SWI boundary conditions in

the mesotrophic Lake Simcoe is predominantly driven (≈80%) by the pathways of aerobic

organic matter mineralization (Fig. 4-8d). The flux of reduced species from sediment to the water

column may constitute a substantial portion of oxygen sink, e.g., 70% in the hyper-eutrophic

Lake Onondaga (Gelda et al., 1995). In Lake Simcoe, the modeled NH4+ flux accounts for ~17%

in SOD, i.e. 0.48 mmol/m2/day or 20 µmol/m2/hr, which is below the reported levels of

1.91±0.98 mmol/m2/day for eutrophic lakes (Muller et al., 2012) but within the range of 10-30

µmol/m2/hr reported for a mesotrophic lake in Denmark (Pelegrí and Blackburn, 1996).

The SOD levels under the same low organic matter deposition, but with high O2SWI (Sc3-

O2highCorgLow) were characterized by a 200-400% increase compared to those under lower

O2SWI (Sc2-O2Avr-CorgLow). This result can be explained by the enhanced aerobic organic

matter mineralization due to high O2SWI (Figs. 4-7k,o and 4-8a). The latter finding is indicative of

the need to distinguish between actual (limited by the available O2 supplied to the sediments) and

potential SOD (maximum oxygen demand with minimal inhibition by O2 availability) in a

system (Bryant et al. 2010). The projected elevated SOD response under the re-oligotrophication

scenario (Sc3-O2High-CorgLow) implies a feedback mechanism that can potentially delay the

restoration of near-bottom oxygen levels even after nutrient-loading reduction strategies take

place. Finally, the scenario of ongoing eutrophication accompanied by an establishment of end-

of-summer hypoxia predicts an additional reduction from 170 to 30 mg O2/m2/day of the actual

SOD values which can still serve, however, as an multiplicative factor for near-bottom hypoxic

waters (Murrell and Lehrter, 2011).

As further validation, we compared the calibrated reactivity rates of organic matter against the

range of sediment reactivity rates known to be associated with freshly settled phytoplankton (Fig.

4-8c). The derived reactivity for all three monitoring stations are in line with Middelburg (1989)

regression curve, as presented in Li et al. (2012), where the first-order reactivity term rdeg is

expected to decrease exponentially with the sediment age and depth (Berner, 1980). Our

diagenetic model consistently demonstrates lower reactivity rates and higher mineralization half-

life periods in recent sediments for stations C9 and K45 (Fig. 4-8c, Table 4-2a). Notably, the

weakly negative slope of the K45 reactivity rate might stem from an O2SWI overestimation and

103

subsequent underestimation of the aerobic Monod inhibition term at this station. The discrepancy

in the half-life period at the C9 station relative to the other two study sites may reflect the

increased terrestrial carbon export from the Holland Marsh agricultural watershed and/or the

submerged aquatic macrophytes in shallow Cook’s Bay (Dittrich et al., 2013). The macrophytes

are characterized by 2-4 times higher half-life periods due to differences in cellulose, lignin,

phenol compounds, and higher C:N:P rations compared to phytoplankton (Marinho et al., 2010;

Bianchini Jr et al., 2008; Meding and Jackson, 2003). This observation is also consistent with the

Hiriart-Baer et al.’s (2011) finding that higher C:N ratios characterize the sediments of K45 and

C9 compared to Kempenfelt Bay (K42). It is worth noting that the abundance of submerged

aquatic macrophytes has tripled, from 1.2 to 3.1 kg/m2, in Cook’s Bay and at the offshore sites in

Lake Simcoe from 1984 to 2008 (Ginn, 2011).

Our modelling analysis provides a convenient framework to track the contribution of sediments

to SOD in Lake Simcoe. The mineralization of recent sediments (0-2 yrs) approximately

represents 70% of SOD, whereas the older sediments (>5 years old) account for less than 4% of

SOD, reflecting the gradual replacement of O2 mineralization with FeS oxidation (Table 4-4).

Importantly, the intermediate layer of 2-5 years is responsible for less than 10% of SOD which

suggests that SOD in Lake Simcoe should respond without a major time lag to an expected

reduction in the organic matter deposition, as a result of exogenous P control (Matzinger et al.

2010). The SOD contribution to total hypolimnetic O2 depletion is estimated at 23.7% and 12.0%

in Kempenfelt Bay and Main Basin, respectively (Fig. 4-8b), which is lower than a lake-wide

estimate of 30% in the 1970-80s (Snodgrass and Holubeshen, 1992). This suggests that the

organic matter mineralization in the water column remains a primary regulator of the

hypolimnetic O2 deficit (>75%), despite the reduction of exogenous phosphorus loading from

more than 25 tonnes P/year since the 1980s. This is in line with the conclusions drawn from

long-term observations of hypolimnetic oxygenated Danish lakes, in that the oxygen treatment

should be accompanied by reduced nutrient inputs if permanent improvements of the lake water

quality are to be obtained (Liboriussen et al., 2009).

4.5. Conclusions

I have used a reaction-transport diagenesis model to examine the impact of SOD on deep

water oxygen levels in three basins of Lake Simcoe. Our modelling framework integrated

104

biogeochemical and physical processes at the sediment-water interface and incorporated dynamic

boundary conditions, such as organic matter sedimentation and oxygen concentration at the

sediment-water interface, while rigorously assessing parameter sensitivity and model

identifiability (McCulloch et al., 2013). The main findings of this study are as follows:

� Our model confirms previous empirical estimates of SOD in Lake Simcoe, suggesting that

SOD contribution to overall hypolimnion DO deficit is less than 30%. Our model also

predicts an order of magnitude difference in SOD levels between Kempenfelt Bay and

Cook’s Bay, which can be attributed to multiple factors, including the differences in primary

production rates, the quality of the settling organic matter, redistribution of sediments and

O2SWI due to differences in morphology and hydrodynamics.

� Porosity and oxygen concentration at the sediment-water interface are among the most

important regulatory factors of the oxygen depth profiles in the sediments. Our model

parameterization downplays the contribution of bioturbation and bioirrigation on sediment

O2 depth profiles. This assumption warrants further examination, given the presence of

dreissenid mussels in extensive areas of the lake.

� My simulations suggest a tenfold higher phosphorus flux from aerobic degradation of

organic matter relative to the contribution of the anaerobic mineralization pathways in Lake

Simcoe. Further, our diffusive P-efflux estimate represents less than 10% of the

sedimentation P fluxes; thus, the deep sediments in Lake Simcoe mainly serve as a sink of

the deposited P.

� The investigated sediment mineralization processes involve both the top (0-5 cm) and deeper

(>10 cm) layers, which are indicative of a "P memory" that extends beyond the recent time

scale.

� Sediment oxygen uptake appears to be sensitive to the variability in organic matter

sedimentation and the oxygen concentrations at the sediment-water interface. In all

scenarios, the rate of organic matter mineralization and associated oxygen fluxes to the

sediments are inhibited by availability of oxygen at SWI during summer stratified period.

The relaxation of O2 inhibition for microbial metabolisms is the reason for the predictions of

increased SOD levels during the fall turnover period after the mixing of the oxygen-

saturated epilimnetic water masses with the hypolimnion. Our long-term model simulations

also predict an increase of the OPD and total phosphorus depletion in the upper sediment

layer following the establishment of conditions of low organic sedimentation flux and high

105

oxygen concentrations in Lake Simcoe (re-oligotrophication scenario). The same exercise

showed spatial SOD heterogeneity with highest SOD levels observed at the Kempenfelt

Bay, suggesting a feedback mechanism in the sediments that affects the oxygen

concentration near the bottom of the lake. This finding enables us to conclude that a lake-

wide nutrient reduction target might not be sufficient to achieve a uniform response in

projected deep-water oxygen concentration in all lake basins.

� The pace of the projected re-oligotrophication and the associated hypolimnetic DO

improvement, induced by nutrient loading reductions, can be hindered over a short-term

time scale due to the potential effects of a number of feedback mechanisms across sediment-

water interface in Lake Simcoe. The increase in hypolimnetic DO can elevate the SOD and

affect the near-bottom water quality, while the expected deepening of OPD can trigger

aerobic mineralization of legacy organic matter that is currently residing in an anaerobic

state.

� My study stresses the importance of a reactive-transport model to predict the response of

Lake Simcoe to management actions while also accounting for the complex interactions

among physical, chemical and biological processes in the sediments.

In conclusion, sediment diagenesis can be a significant driver of oxygen depletion in lakes

and may dramatically impact hypolimnetic oxygen concentrations. Our reactive-transport model

represents a convenient framework to study diagenetic processes in time and space, and thus

offers an essential management tool for addressing "what if?" questions related to the fate and

transport of nutrients in the sediments. A logical next augmentation would be the integration of

the sediment diagenesis processes with a water-quality process-based model to dynamically

examine the interplay among organic matter deposition, sediment dynamics, and dissolved

oxygen patterns in deep waters. The adoption of a more holistic modelling tool will also be

conceptually consistent with the ecosystem management paradigm for restoring beneficial uses

of impaired systems and will likely facilitate a multi-causal way of thinking that can more

effectively accommodate ecosystem complexity (Gudimov et al., 2012).

106

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Table 4-1. Model sediment oxygen consumption pathways.

Reaction* Reactants Products

PR1 Xorg + O2 +H2O NH4 ++HPO4

-+HCO3-+H+ +HS-

SR1 NH4+ +2O2 NO3

− +2H+ +H2O

SR2 H2S+2O2 SO42− +2H+

SR4 FeS+2O2 Fe2+ + SO42-

PBR3 4Fe2++ O2+4HPO42-+ 8HCO3

- 4XFeOOH +4XFe_P+ 8CO2

NA 2Mn2++O2+2H2O 2MnO2 + 4H+

NA CH4+2O2 CO2+2H2O

* see Table 3-2 in Chapter 3 and McCulloch et al.(2013) for complete list of diagenetic reactions

114

Table 4-2a. Limnological characteristics of the three study sites (K45, K42 and C9) in Lake Simcoe.

Station K45 K42 C9

Maximal depth, m 39 42 21

TP 2004-2008 (ice free average), µg/L1) 13.8 14.7 14.8

Chl α, µg/L (±stdev) 1 2.5(1.5) 2.8(1.6) 2.5(1.6)

Flux OM, annual average (2011), g DW/m2/d 2) 0.15 0.37 0.13

Flux OM (2011) seasonal amplitude

(vs annual average), g DW/m2/d 2 25% 25% 25%

Age at 18 cm sediment core, years3) 188 104 70

Mineralization half-life period τSWI, years 2.45 0.55 2.31 1) MOE, 2010. 2) McCulloch et al., 2013. 3) Hiriart-Baer et al., 2011.

Table 4-2b. Scenarios Boundary conditions at three study sites (K45, K42 and C9) in Lake Simcoe. Scenarios / Station K45 K42 C9

Sc.1. Flux OM (annual average) g DW/m2/d 0.18 0.44 0.16

O2SWI summer, mg/L 3.7 2 3.7

Sc. 2. Flux OM (annual average) g DW/m2/d 0.12 0.30 0.10

O2SWI summer, mg/L 3.7 2 3.7

Sc. 3. Flux OM (annual average) g DW/m2/d 0.12 0.30 0.10

O2SWI summer, mg/L 7 7 7

Sc. 4. Flux OM (annual average) g DW/m2/d 0.18 0.44 0.16

O2SWI summer, mg/L 1 1 1

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Table 4-3a. Local sensitivity analysis results for the state variables O2.

* averages over 165,750 data points

Ranking Parameter Roots of mean* squares of

O2 sensitivity functions (mmol/l), ∙10-3 1 Porosity at the SWI 63.67 2 O2

SWI 50.89 3 Refractory OM fraction in total OM flux 19.54 4 Fraction of total OM in total sediment flux 15.17 5 Diffusion coefficient for O2 in sediment 14.71 6 OM flux 11.17 7 Porosity at 19.5 cm (core bottom) 10.75

8 Rate constant of OM degradation with oxygen (PR1)

6.92

9 Half-saturation constant for OM degradation with oxygen

6.84

10 CaCO3 flux 1.40

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Table 4-3b. Local sensitivity analysis results for the state variables Xorg.

Ranking Parameter Roots of mean* squares of Xorg sensitivity functions

(mg/l), ∙104 1 Porosity at the SWI 7.16 2 Porosity at 19.5 cm (core bottom) 5.64 3 Refractory OM fraction in total OM flux 3.38 4 Fraction of total OM in total sediment flux 2.72 5 O2

SWI 1.65 6 Diffusion coefficient for O2 in sediment 0.93

7 Rate constant of OM degradation with oxygen (PR1)

0.68

8 CaCO3 flux 0.29 9 Compaction rate of sediment 0.24 10 Bioturbation coefficient 0.08

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Table 4-3c. Local sensitivity analysis results for the state variables HPO4.-

Ranking Parameter Roots of mean* squares of HPO4

- sensitivity functions

(mmol/l), ∙10-3 1 Flux of FeOOH 7.940 2 O2

SWI 1.954 3 Porosity at 19.5 cm (core bottom) 1.485 4 pH at SWI 1.449 5 Porosity at the SWI 1.014

6 Fraction of total OM in total sediment flux 0.391

7 Fraction of redox-sensitive P 0.339 8 Fraction of inorganic P 0.339 9 NO3 at SWI 0.319 10 Refractory OM fraction in total OM flux 0.242

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Table 4-4. Contribution of the different pathways of sediment oxygen demand in different sediment layers (site K45).

Time Scale SOD, % rdeg O2,

% rnitr, %

roxy H2, %S

roxy

FeS, % rFeOOH,

% FNH4,

% 79.094 0.001 0.019 4.181 0.014 16.691

0-2 yrs 70.902 69.530 0.002 0.010 1.300 0.060 2-5 yrs 9.025 7.830 0.001 0.004 1.190 0.000 5-10 yrs 1.822 1.200 0.001 0.001 0.620 0.000 >10 yrs 1.560 0.480 0.000 0.000 1.070 0.010

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FIGURES LEGENDS

Figure 4-1. Modeled hypolimnetic sites in Lake Simcoe, Ontario, Canada.

Figure 4-2. Vertical profiles of dissolved oxygen concentrations in the central part of Lake

Simcoe (site K45) in 2008 as per Ontario Ministry of Environment dataset.

Figure 4-3. Model sensitivity analysis: (a) conceptual schema of the absolute-relative sensitivity

function, ���������,���������.�. ; (b) depth profiles of sensitivity functions ���,��.�. of the dissolved

O2 to model boundary conditions and model parameters: concentration O2SWI, porosity θsurf,

porosity θdeep, rate constant kO2, half-saturation constant KO2, flux of CaCO3, bioturbation

coefficient Db, rate of sediment compaction kθ, concentration NO3SWI (parameters are defined in

per table 4-SI). Mean prediction and uncertainty bounds for (c) dissolved O2; (d) sediment

porosity; (e) degradation rate of organic matter; and (f) total phosphorus in the sediments; (g)

sensitivity function ����,��.�. of SOD to boundary conditions and model parameters: fraction of

total OM in total sediment flux αOrg, refractory OM fraction in total OM flux αOrg_inert,

concentration O2SWI, rate constant kO2 , half-saturation constant KO2 (as per table 4-SI).

Figure 4-4. (a-d) Specification of the boundary conditions for the four scenarios examined at the

study site K45: varying organic matter sedimentation fluxes and oxygen levels at the sediment-

water interface (O2SWI).

Figure 4-5. Modeled transformation rates of organic P in the aerobic and anaerobic zones in the

central area of Lake Simcoe (site 45).

Figure 4-6. Vertical profiles of dissolved oxygen (a-d), soluble reactive phosphorus (e-h), and

total phosphorus (i-l) in Kempenfelt Bay (site K42), under the four scenarios examined.

Figure 4-7. SRP release rates (a-h) and sediment oxygen demand (i-p) in Lake Simcoe for

March and September, under the four scenarios examined.

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4-8. (a) Sediment oxygen demand (SOD) response to changes in organic matter flux and oxygen

concentration at SWI; (b) contribution of sediment oxygen demand and water column respiration

in K42 (Kempenfelt Bay) and K45 (Main Basin) to hypolimnetic DO depletion; (c) sediment

reactivity rates for organic matter degradation against the Middelburg's (1989) curve for freshly

deposited marine sediments; and (d) partitioning of the relative contribution of the different

pathways of SOD.

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Figure 4-1

122

Figure 4-2

123

Figure 4-3

124

Figure 4-4

125

Figure 4-5

126

Figure 4-6

Figure 4-7

127

128

Figure 4-8

129

Chapter 5 EXAMINATION OF THE ROLE OF DREISSENIDS AND

MACROPHYTES IN THE PHOSPHORUS DYNAMICS OF LAKE SIMCOE, ONTARIO, CANADA4

5.1. Introduction

The invasion of dreissenid mussels has been responsible for a major restructuring of the

biophysical environment in many parts of the Laurentian Great Lakes, with profound alterations

on the nutrient dynamics in the littoral zone (Coleman and Williams, 2002). The nearshore shunt

(sensu Hecky et al., 2004) has been hypothesized to profoundly impact the fate and transport of

particulate matter, and subsequently alter the relative productivity of inshore sites along with

their interactions with the offshore areas. Most notably, dreissenid mussels may filter twice as

many food particles as they can actually ingest, and therefore a large portion of the filtered food

items is subsequently excreted in soluble form or released as (pseudo)feces (Vanderploeg et al.,

2001). When we also consider that the particulate matter is subject to bacterial mineralization, it

can be inferred that dreissenids are likely to mediate the nutrient cycling and may significantly

modulate the nearshore nutrient concentrations (Bierman et al., 2005). In regards to the littoral

algal assemblage, the establishment of dreissenid mussels has been associated with both

desirable (e.g., phytoplankton biomass decline, gradual disappearance of Aphanizomenon and

Oscillatoria) and undesirable (e.g., Microcystis increase) changes in the overall ecosystem

integrity (Nicholls et al., 2002; Vanderploeg et al., 2001). The structural changes in the

phytoplankton community composition could stem directly from the feeding selectivity of

dreissenids or indirectly from the improvements in the transparency of the water column, but the

role of the feedback loop associated with their nutrient recycling activity could conceivably be

another important factor (Bierman et al., 2005).

4 Gudimov, A., Kim, DK., Palmer, M.E., Young, JD, Dittrich, M., Winter, JD and G.B. Arhonditsis."Examination

of the role of dreissenids and macrophytes in the phosphorus dynamics of Lake Simcoe, Ontario, Canada". Manuscript ready for submission to "Ecological Informatics".

Contributions: AG & GA formulated research objectives and modelling methods. AG carried out the analysis, wrote the paper with extensive input from GA. MD, MP, JW, and JY reviewed the paper and offered comments.

130

In Lake Simcoe, the initial year with discernible dreissenid production was 1994, while abundant

colonies of juvenile and adult mussels first occurred on rocky substrates throughout the spring

and summer growing season in 1996 (Evans et al., 2011). In its main basin, dreissenid mussel

distribution is determined by a complex interplay among lake depth, substrate availability, and

exposure to wave disturbance (Ozersky et al., 2011). Specifically, the highest dreissenid biomass

is typically found at areas of intermediate depth, where water movement is high enough to ensure

that the lake bottom is dominated by rocky substrate but not excessively high to cause

catastrophic disturbances to the dreissenid community. On the other hand, Ozersky et al. (2011)

was not able to identify a clear causal connection between the hydrodynamic regime and

dreissenids in Cook's Bay, asserting that the nature of the macrophyte assemblage (composition,

taxon-specific abundance) may be the predominant factor in shaping the dreissenid mussel

distribution. In the same nearshore sites, Schwalb et al. (2013) reported a counterintuitive

positive relationship between phytoplankton abundance and dreissenid biomass, which was

attributed to the horizontal advection and/or the internal wave-mediated transport of deep

chlorophyll a maxima that can temporarily counteract the algal depletion by mussels. Moreover,

the dreissenid-colonized sediments were found to act as a net source of dissolved nutrients to the

water column due to their considerably high excretion rates of dissolved phosphorus and

ammonia (Ozersky et al., 2013). Not surprisingly, the same sites were characterized by higher

amount of periphyton biomass, primary production, and community respiration relative to sites

where mussels were fairly low.

