40
1/40 Modelling deep ventilation of Lake Baikal Deep ventilation in Lake Baikal: a simplified model for a complex natural phenomenon Trento, April 19 th 2013 Department of Civil, Environmental and Mechanical Engineering University of Trento Group of Environmental Hydraulics and Morphodynamics, Trento PhD Candidate: Sebastiano Piccolroaz Supervisor: Dr. Marco Toffolon

Deep ventilation in Lake Baikal: a simplified model for a complex natural phenomenon

Embed Size (px)

DESCRIPTION

Deep ventilation in Lake Baikal: a simplified model for a complex natural phenomenon. Department of Civil, Environmental and Mechanical Engineering University of Trento. Group of Environmental Hydraulics and Morphodynamics, Trento. Trento, April 19 th 2013. Outline. Outline. - PowerPoint PPT Presentation

Citation preview

Page 1: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

1/40Modelling deep ventilation of Lake Baikal

Deep ventilation in Lake Baikal: a simplified model for a complex natural phenomenon

Trento, April 19th 2013

Department of Civil, Environmental and

Mechanical Engineering University of Trento

Group of Environmental Hydraulics and

Morphodynamics, Trento

PhD Candidate:Sebastiano Piccolroaz

Supervisor:Dr. Marco Toffolon

Page 2: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

2/40Modelling deep ventilation of Lake Baikal

Part 1 - A plunge into the abyss of the world's deepest lake

Lake Baikal and deep ventilation

A simplified 1D model

Calibration, validation, sensitivity analysis and main results

Climate change scenarios

Outline

Outline

Part 2 – Back to the surface

A simple lumped model to convert Ta into surface Tw

Conclusions

Page 3: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

3/40Modelling deep ventilation of Lake Baikal

Part 1A plunge into the abyss of the world's deepest lake

Page 4: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

4/40Modelling deep ventilation of Lake Baikal

The lake of records

Lake Baikal - Siberia (Озеро Байкал - Сибирь)

The oldest, deepest and most voluminous lake in the world

Lake Baikal

Page 5: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

5/40Modelling deep ventilation of Lake Baikal

Main characteristics:Volume: 23 600 km3

Surface area: 31 700 km2

Length: 636 kmMax. width: 79 kmMax .depth: 1 642 mAve. Depth: 744 mShore Length: 2 100 kmSurf. Elevation: 455.5 mAge: 25 million yearsInflow rivers: 300Outflow rivers: 1 (Angara River)World Heritage Site in 1996

Lake Baikal in numbers

Divided into 3 sub-basins:South BasinCentral BasinNorth Basin

1461 m

Lake Baikal formed in an ancient rift valley tectonic origin

Lake Baikal

Page 6: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

6/40Modelling deep ventilation of Lake Baikal

Lake Baikal

An impressive bathymetry:maximum depth at 1642 m

average depth at 744 m flat bottom steep sides

Source: The INTAS Project 99-1669 Team. 2002. A new bathymetric map of Lake Baikal. Open-File Report on CD-Rom

Bathymetry

Page 7: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

7/40Modelling deep ventilation of Lake Baikal

1 bar 10 m water

depth 250 m

depth 1000 m

depth 2000 m

Den

sity

ρ [k

g m

-3]

Temperature T [°C]

http://www.engineeringtoolbox.com

e w>e

hc D

EEP

DO

WN

WEL

LIN

G

e w<e

hc N

O D

EEP

DO

WN

WEL

LIN

G

Deep ventilation

The physical phenomenon

Deep ventilation

Phenomenon triggered by thermobaric instability [Weiss et al., 1991]:

− density depends on T and P (equation of state: Chen and Millero, 1976)

− T of maximum density decreases with the depth (P=Patm Tρmax ≈ 4°C)

ehc

e hc

weakexternal forcing

e w

ρparcel< ρlocal

e w

ρparcel > ρlocal

stronghc

Page 8: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

8/40Modelling deep ventilation of Lake Baikal

wind

sinking volume of water

A simplified sketchThe main effects:

− deep water renewal

− a permanent, even if weak, stratified temperature profile

− high oxygen concentration up to the bottom

Presence of aquatic life down to huge depths

deep ventilation at the shore

Deep ventilation

Page 9: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

9/40Modelling deep ventilation of Lake Baikal

− Observations and data analysis:

Weiss et al., 1991; Shimaraev et al., 1993; Hohmann et al., 1997; Peeters et al., 1997, 2000; Ravens et al., 2000; Wüest et al., 2000, 2005; Schmid et al., 2008; Shimaraev et al., 2009, 2011a,b, 2012

− Downwelling periods (May – June, December – January)

− Downwelling temperature (3 ÷ 3.3 °C)

