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Introduction to Modeling
Unit V, Module 21A
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s2
Module 21Introduction to Modeling This module has three main goals. It will help
you: Understand how models help environmental
scientists:Learn about natural systemsPredict how natural systems will behave under different conditions
Evaluate different management scenarios Learn about different approaches to modeling
natural systems See and use examples of watershed, lake,
stream, and biotic models
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s3
Lecture 1 Understanding Models
What is a model? A model is a simplified
representation of the real world
There are two types of models Conceptual Mathematical
Fishing Effort
Equ
ilibr
ium
Yie
ld
Surplus Yield Model (Lackey and Hubert 1978)
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s4
Conceptual Models
What are they? Qualitative, usually based on graphs Represent important system:
componentsprocesses linkages Interactions
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s5
Conceptual Models
When should they be used? As an initial step –
For hypothesis testingFor mathematical model development
As a framework – For future monitoring, research, and management actions at a site
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s6
Conceptual Models
How can they be used? Design field sampling and monitoring programs
Ensure that all important system attributes are measured Determine causes of environmental problems
Identify system linkages and possible cause and effect relationships
Identify potential conflicts among management objectives Anticipate the full range of possible system responses to
management actions Including potential negative effects
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s7
Conceptual Model Example
Macrophytes
Zooplankton refugesNutrient release due to anoxia
+
-
+
+
+
-
-
-Fish cover
Mean zooplankton size
Grazing impact
+
Sedimentation rate
Hypolimnetic oxygen depletion
+
Algal biomass
+
+
+
Increased nutrient loading
Primary productivity
Increased pH
% blue-green algae
+
++
Transparency
+
+
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s8
Mathematical Models
What are they? Mathematical equations that translate a conceptual
understanding of a system or process into quantitative terms (Reckhow and Chapra 1983)
How are they used? Diagnosis
E.g., What is the cause of reduced water clarity in a lake? Prediction
E.g., How long will it take for lake water quality to improve, once controls are in place?
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s9
Categories of Mathematical Models
TypeEmpirical
Based on data analysisMechanistic
Mathematical descriptions based on theory
Time FactorStatic or steady-state
Time-independentDynamic
Describe or predict system behavior over time
Treatment of Data Uncertainty and VariabilityDeterministic
Do not address data variabilityStochastic
Address variability/uncertainty
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s10
Mathematical Models
When should you not use a model? If you do not understand the problem or system well
enough to express it in concise, quantitative terms If the model has not been tested and verified for
situations and conditions similar to your resource It is important to understand model:
Structure Assumptions Limitations
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s11
Remember!
Models do not substitute for logical thinking or other types of data collection and analysis
Models should not be more complicated than is necessary for the task at hand
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s12
Selecting or Developing a Model
Important first steps Define the question or problem to be addressed
with the model Determine appropriate spatial and temporal
scales Identify important ecosystem components and
processes that must be considered to answer the management questions
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s13
Selecting or Developing a Model
Some specific questions to ask Temporal scale
Do I need to predict changes over time or are steady-state conditions adequate?
If time is important, do I need to look at Short-term change (e.g., daily, seasonal) or Long-term change (e.g., trends over years)?
Spatial scale Is my question best addressed:
On a regional scale (e.g., compare streams in a region) or By modeling specific processes within an individual system?
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s14
Lake Models
Most are based on mass balance* calculations * All fluxes of mass to
and from specific compartments in the environment must be accounted for over time
Annual Water Load to Lake
Atmosphere Tributary Groundwater
Runoff40%
22% 17%21%
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s15
Use Lake Models to Ask:
What is the lake’s present water quality? Development:
What was the lake’s water quality before development? How will future watershed development affect water
quality? Nutrients:
What are the most important sources of nutrients to the lake?
What level of nutrient loading can the lake tolerate before it develops algae problems?
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s16
Use Lake Models to Ask:
Nutrient management: How much must nutrients be reduced to eliminate
nuisance algal blooms? How long will it take for lake water quality to improve
once controls are in place? How successful will restoration be, based on water
quality management goals? Are proposed lake management goals realistic and cost
effective?