An important implication of the causal linkage between dreissenids and nutrient variability in the

littoral zone is the weakening of the signal of the external loading, which forced Hecky et al.

(2004) to question the structural adequacy of the conventional phosphorus mass-balance models

developed during the pre-dreissenid period in the Great Lakes. In this regard, Zhang et al. (2013)

showed that failure to explicitly account for the role of dreissenids (or other factors associated

with the internal nutrient loading) compromised the capacity of a model to capture the TP peaks

typically experienced towards the late summer-early fall period in the upper Bay of Quinte. In

particular, the modeled range of the monthly TP concentrations was much narrower than the

actual values and the predicted patterns failed to reproduce the substantial inter-annual variability

characterizing the system (Zhang et al., 2013). In Lake Simcoe, Gudimov et al. (2012) recently

introduced a spatially-explicit simple mass-balance model forced with idealized sinusoidal P

131

loading to predict total phosphorus concentrations. The study reported a two-fold discrepancy

between empirical gross and predicted net TP sedimentation rates, presumably reflecting the role

of macrophytes and dreissenids, the sediment resuspension induced by wind forcing, the

diffusive release of phosphorus from the sediments, and the complex interplay between offshore

waters and the two embayments of Lake Simcoe (Cook's Bay and Kempenfelt Bay). In this

regard, Nürnberg et al. (2013) provided evidence of substantial internal loading in all lake

sections, but especially in the stratified Kempenfelt Bay and the main basin. The same study also

asserted that internal loading may also occur in the polymictic Cook's Bay, as the warmer

temperatures may elevate the sediment oxygen demand and phosphorus release rates. By

contrast, Dittrich et al. (2013) reported empirical estimates that are significantly lower than

Nürnberg et al. (2013) internal loading fluxes (see also Discussion section).

In this study, we use mathematical modelling to test the hypothesis that the phosphorus dynamics

in Lake Simcoe is predominantly driven by internal mechanisms, after the establishment of

dreissenids and the proliferation of macrophytes. First, we present the mechanistic foundation of

phosphorus mass-balance model, recently developed by Kim et al. (2013), aiming to account for

the role of macrophyte dynamics, to explicitly represent the impact of dreissenids in the system,

and to sensibly portray the interplay between the water column and sediments. We provide the

rationale behind the model structure adopted, the simplifications included, and the mathematical

formulations used. We then present the results of a calibration exercise and examine the capacity

of the model to sufficiently reproduce the observed patterns in Lake Simcoe during the 1999-

2007 study period. We also present the results of a local sensitivity analysis striving to identify

the most influential components of the model and to shed light on the spatiotemporal role of the

various ecological processes and cause-effect relationships, as postulated by the model parameter

specification. We also critically discuss several of the lessons learned from our modelling

analysis regarding the ecosystem functioning relative to our contemporary understanding of the

Lake Simcoe dynamics.

5.2. Methods

5.2.1. Site description - Dataset

Lake Simcoe has experienced severe eutrophication problems as a result of the agricultural

activities and increasing urbanization in its catchment (North et al., 2013). In particular, Lake

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Simcoe currently receives phosphorus loads from fourteen municipal wastewater treatment

plants, 6±1 tonnes yr-1, the atmospheric deposition (18±4 tonnes yr-1) and other non-point

pathways, including runoff from agricultural, urban and natural areas (43±5 tonnes yr-1), and

rural septic systems (4.4±0.1 tonnes yr-1) (Gudimov et al., 2012). The exogenous phosphorus

loading determine the ambient total phosphorus (TP) levels, stimulate phytoplankton production,

and the subsequent decomposition of the excessive organic matter in the sediments likely

contributes to hypolimnetic dissolved oxygen (DO) depletion (Dittrich et al., 2013; McCulloch et

al., 2013). Prior to the mid-1990s, end-of-summer hypolimnetic DO levels reached nearly lethal

levels for many coldwater fish species, <3 mg/L (Evans, 2007). As a result, fish biomass declined

for several commercially important fish species, such as lake trout (Salvelinus namaycush), lake

whitefish (Coregonus clupeaformis), and lake herring (Coregonus artedi) (Evans, 2007). To

assist with the restoration of a self-sustaining coldwater fishery, the on-going reduction of point

and non-point phosphorus inputs aim to control excessive phytoplankton biomass production and

to gradually alleviate hypoxic conditions in order to obtain an end-of-summer minimum volume-

weighted hypolimnetic dissolved oxygen of 7 mg/L (Young et al., 2011).

Lake Simcoe is a well studied system with detailed long-term records of major sources and sinks

of phosphorus at both lake top (water surface) and bottom (sediment bed) boundaries. Most of

the datasets have been received from the Ontario Ministry of the Environment (MOE) and Lake

Simcoe Region Conservation Authority (LSRCA), i.e., lake bathymetry, total phosphorus

loading estimates, bi-monthly water quality samples from the ice-free period at different

monitoring stations, water temperature, start and end dates of stratification period, data on

photosynthetic active radiation (PAR).Our model segmentation of Lake Simcoe resembles

Nicholls’ (1997) conceptualization, in that the two embayments (Kempenfelt Bay and Cook's

Bay) along with the shallow littoral zone at the east end are separated from the main basin (Fig.

5-1). Data on monthly tributary discharges and phosphorus exogenous loading into Lake Simcoe

for the 1999-2007 period were provided by (LSRCA, 2006) and (LSRCA, 2012), based on the

midpoint method of interpolation to fill the gaps between bi-monthly samples of phosphorus

concentrations and flow discharges. Wind data have been compiled from Weather Canada

database in an hourly scale. Information on macrophytes abundance has been compiled from

several published sources (Ginn, 2011; LSRCA, 2011; Depew et al., 2011a,b; Stantec, 2007),

while dreissenids spatial distribution and physiological parameters have been studied by Ozersky

133

et al. (2011), Evans et al. (2011) and Ozersky et al. (2013). Sediment profiles measurements have

been published in Dittrich et al. (2013) and include sediment porosity (φ), total phosphorus

(TPsed), organic bound P (OPsed), particulate inorganic (PIPsed), and dissolved inorganic (DIPsed)

phosphorus concentrations. Scenario analysis of sediment internal P loading reflect estimated

fluxes presented by Dittrich et al. (2013) and Nürnberg et al. (2013). Organic microbial

decomposition rates in sediments are based on the McCulloch et al. (2013) modelling study,

while sediment burial rates at different monitoring stations have been adopted from Hiriart-Baer

et al. (2011).

5.2.2. Model description

The present study is based on a TP mass-balance model which represents Lake Simcoe as four

completely mixed tank reactors, while explicitly accommodating the stratification patterns

typically shaping the water quality patterns in Kempenfelt Bay, Cook's Bay, and the main basin

(Fig. 5-1). The four epilimnetic segments are interconnected through bi-directional hydraulic

exchanges to account for wind-driven flows and tributary discharges from adjacent watersheds.

The present model follows the approach presented by Kim et al. (2013) to improve the fidelity of

epilimnetic TP simulations through detailed specification of internal P recycling pathways (Fig.

5-2), such as the macrophyte dynamics and dreissenid activity as well as the fate and transport of

phosphorus in the sediments, including the sediment resuspension, sorption/desorption in the

sediment particles, and organic matter decomposition (see Table 1C-SI in the Appendix C).

Thus, the ordinary differential equations describing the dynamics of phosphorus in the water

column consider all the external inputs, advective horizontal mass exchanges between adjacent

segments, macrophyte uptake, macrophyte phosphorus release through respiration, dreissenid

filtration, dreissenid excretion and pseudofeces egestion, vertical diffusive exchanges when

stratification is established, and refluxes from the bottom sediments. The model considers a

weighted average TP sedimentation rate to account for the differences in settling velocities of

autochthonous and allochtonous biogenic particles (Ramin et al., 2011). Because the model does

not distinguish between soluble and particulate P in the water column to constrain model

complexity, the phytoplankton and detritus concentrations are introduced as forcing functions,

which ultimately allows the characterization of the site-specific settling fluxes and the

reproduction of the TP gradient from the eutrophic Cook's Bay to the mesotrophic main basin.

134

5.2.2.1. Intersegment circulation flows

In the Gudimov et al. (2012) feedforward model, the hydraulic exchanges between the two

embayments and the main basin have been reproduced through a set of annually averaged

unidirectional net flows, which were subject to Bayesian updating. Here, we improve the

representation of the horizontal advection patterns with the consideration of daily bi-directional

flows while maintaining lake-wide hydraulic mass-balance. The embayment outflows comprise

the watershed inflow discharges and the horizontal advection movement due to wind-induced

wave propagation and current drifts controlled by the water surface shear stress (Tsanis, 1992).

Wave movements were calculated based on the premise that the wave height is a function of

wind speed, fetch, and storm duration (Smith, 1979; see Table 1C-SI), while drift currents are

assumed to follow the Ekman exponential decline of current speed with depth and are also driven

by the Coriolis force (Smith, 1979). The bi-directional circulation patterns across the interface

between the main basin and the two embayments meet equilibrium conditions by considering

backflows that counterbalance the displaced volume of water (Tsanis, 1992; Baird & Associates,

2006).

5.2.2.2. Macrophyte Submodel

The contribution of macrophytes to the phosphorus cycle is based on Asaeda et al. (2000) dry-

mass biomass submodel as modified by Kim et al. (2013). The macrophyte governing equation

considers growth through uptake of interstitial inorganic phosphorus by their roots, mortality

representing the deposition of senesced plant tissues to the sediment organic phosphorus pool,

and respiration through tubers to release P back to the water column. All biological processes are

temperature dependent based on the Arrhenius equation with maxima occurring during the

summer stratified period (Chapra, 1997). The growth term is also controlled by light intensity

with extinction coefficients reported by Depew et al. (2011b). The predicted macrophyte

abundance (g dry weight or dw m-2) is prorated to a segment-specific vegetation littoral zone

(Table 1C-SI), while the tissue phosphorus content is based on existing empirical estimates from

Lake Simcoe (Depew et al., 2011b).

5.2.2.3. Dreissenid submodel

Our dreissenid submodel adopts the bioenergetic representation of the physiological activity of

individual mussels (Schneider, 1992; Bierman et al., 2005). The dreissenid interaction with the

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water column and sediment layers depends on their filtration rates, food ingestion, respiration,

excretion metabolism, production of feces, pseudofeces, and dissolved P as end-products (Fig. 5-

2). Filtering rate represents the volume of water swept clear of particles per unit time, which was

modeled following assumption of Bierman et al. (2005) that mussels maintain a maximum

ingestion rate for all food concentrations below a saturation value and are negatively related to

food abundance when this threshold is exceeded (Sprung and Rose, 1988). The capacity of

dreissenid filtration to impact the entire water column is dependent upon the wind-induced

turbulent mixing and the resultant eddy diffusivity in the water column (Edwards et al., 2005).

This process can suppress the dreissenid filtration effect on algae and other biogenic particles

from littoral to pelagic zones, resulting in the formation of boundary layers near dreissenid

mussel beds in stratified waters (Boegman et al., 2008). The latter effect is introduced in the

model with a segment-specific and depth-dependent scaling clearance rate coefficient (Daunys et

al., 2006). The rejected suspended solids and the rest biodeposited particulate material is

distributed between the water column and sediments (Fig. 5-2; Yu and Culver, 1999). The

production rate of pseudo-feces is calculated as the difference between filtered and ingested

food, assuming that the latter fraction corresponds to 34% (Walz, 1978). Counter to the Bierman

et al. (2005) study, our approach does not explicitly consider age cohort classes, while the

dynamics of individual dreissenid mussels are converted to an ecosystem-scale effect by

multiplying the areal biomass estimates with a used-specified colonization area.

5.2.2.4. Sediment submodel

Modeled sediment phosphorus considers three P fractions: particulate organic P (OPsed),

particulate inorganic P (PIPsed) and dissolved interstitial P (DIPsed) (Kim et al., 2013). The model

approximates the dynamic P transformation processes in the upper sediment layers with an active

P pool constrained by measured data by Dittrich et al. (2013). The sediment accumulation depths

in most model segments extend beyond the simulation time period of 9 years (1999-2007) with

10 years of sediment accumulation history in Cook's Bay, 22 years in Kempenfelt Bay, and 36

years in Main Basin (Hiriart-Baer et al., 2011). Being the residues of algae, dead macrophyte

tissues, and dreissenid egested/excreted material, organic phosphorus is transported towards the

deeper sediments through burial. Temperature-dependent biological decomposition of organic

phosphorus in the sediments leads to the regeneration of dissolved phase phosphorus. Dissolved

phosphorus is subjected to diffusion and adsorption-desorption to/from the sediment particles.

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Following findings of Hiriart-Baer et al. (2011), the sediment burial of particulate fractions

(OPsed and PIPsed) was assumed to be the lowest in the main basin and the highest in Cook's Bay.

We use Michaelis–Menten kinetics and the Arrhenius equation to describe the release rate of

dissolved phosphorus from the surface layer into the overlying water as a function of the

concentration gradients, the dissolved oxygen availability, and temperature. Exchangeable

particulate phosphorus may act as a sink or source, depending on the difference between the

concentration in interstitial waters and a dynamic equilibrium concentration of dissolved

phosphorus. The latter concentration was estimated from exchangeable particulate phosphorus

in sediments, assuming non-linear sorption partitioning described by the Langmuir isotherm

(Wang et al., 2003a, b). Sediment resuspension is another potentially important sink of the

phosphorus pool that depends strongly upon the magnitude of the bottom shear stress (Lick,

1986; Mehta et al., 1982; Tsai and Lick, 1986). Similar to Kim et al. (2013), we used an

empirical expression that postulates a linear relationship between sediment resuspension rate and

the excess bed shear stress (Mehta et al., 1982; Chao et al., 2008). The bottom shear stress

associated with the near-bed wave velocity was assumed to be much larger than that associated

with the near-bed current velocity (Mian and Yanful, 2004). The Sverdrup–Munk–Bretschneider

(SMB) method for shallow water bodies was then used to quantify the bed shear stresses, as a

function of the wave characteristics (height, period length), the water depth, the wind speed and

fetch length (CERC, 1994).

We used the average error (AE), the relative error (RE), and the root mean square error (RMSE)

to estimate the agreement of the daily TP predictions with the corresponding observed values

(Stow et al., 2003). A sensitivity analysis was conducted to quantify the dependence of model

predictions on model inputs. Specifically, we reported the 95% predictive intervals associated

with the uncertainty of the exogenous TP loading and hydrodynamic inter-segment exchanges.

These forcing functions were treated stochastically using Latin Hypercube sampling. Model

inputs have been sampled independently from uniform distributions based on relevant coefficient

of variations (Table 5-1). Additionally, the sensitivity of model endpoints to parameters related

to the dynamics of macrophytes, dreissenids or sediment P release was tested by inducing

perturbations around the values assigned during the calibration exercise.

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5.3. Results

The comparison between the observed and predicted TP concentrations in the different model

segments is illustrated in Fig. 5-3, while the associated fit statistics are provided in Table 5-2. The

fit statistics are on par with the error values reported for other TP mass-balance models developed

in the Great Lakes (Chapra and Dolan, 2012). The RMSE values varied from 4.5 to 6.5 µg TP L-1

for daily concentrations and 2.5-4.1 µg TP L-1 for seasonal mean values. The RE values ranged

from 32-37% and 11-23% for daily and seasonal TP concentrations, respectively. The TP levels

are overestimated in the Main Basin and the East End of Lake Simcoe with average error (AE) of

1.2-2.4 µg TP L-1, but they are underestimated in Cook’s Bay with negative AE ≈ -1.7 µg TP L-1.

Interestingly, our sensitivity analysis showed that both exogenous P loading and hydrodynamic

forcing can induce significant variability in the two embayments, whereby conditions of long

residence time and increased nutrient inflows result in simulated TP levels of 40-50 µg L-1 at

Cook’s Bay and 20-30 µg L-1 at Kempenfelt Bay. The present model improved the fit to the

observed TP patterns in Cook’s Bay relative to Gudimov et al. (2012) continuous stirred-tank

reactor (CSTR) model, as the RMSE values decreased from 10.8 to 6.4 µg TP L-1. In the Main

Basin, the RMSE values remained practically unaltered, ≈4.0-4.5 µg TP L-1, while the fit in

Kempenfelt Bay worsened from 3.2 to 5.7 µg TP L-1. Similar to Gudimov et al's (2012) results,

our model appears to underpredict the intra-annual epilimnion TP concentration dynamics,

indicative of a more complex interplay among exogenous loading, hydrodynamics, and biological

productivity that most likely modulates in-lake TP variability.

The specification of the settling velocities in the different model segments are provided in Table

5-1. The average TP settling rate of 6.5 m yr-1 falls within the 4-13 m yr-1 range reported for

mesotrophic embayments in Lake Superior (Chapra and Dolan, 2012). The annual settling

velocities are also comparable with those derived by the CSTR model with the highest rate in

Cook’ Bay and the lowest in the main basin (Gudimov et al., 2012). According to our model, the

amount of phosphorus exported from the main basin through the outlet in Atherley Narrows was

estimated to be 12.1 tonnes P yr-1, which falls within the typically reported range of 6.9-14.3

tonnes P yr-1 and corresponds to an average of 83% P retention in Lake Simcoe (LSRCA, 2006;

2012). The net export of 13.1 tonnes P yr-1 from Cook’s Bay to the main basin is distinctly higher

from Gudimov et al.'s (2012) estimate of 3.4 tonnes P yr-1, but the latter model also predicted an

elevated epilimnetic loss of 13.1 tonnes P yr-1 at the middle area of the embayment (Gudimov et

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al., 2012). Likewise, the net export of 7.3 tonnes P yr-1 from Kempenfelt Bay is higher than

Gudimov et al.'s (2012) net export of 3.0 tonnes P yr-1, and instead the CSTR model suggested

an elevated loss of 4.5 tonnes P yr-1 at the inner segment of this embayment (segment K39). The

explicit consideration of macrophytes and dreissenids modified significantly the P sedimentation

fluxes reported by Gudimov et al. (2012) in Cook’s Bay (62-976 versus 51 mg P m-2 yr-1),

Kempenfelt Bay (83-496 versus 50.6 mg P m-2 yr-1), and East End (72 versus 124 mg P m-2 yr-1),

while the main basin remained mostly unaffected (44-83 versus 71 mg P m-2 yr-1).

Our model predicts that the macrophytes biomass values in the end of summer can reach values

up to 120 g dw m-2 in the Cook’s Bay epilimnion and 100 g dw m-2 at the littoral zone of the East

End, which correspond to annual average values of ≈75 and 70 g dw m-2, respectively. These

predictions are on par with the empirical estimates of 60-80 g dw m-2 reported for the nearshore

areas in the middle and outer Cook’s Bay, but underestimate the biomass values (> 80 g dw m-2)

at the innermost sites of this embayment (Ginn, 2011). The reason for the discrepancy in the

inner Cook's Bay is that our model predicts a severe macrophyte limitation stemming from the

nutrient availability in the interstitial waters of the top sediment layer, which in turn represents

the accumulation history over the last 10 years. The annual P loading in Cook’s Bay has

dramatically fallen from 70 tonnes P yr-1 in 1990-1991 to an approximate average of 20 tonnes P

yr-1 during the 1998-2008 period. Thus, higher macrophyte biomass values could be achieved by

considering higher "legacy P" stored in the deeper sediments during the eutrophic past (see Fig.

4C-SI), especially directly at the outlet from Holland Marsh dykes where most of the terrestrial P

load settles down (Depew et al., 2011a). The model also overestimates somewhat the observed

macrophyte abundance in the nearshore sites of Kempenfelt Bay and main basin, 20-40 g dw m-

2. Our model postulates that the metabolic by-products excreted through respiration represent a

direct gain for the TP pool in the water column, and as such the macrophyte parameter

specification could partly drive the model predictions (Fig. 1-3C SI). The scenario of light

deficiency for macrophytes in Cook’s Bay and East End results in a decrease by 1-2 µg TP L-1

(Fig. 1C SI; lines A), while the opposite holds true for the scenario of optimal illumination (Fig.