− Downwelling volumes estimations (10 ÷ 100 km3 per year)

− Numerical simulations:

Akitomo, 1995; Walker and Watts, 1995; Killworth et al., 1996; Tsvetova, 1999; Peeters et al., 2000; Botte and Kay, 2002; Lawrence et al., 2002

− 2D or 3D numerical models

− Simplified geometries or partial domains

− Main aim: understand the phenomenon (triggering factors/conditions)

Putin turns submariner at Lake BaikalMIR: Deep Submergence VehicleField measurement campaign (photo credit: C. Tsimitri)

Deep ventilation

The state of the art

Wal

ker a

nd W

atts,

199

5

Page 10: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

10/40Modelling deep ventilation of Lake Baikal

The input data─ surface water temperature (measurements + reanalysis)

─ wind speed and duration (observations + reanalysis)

• Courtesy of Prof. A. Wüest and his research team (EAWAG)• ERA-40 reanalysis dataset, thanks to Clotilde Dubois and Samuel

Somot (Meteo France)

• Rzheplinsky and Sorokina, 1977• ERA-40 reanalysis dataset, thanks to Clotilde Dubois and Samuel

Somot (Meteo France)

A simplified 1D numerical model

A simplified 1D model

The aims− simple way to represent the phenomenon (at the basin scale)

− just a few input data required (according to the available measurements)

− suitable to predict long-term dynamics (i.e. climate change scenarios)

The site− South Basin of Lake Baikal

South B

asin

Page 11: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

11/40Modelling deep ventilation of Lake Baikal

Required energy→

ehc

The model in three parts

A simplified 1D numerical model

1. simplified downwelling algorithm(wind energy input vs energy required to reach hc)

specific energy input ew ew=ξCD0.5W

downwelling volume Vd Vd=ηCDW2Δtw

Wind - based parameterization:

Available energy(downwelling volume)

ξ and η: main calibration parameters of the model

e w<e

hc N

O D

EEP

DO

WN

WEL

LIN

G

T profile

Compensation depth - hc

ehc

e w>e

hc D

EEP

DO

WN

WEL

LIN

G

(mainly dependent on the geometry)

Page 12: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

12/40Modelling deep ventilation of Lake Baikal

The model in three parts

2. Lagrangian vertical stabilization algorithm(re-arrange unstable regions, move the sinking volume)

z

− re-sorting starting form the pair of sub-volumes showing the higher instability

− the mixing exchanges are accounted for at every switch

where is the generic tracer and the mixing coeff. Stable

Unstable

°C ρ

T ρmax

A simplified 1D numerical model

Page 13: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

13/40Modelling deep ventilation of Lake Baikal

3. vertical diffusion equation solver with source (reaction) terms (for temperature, oxygen and other solutes)

The model in three parts

°C

z

DO

− the diffusion equation is solved for any tracer

given the BC at the surface

and R along the water column.

cooling higher sat. conc.

T ρmax

geothermal heat flux

geot

herm

al h

eat fl

ux

oxygen consumption

flux

source

A simplified 1D numerical model

Page 14: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

14/40Modelling deep ventilation of Lake Baikal

… it is a matter of feedback

Lacustrine systems are regulated by a complex network of feedback loops, controlled by the external forcing

Self-consistent procedure to dynamically

reconstruct Dz

A simplified 1D numerical model

Page 15: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

15/40Modelling deep ventilation of Lake Baikal

Calibration

Calibration

Thanks to S. Somot and C. Dubois (Meteo France)

Calibration procedure (ξ, η, cmix and Dz,r)

Medium term simulations during the second half of the 20th century:

─ comparison of simulated temperature and oxygen profiles with measured data

─ formation of the CFC profile (1988-1996) unambiguous tracer: non-reactive, high chemical stability [e.g. England,

2001]

Objective: numerically reproduce particular conditions of the lake during a specific historical period (1980s- 1990s).

Available data: reanalysis dataset the reprocessing of past climate observations combining together data assimilation techniques and numerical modeling (GCMs)

ERA-40 datasets: wind speed (W) and air temperature (Ta) every 6 hours from 1958 to 2002

Page 16: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

16/40Modelling deep ventilation of Lake Baikal

Calibration

Reanalysis data: limitations

─ reanalysis horizontal resolution is too coarse ( ∼ 100 km x 100 km) for the purpose of many practical applications (mismatch of spatial scales)

─ reanalysis data are often affected by inconsistencies due to the lack of fundamental feedback between the numerous natural processes

─ air temperature is available, but the model requires surface water temperature

Post-processing (downscaling) is necessary

Page 17: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

17/40Modelling deep ventilation of Lake Baikal

Calibration

Statistical downscaling

Transfer function approach: establishes a relationship between the cumulative distribution functions (CDFs) of observed local climate variables (predictands) and the CDFs of large-scale GCMs outputs (predictors)