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s17
Eutrophication Modeling
Excessive nutrients that promote algal growth were identified as the most important problem in 44% of all U.S. lakes surveyed in 1998 (U.S. EPA 2000)
e.g., Lake Onondaga, NY
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s18
Phosphorus Dynamics in Temperate Lakes – Observations
Algal growth is usually limited by the supply of phosphorus (P) An increase (or decrease) in P entering the lake over a
year or season will increase (or decrease) the average concentrations of P and algae
A lake’s capacity to absorb increased P loading without consequent algal blooms increases with: Volume Depth Flushing Sedimentation rates
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s19
Mass Balance Loading Models
Assumptions Water quality is
degraded by excess phosphorus in the lake
Phosphorus comes in from the watershed (including sewage outfalls)
Phosphorus leaves the lake via outflows and by sedimentation
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s20
Conceptual Model of Nutrient Effects on Water Quality
Natural phosphorus loading Geology/land use Precipitation Hydrology Lake morphometry
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s21
Model Goals
Estimate how much phosphorus is entering the lake in order to estimate the lake water concentration under different scenarios
Once you can predict the lake phosphorus concentration, use empirical relationships to deduce other water quality parameters such as:
Chlorophyll-a (algae)
Secchi depth (clarity)
Dissolved oxygen in the hypolimnion (bottom layer)
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s22
Model Assumptions
Algal growth is limited by phosphorus Not limited by nitrogen, light, grazers or other
factors The whole lake volume is well-mixed Water inflow equals water outflow Phosphorus obeys mass balance principles
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s23
Model Steps
1. Develop hydrological and nutrient budgets2. Calculate lake phosphorus concentrations
from external and internal phosphorus loading
3. Predict water quality from lake phosphorus concentration
4. Verify the model5. Forecast and track changes in water quality
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s24
Step 1 – Hydrologic Budget
Inflow + precipitation = outflow + evaporation + change in storage
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s25
Step 1 – Phosphorus Budget
External load = outflow load + sedimentation – internal load + change in storage
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s26
Step 2 – Predicting Phosphorus Concentrations
Four variables are calculated:
Ave. input P concentration = external P load / outflow
Ave. water residence time = lake volume / outflow
Mean depth = lake volume / lake surface area
Net P retention = (sedimentation – internal load) / external load
Annual Water Load
Atmosphere Tributary Groundwater
Runoff40%
22% 17%21%
Annual P Load
Internal 64% Runoff 22%
Groundwater 3% Tributary 3%Atmospheric
8%
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s27
Step 3 – Relationships Between P and Other Water Quality Variables
Log
chla
Log Total P
Total PSecc
hi T
rans
pare
ncy
(m)
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s28
Step 4 – Model Verification
Water quality models must be tested with real field data under baseline conditions to ensure that they work! Field sampling must consider several dimensions:
Depth Sampling location Seasonality Annual variation
Analytical error and natural variability must be considered
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s29
Step 5 – Forecasting and Tracking Changes in Water Quality
• Reducing inflow P led to reduced
in-lake P concentrations
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s30
Example – Lake Washington, WA
Urbanized lake east of Seattle
Sewage was diverted from the lake into Puget Sound
Eutrophic lake recovered to meso-oligotrophic
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s31
Example – Lake Washington
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s32
Example – Shagawa Lake, MN
Adjacent to the Boundary Waters Canoe Area Wilderness
Moderate size, shallow Eutrophic from Ely, MN
sewage Recovery slower than
expected after new Advanced Wastewater Treatment System put in
Slow recovery due to long-term sediment phosphorus release
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s33
Example – Shagawa Lake
• Annual temperature and dissolved oxygen data
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s34
References
Reckhow and Chapra Terrene Institute
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s35
End of Lecture One
Developed by: Hagley Updated: May 30, 2004 U5-m21a-s36
Watershed Models
This section has three main purposes. It should help you to: Understand when and how modeling can contribute to
watershed assessment Learn approaches and tools that are useful for watershed
modeling Note: watershed assessment can require different tools and
approaches from traditional point source modeling Understand the considerations in choosing models for
watershed assessments
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