1C SI; lines B), except from Cook’s Bay in which sediment DIP is the predominant limiting

factor. Similar to findings of Kim et al. (2013), the TP increase with the scenario of optimal

illumination of the water column can be offset by assigning a higher value to the optimal solar

radiation for macrophyte growth (Fig. 1C SI; lines C). Model sensitivity to the specification of

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the macrophyte affinity for sediment DIP is comparable with the light limitation effects (Fig. 2C

SI). Similar influence on the water column TP concentrations can be obtained by the values

assigned to macrophyte growth, metabolic losses and sediment mineralization rates, i.e., a faster

macrophyte growth and metabolic rates coupled with active sediment decomposition can shift up

the ambient levels by 1.5-2.0 µg TP/L relative to the reference conditions (Fig. 3C SI; lines A-

C).

The model parameter specification reflects the filtration behavior of an individual dreissenid

mussel of an average size of 11 mm, which falls within the reported range of 5-24.6 mm/ind

(Ozersky et al., 2013). The simulated mussel clearance rate of 23 ml/ind/hr (1.2-7.5 L/g shell-

free dry mass or SFDM/h) falls within the reported range of 20.9±30.2 ml/ind/hr (3.6±4.7 L/g

SFDM/h) (Ozersky et al., 2013). Taking into account the dreissenid area distribution reported by

Ozersky et al. (2011) along with a whole-lake average population density of 7,000 ind/m2

(Evans et al., 2011), the model predicts a total dreissenid biomass of 12 tonnes SFDM (11,879

MT SFDM in Ozersky et al. (2011). This predicted biomass in turn corresponds to a nominal

areal grazing rate of 2.6-3.8 m3 m-2 day-1, which is comparable to the empirical estimate of 0.2-

6.4 m3 m-2 day-1 in Lake Simcoe (Schwalb et al., 2013). If nominal clearance rates are taken into

account, the whole lake volume can be filtered every ten days (Ozersky et al., 2013), based on

Coughlan (1969) assumption that the suspended particles are homogeneously mixed with

dreissenids having access to the whole water volume and the filtered particles are permanently

deposited and thus not filtered again. Nonetheless, our model does not support such extreme

predictions about the role of the dreissenids, as we postulate a reduced clearance rate due to

refiltration of suspended particles (i.e., 71-86% of the inhaled water is refiltered), reflecting the

limited effect of turbulence in the water column mixing as well as the refiltration due to high

dreissenid density (Yu and Culver, 1999). The model also approximately mimics the formation

of a boundary layer in areas below the mixed layer (> 8 m deep), where dreissenids have access

mostly to particles settled from epilimnion (Boegman et al., 2008), as the predictions of a filtered

TP of ~60 tonnes P yr-1 far exceed the epilimnetic fluxes of ~40 tonnes P yr-1 settling in the

hypolimnion of the main basin (Fig. 5-4a).

The sensitivity analysis of the dreissenid submodel shows that ambient TP increases by 5-8 TP

L-1 in response to dreissenid low density population of 1,000 ind/m2 (e.g., 3.5 g SFDM m-2 at the

East End compared to 22 g SFDM m-2 under the reference conditions), whereas an increased

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abundance of 10,000 ind m-2 (or 33 g SFDM m-2) results in a decrease by 2-3 µg TP L-1

depending on the embayment considered (Fig. 4C-SI). Interestingly, the characterization of the

dreissenid ingestion and metabolic strategies does not appear to be particularly influential to the

TP model predictions (Fig. 5C-SI). Finally, we note that the modeled dreissenid P excretion rate

is 4.0 µg P g SFDM-1 day-1, which falls within Ozersky et al. (2013) estimate of 1.6-12.8 µg P g

SFDM-1 day-1.

The sediment submodel predictions are the result of a complex dynamic equilibrium among

phosphorus in the water column, macrophytes, dreissenid mussel activity, and sediment

processes. The model predictions for sediment organic phosphorus closely match the measured

concentration profile of organic bound P fraction at stations K45, K42 and C9, as represented by

the NaOH-NRP fraction under the sequential phosphorus fractionation schema reported in

Dittrich et al. (2013). The model predicts segment-specific concentrations of 0.11 mg P/g dw at

station C9 in Cooks Bay (compared to a measured active pool of 0.12 mg P g dw-1), 0.25 mg P g

dw-1 at station K42 in Kempenfelt Bay (measured value of 0.22 mg P g dw-1) and 0.14 mg P g

dw-1 at station K45 in the main basin (compared to 0.17 mg P g dw-1). The modeled sediment

diffusive fluxes are in complete agreement with the values reported by McCulloch et al. (2013),

i.e., 0.1 mg P m-2 day-1 at station C9, 0.2 mg P m-2 day-1 at K42, and 0.07 mg P m-2 day-1 at K45.

According to our sensitivity analysis, the value assigned to the sediment porosity moderately

affects the water column TP concentrations, <2 µg L-1 (Fig. 6C-SI). In a similar manner, shifting

the sediment characterization towards the predominance of adsorption or desorption processes

can vary the ambient TP levels by 2-4 µg L-1 (Fig. 7C-SI). Finally, our model demonstrates low

dependence on the parameters related to P diffusive fluxes; namely, the diffusion coefficient and

sediment thickness. This limited response can be potentially enhanced if we consider the legacy

TP in the deeper sediments, which requires consideration of non-steady-state behavior and

complete accumulation history.

Based on the model parameter specification, the various external and internal TP flux rates in Lake

Simcoe are presented in Figure 5-4 and Table 5-5. The net TP contributions (sources or sinks)

represent the mass of phosphorus associated with the various compartments (water column,

sediments, macrophytes, dreissenids) averaged over the 1999-2007 period. In Cook's Bay, the

phosphorus budget is predominantly driven by the external sources (phosphorus loading: 18.3

tonnes P yr-1) and sinks (outflows: 13.1 tonnes P yr-1). Dreissenids approximately filter 68.5 tonnes

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P yr-1 from the water column and subsequently egest 58.5 tonnes P yr-1 via their metabolic

excretion and particle rejection, whereas an additional 6.7 tonnes P yr-1 of pseudofeces are

deposited onto the sediments. Interestingly, our model suggests that the sediments (resuspension

and diffusion from the sediments to the water column minus particle settling) act as a net sink on

an annual scale in this segment (2.7 and 1.2 tonnes P yr-1 in the epilimnion and hypolimnion,

respectively). Likewise, the macrophyte intake of phosphorus from the interstitial waters is

responsible for a net loss of 8.6 tonnes P yr-1 from the sediments, and an approximately equal

amount is returned into the water column through respiration/excretion. In a similar manner, the

macrophyte intake minus the amount of P regenerated from the decomposition of the dead plant

tissues can take away 12.7 tonnes P yr-1 from the sediments in the eastern part of Lake Simcoe,

while the subsequent release of their metabolic by-products is responsible for 12.8 tonnes P yr-1.

The particulate P settling clearly dominates over the resuspension and diffusion from the

sediments to the water column with the corresponding net fluxes being equal to 5.8 tonnes P yr-1.

Kempenfelt Bay receives 9.3 tonnes P yr-1 from exogenous sources, while 7.3 tonnes P yr-1 are

transported into the main basin. The total net loss to the sediments accounts for 1.6 tonnes P yr-1,

while dreissenids on average reduce the ambient TP levels by 0.8 tonnes P yr-1. In the main basin,

the dreissenids filter 103.1 tonnes P yr-1 and approximately 90% of that amount (93.5 tonnes P yr-

1) is returned into the water column as pseudofeces or other metabolic excreta. In the same area,

external TP loading accounts for about 21.7 tonnes P yr-1, while an average of 12.1 tonnes P yr-1

are exported through the outflows into Lake Couchiching. Our model postulates that the burial into

the deeper sediment layers of the main and eastern basin represents a significant pathway (15.6-

39.1 tonnes P yr-1) through which phosphorus is permanently lost from the system.

5.4. Discussion

In the context of eutrophication modelling, Gudimov et al. (2012) cautioned that the recent trend

to increase model complexity, without ensuring that commensurate empirical knowledge from

the studied system exists, can compromise our ability to effectively constrain parameters from

observations. As a result of this practice, the inflated uncertainty undermines model credibility

for supporting environmental management decisions. For this reason, the same study advocated

the use of simple models as adequate first-order approximations until simplicity can be gradually

traded for increased explanatory power (Gudimov et al., 2012). However, Kim et al. (2013)

argued that the conventional TP (Vollenweider-type) models are structurally inadequate to

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represent one of the most critical facets of eutrophication, i.e., the causal linkage among external

loading, internal recycling, and summer ambient concentrations. In Lake Simcoe, recent

empirical evidence has made it abundantly clear that the complex interplay among macrophytes,

dreissenids, and sediment diagenesis appears to modulate the TP dynamics in the system. From a

management standpoint, the presence of a significant positive feedback loop could suggest a

disconnect between external loading and ambient nutrient levels, and thus the anticipated water

quality improvements by additional exogenous nutrient loading reductions may not be realized

within a reasonable time frame. By invoking extra complexity, the present model structure

offered the opportunity to examine (and potentially shed light) on the role of different nutrient

recycling pathways.

What is the influence of macrophytes on the phosphorus cycling in Lake Simcoe? The

macrophyte community in Lake Simcoe is currently dominated by Ceratophyllum demersum

(39.1% of the total biomass), the invasive species Myriophyllum spicatum (27.4%), Elodea

canadensis (10.7%) and Chara spp. (9.7%). The controlling factors of the submerged

macrophyte distribution and abundance are the depth, the fetch/wave exposure, the sediment

texture and stability, and the phosphorus loading from the closest tributary along with the size of

the area drained (Ginn, 2011). A nearly threefold increase in aquatic plant biomass has been

recorded after the invasion of zebra mussels, and existing empirical evidence indicates that

macrophytes have proliferated into much deeper (from 6.0 m in 1984 to 10.5 m in 2008) waters

with increasing water clarity (Ginn, 2011). Several mechanisms have been proposed to determine

the role of aquatic macrophytes as either nutrient sources or sinks in the surrounding water

(Wigand et al., 1997; Barko and James, 1998; Sand-Jensen, 1998; Christensen, 1999; Eriksson

and Weisner, 1999; Zimmer et al., 2001; Bini et al., 2010). Submerged macrophytes obtain

phosphorus both from the water column and the sediment substrate, but under normal pore and

ambient phosphorus concentrations, nutrient intake from the sediments dominates. In doing so,

they can provide a significant pathway for the rapid transport of the nutrients assimilated from

the sediments into the water column; a process known as "nutrient pump effect" (Howard-

Williams and Allanson, 1981; Asaeda et al., 2000). Macrophytes also demonstrate high luxury

uptake capacity and tend to accumulate nutrients in levels higher than their physiological

requirements, and therefore the decomposition of dead plant tissues may be an important source

of nutrients (Bini et al., 2010). Productive macrophyte stands could also cause hypoxia at night-

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time, thereby increasing sediment P fluxes (Bini et al., 2010), but even in well-oxygenated water

the increased photosynthetic rates elevate water pH (>9) which can accelerate P release from the

sediments (Barko and James, 1998). Nonetheless, there is another suite of mechanisms that can

potentially minimize the phosphorus release from decaying macrophytes, such as foliar

absorption or rapid phytoplankton uptake, and thus their presence may not always be positively

related to the ambient nutrient concentrations (Rørslett et al., 1986).

In accordance with empirical evidence, our model consistently predicts that macrophyte intake

from the interstitial waters is responsible for a significant loss of phosphorus from the sediments.

For example, in Cook's Bay, Johnson and Nicholls (1989) found a sediment TP ≈1040 μg·g−1

relative to a recently reported mean value of 518 μg·g−1, with ≈ 300 μg·g−1 in the southern area

of this embayment where the highest plant biomass is recorded (Ginn, 2011). Our study also

postulates that approximately equal phosphorus mass is returned into the water column as

metabolic excreta. The latter characterization presumably deviates from the notion that the

release of sediment-derived phosphorus from actively growing macrophytes is of minor

importance compared to the quantities of nutrients released during macrophyte decay (Rørslett et

al., 1986). In this study, there are two basic reasons why we opted for a parameter specification

that likely overstates the direct P release from macrophytes relative to the indirect path of the

bacteria-mediated decomposition of dead plant tissues on the sediments: (i) it makes it easier to

parse out the influence of macrophytes on the phosphorus cycling in the water column, given the

simplified mathematical description of the actual nature of the processes associated with the

breakdown of the fallen litter (e.g., dependence on the content of structural carbohydrates and

nutrients); and (ii) it does facilitate the reproduction of the ambient TP levels in Lake Simcoe

during our calibration exercise. In particular, depending on the macrophyte characterization as r

or K strategists (i.e., organisms with faster/slower maximum growth and metabolic rates)

combined with fast or slow sediment decomposition rates, the macrophyte activity can vary the

ambient TP levels by 2.0-4.0 µg L-1.

How critical is the role of the TP fluxes associated with the dreissenid mussels in Lake Simcoe?

In Lake Simcoe, according to the Ozersky et al. (2011) survey, 3.5% of the total dreissenid

biomass (≈12 tonnes SFDM) is found in Cook's Bay. In Kempenfelt Bay and the main basin

more than 25% of total dreissenid biomass was estimated to be in the 0-3.5 m depth interval,

≈32% of dreissenid biomass in the 3.5-8 m depth interval, and only a minor proportion of

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dreissenids can be found at depths greater than 20 m (see Fig. 1 in Schwalb et al., 2013). Our

model predicts that dreissenids filter a considerable amount of particulate phosphorus from the

water column (6.2-238 tonnes P yr-1), but the effective clearance rate is significantly lower (0.8-

22.8 tonnes P yr-1) with a substantial amount of the filtered particles (>85%) returned into the

water column as feces, pseudofeces or other metabolic excreta. The latter finding is not

surprising as the ratio between zebra mussel filtration and effective clearance rate can vary

between 3.4 and 6.9 (Yu and Culver, 1999). In particular, our model highlights the critical role of

dreissenids in the shallow eastern end of Lake Simcoe, where they filter 238.5 tonnes P yr-1 from

the water column and subsequently egest 215.0 tonnes P yr-1, while an additional 22.4 tonnes P

yr-1 of metabolic excreta are deposited onto the sediments. Because of its shallow morphometry,

a large portion of the eastern area is located within the euphotic and well-mixed zone, and

therefore the elevated benthic photosynthesis and access of the dreissenids to sestonic algae

create favourable conditions for biodeposition and nutrient recycling (Ozersky et al., 2013).

Importantly, the large fetch of Lake Simcoe, the relatively deep epilimnion, and the fairly rapid

horizontal mixing often induce hydrodynamic conditions that may allow the localized impacts of

dreissenids to shape ecosystem-scale patterns (Schwalb et al., 2013).

In a recent synthesis paper, North et al. (2013) provided evidence that six out of eleven predicted

effects of the nearshore P shunt hypothesis are supported by the long-term patterns in Lake

Simcoe. For example, the littoral benthos has been characterized by an increase in abundance

and diversity (Ozersky et al., 2011), while the biomass of non-dreissenid profundal benthos

demonstrates decreasing trends (Jimenez et al., 2011; Rennie and Evans, 2012). Counter to the

expected responses though (Higgins and Zanden, 2010), there was no evident change in the ice-

free TP concentrations, phytoplankton biovolume levels, and relative abundance of filamentous

benthic algae. Regarding the TP concentrations, the same study attributed the lack of a declining

trajectory to the year-to-year variability of the exogenous TP loading that tends to prevail over

the nearshore dreissenid filtration effects. Given the current mesotrophic state of Lake Simcoe, it

is not unreasonable to postulate a stronger reliance of the ambient TP dynamics upon the external

nutrient subsidies. However, our modelling analysis suggests that the presence of active nutrient

recycling pathways, potentially magnified by the particular morphological features and

hydrodynamic patterns of Lake Simcoe, could alleviate the direct effects of dreissenid filtration

and therefore the system has not experienced distinct decreasing trends in regard to its TP levels.

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What is our contemporary understanding of the role of the sediments? The sediment submodel is

an adaptation of the McCulloch et al. (2013) dynamic reactive-transport model, based on the

calibration dataset derived from Dittrich et al.'s (2013) sediment core analysis. From a

management point of view, the primary interest is to estimate how P loading into the different

basins will impact the local net P sedimentation (or retention) rates and consequently the Lake

Simcoe water quality. For example, using the characterization of the phosphorus cycle presented

in Fig. 5-4, we can calculate the retention capacity in Cook's Bay to be about 28%, which is

fairly close to Dittrich et al.'s (2013) value of 36% but significantly lower than Johnson and

Nicholls' (1989) estimate of 48% in 1980s. Thus, the colonization of the embayment by

dreissenids and the recent proliferation of macrophytes appear to render support to Dittrich et

al.'s (2013) hypothesis that the P retention in Cook's Bay may have decreased. The predominant

fraction of TP is carbonate-bound P (apatite-P) mainly due to the accelerated erosion in the

catchment. Furthermore, the TP content in the sediments of Cook’s Bay is the lowest among the

three studied basins in Lake Simcoe, providing evidence that the high sedimentation rates and

natural watershed sources may lead to a "dilution" of P in the sediment dry matter. In contrast,

Kempenfelt Bay typically receives half of the external P loading than Cook's Bay and the model

predicts a P retention of 22% (2.0 tonnes P yr-1), which is practically similar to the 25% estimate

in the 1980s (Johnson and Nichols, 1989) but much lower than Dittrich et al.'s (2013)

sedimentation rate (≈70%). In the same segment though, the hypolimnetic sediments are

responsible for a fairly high diffusive P flux into the water column (≈1.7 tonnes P yr-1),

presumably reflecting the highest proportion of the redox-sensitive P sediment pool compared to

other lake segments as well as the frequent hypoxic conditions in the Kempenfelt Bay

hypolimnion (Eimers et al., 2005). Phosphorus release from the sediments occurs within a short

time scale (58%), but a substantial fraction (42%) of diagenetically mobile P in the sediments

represents a long-term source in this site (Dittrich et al., 2013). The main basin receives 48.5

tonnes P yr-1 from the watershed and the adjacent basins, while 12.1 tonnes P yr-1 are exported

through Atherley Narrows, resulting in a P retention (75%) that is quite close to the lake-wide

estimate (83%). The sediments in the main basin are mostly driven by fast diagenetic processes

of settling organic matter from lake epilimnion (Dittrich et al., 2012), which in turn may be

partly reflected in our predictions of a 9.2 tonnes P yr-1 internal P loading. Overall, consistent

with the Dittrich et al.'s (2013) estimates, our modelling analysis suggests that the P diffusive

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fluxes from the sediments account for less than 30-35% of the exogenous P loading in Lake

Simcoe.

In a recent study, Nurnberg et al. (2013) attempted to quantify the long-term internal P loading in

Lake Simcoe using two different methods: (i) an in situ estimation based on the difference of the

TP concentrations between July and October; and (b) a gross estimation based on the product of

experimental P release rates with the spatiotemporal hypoxic extent of the sediments (Loh et al.,

2013). The whole lake internal P loading was estimated to be 37.4 tonnes P yr-1 (53% of the

external loading) and 62.9 tonnes P yr-1 (89% of the external loading), respectively. Because of

the significant discrepancy between our internal P fluxes and those reported by Nurnberg et al.

(2013), we attempted to shed light on the implications for the predicted phosphorus cycling in

Lake Simcoe. In particular, we simulated conditions of elevated internal P fluxes mediated

through the sediments by assigning a higher fraction of egested/refiltered seston and metabolic

excreta to be directly deposited onto the sediments in conjunction with increased sediment P

mobility (Table 5-6). Consequently, the active dreissenid biodeposition has increased from 22.4

to 111.3 tonnes P yr-1 in the eastern Lake Simcoe, from 9.7 to 49.5 tonnes P yr-1 in main basin,

and from 6.7 to 33.1 tonnes P yr-1 in Cook's Bay, accompanied by an increase in the upward

fluxes in the sediment-water column interface (difference between P release from sediments and

particle settling) from -5.8 to -0.9, -32.3 to +0.6 and -3.9 to -2.9 tonnes P yr-1, respectively.

Notably, the ambient TP levels after the reallocation of the dreissenid egesta on the sediments

could not be completely counterbalanced by (realistically) elevated sediment reflux rates, while

any other calibration strategy invoking additional subsidies in the water column (e.g.,

intensification of macrophyte metabolic P release) resulted in a severe depletion of the sediment

P pool. In this regard, we note that the unaccounted role of benthic algae could conceivably

provide an alternative pathway of P recycling (Buzzelli et al., 2000), especially since

measurements of the P tissue content in Lake Simcoe periphyton (Dichotomosiphon Tuberosus)

are comparable to the storage values reported for macrophytes (6-8 tonnes P). In all basins of

Lake Simcoe, organic P (NaOH-NRP) represents a substantial part of P released from the

sediments (Dittrich et al., 2013). Prior to 1995, phytoplankton biomass predominantly

contributed to the organic P fraction (Eimers et al., 2005), but the periphyton (or biofilm)

supported by macrophytes likely contributes to the currently elevated NaOH-NRP fraction which

in turn can be an indicator of the microbial activity in the sediments (Jaschinski et al., 2011).

147

In conclusion, we examined the relative importance of the causal linkages between exogenous

loading and internal nutrient recycling with the phosphorus dynamics in Lake Simcoe, Ontario,

Canada. Our intent was to shed light on the spatial variability of the role and the broader

ramifications for the ecosystem functioning of the dreissenid activity, the recent macrophyte

proliferation, and the interplay between water column and sediments (Fig. 5-5). Consistent with

empirical evidence from the system, our model predicts that macrophyte intake from the

interstitial waters, thereby providing a significant pathway for the rapid transport of the nutrients

assimilated from the sediments into the water column. Dreissenids filter a significant amount of

particulate phosphorus from the water column, but the effective clearance rate is significantly

lower with a substantial amount of the filtered particles (>85%) returned into the water column

as feces, pseudofaeces or other metabolic excreta. This pattern is particularly pronounced in the

shallow eastern end of Lake Simcoe, where a large portion is located within the euphotic and

well-mixed zone, and therefore the elevated benthic photosynthesis and access of the dreissenids

to sestonic algae create favourable conditions for biodeposition and nutrient recycling.

Importantly, the large fetch of Lake Simcoe and the fairly rapid hydrodynamic mixing may

facilitate the localized impacts of dreissenids to modulate ecosystem-scale patterns. P diffusive

fluxes from the sediments account for about 30-35% of the exogenous P loading in Lake Simcoe.

The retention capacity in Cook's Bay is estimated to be about 28%, which is distinctly lower than

estimates from the 1980s. Thus, the colonization of the embayment by dreissenids and the recent

proliferation of macrophytes appear to have decreased the P retention in Cook's Bay, where the

predominant fraction of TP is carbonate-bound P (apatite-P) mainly due to the accelerated

erosion in the catchment. The sediments in the main basin are mostly driven by fast diagenetic

processes of settling organic matter from the epilimnion, resulting in internal P loading of 9.2

tonnes P yr-1. In a similar manner, the hypolimnetic sediments in Kempenfelt Bay are responsible

for a fairly high diffusive P flux into the water column (≈1.7 tonnes P yr-1), presumably

reflecting the highest proportion of the redox-sensitive P sediment pool compared to other lake

segments as well as the occurrence of hypoxic conditions. Finally, regarding the absence of

decreasing trend in the TP concentrations after the invasion of dreissenid mussels, we argue that

the presence of active nutrient recycling pathways, potentially enhanced by the particular

morphological features and water mass circulation patterns in Lake Simcoe, could offset the

direct dreissenid filtration effects. We believe that the role of the different feedback loops

associated with nutrient recycling should be explicitly considered from the on-going restoration

148

efforts in Lake Simcoe, as it can considerably shape the relationship between external loading

and ecosystem response in both space and time.

5.5. Acknowledgements

This project was undertaken with the financial support of the Government of Canada provided

through the Department of the Environment. Alexey Gudimov has also received financial

support from a Doctoral Scholarship from the Natural Sciences and Engineering Research

Council of Canada. All the material pertinent to this analysis is available upon request from the

corresponding author.

149

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157

Table 5-1. Forcing functions of exogenous loading, intersegment flow and mass exchanges, model estimates of settling P fluxes.

TP mass balance model CSTR model by Gudimov et al. (2012), see Chapter 2

Segment TP load tonnes P yr-1

min-max (CV)

Flow, x106

m3 day-1

Settling velocity,

m yr-1

TP export, tonnes P yr-1

Settling flux from

epilimnion, mg P m-2 yr-1

Segment TP load

tonnes P yr-1

Settling velocity,

m yr-1

TP export,

tonnes P yr-1

Settling flux from

epilimnion, mg P m-2 yr-1

Cook's 12.1- 1.6- C1 16.1 2.0 15.3 62

Bay 24.5 18.2 6.6 13.1 51 C6 2.3 52.1 4.2 976

(17%) (42%) C9 2.2 6.6 3.4 94

Kempenfelt 7.4- 2.3 K39 8.3 33.5 3.8 491

Bay 11.2

(10%)

23.5

(41%)

6.5 7.3 51 K42 1.4 6.2 3.0 83

East End

14.4-

25.6

(14%)

8.1

107.0

(43%)

6.6

6.4

124

E51

21.9

6.2

4.2

72

Main 15.6- - S15 7.0 3.6 3.3 44

Basin 27.8

(14%)

-

-

6.5 12.1 71 K45 15.5 6.9 9.6 83

158

Table 5-2. Goodness-of-fit statistics for TP predictions based on root-mean-squared error (RMSE), average error (AE), and relative error (RE).

Model Segment RMSE µg P/L

AE µg P/L

RE %

Cook’s Bay 6.4*/ 3.0** -1.7 / 2.5** 32 / 11** Kempenfelt Bay 5.7 / 4.1 2.9 / 3.0 37 / 23 East End 4.7 / 2.9 2.4 / 2.4 36 / 19 Main Basin 4.5 / 2.5 1.2 / 1.2 32 / 16

*Daily TP predictions, **Summer stratified average TP values

159

Table 5-3: Model predictions and measured values for aquatic macrophytes, dreissenids and sediments.

Segment/ Cook's Bay Kempenfelt Bay East End Main Basin Total

Model Endpoint Model Obs. Model Obs. Model Obs. Model Obs. Model Obs.

Macrophytes abundance

35-116

75 21-67 20-40 32-95 70 32-95 20-40 - -

Macrophytes colonization area, km2

17.8 17.8 1.5 NA 24.9 NA 11.6 NA 56 56

Macrophytes biomass, tonnes dw

1,000 NA 58 NA 1,500 NA 700 NA 3,300 NA

Macrophytes P content

2,800 1,169* 120 NA 3,600 NA 1,500 NA 8,000 NA

Dreissinids biomass, tonnes SFDM

600 450 200 200 3,200 3,600 7,000 7,400 11,000 11,500

Sediment OP (fast degradable) accumulation mg P g dw-1

0.11 0.12 0.25 0.22 NA NA 0.14 0.17 - -

Flux from sediments, mg P m-2 day-1

0.07-0.11

0.10 0.18-0.21

0.20 0.07-0.08

NA 0.07-0.08

0.07 - -

*Estimated in 1988 under eutrophic conditions.

160

Table 5-4: Calibration parameters for Lake Simcoe TP model.

Symbol Variables and Parameters Value Units

Kd20 Decomposition rate coefficients at 20 °C

Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

0.0025 0.00075 0.0078 0.0006 0.0006 0.00065 0.00013

day-1

Dmac Macrophyte mortality rate 0.001 day-1 Kp Half saturation constant for phosphate in sediment pore water 5 µg L-1

PIPmax Maximum sorption capacity

Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

1.0

1.0 0.4

0.4

0.8

0.8

mg g-1

Pm Maximum gross photosynthesis rate 0.030 day-1 Rmac20 Macrophyte respiration rate at 20°C 0.018 day-1

Vs-chla Settling rate of phytoplankton 0.005 m day-1

Vs-pp Settling rate of organic matter other than phytoplankton 0.020 m day-1

α2 Phytoplankton self shading effect 0.02 m2 mg chla-1

FR Dreissenid filtration rate 500/350÷500* mL ind-1 day-1 Dreissenid filtration rate 23/20.9±30.2* mL/ind/hr Bzm Individual weight of a dreissenid mussel 14* mg WW/ind Lzm Length of an individual dreissenid 11 /5÷24.6* mm/ind αsdR Resuspension coefficient 2 mg P m2 day-1

*Ozersky et al. 2013;

**Evans et al. 2011.

161

Table 5-5: TP fluxes (tonnes P yr-1) from different mechanisms considered by the model under the

characterization of the sediment P release as per Dittrich el al. (2013).

•water-sed: (resuspension and diffusion from the sediments to water column) - (particle settling)

•water mac: (macrophyte respiration)

•water-ZM: (respiration, 0.4×excretion and refiltration rejection of dreissenids) - (particle filtration of dreissenids)

•sed-ZM: 0.6×excretion, egestion and direct rejection to sediments from dreissenids

•sed-mac: (macrophyte mortality) - (macrophyte intake from sediment)

•burial: burial rate into deeper layers

•water in: upstream inflow and external loading

•water out: downstream outflow

Site water-sed water-mac water-ZM sed-ZM sed-Mac burial water in water out

KBe -0.4 0.5 -0.8 0.6 -0.5 0.6 9.3 7.3

KBh -1.2 0.0 0.0 0.0 0.0 1.3 0.0 0.0

CBe -2.7 8.6 -10.0 6.7 -8.6 0.7 18.3 13.1

CBh -1.2 0.0 0.0 0.0 0.0 1.2 0.0 0.0

E1 -5.8 12.8 -22.8 22.4 -12.7 15.6 20.0 6.4

MBe -2.7 5.5 -3.8 3.8 -5.5 1.0 21.7 12.1

MBh -29.6 0.0 -5.8 5.9 0.0 39.1 0.0 0.0

162

Table 5-6: TP fluxes (tonnes P yr-1) from different mechanisms considered by the model under a

characterization of a faster sediment P release.

•water-sed: (resuspension and diffusion from the sediments to water column) - (particle settling)

•water mac: (macrophyte respiration)

•water-ZM: (respiration, 0.4×excretion and refiltration rejection of dreissenids) - (particle filtration of dreissenids)

•sed-ZM: 0.6×excretion, egestion and direct rejection to sediments from dreissenids

•sed-mac: (macrophyte mortality) - (macrophyte intake from sediment)

•burial: burial rate into deeper layers

•water in: upstream inflow and external loading

•water out: downstream outflow

Site water-sed water-mac water-ZM sed-ZM sed-Mac burial water in water out

Kbe -0.3 1.7 -3.0 3.0 -1.7 0.7 9.3 7.0

KBh -0.6 0.0 0.0 0.0 0.0 0.8 0.0 0.0

CBe -2.1 34.0 -35.5 33.1 -33.8 0.9 18.3 13.8

CBh -0.8 0.0 0.0 0.0 0.0 0.9 0.0 0.0

E1 -0.9 78.3 -108.4 111.3 -78.3 26.2 20.0 -8.1

MBe -1.4 21.9 -19.3 20.0 -22.1 1.1 21.7 9.5

MBh 2.0 0.0 -27.9 29.5 0.0 33.0 0.0 0.0

163

FIGURES LEGENDS

Figure 5-1: Lake Simcoe map with adjacent watershed areas (left panel); Lake Simcoe spatial

segmentation and intersegment flow diagram (right panel).

Figure 5-2: Conceptual diagram of phosphorus pathways in P mass-balance model of Lake Simcoe.

Figure 5-3: Model fit with 95% uncertainty bounds related to the error in the characterization of the

TP loading and hydraulic intersegment exchanges.

Figure 5-4: Simulated phosphorus fluxes (tonnes P yr-1) in water column and sediment layer in the

four spatial segments of Lake Simcoe

Figure 5-5: (a) Sankey diagram for comparative description of the phosphorus flows from

exogenous and endogenous P sources (tonnes P yr-1). Width of the flow pathways is proportional to

annual estimates of relevant fluxes. Dreissenids pathways indicate negative fluxes associated with

the particle rejection/egestion of metabolic excreta minus particle filtration; (b) comparative

diagram of P sinks at sediment-water interface (tonnes P yr-1).

164

Figure 5-1

165

Figure 5-2

166

Figure 5-3

167

Figure 5-4

Figure 5-5 (a)

(b)

168

169

Chapter 6 CONCLUSIONS

In Lake Simcoe, a variety of statistical (data-driven) and mathematical (process-based) models

have been developed to understand ecological interactions, to gain insights into the role of

specific facets of the ecosystem functioning (internal loading, dreissenids), and to predict the

response of the lake to external nutrient loading reductions. Generally, model-based

environmental management is preferred to have stronger mechanistic foundation, as this provides

additional assurance that the models can reflect the functional changes in the studied system

induced by significantly different external conditions. Nonetheless, developing a process-based

model and invoking extra complexity raises critical questions in regard to the existence of

commensurate knowledge of the multifaceted aspects of the system dynamics or even the

capacity to depict them mathematically. Striving for the optimal balance between models that our

prior knowledge tells us "much about little" or "little about much", modellers mainly opt for the

latter option, and thus offer mainly heuristic tools to examine different ecological hypotheses and

possibly dictate future data collection efforts. The majority of the recent process-based models

are profoundly overparameterized and have little capacity to support robust predictive

statements. What seems to be missing is a rigorous uncertainty assessment of the available

models along with efforts to base the (much needed) ecological forecasts upon that uncertainty

(Pappenberger and Beven, 2006).

In this regard, the second chapter aimed to counterbalance the problem of overparameterized

models by extending the work of Vollenweider (1968), Dillon and Rigler (1974), Janus and

Vollenweider (1981). My objective was to improve the applicability of P mass-balance models

by offering a novel methodology to reproduce intra- and inter-annual TP variability. The model

postulated idealized sinusoidal external P loading and applied hierarchical Bayesian optimization

for deriving segment-specific parameter estimates to accommodate system heterogeneity. Model

goodness-of-fit support the hypothesis that the sinusoidal approximation of seasonal TP loading

does provide an adequate explanation of measured TP concentration in two lake embayments

(Cook’s Bay and Kempenfelt Bay) and nearshore littoral zone at East End, but demonstrates less

predictive power in offshore sites of main basin. The model also accounted for variability of

exogenous loading, model structural and parametric errors and ultimately provided probabilistic

170

estimates of exceedance frequencies of TP violations in different lake segments under nutrient

loading reduction scenarios. Specifically, the model demonstrated a lake-wide decrease in

ambient TP concentrations in response to stringent P control measures in all lake segments

except Cook’s Bay.

Abiotic and biotic interactions characterizing the lower food web of Lake Simcoe were

investigated through a spatially explicit hierarchical structural equation model (SEM). Being a

multivariate statistical technique, the proposed SEM comprised a series of linear inter-connected

relationships between phyto- and zooplankton abundance and multiple abiotic predictors, such as

limiting nutrients (nitrogen, phosphorus), water temperature, and light availability. The SEM

exercise delineated the existence of strong relationships between ambient TP concentration and

planktonic biomass in nearly all lake segments. SEM was subsequently integrated with the P

mass balance model, which was used to perform Monte Carlo analysis of scenarios linking

phytoplankton response to management P reduction plans of 15% and 30%. The applied

probabilistic framework allowed estimating exceedance frequencies of chlorophyll-α violations

of the 4 µg/L threshold in different lake segments. My analysis identified two areas at the

southern end of Cook’s Bay and western end of Kempenfelt Bay near the city of Barrie, where

elevated algal abundance levels can be expected to occur even under stringent 30% nutrient

reduction. The latter prediction of phytoplankton resilience coupled with the registered elevated

P net settling rates in Cook’s Bay and Kempenfelt Bay has been hypothesized to be driven by

lake internal P recycling mechanism, which can support primary production during summer

stratified period and disconnect system response from the variability of external nutrient loading.

The third chapter aimed to investigate the role of lake sediments and associated internal P

loading through the development of a non-steady-state process-based diagenesis modelling

framework. The proposed model simulated geochemical transformations of organic matter and

major P binding forms as defined by the sequential fractionation technique of Psenner and Pusco

(1988). Early diagenesis has been formulated within a reactive-transport modelling framework to

account for combined effect of physical, chemical, and biological processes. Physical processes

in sediments were represented by burial and compaction rates, chemical processes accounted for

multiple precipitation-dissolution reactions and acid-based equilibrium conditions. Biological

processes were represented by a sequence of microbially-mediated redox transformations of

organic matter, while benthic invertebrates activity was incorporated through sediment

171

bioturbation and bioirrigation processes. The model successfully reproduced the P fractionation

data, i.e., adsorbed P, organic P, apatite P, Al–P and redox sensitive (Fe–P), as well as the total

phosphorus levels at each studied site. The model also rendered support to the hypothesis of

spatial heterogeneity of sediment diagenesis, challenging the practice of assigning lake-wide

boundary conditions and diagenetic parameter vectors across large lakes with complex

morphology. Kempenfelt Bay sediments showed a large amount of redox sensitive P at the

surface, implying that a much greater P flux from the sediments to the water column should be

expected if conditions at the sediment–water interface become anoxic. Meanwhile, P release in

the deep sites of Cook's Bay and Main Basin mainly stemmed from the organic P fraction.

Consistent with the on-going scientific debate (Hupfer and Lewandowski, 2008), my study

challenges the validity of the paradigm of oxygen-mediated P release from lake sediments,

representing P internal loading as a complex process driven by an array of multifaceted

diagenetic reactions. The results of this chapter also consolidate the usability of reactive-

transport models as an essential research tool in biogeochemistry (Steefel et al., 2005). Sediment

diagenesis models can serve as an inverse paleolimnological tool to infer about the history of P

mobilization and its impact on the development of lake trophic status. From a lake management

perspective, reactive-transport models can provide decision makers with a predictive tool to

estimate diffusive P flux from the sediments into the water column under varying management

scenarios, including re-oligotrophication, climate-induced hydrodynamic changes, hypolimnetic

artificial oxygenation, and introduction of binding agents for P precipitation and inactivation in

sediments. Importantly, due to the increased structural complexity, these models can be prone to

poor identifiability problems, which in turn may limit the credibility of the predictive statements

drawn (Brun et al., 2001; Omlin et al., 2001). Nonetheless, my research has showed that these

limitations can be overcome by increasing the availability of experimental data with respect to

the number of measured chemical species as well as by refining the spatiotemporal resolution of

samples.

Fourth chapter investigated the forecasting capacity of diagenetic RTM models to generate

estimates of P diffusive fluxes and sediment oxygen demand (SOD) at different sites of Lake

Simcoe under multiple scenarios of varying carbon fluxes and O2 at the sediment-water interface.

The simulated TP response in sediments reinforced the hypothesis that the long-term sediment P

retention in lakes is controlled by P burial in anaerobic sediments layers (Katsev and Dittrich

172

2013). In a similar context, the results of the present study are on par with recent findings that TP

in the upper sediment layers of mesotrophic lakes are not necessarily correlated with

contemporaneous water column TP concentrations (Ginn et al., 2012; Carey and Rydin, 2011).

Reactive-transport modelling framework has been applied to examine the hypothesis that the

magnitude of hypolimnetic oxygen depletion in Lake Simcoe could be directly associated with

sediment diagenesis processes. Although the model predictions were consistent with previous

historic sediment oxygen demand (SOD) records, the final contribution of sediments to O2

depletion was limited to 23.7% and 12% in Kempenfelt Bay and Main Basin, respectively. As a

result, we hypothesized that microbial mineralization in water column or benthic algae

respiration at sediment-water interface can also contribute to hypolimnetic O2 depletion, unlike

eutrophic lakes where sediment fluxes of reduced substances to hypolimnion can contribute up to

70% to O2 deficit (Gelda et al., 1995). Further, the identified differences in the quality of settling

organic matter at different lake segments suggested a variant contribution of the export of

terrestrial carbon from agricultural tributaries and/or senesced aquatic macrophytes. Taking into

account the spatial SOD variability, especially the elevated SOD levels at the Kempenfelt Bay, a

new hypothesis was formulated that remedial measures targeted on lake-wide nutrient reduction

might not be sufficient to achieve a uniform response in deep-water oxygen concentration in all

lake basins.

The fourth chapter of the present thesis explicitly accounted for the role of nutrient regeneration

mechanisms associated with macrophytes, dreissenids, and sediments. Consistent with empirical

evidence, the model highlighted their overall importance in nutrient redistribution among the

different spatial segments of Lake Simcoe. Macrophyte intake from the interstitial waters

represents a significant pathway for the rapid transport of the nutrients assimilated from the

sediments into the water column. Dreissenids filter a significant amount of particulate

phosphorus from the water column, but the effective clearance rate is significantly lower with a

substantial amount of the filtered particles (>85%) returned into the water column as feces,

pseudofeces or other metabolic excreta. This pattern is particularly pronounced in the shallow

eastern end of Lake Simcoe, where a large portion is located within the euphotic and well-mixed

zone, and therefore the elevated benthic photosynthesis and access of the dreissenids to sestonic

algae create favourable conditions for biodeposition and nutrient recycling. Importantly, the

large fetch of Lake Simcoe and the fairly rapid hydrodynamic mixing may facilitate the localized

173

impacts of dreissenids to modulate ecosystem-scale patterns. P diffusive fluxes from the

sediments account for about 30-35% of the exogenous P loading in Lake Simcoe. The sediments

in the main basin are mostly driven by fast diagenetic processes of settling organic matter from

the epilimnion, resulting in internal P loading of 9.2 tonnes P yr-1. In a similar manner, the

hypolimnetic sediments in Kempenfelt Bay are responsible for a fairly high diffusive P flux into

the water column (≈1.7 tonnes P yr-1), presumably reflecting the highest proportion of the redox-

sensitive P sediment pool compared to other lake segments as well as the occurrence of hypoxic

conditions. The retention capacity in Cook's Bay is estimated to be about 28%, which is

distinctly lower than estimates from the 1980s. Thus, the colonization of the embayment by

dreissenids and the recent proliferation of macrophytes appear to have decreased the P retention

in Cook's Bay, where the predominant fraction of TP is carbonate-bound P (apatite-P) mainly

due to the accelerated erosion in the catchment. Regarding the absence of decreasing trend in the

TP concentrations after the invasion of dreissenid mussels, my study suggests that the presence

of active nutrient recycling pathways, potentially enhanced by the particular morphological

features and water mass circulation patterns in Lake Simcoe, could offset the direct dreissenid

filtration effects. To summarize, the present work suggests that the role of the different feedback

loops associated with nutrient recycling should be explicitly considered from the on-going

restoration efforts in Lake Simcoe, as it can considerably shape the relationship between external

loading and ecosystem response in both space and time.

The present modelling work highlights the spatial heterogeneity of the limnological factors that

predominantly control P dynamics at different Lake Simcoe embayments. Their relative

importance is determined by the morphological features of the basins, the land use patterns of the

adjacent watersheds, the contribution of point and non-point P exogenous sources, and the recent

establishment of potentially important biological P mediators, such as macrophytes and

dreissenids (Figure 6-1a,b). In summary, the ambient TP concentrations in Kempenfelt Bay

depends on exogenous P loading from the highly urbanized area of the city of Barrie, while

macrophytes and dreissenids play minimal role due to the steep shores and deep bathymetry

which impede their massive colonization (Fig. 6-1b). Meanwhile, the amount of accumulated

redox-sensitive P pool in Kempenfelt Bay sediments may serve as an internal source that can

result in P hypolimnetic accumulation under hypoxic conditions. In contrast, TP dynamics at the

shallow Cook’s Bay emphasize the importance of internal P pathways mediated by macrophytes

174

and dreissenids along with the massive P loading from Holland Marsh agricultural cluster. Our

results from the shallow littoral zone at the eastern end of the main basin provided overwheming

evidence of the establishment of a near-shore nutrient shunt induced by the invasion of

dreissenids, which in turn redirects energy and nutrients from the water column to littoral

sediments. In the same location, the exposure of waters to wind driven turbulence triggers

resuspension of biodeposited (pseudo)feces from the lake bottom, thereby serving as an

additional feedback mechanism of P cycling. Finally, the main basin does not necessarily depend

on one single mechanism, but rather our analysis provides evidence for the presence of several

factors of equal importance. Because of the significant hypolimnetic sediment area in the main

basin (~50% of total lake area), the internal P release plays a significant role; more than any

other segment. The intersegment P transport from adjacent embayments to the main basin

represent an additional source of P, which is comparable to the corresponding external P loading

driven by air deposition and tributary inflows.

Future directions: To improve overall model performance and to strengthen our forecasting

capacity, I propose the following model augmentations to guide the Lake Simcoe management.

(i) The mass-balance model has demonstrated a reliance of the main basin TP concentrations on

intersegment nutrient delivery from the neighboring embayments of Cook’s Bay, Kempenfelt

Bay and East End, which invites the development of an explicit lake-wide hydrodynamic model.

The hydrodynamic model proposed can also assist with the estimation of the amount of

exogenous P loading short-circuited to hypolimnion as well as the amount of P transported from

epilimnion to hypolimnion through the wind-induced mixing. (ii) The eutrophication models

presented successfully reinstated the existing correlation between exogenous nutrient loading and

the ambient TP concentrations. According to presented information by the Lake Simcoe Region

Conservation Authority, the potential underestimation of P tributary loading following the

summer storm events can contribute ~ 20% and can profoundly modulate TP concentrations and

overall phytoplankton dynamics during the summer stratified period. Thus, the development of a

hydrological watershed model to predict daily P tributary loading, which can be subsequently

integrated with the lake model in order to propagate the variability of exogenous loading through

a complex network of ecological interactions in the water column and ultimately simulate the

planktonic food web response. (iii) As the sediment and macrophyte predictions indicate, an

additional sediment layer should be incorporated in Cook’s Bay to account for the storage of

175

legacy P. Further, my research mostly revolved around the correct representation of phosphorus

dynamics and primary production in response to exogenous and internal nutrient loading,

although the major lake management concern is the hypolimnetic oxygen depletion. The

proposed analysis indicates that oxygen demand driven by decay of settled organic matter in the

water column is a major contributor to oxygen deficit as compared to sediment oxygen demand.

Recent measurements of temporal and spatial variability of bacterial activity in Lake Simcoe

indicate that heterotrophic bacteria production in Lake Simcoe is low compared to other

mesotrophic lakes, leading to a newly formulated hypothesis that bacterial activity is not the

primary cause of hypoxia (Quinn et al., 2013). This finding requires further research to elucidate

the driving mechanisms of oxygen depletion.

On a final note, the present evaluation of wide range of mathematical/statistical models

implicitly pinpoints the uncertainty pertaining to the selection of the optimal model structure for

a specific environmental management problem. However, I believe that the presence of various

models with different strengths and weaknesses offers a unique opportunity for synthesis and

improvement of the contemporary modelling practice in Lake Simcoe. Despite their simplicity,

statistical models offer straightforward cause-effect relationships coupled with uncertainty

estimates (e.g., response curves). Since they are founded upon the available data from the

system, they offer a less risky choice to move forward and indeed offer a pragmatic means to

obtain insight about the response of the system. Nevertheless, there are major limitations in their

capacity to guide predictions outside the range associated with the dataset used. As an

alternative, existing mechanistic models have significant heuristic value and potential to be used

for predictive purposes, once rigorously evaluated. Recognizing that there is no true model of an

ecological system, but rather several adequate descriptions of different conceptual basis and

structure, model averaging is a means for obtaining weighted averages of the forecasts from

multiple models of varying complexity (Ramin et al., 2012). Perhaps, one of the most promising

ways to overcome the problem of structural uncertainty in aquatic ecosystem modelling may be

to draw inference from this type of integrative statements. A number of methods exist to

synthesize predictions across groups of models (ensembles), including sequential data

assimilation approaches, such as the ensemble Kalman filter and ensemble particle filters (Vrugt

and Robinson, 2007; Moradkhani et al., 2006) and post-hoc ensemble integration strategies, such

as the Bayesian model averaging commonly used in weather forecasting (Raftery et al., 2005). In

176

the context of ecological process-based modelling though, this approach should not be viewed

solely as a framework to improve our predictive devices, but rather as an opportunity to compare

alternative ecological structures, to challenge existing ecosystem conceptualizations, and to

integrate across different (and often conflicting) paradigms.

177

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of sediment phosphorus: Limnology and Oceanography 56, p. 2051-2063.

Dillon, P., and Rigler, F., 1974. The phosphorus-chlorophyll relationship in lakes: Limnol.

Oceanogr 19, p. 767-773.

Gelda, R., Auer, M., and Effler, S., 1995. Determination of sediment oxygen demand by direct

measurement and by inference from reduced species accumulation: Marine and

Freshwater Research 46, p. 81-88.

Ginn, B.K., Rühland, K.M., Young, J.D., Hawryshyn, J., Quinlan, R., Dillon, P.J., and Smol,

J.P., 2012. The perils of using sedimentary phosphorus concentrations for inferring

long-term changes in lake nutrient levels: Comments on Hiriart-Baer et al., 2011:

Journal of Great Lakes Research.

Hupfer, M., and Lewandowski, J., 2008. Oxygen Controls the Phosphorus Release from Lake

Sediments–a Long‐Lasting Paradigm in Limnology: International Review of

Hydrobiology 93, p. 415-432.

Janus, L., and Vollenweider, R., 1981. The OECD cooperative report on eutrophication:

Canadian contribution: Summary Rep. Sci. Ser.

Katsev, S., and Dittrich, M., 2013. Modelling of decadal scale phosphorus retention in lake

sediment under varying redox conditions: Ecological Modelling 251, p. 246-259.

Moradkhani, H., Hsu, K., Hong, Y. and Sorooshian, S., 2006. Investigating the impact of

remotely sensed precipitation and hydrologic model uncertainties on the ensemble

streamflow forecasting. Geophysical Research Letters 33, 12401-12406

Omlin, M., Brun, R., and Reichert, P., 2001. Biogeochemical model of Lake Zürich: Sensitivity,

identifiability and uncertainty analysis: Ecological Modelling 141, p. 105-123.

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Pappenberger, F. and Beven, K. J., 2006. Ignorance is bliss: Or seven reasons not to use

uncertainty analysis. Water Resources Research 42(5), 5302-5310 .

Psenner, R., and Pucsko, R., 1988. Phosphorus fractionation: Advantages and limits of the

method for the study of sediment P origins and interactions: Advanced Limnology30, p.

43-59.

Raftery, A. E., T. Gneiting, F. Balabdaoui, and Polakowski, M., 2005. Using Bayesian model

averaging to calibrate forecast ensembles, Mon. Weather Rev., 133, 1155 – 1174.

Ramin, M., Labencki, T., Trolle, D., Boyd, D., Arhonditsis, G.B., 2012. A Bayesian synthesis of

predictions from different models for setting water quality criteria. Ecological

Modelling 242, 127–145.

Quinn, C.J., North, R.L. and Dillon, P.J., 2013. Year-round patterns in bacterial production and

biomass in Lake Simcoe, Ontario, Canada: are heterotrophic bacteria a significant

contributor to low hypolimnetic oxygen? Inland Waters, Vol 3, No 2.

Steefel, C.I., DePaolo, D.J., and Lichtner, P.C., 2005. Reactive transport modelling: An essential

tool and a new research approach for the Earth sciences: Earth and Planetary Science

Letters 240, p. 539-558.

Vollenweider, R.A., 1968. The scientific basis of lake and stream eutrophication, with particular

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179

FIGURES LEGENDS

Figure 6-1: a) Bubble treemap diagram indicating the relative importance of P fluxes in different

lake segments; b) Bathymetric map of Lake Simcoe with superimposed factors that drive

phosphorus dynamics in the different lake segments.

Figure 6-1

a) b)

180

181

Appendix A

Supporting Information for Chapter 2

A) DATA SET DESCRIPTION

Exogenous nutrient loading values during the 1999-2004 period were obtained by the Ministry of

the Environment of the Province of Ontario (OMOE), while loading estimates from 2004 to 2007 were

provided by the Lake Simcoe Regional Conservation Authority (LSRCA). Non-point sources included

tributary loads, polders, and air deposition. Point sources included loadings from septics, Water Control

Pollution Stations (WCPC), and urban runoff. Phosphorus inputs from precipitation were assumed

proportional to segment areas. The air deposition fluxes were based on both monthly (1999-2004) and

daily (2004-2007) estimates. Chlorophyll α, TP, TN, NO3, and DIN concentrations were based on

samples collected twice a month during the ice-free period1. Composite samples from the euphotic zone

were collected from nine (9) stations (Fig. 1a): ATH (Atherley Narrows segment), E51 (Eastern

Segment), K45 and S15 (Central Segment), K42 and K39 (Kempenfelt Bay segment), C1, C6 and C9

(Cook’s Bay segment). Missing data were imputed by linear interpolation between adjacent dates. In

cases where the monitoring of a particular variable was discontinued, the data were imputed by linear

regressions, in which past information from neighbouring stations was used as predictor variable.

Number of animals and average lengths of identified zooplankton species were used to derive

biomass estimates with dry weight-length regression models (Table A1):

lnW = lna + blnL (A-1)

where lnW is the natural logarithm of the dry weight (µg), and lnL is the mean of the natural log-

transformed lengths (mm) of all the individuals of the same species in a particular sample. Zooplankton

biomass estimates in the original scale were obtained by back-transformation and correction for the

retransformation bias2:

W=aLbexp(0.5

SEE2) (A-2)

182

where SEE is the standard error of the model. When the standard error was not provided for a specific

regression model, the global mean error from all the regression models was used to fill the missing

value. In addition, we accounted for the reduction of dry weight from the chemical preservation of

organisms3 by classifying zooplankton length measurements into two size fractions (large>0.25mm,

small<0.25mm). The derived dry weight estimates from equation (2) were then reduced by 37% and

43% for large and small size animals, respectively.

Based on their feeding patterns, identified species were classified into herbivorous and

omnivorous/carnivorous zooplankton. The classification “herbivorous” comprised species that feed upon

a variety of small particles including bacteria, algae, ciliates, small rotifers and copepod nauplii as large

as 100 µm4. With this categorization, meiobenthic cladocerans, such as Disparalona hamata and

Pseudochydorus globosus, were specified as herbivores. Major zooplankton taxonomic groups during

the study period (1997-2007) are shown in Fig. 8-SI. Daphnia galeata mendotae had the largest

contribution to the total zooplankton biomass. Calanoid and cyclopoid copepodids also consistently

appeared in all sampling stations. These three major groups accounted for approximately 50% of the

total zooplankton biomass. Other major species included Eubosmina longispina, Eubosmina coregoni,

Leptodiaptomus minutes, Skistodiaptomus oregonensis, and Daphnia longiremis. Large zooplankton

species, such as Bythotrephes longimanus and Leptodora kindtii, contribute about 3-4% to the total

zooplankton biomass in Lake Simcoe, although some large species are not adequately represented in the

routine zooplankton collections due to the size of the net used.

183

Table A1. Zooplankton biomass estimation based on dry weight-length regression models collected from the literature. Counts (N), average length (L), and associated length ranges of the different species in Lake Simcoe.

Species Category N L Range ln a b SEE Reference

CLADOCERA

Daphnia ambigua Herbivorous 29 0.91 0.53-1.48 1.54 2.29 0.0312 5

Daphnia parvula Herbivorous 33 0.85 0.46-1.24 1.08 2.16 0.0312 6

Daphnia pulicaria Herbivorous 1 1.04 N/A 1.3585 3.14 0.0312 7

Daphnia retrocurva Herbivorous 915 0.97 0.46-1.81 0.8637 3.1262 0.0441 8

Daphnia galeata mendotae Herbivorous 12631 0.97 0.25-4.00 1.0797 2.7188 0.0352 9

Daphnia longiremis Herbivorous 1294 0.87 0.34-1.48 1.6274 3.3367 0.0136 9

Daphnia sp. Herbivorous 1 0.65 N/A 1.0797 2.7188 0.0352 9

Ceriodaphnia sp. Herbivorous 89 0.48 0.26-0.75 2.7286 3.337 0.0617 8

Simocephalus serrulatus Carnivorous/Omnivorous 3 0.83 0.76-0.91 1.3863 3.81 0.0312 5

Bosmina freyi, liederi or longispina Herbivorous 3102 0.36 0.16-0.72 3.5274 3.5859 0.0936 10

Bosmina longirostris Herbivorous 6569 0.37 0.21-1.15 2.4751 3.3614 0.0083 8

Eubosmina coregoni Herbivorous 5089 0.47 0.24-1.19 3.0871 2.3371 0.0046 11

Eubosmina longispina Herbivorous 7339 0.44 0.15-0.89 3.5274 3.5859 0.0936 10

Alona affinis Herbivorous 2 0.70 0.48-0.91 2.7676 3.84 0.0312 5

Alona guttata Herbivorous 1 0.34 N/A 2.2367 2.7418 0.0231 8

Alona sp. Herbivorous 12 0.48 0.29-0.78 2.2367 2.7418 0.0231 8

Disparalona hamata Herbivorous 1 0.25 N/A 3.5276 3.264 0.0312 12

Camptocercus sp. Herbivorous 3 0.76 0.69-0.81 9.05 0.85 0.0312 5

Chydorus sphaericus Herbivorous 155 0.28 0.15-0.51 3.127 3.3678 0.0011 8

Pseudochydorus globosus Herbivorous 53 0.53 0.37-0.75 3.127 3.3678 0.0312 8

Diaphanosoma birgei Herbivorous 575 0.37 0.005-1.12 1.072 2.9054 0.0378 8

Diaphanosoma brachyurum Herbivorous 75 0.76 0.38-1.08 1.6242 3.0468 0.1370 10

Sida crystallina Herbivorous 6 0.89 0.75-1.08 2.0539 2.189 0.0312 12

Holopedium sp. Carnivorous/Omnivorous 43 0.80 0.43-1.16 2.788 3.2102 0.0515 8

Polyphemus pediculus Carnivorous/Omnivorous 12 0.75 0.35-1.13 2.7792 2.152 0.0312 12

Bythotrephes longimanus Carnivorous/Omnivorous 348 2.91 0.74-5.76 1.23 2.09 0.0312 13

Leptodora kindtii Carnivorous/Omnivorous 124 4.99 0.96-12* 0.445 1.873 0.0037 11

184

Species Observed Diet Category N L Range ln a b SEE Reference

COPEPODA

Calanoid copepodids Herbivorous 22755 0.66 0.21-1.84 0.9799 2.7765 0.0093 8

Calanoid nauplius Herbivorous 17321 0.20 0.06-1.11 0.9926 2.0997 0.0172 8

Leptodiaptomus minutus Herbivorous 13506 0.82 0.15-1.31 1.0377 2.8255 0.0157 8

Leptodiaptomus sicilis Herbivorous 450 1.23 0.88-1.52 0.9311 3.036 0.0026 8

Skistodiaptomus oregonensis Herbivorous 4115 1.13 0.70-1.59 0.9717 2.7323 0.0071 8

Epischura lacustris Carnivorous/Omnivorous 1264 1.51 0.91-2.02 1.2702 2.485 0.0116 8

Epischura lacustris (copepodids) Carnivorous/Omnivorous 2112 0.82 0.29-1.61 0.8655 2.9373 0.0086 8

Cyclopoid copepodids Carnivorous/Omnivorous 30878 0.50 0.15-1.20 1.03 2.505 0.0479 8

Cyclopoid nauplius Herbivorous 25848 0.16 0.06-0.44 1.6388 2.4474 0.0196 8

Acanthocyclops robustus Carnivorous/Omnivorous 12 0.74 0.63-1.01 1.2177 3.4934 0.0199 8

Acanthocyclops vernalis Carnivorous/Omnivorous 28 0.91 0.7-1.23 1.2177 3.4934 0.0199 8

Cyclops scutifer Carnivorous/Omnivorous 2 0.92 0.53-1.31 1.2286 2.6398 0.0782 10

Diacyclops bicuspidatus thomasi Carnivorous/Omnivorous 12108 0.80 0.52-1.20 0.8066 4.0823 0.0173 8

Eucyclops neomacruroides Carnivorous/Omnivorous 1 1.02 N/A 1.1615 2.9559 0.0263 8

Eucyclops serrulatus Carnivorous/Omnivorous 13 0.70 0.6-0.89 1.1615 2.9559 0.0263 8

Macrocyclops albidus Carnivorous/Omnivorous 1 0.65 N/A 1.3169 2.7917 0.0254 8

Mesocyclops americanus Carnivorous/Omnivorous 2 1.16 1.12-1.19 1.3169 2.7917 0.0254 8

Mesocyclops edax Carnivorous/Omnivorous 4072 0.90 0.58-1.44 1.3169 2.7917 0.0254 8

Tropocyclops extensus Herbivorous 3003 0.49 0.35-0.69 1.1615 2.9559 0.0263 8

Tropocyclops prasinus Herbivorous 3735 0.48 0.35-1.01 1.1615 2.9559 0.0263 8

Harpacticoid sp. Herbivorous 16 0.47 0.21**-0.62 -5.32 13.95 0.0312 14

* The maximum length was set equal to 12 mm to correct the measurement error ** The minimum length was set equal to 0.21 mm to avoid negative values

185

References

1. Young, J. D.; Winter, J. G.; Molot, L., 2011. A re-evaluation of the empirical relationships

connecting dissolved oxygen and phosphorus loading after dreissenid mussel invasion in Lake

Simcoe. Journal of Great Lakes Research 37, 7-14.

2. Stow, C.A.; Reckhow, K.H.; Qian S.S., 2006. A Bayesian approach to retransformation bias in

transformed regression. Ecology 87: 1472-1477.

3. Giguere, L. A.; St-Pierre, J. F.; Bernier, B.; Vezina, A.; Rondeau, J. G., 1989. Can we estimate the

true weight of zooplankton samples after chemical preservation? Canadian Journal of Fisheries

and Aquatic Sciences 46, 522-527.

4. Porter, K. G.; Gerritsen, J.; Orcutt, J. D., 1982. The effect of food concentration on swimming

patterns, feeding-behavior, ingestion, assimilation, and respiration by Daphnia. Limnology &

Oceanography 27, 935-949.

5. Dumont, H. J.; Vandevelde, I.; Dumont, S.,1975. Dry weight estimate of biomass in a selection of

cladocera, copepoda and rotifera from plankton, periphyton and benthos of continental waters.

Oecologia 19, 75-97.

6. Pace, M. L.; Orcutt, J. D., 1981. The relative importance of protozoans, rotifers, and crustaceans in

a fresh-water zooplankton community. Limnology & Oceanography 26, 822-830.

7. Snow, N. B., 1972. Effect of season and animal size on caloric content of daphnia-pulicaria forbes.

Limnology & Oceanography, 17, 909-913.

8. Malley, D. F.; Lawrence, S. G.; Maciver, M. A.; Findlay, W. J., 1989. Range of variation in

estimates of dry weight for planktonic crustacea and rotifera from temperate North American

lakes. Canadian Technical Report of Fisheries and Aquatic Sciences, 1666.

9. Lawrence, S. G.; Malley, D. F.; Findlay, W. J.; Maclver, M. A.; Delbaere, I. L., 1987. Method for

estimating dry-weight of fresh-water planktonic crustaceans from measures of length and shape.

Canadian Journal of Fisheries and Aquatic Sciences 44, 264-274.

10. Bottrell, H. H.; Duncan, A.; Gliwicz, Z. M.; Grygierek, E.; Herzig, A.; Hillbricht-Ilkowska, A.;

Kurasawa, H.; Larsson, P.; Weglenska, T., 1976. Review of some problems in zooplankton

production studies. Norwegian Journal of Zoology 24, 419-456.

11. Culver, D. A.; Boucherle, M. M.; Bean, D. J.; Fletcher, J. W., 1985. Biomass of fresh-water

crustacean zooplankton from length weight regressions. Canadian Journal of Fisheries and

Aquatic Sciences 42, 1380-1390.

186

12. Rosen, R. A., 1981. Length-dry weight relationships of some freshwater zooplankton. Journal of

Freshwater Ecology 1, 225-229.

13. Makarewicz, J. C.; Jones, H. D., 1990. Occurrence of bythotrephes-cederstroemi in lake-ontario

offshore waters. Journal of Great Lakes Research 16, 143-147.

14. Goodman, K. S., 1980. The estimation of individual dry-weight and standing crop of harpacticoid

copepods. Hydrobiologia 72, 253-259.

187

B) FIGURES LEGENDS

Figure A1-SI: Conceptual model of the epilimnetic plankton dynamics in Lake Simcoe.

Figure A2-SI: Comparison of the observed and mean predicted (along with 95% credible intervals)

total phosphorus concentrations in the nine segments of the continuously-stirred-talk reactor (CSTR)

model, forced with idealized sinusoidal loading.

Figure A3-SI: Scatter plots of the segment-specific sedimentation rates against the residence times for

the year 2007.

Figure A4-SI: Posterior estimates of the total phosphorus sedimentation rates (year-1) at the

different segments of Lake Simcoe.

Figure A5-SI: Predicted annual phosphorus mass balance and net exchange rates at the different

segments of Lake Simcoe during the study period (1999-2007).

Figure A6-SI: Comparison of the observed and mean predicted (along with 95% credible intervals)

chlorophyll a and zooplankton biomass values in the nine segments of the Lake Simcoe structural

equation model.

Figure A7-SI: Predictions of the Bayesian network for the average total phosphorus and

chlorophyll a concentrations in Lake Simcoe under the present conditions and two scenarios of

phosphorus loading reduction.

Figure A8-SI: Zooplankton composition by biomass in Lake Simcoe during the study period (1997-

2007).

188

Figure A1-SI

189

Figure A2-SI

190

Figure A3-SI

191

Figure A4-SI

192

Figure A5-SI

193

Figure A6-SI

194

Figure A7-SI

195

Figure A8-SI

DAPHNIA

GALEATA

MENDOTAE

21%

CALANOID

COPEPODIDS

16%

CYCLOPOID

COPEPODIDS

15%

EUBOSMINA

LONGISPINA

9%

LEPTODIAPTOMUS

MINUTUS

7%

EUBOSMINA

COREGONI

4%

DIACYCLOPS

BICUSPIDATUS

THOMASI

4%

BOSMINA FREYI,

LIEDERI

4%

SKISTODIAPTOMUS

OREGONENSIS

4%

DAPHNIA

LONGIREMIS

3%

OTHER

13%

196

C) TABLES

Table A2-SI: Continuously Stirred Tank Reactor Model: Summary statistics of the posterior parameter distributions for

the nine segments in Lake Simcoe.

Cook’s Bay Kempenfelt Bay Main Basin East End Outflow

C1 C6 C9 K39 K42 S15 K45 E51 ATH

Stochastic

Nodes

Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

κ2 1999j 0.91 0.37 8.42 1.78 0.92 0.27 7.40 1.68 1.04 0.30 0.77 0.19 1.03 0.20 1.39 0.25 0.89 0.35

κ2 2000j 0.90 0.36 8.81 1.72 0.99 0.27 6.04 1.66 0.89 0.29 0.72 0.17 1.00 0.19 1.15 0.21 0.99 0.37

κ2 2001j 0.92 0.37 7.02 1.60 0.82 0.28 2.60 1.13 0.74 0.28 0.23 0.10 0.66 0.16 0.65 0.16 0.91 0.35

κ2 2002j 0.91 0.37 3.67 0.98 0.79 0.27 2.84 1.16 0.73 0.29 0.21 0.09 0.60 0.15 0.63 0.15 0.91 0.35

κ2 2003j 0.92 0.36 8.02 1.93 0.85 0.27 2.98 1.20 0.75 0.28 0.43 0.14 0.78 0.17 0.96 0.24 0.96 0.36

κ2 2004j 0.92 0.36 6.46 1.48 0.88 0.27 2.30 0.97 0.81 0.27 0.44 0.13 0.78 0.16 0.68 0.15 0.93 0.35

κ2 2005j 0.93 0.37 13.14 2.29 1.03 0.29 6.30 1.56 0.93 0.29 0.53 0.14 1.12 0.19 1.03 0.19 1.02 0.37

κ2 2006j 0.93 0.36 10.68 2.47 0.94 0.28 6.11 1.59 0.87 0.29 0.48 0.13 1.00 0.18 0.89 0.17 1.00 0.36

κ2 2007j 0.92 0.36 10.77 2.34 0.91 0.28 4.59 1.46 0.83 0.29 0.41 0.13 0.76 0.17 1.10 0.24 0.94 0.36

σκ2j 0.36 0.09 6.31 1.33 0.32 0.07 3.29 0.79 0.33 0.08 0.42 0.09 0.31 0.06 0.34 0.08 0.36 0.10

τ 0.39, 0.01

κ2 0.86, 0.07

κ2μ 0.78, 0.27

σκ2 0.36, 0.10

197

Table A3-SI: Structural Equation Model: Summary statistics of the posterior parameter distributions for the nine segments in Lake

Simcoe.

C1 C6 C9 K39 K42 S15 K45 E51 ATH

Parameters Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD

γ(Nitrogen)j 0.13 0.16 -0.22 0.15 -0.36 0.15 -0.08 0.18 -0.36 0.16 0.00 0.14 -0.34 0.17 -0.20 0.12 0.08 0.14

γ(Phosphorus)j 0.30 0.11 -0.02 0.11 0.27 0.09 0.27 0.11 0.29 0.10 0.17 0.10 0.20 0.10 0.46 0.10 0.10 0.10

γ(Light)j -0.42 0.11 -0.38 0.11 -0.38 0.11 -0.18 0.13 -0.26 0.11 -0.37 0.13 -0.28 0.11 -0.32 0.10 -0.47 0.12

γ(Temperature)j 0.42 0.10 0.43 0.11 0.47 0.11 0.46 0.11 0.46 0.11 0.48 0.10 0.50 0.10 0.49 0.10 0.50 0.11

β(Zooplankton)j -0.18 0.10 -0.12 0.10 -0.20 0.09 -0.23 0.10 -0.20 0.09 -0.10 0.10 -0.19 0.09 -0.20 0.09 -0.23 0.10

β(Chlorophyll)j 0.06 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.05 0.04 0.03 0.03 0.04 0.03 0.03 0.03

λ(TN)j 0.88 0.20 0.32 0.12 0.15 0.10 0.10 0.08 0.25 0.12 0.45 0.15 0.28 0.13 0.55 0.12 0.16 0.10

var(δDIN) j 0.44 0.19 0.31 0.15 0.31 0.16 0.38 0.17 0.29 0.15 0.35 0.17 0.42 0.18 0.29 0.15 0.36 0.18

var(δTN) j 0.65 0.16 0.99 0.07 1.03 0.07 1.05 0.08 0.99 0.07 0.94 0.07 0.99 0.07 0.88 0.06 0.90 0.07

var(δTP) j 0.32 0.16 0.28 0.15 0.31 0.15 0.34 0.16 0.32 0.16 0.33 0.17 0.33 0.15 0.21 0.11 0.26 0.14

var(δLight) j 0.29 0.16 0.29 0.14 0.32 0.16 0.35 0.16 0.36 0.16 0.25 0.13 0.27 0.15 0.27 0.14 0.23 0.11

var(δTemperature) j 0.31 0.15 0.31 0.14 0.31 0.15 0.29 0.15 0.31 0.15 0.29 0.15 0.30 0.15 0.28 0.15 0.23 0.11

var(εphytoplankton) j 0.20 0.10 0.39 0.16 0.19 0.09 0.47 0.17 0.28 0.13 0.43 0.16 0.30 0.15 0.22 0.11 0.33 0.16

var(εzooplankton) j 0.25 0.13 0.31 0.14 0.34 0.14 0.29 0.14 0.34 0.15 0.26 0.14 0.29 0.14 0.28 0.13 0.22 0.12

φ(Nitrogen) j 0.84, 0.08

φ(TP) 0.90, 0.06

φ(Light) 0.85, 0.06

φ(Temp) 0.89, 0.06

ψ1 0.65, 0.06

ψ2 0.70, 0.06

198

D) FEEDFORWARD SYSTEM OF CONTINUOUSLY-STIRRED TANK REACTORS WITH

SINUSOIDAL LOADING FORCING

D1) Model assumptions and limitations: The feedforward series of completely mixed reactors is a

pragmatic approach to accommodate the spatial variability in Lake Simcoe, given the lack of

hydrodynamic information from the system to support a more sophisticated modelling construct, e.g.,

lack of chloride concentrations to properly constrain the intersegment mixing processes during the study

period. Relative to the feedback framework (i.e., bidirectional mass exchange among the spatial

compartments), the feedforward setup is founded upon the assumption of a net unidirectional flow,

thereby simplifying both steady-state and time-variable solutions. Yet, while this approach is

conceptually suitable to model horizontal mass exchanges in a chain of lakes or a stream, its validity to

accommodate the spatial heterogeneity of a single lake holds true only under certain conditions. In

particular, the net mass of phosphorus transported from segment A to segment B is:

AA

NET

A

BBAA CV

Q

V

CQCQ −=

+− (D-1)

or 0>−=A

BBANET C

CQQQ (D-2)

In Lake Simcoe, the feedforward spatial configuration postulates three chains of reactors that connect

Cook’s Bay (C1→C6→C9→S15→K45), Kempenfelt Bay (K39→K42→K45), and the eastern segment

(E51→K45) with the main basin of the lake, which subsequently discharges to Atherley Narrows

(K45→ATH).

199

Depending on the magnitude of the net outflows relative to the volume of a specific spatial compartment,

Eq. D1 distinguishes between two cases:

1) The net outflows are non-negligible relative to the compartment volume or 0>A

NET

V

Q. This condition

refers to small and moderate sized compartments, such as C1, C6, C9, K39, K42, and ATH (Table D1).

First, because the observed TP concentrations suggest that the scenario CB>CA rarely holds true (Table

D1), the validity of Eq. D2 could be examined in the following conditions:

a) QA>QB: This scenario is related to the impact of the spring freshet and/or extreme precipitation

events that result in high hydraulic loading into the two embayments. Under these conditions, the

mass exchanges are indeed predominantly unidirectional from the nearshore areas to the outer lake.

b) QA≈QB: When the water volume exchanges among adjacent segments are approximately equal,

then the validity of Eq. D2 depends on the corresponding TP concentrations.

i) CA≈CB: If the two concentrations are also equal, then the two segments are approximately on

a steady state. This scenario may represent the conditions frequently experienced in Kempenfelt

Bay (K39→K42) or the outer area of Cook’s Bay and the main basin (C9→S15).

ii) CA>CB: This scenario reproduces the concentration gradient established at the inner segments

of Cook’s Bay (C1→C6→C9) or the interface between the main basin and Atherley Narrows

(K45→ATH). Thus, both areas can be assumed to be on par with the patterns postulated by the

feedforward model.

c) QA<QB: This condition mainly refers to wind-induced circulation patterns that predominantly

drive water masses to south- or westward directions. In this case, Eq. D2 is violated and the model

used in this analysis cannot describe the day-to-day TP variability. In particular, because of the

spatial TP trends typically experienced in the system, the model fails to account for the dilution

effects of the water masses from the outer lake on the two embayments. The latter likelihood also

suggests that the net TP loss rates presented in the study may overestimate the actual net

sedimentation occurring in the nearshore sites.

200

2) The net outflows are negligible relative to the compartment volume or 0→A

NET

V

Q. This condition

refers to large compartments, such as S15, K45, and E51 (Table D1). In this scenario, the main

implication of the feedforward model is that the largest fraction of the inflowing TP loads from the

watershed and/or antecedent lake segments is being subjected to sedimentation within those

compartments, rather than carried forward to the subsequent segments. Notably, this simplification could

have led to an overestimation of the sedimentation rates in the eastern basin, if there were substantial

exogenous loads and a distinct gradient of TP concentrations.

201

D2) Analytical solutions: A-level segments that initiate a chain of reactors: sites K39, C1, E51

)](sin[22 AAAA

AAA

Aamp

AA

avgAA t

V

W

V

WC ωφθω

ωλλ−−

++=

T

πω 2= )arctan()(A

AAA λ

ωωφ =

B-level segments that receive mass from the A-level segments K39, C1: sites K42, C6

)](sin[22 BBBB

BBB

Bamp

BB

avgB

BBAA

avgAAB t

V

W

V

W

VV

WQC ωφθω

ωλλλλ−−

+++=

)]()(sin[2222 BBAAA

BBAABA

AampAt

VV

WQωφωφθω

ωλωλ−−−

+++

)arctan()(B

BBB λ

ωωφ =

C-level segment that receives mass from the A-level segment C1 and the B-level segment C6: site C9

99

9

6699

66

116699

1169

CC

avgC

CCCC

avgCC

CCCCCC

avgCCCC V

W

VV

WQ

VVV

WQQC

λλλλλλ++=

)](sin[ 999929

299

9CCCC

CCC

Campt

V

Wωφθω

ωλ−−

++

)]()(sin[ 99666629

29

26

2669

66

CCCCCC

CCCCCC

CampCt

VV

WQωφωφθω

ωλωλ−−−

+++

)]()()(sin[ 9966111129

29

26

26

21

21619

116

CCCCCCCC

CCCCCCCCC

CampCCt

VVV

WQQωφωφωφθω

ωλωλωλ−−−−

++++

)arctan()(9

999

C

CCC λ

ωωφ =

202

D-level segment that receives mass from the A-level segment C1, the B-level segment C6, and the C-level segment C9: site S15

1515

15

991515

99

66991515

669

1166991515

116915

SS

avgS

CCSS

avgCC

CCCCSS

avgCCC

CCCCCCSS

avgCCCCS V

W

VV

WQ

VVV

WQQ

VVVV

WQQQC

λλλλλλλλλλ+++=

)](sin[ 15151515215

21515

15SSSS

SSS

Sampt

V

Wωφθω

ωλ−−

++

)]()(sin[ 15159999215

215

29

29915

99

SSCCCC

SSCCCS

CampCt

VV

WQωφωφθω

ωλωλ−−−

+++

)]()()(sin[ 151599666626

26

29

29

215

2156915

696

SSCCCCCC

CCCCSSCCS

CampCCt

VVV

WQQωφωφωφθω

ωλωλωλ−−−−

++++

)]()()()(sin[ 15159966111121

21

26

26

29

29

215

21516915

1961

SSCCCCCCCC

CCCCCCSSCCCS

CampCCCt

VVVV

WQQQωφωφωφωφθω

ωλωλωλωλ−−−−−

+++++

E-level segment that receives mass from the A-level segment E51, and the series of reactors from Kempenfelt Bay and Cook’s Bay: site K45

_chainCook's Bay Bay_chainKempenfeltEKE CCCCC +++= 5145

)](sin[ 4545454522

4545

45

4545

4545 KKKK

KK

Kamp

KK

avgKK t

V

W

V

WC ωφθω

ωλλ−−

++=

)]()(sin[ 454551515151245

245

251

2514551

5151

45455151

515151 KKEEEE

KKEEKE

EampE

KKEE

avgEEE t

VV

WQ

VV

WQC ωφωφθω

ωλωλλλ−−−

+++=

203

42424545

4242

424239394545

393942_

KKKK

avgKK

KKKKKK

avgKKKchainBayKempenfelt VV

WQ

VVV

WQQC

λλλλλ+=

)]()(sin[ 454542424242245

245

242

2424245

4242

KKKKKK

KKKKKK

KampKt

VV

WQωφωφθω

ωλωλ−−−

+++

)]()()(sin[ 4545424239393939245

245

242

242

239

239423945

393942

KKKKKKKK

KKKKKKKKK

KampKKt

VVV

WQQωφωφωφθω

ωλωλωλ−−−−

++++

15154545

1515

9915154545

9915

669915154545

66915

11669915154545

116915

SSKK

avgSS

CCSSKK

avgCCS

CCCCSSKK

avgCCCS

CCCCCCSSKK

avgCCCCS_chainCook's Bay VV

WQ

VVV

WQQ

VVVV

WQQQ

VVVVV

WQQQQC

λλλλλλλλλλλλλλ+++=

)]()(sin[ 454515151515245

245

215

2151545

1515

KKSSSS

KKSSSK

SampSt

VV

WQωφωφθω

ωλωλ−−−

+++

)]()()(sin[ 45451515999929

29

215

215

245

24591545

9159

KKSSCCCC

CCSSKKCSK

CampSCt

VVV

WQQωφωφωφθω

ωλωλωλ−−−−

++++

)]()()()(sin[ 4545151599666626

26

29

29

215

215

245

245691545

61596

KKSSCCCCCC

CCCCSSKKCCSK

CampSCCt

VVVV

WQQQωφωφωφωφθω

ωλωλωλωλ−−−−−

+++++

2

12

12

62

62

92

92

152

152

452

451691545

115961

CCCCCCSSKKCCCSK

CampSCCC

VVVVV

WQQQQ

ωλωλωλωλωλ ++++++

)]()()()()(sin[ 4545151599661111 KKSSCCCCCCCC t ωφωφωφωφωφθω −−−−−−×

204

F-level segment that receives mass from the E-level segment K45: site ATH

_chainCook's Bay Bay_chainKempenfeltEKATHF CCCCCC ++++= 5145

)](sin[22

45ATHATHATHATH

ATHATHATH

ATHamp

ATHK

avgATHATH t

V

W

V

WC ωφθω

ωλλ−−

++=

)]()(sin[ 45454545245

245

2245

4545

4545

454545 ATHATHKKKK

KKATHATHATHK

KampK

KKATHATH

avgKKK t

VV

WQ

VV

WQC ωφωφθω

ωλωλλλ−−−

+++=

)]()()(sin[ 45455151515122245

245

251

2514551

515145

51515151

51514551 ATHATHKKEEEE

ATHATHKKEEKEATH

EampEK

EEEEATHATH

avgEEKE t

VVV

WQQ

VVV

WQQC ωφωφωφθω

ωλωλωλλλλ−−−−

++++=

45454242

424245

393942424545

39394245

KKKKATHATH

avgKKK

KKKKKKATHATH

avgKKKK Bay_chainKempenfelt VVV

WQQ

VVVV

WQQQC

λλλλλλλ+=

)]()()(sin[ 454542424242242

242

245

245

224245

424542

ATHATHKKKKKK

KKKKATHATHKKATH

KampKKt

VVV

WQQωφωφωφθω

ωλωλωλ−−−−

++++

)]()()()(sin[ 4545424239393939239

239

242

242

245

245

22394245

39454239

ATHATHKKKKKKKK

KKKKKKATHATHKKKATH

KampKKKt

VVVV

WQQQωφωφωφωφθω

ωλωλωλωλ−−−−−

+++++

205

_chainCook's BayC = 11669915154545

11691545

CCCCCCSSKKATHATH

avgCCCCSK

VVVVVV

WQQQQQ

λλλλλλ

15154545

151545

9915154545

991545

669915154545

6691545

SSKKATHATH

avgSSK

CCSSKKATHATH

avgCCSK

CCCCSSKKATHATH

avgCCCSK

VVV

WQQ

VVVV

WQQQ

VVVVV

WQQQQ

λλλλλλλλλλλλ+++

)]()()(sin[ 454515151515215

215

245

245

221545

151545

ATHATHKKSSSS

SSKKATHATHSKATH

SampSKt

VVV

WQQωφωφωφθω

ωλωλωλ−−−−

++++

)]()()()(sin[ 45451515999929

29

215

215

245

245

2291545

945159

ATHATHKKSSCCCC

CCSSKKATHATHCSKATH

CampKSCt

VVVV

WQQQωφωφωφωφθω

ωλωλωλωλ−−−−−

+++++

26

26

29

29

215

215

245

245

22691545

6451596

CCCCSSKKATHATHCCSKATH

CampKSCC

VVVVV

WQQQQ

ωλωλωλωλωλ ++++++

)]()()()()(sin[ 45451515996666 ATHATHKKSSCCCCCC t ωφωφωφωφωφθω −−−−−−×

21

21

26

26

29

29

215

215

245

245

221691545

14515961

CCCCCCSSKKATHATHCCCSKATH

CampKSCCC

VVVVVV

WQQQQQ

ωλωλωλωλωλωλ +++++++

)]()()()()()(sin[ 4545151599661111 ATHATHKKSSCCCCCCCC t ωφωφωφωφωφωφθω −−−−−−−×

206

E) STRUCTURAL EQUATION MODEL FOR LAKE SIMCOE

Using the classical SEM notation, we present the matrices’ forms and the specific

assumptions made for the non-recursive structural equation model for Lake Simcoe (Fig. 1b & Fig.

A1-SI). The exogenous latent variable measurement model consists of four matrices; i.e. X is a q x 1

vector of observable indicators of the independent latent variables ξ; Λx is a q x n matrix of

coefficients relating X to ξ; ξ is a n x 1 vector of independent (exogenous) latent variables; and, δ is a

q x 1 vector of measurement errors for X. In the present model, we included four (n = 4) exogenous

latent variables ξ which were described from five (q = 5) indicator variables; i.e., TN and DIN were

used for the latent variable “Nitrogen”; Secchi Disc Depth for the latent variable “Light”; TP for the

latent variable “Phosphorus” and Temperature for the respective latent variable. Thus,

=====

=

eTemperaturX

TPX

c DepthSecchi DisX

DINX

TNX

X

5

4

3

2

1

,

=

5

4

3

2

1

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

λλ

λλλ

XΛ ,

====

=

eTemperaturξ

Phosphorusξ

Lightξ

Nitrogenξ

ξ

4

3

2

1

,

=

5

4

3

2

1

δδδδδ

δ

The endogenous latent variable measurement model also consists of four matrices; i.e., Y is a p x 1

vector of observable indicators of the dependent latent variables η; Λy is a p x m matrix of

coefficients relating Y to η; η is a m x 1 vector of dependent (endogenous) latent variables; ε is a p x

1 vector of measurement errors for Y; For our model, two indicator variables (p = 2) were used for

the representation of two (m = 2) endogenous latent variables; i.e., Chlorophyll a and Zooplankton

biomass were used as indicators for the latent variables “Phytoplankton” and “Herbivorous

Grazing”. Thus, the exogenous latent variable measurement model can be described by the four

matrices:

==

=nZooplanktoY

l aChlorophylYY

2

1 ,

=

7

6

0

0

λ

λΛY ,

==

=GrazingsHerbivorouη

tonPhytoplankηη

2

1 ,

=

2

1

εε

ε

The additional three matrices for the latent variable model are:

207

=

4

321

00 0

0

γγγγ

Γ , [ ]21 ββΒ= ,

=

2

1

ζζ

ζ

where Γ and Β are the matrices of coefficients for the latent exogenous and endogenous variables,

respectively; ζ is the vector of latent (structural) errors. As inferred from the path diagram, the

associated covariance matrices of the model, Cov(ξ) = Φ(n x n): lake-wide covariances between the

independent variables ξ; Cov(ε) = Θε(p x p): segment-specific covariances between the

measurement errors in Y; Cov(δ) = Θδ(q x q): segment-specific covariances between the

measurement errors in X; Cov(ζ) = Ψ(m x m): lake-wide covariances between the structural errors ζ,

have the off-diagonal elements equal to zero:

=

)var( 0

)var(

2

1

εε

ε

Θ ,

=

)var( 0 0 0 0

)var( 0 0 0

)var( 0 0

)var( 0

)var(

5

4

3

2

1

δδ

δδ

δ

δ

Θ ,

=

22

11

0 ψψ

Ψ ,

=

44

33

22

11

0 0 0

00

0

φφ

φφ

Φ

The metric of the latent variables was set by fixing one loading in each column of ΛX and ΛY to 1.0.

In this particular case, we assumed that λ2 = λ3 = λ4 = λ5 = λ6 = λ7 = 1.0. The hierarchical Bayesian

configuration of the Lake Simcoe SEM for an arbitrary observation i at segment j can be specified as

follows:

X1ij = λ1jξ1ij + δ1j, X2ij =ξ1ij + δ2ij

X3ij = ξ2ij + δ3ij

X4ij = ξ3ij + δ4ij

X5ij = ξ4ij + δ5ij

δ.j ~ N(0,Θδj), ξ. ~ N(0,Φ)

208

Y1ij = η1ij + ε1ij

Y2ij = η2ij + ε2ij

ε.j ~ N(0,Θεj)

η1ij = γ1jξ1ij + γ2jξ2ij + γ3jξ3ij + β1jη2ij + ζ1ij

η2ij = γ4jξ4ij + β2jη1ij + ζ2ij

ζ. ~ N(0,Ψ)

We used independent non-informative conjugate gamma priors (0.001, 0.001) for the elements of the

matrices Θδj-1, Θεj

-1, Φ-1 and Ψ-1. Effectively “flat” normal prior distributions with means equal to 0

and precisions equal to 0.0001 along with diffuse gamma priors were used for the hierarchical

treatment of the structural parameters and the factor loading λ1 or λTN. MCMC simulation was used as

the computation tool implemented in the WinBUGS software (Lunn et al., 2000). We used two chain

runs of 50,000 iterations and samples were taken every 20th iteration to avoid serial correlation, and

convergence was assessed using the modified Gelman-Rubin convergence statistic (Brooks and

Gelman, 1998). Generally, the sequences converged rapidly (≈ 2,000 iterations), while the summary

statistics reported in this study were based on the last 40,000 draws. The accuracy of the posterior

estimates was inspected by assuring that the Monte Carlo error (an estimate of the difference

between the mean of the sampled values and the true posterior mean; see Lunn et al., 2000) for all

the parameters was less than 5% of the sample standard deviation. In the context of aquatic ecology,

a simple illustration of a Bayesian SEM configuration can be found in Arhonditsis et al. (2006).

Finally, we note that the present formulation differs from the spatially-explicit Bayesian SEM

developed for the Neuse River Estuary (Arhonditsis et al., 2007a,b) in that (i) none of the latent

variables is treated as perfectly measured, i.e., all the measurement errors were explicitly considered;

(ii ) the covariance matrices of the exogenous latent variables and the structural errors were common

over the entire lake rather than segment-specific.

209

References

Arhonditsis, G.B., C.A. Stow, H.W. Paerl, L.M. Valdes, L.J. Steinberg, and K.H. Reckhow, 2007.

Delineation of the role of nutrient dynamics and hydrologic forcing on phytoplankton patterns

along a freshwater-marine continuum. Ecological Modelling 208, 230-246.

Arhonditsis, G.B., H.W. Paerl, L.M. Valdes, C.A. Stow, L.J. Steinberg, and K.H. Reckhow, 2007.

Application of Bayesian Structural Equation Modelling for examining the Neuse River Estuary

(NC, USA) phytoplankton dynamics. Estuarine Coastal & Shelf Science 73, 63-80.

Arhonditsis, G.B., C.A. Stow, L.J. Steinberg, M.A. Kenney, R.C. Lathrop, S.J. McBride, and K.H.

Reckhow, 2006. Exploring ecological patterns with structural equation modelling and Bayesian

analysis. Ecological Modelling 192, 385-409.

Brooks, S.P. and Gelman, A., 1998. Alternative methods for monitoring convergence of iterative

simulations. Journal of Computational and Graphical Statistics 7, 434-455.

Lunn, D.J., Thomas, A., Best, N., and D. Spiegelhalter, 2000. WinBUGS a Bayesian modelling

framework: concepts, structure, and extensibility. Statistics and Computing 10, 325–337.

210

Appendix B

Supporting Information for Chapter 4

Table B2-SI (next page) is based on the IDENT procedure from UNCSIM software package

(Reichert, 2005). The matrix is a part of the identifiability analysis presented in detail in

(McCulloch et al., 2013). Each parameter is varied within 10% of its standard deviation under

the assumption of a normal distribution. The standard deviations of Si concentrations are

proportional to values of scaling parameters to make concentrations of different species

comparable (McCulloch et al., 2013). For more details, the reader is referred to the links

http://www.uncsim.eawag.ch/ and http://www.eawag.ch/forschung/siam/software/ident/index

Table B1-SI. Scaling factor for sensitivity analysis.

yi sci SO2 0.219 mmol/l

SCa 1 mmol/l

SCO3 0.001 mmol/l SHPO4 0.0009 mmol/l SNO3 0.022 mmol/l SHS 0.007 mmol/l

SNH4 0.05 mmol/l SS2 2.4 10-10 mmol/l SSO4 0.03 mmol/l SMn 0.02 mmol/l SFe 0.0088 mmol/l pH 8.19 -

Xorgfast 35 mg/gDM Xorgine 10 mg/gDM XMnO2 1.4 mg/gDM XMnCO3 3.8 10-4 mg/gDM XCaCO3 2.2 mg/gDM

XP_Apatite 0.44 mg/gDM XFeOOH 151 mg/gDM XFe_Other 1.5 mg/gDM

XP_Absorbed 0.16 mg/gDW XFeCO3 1.7 10-4 mg/gDW XP_BD 0.4 mg/gDW

XInorg_Other 0.3 mg/gDW

211

Table B2 -SI. Correlation matrix of the model parameters*. Correlation coefficients with absolute value higher than 0.50 are reported in a bold font

S O2S

WI

αO

rg_

ine

rt

αO

rg

k O2

Ksa

tur O

2

f CaC

O3

k θ

S NO

3 SW

I

DB

k NO

3

Ksa

tur N

O3

αbio

irri

g

1 0;�+

�56

S Ca S

WI

S HS

WI

k oxi

HS

S HS S

WI

S Fe S

WI

S Mn

SW

I

k FeO

OH

KF

eOO

H

k de

gF

e-P

k Fe-

P

k nitr

i

SO2SWI

1.00 -0.20 0.14 0.00 -0.02 -0.01 0.03 -0.76 -0.12 0.13 0.18 -0.61 0.97 -0.08 -0.04 0.07 -0.02 -0.24 -0.11 0.40 -0.10 0.17 0.06 -0.34

αOrg_inert -0.20 1.00 0.02 -0.06 -0.23 0.15 -0.24 -0.08 -0.18 -0.04 -0.13 0.27 -0.11 0.04 0.03 -0.10 0.02 0.05 0.08 -0.06 0.02 -0.01 0.00 0.28

αOrg 0.14 0.02 1.00 0.00 0.11 0.13 0.18 0.05 0.14 -0.05 0.01 -0.18 0.08 -0.03 -0.02 0.06 -0.01 -0.05 -0.06 -0.04 0.02 0.05 0.05 -0.19

kO2 0.00 -0.06 0.00 1.00 0.97 0.03 0.10 0.19 0.61 -0.14 -0.17 0.27 -0.05 -0.05 -0.03 0.83 0.02 -0.18 -0.15 0.16 0.60 -0.25 -0.74 -0.25

KsaturO2 -0.02 -0.23 0.11 0.97 1.00 -0.01 0.18 0.20 0.61 -0.18 -0.18 0.27 -0.06 -0.04 -0.02 0.83 0.02 -0.17 -0.15 0.16 0.58 -0.29 -0.72 -0.24

fCaCO3 -0.01 0.15 0.13 0.03 -0.01 1.00 0.13 -0.01 0.00 -0.05 -0.07 0.03 -0.01 0.01 0.00 0.02 0.00 0.00 0.04 -0.01 -0.02 0.00 0.03 0.02

kθ 0.03 -0.24 0.18 0.10 0.18 0.13 1.00 0.16 0.03 -0.01 0.02 -0.24 -0.04 -0.02 0.03 0.05 -0.02 0.00 -0.01 -0.05 -0.19 -0.43 0.11 -0.10

SNO3 SWI

-0.76 -0.08 0.05 0.19 0.20 -0.01 0.16 1.00 0.47 0.05 -0.02 0.21 -0.89 0.01 0.00 0.03 -0.01 0.14 0.02 -0.43 0.15 -0.08 -0.06 -0.11

DB -0.12 -0.18 0.14 0.61 0.61 0.00 0.03 0.47 1.00 -0.22 -0.19 0.39 -0.20 -0.06 0.15 0.45 0.00 -0.10 -0.03 -0.04 0.35 -0.30 -0.24 -0.35

kNO3 0.13 -0.04 -0.05 -0.14 -0.18 -0.05 -0.01 0.05 -0.22 1.00 0.98 -0.45 0.03 -0.15 -0.11 -0.51 -0.04 -0.01 0.10 0.20 0.04 0.58 0.19 -0.17

KsaturNO3 0.18 -0.13 0.01 -0.17 -0.18 -0.07 0.02 -0.02 -0.19 0.98 1.00 -0.42 0.11 -0.16 -0.10 -0.53 -0.04 -0.02 0.12 0.26 0.00 0.52 0.24 -0.16

αbioirrig -0.61 0.27 -0.18 0.27 0.27 0.03 -0.24 0.21 0.39 -0.45 -0.42 1.00 -0.45 0.07 0.19 0.23 0.04 0.09 0.13 -0.04 0.25 -0.43 -0.22 0.40

SHCO3 SWI

0.97 -0.11 0.08 -0.05 -0.06 -0.01 -0.04 -0.89 -0.20 0.03 0.11 -0.45 1.00 -0.06 0.02 0.06 -0.02 -0.22 -0.08 0.44 -0.12 0.11 0.07 -0.20

SCa SWI

-0.08 0.04 -0.03 -0.05 -0.04 0.01 -0.02 0.01 -0.06 -0.15 -0.16 0.07 -0.06 1.00 0.00 -0.05 0.00 -0.01 0.00 -0.42 0.00 -0.07 0.10 -0.09

SHSWI

-0.04 0.03 -0.02 -0.03 -0.02 0.00 0.03 0.00 0.15 -0.11 -0.10 0.19 0.02 0.00 1.00 -0.02 0.00 -0.01 0.04 -0.02 0.02 -0.08 0.06 0.04

koxi HS 0.07 -0.10 0.06 0.83 0.83 0.02 0.05 0.03 0.45 -0.51 -0.53 0.23 0.06 -0.05 -0.02 1.00 0.04 -0.14 -0.33 0.09 0.56 -0.25 -0.86 -0.02

SHS SWI

-0.02 0.02 -0.01 0.02 0.02 0.00 -0.02 -0.01 0.00 -0.04 -0.04 0.04 -0.02 0.00 0.00 0.04 1.00 0.01 0.00 -0.11 -0.04 0.00 -0.02 0.06

SFe SWI

-0.24 0.05 -0.05 -0.18 -0.17 0.00 0.00 0.14 -0.10 -0.01 -0.02 0.09 -0.22 -0.01 -0.01 -0.14 0.01 1.00 0.03 -0.17 -0.11 -0.03 0.11 0.16

SMn SWI

-0.11 0.08 -0.06 -0.15 -0.15 0.04 -0.01 0.02 -0.03 0.10 0.12 0.13 -0.08 0.00 0.04 -0.33 0.00 0.03 1.00 -0.05 -0.15 -0.10 0.26 0.10

kFeOOH 0.40 -0.06 -0.04 0.16 0.16 -0.01 -0.05 -0.43 -0.04 0.20 0.26 -0.04 0.44 -0.42 -0.02 0.09 -0.11 -0.17 -0.05 1.00 0.06 0.01 -0.09 -0.02

KFeOOH -0.10 0.02 0.02 0.60 0.58 -0.02 -0.19 0.15 0.35 0.04 0.00 0.25 -0.12 0.00 0.02 0.56 -0.04 -0.11 -0.15 0.06 1.00 0.29 -0.74 -0.19

kdegFe-P 0.17 -0.01 0.05 -0.25 -0.29 0.00 -0.43 -0.08 -0.30 0.58 0.52 -0.43 0.11 -0.07 -0.08 -0.25 0.00 -0.03 -0.10 0.01 0.29 1.00 -0.10 -0.06

kFe-P 0.06 0.00 0.05 -0.74 -0.72 0.03 0.11 -0.06 -0.24 0.19 0.24 -0.22 0.07 0.10 0.06 -0.86 -0.02 0.11 0.26 -0.09 -0.74 -0.10 1.00 -0.21

knitri -0.34 0.28 -0.19 -0.25 -0.24 0.02 -0.10 -0.11 -0.35 -0.17 -0.16 0.40 -0.20 -0.09 0.04 -0.02 0.06 0.16 0.10 -0.02 -0.19 -0.06 -0.21 1.00

212

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ammonia and the stoichiometric dissociation constant of ammonia in estuarine water and

seawater from− 2 to 40° C: Geochimica et cosmochimica acta 59, 2403-2421.

Dittrich, M., Wehrli, B., and Reichert, P., 2009. Lake sediments during the transient

eutrophication period: Reactive-transport model and identifiability study: Ecological

Modelling 220, 2751-2769.

Dong, L., Yang, Z., and Liu, X., 2011. Phosphorus fractions, sorption characteristics, and its

release in the sediments of Baiyangdian Lake, China: Environmental monitoring and

assessment 179, 335-345.

Katsev, S., Tsandev, I., L'Heureux, I., and Rancourt, D.G., 2006. Factors controlling long-term

phosphorus efflux from lake sediments: Exploratory reactive-transport modelling:

Chemical Geology 234, 127-147.

Kopácek, J., Borovec, J., Hejzlar, J., Ulrich, K.-U., Norton, S.A., and Amirbahman, A., 2005.

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technology 39, 8784-8789.

McCulloch, J., Gudimov, A., Arhonditsis, G., Chesnyuk, A., and Dittrich, M., 2013. Dynamics

of P-binding forms in sediments of a mesotrophic hard-water lake: Insights from non-

steady state reactive-transport modelling, sensitivity and identifiability analysis:

Chemical Geology.

Reed, D.C., Slomp, C.P., and Gustafsson, B.G., 2011. Sedimentary phosphorus dynamics and the

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Limnology and Oceanography 56, 1075-1092.

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waters: Environmental Science And Technology.

213

Appendix C

Supporting Information for Chapter 5

Figures Legends

Figure C1-SI: Sensitivity of TP predictions on macrophyte light limitation: black lines:

reference simulation; gray lines represent scenarios: a) dotted line: scenario of light deficiency

(α1=0.3, α2=0.025), b) dash-dot line: scenario of optimal illumination of the water column

(α1=0.18, α2=0.015); gray solid line: scenario of increased water clarity coupled with an increase

of the optimal solar radiation for macrophyte growth (α1=0.18, α2=0.015, Iopt=34).

Figure C2- SI: Sensitivity of TP predictions on macrophyte phosphorus limitation: black lines:

reference simulation; dotted line: high affinity for phosphorus (Kp=3.8); dash dot line: low

affinity for phosphorus (Kp=6.3).

Figure C3- SI: Sensitivity of TP predictions on phosphorus recycling regimes mediated by

macrophytes: black lines: reference simulation; dotted line: fast macrophytes growth and

metabolic rates and fast sediment decomposition rates (Pm=0.03+50%, Rmac20=0.018+50%,

Dmac=0.001+15%, Kd20=+50% increase to the segment-specific value); dash-dot line: fast

macrophytes growth and metabolic rates and slow sediment decomposition rates (Pm=0.03+50%,

Rmac20=0.018+50%, Dmac=0.001+15%, Kd20=-50% increase to the segment-specific value; gray

solid line: slow macrophytes growth and metabolic rates and slow sediment decomposition rates

(Pm=0.03-50%, Rmac20=0.018-50%, Dmac=0.001-15%, Kd20=-50% increase to the segment-

specific value).

Figure 4C- SI: Projected biomass response of submerge aquatic macrophytes in Cook's Bay

according to scenarios of Holland Marsh P loading from 1999-2007 (18.3 MT P/year), 1990-

1993 (56.0 MT P/year), and 1999-2007 loading coupled with legacy P in older sediments (22

cm).

214

Figure C5- SI: Sensitivity of TP predictions on different dreissenids colonization densities:

black lines: reference simulation; gray dotted line: areal abundance of 1000 ind/m2; gray dot-

dash line: areal abundance of 10,000 ind/m2.

Figure C6-SI: Sensitivity of TP predictions on phosphorus recycling regimes mediated by

dreissenids: black lines: reference simulation; gray dotted line: fast dreissenid ingestion and

respiration rates and fast sediment decomposition rates (ac, ar, Kd20 = reference +25%); gray dash-

dot line: slow dreissenid ingestion and respiration rates and slow sediment decomposition rates

(ac, ar, Kd20 = reference -25%).

Figure C7- SI: Sensitivity of TP predictions on sediment porosity: black lines: reference

simulation; gray dotted line: high sediment porosity (φ=0.98); gray dash-dot line: low sediment

porosity (φ=0.85))

Figures C8- SI: Sensitivity of TP predictions on phosphorus adsorption/desorption processes in

the sediments: black lines: reference simulation; gray dotted line: predominance of adsorption

fluxes (Kad=5.4, PIPmax=1, E=10.925), gray dash-dotted line: predominance of desorption fluxes

(Kad=7.56, PIPmax =0.6, E=9.025).

Figure C9- SI: Sensitivity of TP predictions on phosphorus diffusion from the sediments: black

lines: reference simulation; gray dotted line: high diffusivity with thicker sediments (Kdiff,

δ=125%); gray dash-dotted line: low diffusivity with thinner sediments (Kdiff, δ =75%).

215

Figure C1- SI

216

Figure C2- SI

217

Figure C3- SI

218

Figure C4- SI

219

Figure C5- SI

220

Figure C6- SI

221

Figure C7- SI

222

Figure C8- SI

223

Figure C9- SI

224

Table C1-SI: Mathematical equations of the total phosphorus model.

Process Symbol Equation

Water column dTP9dt

TP�" + TP,DE+TP,D� + TP��FE + TPG�E + TPG�H + TPG�E�I − TPI� − TPG�/+ KTPLMNOP789 − TP8QR + TPDTU.T2V TP,DE

AV9 RZU[Q[ TP[\] D[U\^DIP[U\ − DIP9`

TPaMNb αaMN AV9 ^RaMNBPaMN`BaMN

TPdab e��AV9 BPdawZRdaBda

TPdag αda e��AV9 BPda^1 − fjklmn` woUdaBda

TPdaq FTdaV9

TPG�E�I ^1 − a[U\`^FTda − woIdae��ABdaBPda`

TP9' V[z ∙ TP9

V[ vℎxyz{| {}vℎxy} ~,lF��� + �1 − vℎxyz{| {}vℎxy}� ~,l��

TPLMNOP789, TP8QR TP9 QP789V9

TPDTU,T2 1VTU,T2^t` �AT2 �K^[RZ/�[RZ`�∆TPTU/T2�∆z ��

Macrophytes dBaMNdt ^GaMN − RaMN − DaMN` ∙ BaMN

GaMN Pa DIP[U\K� + DIP[U\ fT^t` fT^t` 2.718 FDKU�R ZaMN �el�� − el��� x1

I�el����m���FD I8�R x2

I�FD I8�R KU�R α� + α�chly

RaMN RaMN�� ∙ θZaMN^¢l��` £��F�¤��� ¥ ¦��FA[U4aU�R[ BaMN Dreissenids

dBdadt ^woIda − ^wZRda + woFda + woUda``Bda

Ida αNZBdaL� ∙ f§^t` ∙ min «PP9KN� , 1¬

225

Process Symbol Equation

f§^t` K�eγ­^RlR­`1 + K�^eγ­^RlR­` − 1` ∙ K:eγ®^R¯lR`

1 + K:^eγ®^R¯lR` − 1`

αNZ αNel�.+d

γ� 1t� − t� ∙ ln K�^1 − K�`K�^1 − K�`

γ� 1t: − t+ ∙ ln K+^1 − K:`K:^1 − K+`

Rda

αNZBdaL° ∙ fZ^t` + wowZ ∙ SDA^Ida − Fda`

aZ ZUP37R αZel�.+d

fZ^t` V�e�^�l²` V

ta − tta − t�

x «w�1 + ³1 + 40/y�20 ¬�

w lnQ^ta − t�`

y lnQ^ta − t� + 2`

PP9 TP9^1 − w]§k` Fda αoexp ¸γo ∙ min «PP9KN� , 1¬¹ ∙ Ida

Uda αQ^Ida − Fda`

FR

ºG���= KN� ∙ 0.34 if PP9 < KN�

ºG���= PP9 ∙ 0.34 if PP9 > KN�

FTda FR Bda αda Ae�� PP9

£d�R8RM7 ¥ Bmn¾¦G�¿A3:

3À� e��¿

Dissolved Inorganic Phosphorus

dDIP[U\dt

−D[U\^DIP[U\ − DIP9` + S[U\^DIP[U\U − DIP[U\` + K\UN8a ∙ ρφ

· OP[U\ −

−GaMN ∙ yaMN · ^ AφV[U\` · BaMN · BPaMN

D[U\ θ[¢l�� ∙ K]jK]j + DO ∙ φδ� K\3oo1 − ln ^Ã`

S[U\ φKM\

DIP[U\U PIP[U\E ∙ ^PIPaM� − PIP[U\`

K\UN8a K\�� ∙ θ[¢l��

226

Process Symbol Equation

Particulate Inorganic Phosphorus

dPIP[U\dt −fZU[Q[ ∙ Aρ ∙ V[U\ RZU[Q[ − S[U\^DIP[U\U − DIP[U\` ∙ φ

ρ− B[U\lk§k ∙ PIP[U\

B[U\lkk SLQZδ

Organic Phosphorus dOP[U\dt

V[ ∙ TP9z ∙ Aρ ∙ V[U\ − ^1 − fZU[Q[` ∙ A

ρ ∙ V[U\ ∙ RZU[Q[ − B[U\lkk ∙ OP[U\ − K\UN8a ∙ OP[U\ + DaMN ∙ BaMN∙ αaMN ∙ Aρ ∙ V[U\ ∙ BPaMN + Dda ∙ Bda ∙ αda ∙ A

ρ ∙ V[U\ ∙ BPda + Psdfdaρ ∙ V[U\

Dda wo ∙ ^fjklmn ∙ Uda + Fda` Psdfda a[U\^FTda − wo ∙ Ida ∙ A ∙ Bda ∙ BPda`

Sediment resuspension

RZU[Q[ a,DE �τ− τNτN ��ÇÈÉ if τ ≥ τN , 0 if τ < τN

Inflow from Main Basin to a segment Outflow from a segment to Main Basin

Qbackflow

Qoutflow

(Mw+Md)Lsegment

Qbackflow + Qtrib

Mw

Md

Ë,�ÌÍÎ32 ℎ where ÎË,Ð�� = 0.0026 ÒÎÓUM� Ô�.:Õ

ÖD = 0.0298 Óz,

Ë�,Ë, = 8.98 Ö,ÖDØ1 + 7.95 Ö,ÖDÚ

z�,z, = 4.35 Ö,ÖDØ1 + 3.35 Ö,ÖDÚ

Û = 4.605ÜF���

ÜF��� = 30.47 Ý,Þßà∅Ð, Ý, = }�â�Ð�� Ð, = 0.035 Ð� }� = 0.001�0.75 + 0.067Ð� �

ãÇ ^1 − äl G`, where

227

Table 2C- SI: State variables and parameters of the total phosphorus model.

Symbol Variables and Parameters Value Unit

A Segment area: Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

5,795,000

29,942,500 26,220,000 12,500,000

124,630,000 46,445,000 470,472,500

m2

m2

m2

m2

m2

m2

m2

ALh Epilimnion/Hypolimnion interface m2 bc Exponent for weight effect on dreissenid ingestion -0.39(1) Bmac Macrophyte biomass (dry weight) g m-2 £��F�¤��� Total macrophyte biomass in a segment (dry weight) MT BPmac Phosphorus content in macrophyte biomass 0.0021(2) g P g dry weight-1

BPzm Phosphorus content in dreissenid biomass 0.006(3) g P g wet weight-1

br Exponent for weight effect on respiration -0.25(1) bsdR Sediment bed shear stress exponent 1(4) Bsed-PP Burial rate of particulate phosphorus: day-1 Bzm Dreissenid biomass g mussel WW / ind £d�R8RM7 Total lake dreissenid biomass MT chla Chlorophyll α concentration µg L-1 chlaC Chlorophyll α to carbon ration in phytoplankton 0.05 CD Wind drag coefficient DIPsed DIP in the sediments µg L-1 Dcrit Depth of frictional resistance m DIPsede Equilibrium phosphorus concentration in the solid phase of sediments µg L-1

DIPw DIP in the water column µg L-1 Dmac Macrophyte mortality rate 0.001 day-1 DO Dissolved oxygen concentration mg O2 L

-1 Dsed Diffusion exchange rate between sediment pore water and water column day-1 Dzm Dreissenid egestion and excretion g food g mussel -1 day-1 E Langmuir sorption constant 9.5 L mg-1 F Wind fetch m FD Time fraction of daily solar radiation fI(t) Temperature dependence of ingestion fOP-ZM Fraction of organic phosphorus in dreissenid excretion 0.6(3) FR Dreissenid filtration rate L g mussel-1 day-1 fr(t) Temperature dependence of respiration fresus Inorganic fraction of resuspended phosphorus 0.5(3) FTzm Phosphorus mass filtered by dreissenids kg day-1 Fzm Dreissenid egestion g food g mussel -1 day-1 Gmac Macrophyte growth rate day-1 Io Solar radiation on the surface MJ m-2 day-1 Hs Wave height Iopt Optimal solar radiation for macrophyte growth 18 MJ m-2 day-1 Izm Dreissenid food ingestion g food g mussel -1 day-1 k Exponential decay coefficient in drift current equation K1 Empirical coefficient representing temperature effect on ingestion at t1 0.1(1)

1 Schneider, 2002. 2 Depew, 2011. 3 Kim et al. 2013

228

Symbol Variables and Parameters Value Unit

K2 Empirical coefficient representing temperature effect on ingestion at t2 0.98(3) K3 Empirical coefficient representing temperature effect on ingestion at t3 0.98(3) K4 Empirical coefficient representing temperature effect on ingestion at t4 0.02(3) Kad First-order desorption/sorption rate 7.2 day-1

Kcp Saturation particulate phosphorus concentration 1 mg P L-1 Kd20 Decomposition rate coefficients at 20 °C

Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

0.0025 0.00075 0.0078 0.0006 0.0006 0.00065 0.00013

day-1

Kdecom Sediment decomposition rate day-1 Kdiff Molecular DIP diffusion coefficient at reference temperature (20oC) 7.38 10-10 (1) m 2 day-1 KDO Half saturation constant for anaerobic phosphorus sediment release 0.5 mg O2 L

-1 Knstr Diffusivity in non-stratified conditions 10 m2 day-1 Kp Half saturation constant for phosphate in sediment pore water 5 µg L-1 Kstr Diffusivity in stratified conditions 0.15(4) m2 day-1 Lseg Lake width between shores at cross section between adjacent segments m Lzm Length of individual dreissenid m Mw Flow per unit width due to orbital wave action m2/sec Md Flow per unit width in a drift current m2/sec Nab Abundance of zebra mussels per unit area 7,0002 ind/m2 OPsed Organic phosphorus in the sediments mg g-1 PC Intracellular P:C ratio in phytoplankton 0.024 PIPmax Maximum sorption capacity

Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

1

1 0.4

0.4

0.8

0.8

0.8

mg g-1

PIPsed PIP in the sediments mg g-1 Pm Maximum gross photosynthesis rate 0.03 day-1 PPw Particulate phosphorus in water µg L-1 Psdfzm Pseudofecal mass from dreissenids kg day-1 Q Slope estimate, approximately Q10 3.1(2) Rmac Macrophyte respiration rate day-1 Qtrib Tributary inflow from adjacent watershed Rmac20 Macrophyte respiration rate at 20°C 0.018(2) day-1 Rresus Sediment resuspension rate kg day-1 Rzm Dreissenid respiration g O2 g mussel-1 day-1

1 Li and Gregory, 1974. 2 Evans et al. 2011. 3 Schneider, 2002. 4 Kim D.K. et al., 2013.

229

Symbol Variables and Parameters Value Unit

Sbur Burial coefficient Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

5.86 × 10-6 (1)

1.17 × 10-6

5.86 × 10-6

5.86 × 10-6

5.86 × 10-6

1.17 × 10-6

2.34 × 10-6

m day-1

SDA Fraction of ingestion spent on feeding energy 0.285 (1) Ssed Sediment desorption/sorption rate day-1 Ý, Wind stress on water surface N/m2 T Water temperature ºC Ts Wave period sec

t0 Optimum temperature for standard respiration 28(2) ºC

t1 Lower temperature at which consumption is K1 x maximum ingestion 2(2) ºC t2 Lower temperature at which consumption is K2 x maximum ingestion 12(2) ºC t3 Higher temperature at which consumption is K3 x maximum ingestion 21(2) ºC t4 Higher temperature at which consumption is K4 x maximum ingestion 32(2) ºC tm Maximum temperature for standard respiration 31(2) ºC td Minimum storm duration minutes TPbackflow TP fluxes through backflow transport from adjacent segment kgP day-1 TPDLe,Lh Total phosphorus exchanges between epilimnion and hypolimnion kgP day-1 TPin Total phosphorus fluxes from exogenous sources and antecedent segments kgP day-1 TPmacR Total phosphorus fluxes from macrophyte respiration kgP day-1 TPout Total phosphorus outflow fluxes kgP day-1 TPsdD Total phosphorus fluxes from sediment diffusion kgP day-1 TPsdR Total phosphorus fluxes from resuspension kgP day-1 TPw Total phosphorus concentration in the water column kgP day-1 TPwS Total phosphorus settling kgP day-1 TPzmF Total phosphorus filtration kgP day-1 TPzmR Total phosphorus fluxes from dreissenid respiration kgP day-1 TPzmRjw Total phosphorus fluxes from dreissenid rejection to water column kgP day-1 TPzmRjsd Total phosphorus fluxes from dreissenid rejection to sediments kgP day-1 TPzmX Total phosphorus fluxes from dreissenid excretion kgP day-1 Uzm Dreissenid excretion g food g mussel -1 day-1 Ua Wind speed m/sec Us Surface current velocity m/sec

Vw Segment-specific volume as a function of time, determined by the water balance

m3

Vs Weighted average settling rate for phytoplankton and detritus particles m day-1 Vs-chla Settling rate of phytoplankton 0.005 m day-1 Vs-pp Settling rate of organic matter other than phytoplankton 0.020 m day-1 Vsed Segment-specific sediment volume m3 wDIP Proportion of ambient dissolved phosphorus wf Conversion efficiency 1.724138 (2) g mussel g food-1 wr Respiration efficiency 5.586207 (2) g mussel g O2

-1 z Water depth m

Zmac Water depth from the water surface to the top of macrophyte bed 4.3 m α1 Background extinction coefficient 0.24(1) m-1 α2 Phytoplankton self shading effect 0.02 m2 mg chla-1 αc Maximum dreissenid ingestion rate 1.86 mg food g mussel -1 day-1

αc refilt Maximum dreissenid ingestion rate scaled for water turbulence attenuation with depth to represent formation of concentration boundary layer at lake

1 Ozersky et al., 2011 2 Schneider, 2002

230

Symbol Variables and Parameters Value Unit

bed and enhanced refiltration αf Minimum fraction of food egested 0.315(2) αmac Segment-specific fraction of macrophyte areal coverage

Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

25(1) 0 68(1) 20(1) 25(1) 0

%

αzm Segment-specific fraction of dreissenid areal colonization Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

100(3)

0 100(3) 0 100(3) 100(3) 53(3)

%

αr Maximum effective dreissenid respiration rate (including reproduction) 0.014 mg O2 g mussel-1 day-1 αcr Clearance coefficient for water turbulence attenuation with depth to

represent enhanced refiltration and formation of concentration boundary layer at lake bed

αsdR Resuspension coefficient 2 mg P m2 day-1

αu Fraction of assimilated food excreted 0.064 αsed Fraction of filtered food biodeposited directly to sediment 0.01 γf Coefficient for egestion dependence on food availability 0.88 δ Sediment thickness cm

Kempenfelt Bay epilimnion Kempenfelt Bay hypolimnion Cook’s Bay epilimnion Cook’s Bay hypolimnion East End epilimnion Main Basin epilimnion Main Basin hypolimnion

6.5(1) 2.0 6.5 6.5 6.5 6.5 6.0

cm

ΔTPLe/Lh TP gradient between epilimnion and hypolimnion µg L-1 Δz Distance between epilimnion and hypolimnion centroids m θd Temperature coefficient for decomposition 1.08

θrmac Temperature dependence of macrophyte respiration 1.08 θs Temperature dependence of sediment diffusion 1.08 νsdR Sediment resuspension mass kg m-2 day-1

ρ Sediment solid density 2.55(2)

g cm-3

ρa Air density kg/m3 τs Wind stress on water surface N m-2 τ Sediment bed shear stress N m-2

τc Critical sediment bed shear stress 0.03 N m-2 φ Sediment porosity 0.947 (4) ∅ Latitude 44.39oN grad

1Ginn et al, 2011. 2 Schneider, 2002, Kim et al., 2013. 3 Ozersky et al., 2011; Ozersky et al. 2013; Evans et al. 2011; Schwalb et al. 2013. 4Avnimelech et al., 2001, Dittrich et al., 2012

231

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