Quantile – mapping method [Panofsky and Brier, 1968]:

assumption

xr = generic climatic variable of re-analysis (W, Ta)Xr,adj = generic climatic variable adjusted CDFr = cumulative distribution function of re-analysis dataCDFo = cumulative distribution function of observations

Drawbacks:─ it does not include information of future climate patterns

─ it is stationary in the variance and skew of the distribution, and only the mean changes

─ it is not indicated to be applied for climate change analysis

[e.g. Minville et al.,2008; Diaz-Nieto and Wilby, 2005; Hay et al., 2000]

Page 18: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

18/40Modelling deep ventilation of Lake Baikal

Quantile-mapping approach

Wind: seasonal CDFs Temperature: daily CDFs

Wr Wr,adj Ta,r Tw,adj

Calibration

From reanalysis (large scale) to observations (local scale)

Page 19: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

19/40Modelling deep ventilation of Lake Baikal

15th of February 15th of September

Calibration

Temperature profiles

Page 20: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

20/40Modelling deep ventilation of Lake Baikal

CFC and dissolved oxygen profiles

Calibration

Mean annual

Page 21: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

21/40Modelling deep ventilation of Lake Baikal

Sensitivity analysis

Sensitivity analysis

Sensitivity analysisAimed at evaluating the robustness of the calibration and the role played by each of the main parameters of the model.

Procedure: a new set of 40-year simulations, changing ξ, η and cmix (one by one) within the interval of ± 50% of the calibrated value.

Results:

─ an evident deviation from measurements and calibrated solution suggesting that a proper calibration has been achieved

─ no dramatic changes are observed in the behavior of the limnic system indicating the suitability and robustness of the fundamental algorithms

Page 22: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

22/40Modelling deep ventilation of Lake Baikal

Validation

Validation

Validation procedureLimited amount of available information

a classical validation of this model with an independent set of data is not possible

Indirect validation: long-term simulation, starting from arbitrarily set initial conditions and verifying the achievement of proper equilibrium profiles of the main variables.

─ Initial conditions: isothermal (T=3.98°C) and anoxic profiles (DO=0 mgO2 l-1)

─ Boundary conditions: a series of 1000 years randomly generated from the ERA-40 reanalysis datasetSame external forcing as those of current conditions

numerical results are expected to converge toward the actual observed conditions, after an adjustment phase depending on the IC.

adjustment phase ∼ 50 – 100 years

asymptotic equilibrium T 3.37°C∼

Page 23: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

23/40Modelling deep ventilation of Lake Baikal

15th of February

Validation

Temperature and dissolved oxygen profiles

Mean annual

Page 24: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

24/40Modelling deep ventilation of Lake Baikal

Main results

Main results

Characterization of seasonal dynamics─ cycle of temperature

─ thickness of the epilimnion

─ diffusivity profile

─ N2, S2 and Ri profiles

In-depth analysis of deep ventilation─ timing of deep ventilation

─ vertical distribution of downwellings

─ main downwelling properties: and

─ energy demand vs.

Page 25: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

25/40Modelling deep ventilation of Lake Baikal

Seasonal cycle of temperature (mean year)

Measurements (data courtesy of Prof. A. Wüest, unpublished data)

Simulation(1000-year simulation, mean year) Map of residuals

(modeled - measured temperature profiles).

RMSE 0.07°C∼MAE 0.03°C∼MaxAE 0.78°C∼

Main results

Page 26: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

26/40Modelling deep ventilation of Lake Baikal

Present model: statistics based on the 1000-year simulation results (long dataset) events beneath 1300 m depth

Literature estimates: measurements collected near the bottom short observational periods (from a few years to a decade) significant variability between the single authors (depending on analyzed events)

is probably underestimated [Wüest et al., 2005; Schmid et al., 2008]

Downwelling properties mean annual sinking volume ( ) and temperature ( )

Main results

Warm season: smaller and colder eventsCold season: larger and warmer events

Page 27: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

27/40Modelling deep ventilation of Lake Baikal

Downwelling properties relationship between and the specific energy required to reach hc

Main results

e c is

high

erin

win

ter

Warm season: smaller and colder eventsCold season: larger and warmer events

Wind is stronger during the cold season (Oct-Dec)

specific energy input ew ew=ξCD0.5W

downwelling volume Vd Vd=ηCDW2Δtw

Wind-speed parameterization:

is larger during this period …

… and is higher.

One would expect colder in winter than in summer

Is this a contradictory result?

Seasonality of ec due to the typical thermal structure of the epilimnion

Page 28: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

28/40Modelling deep ventilation of Lake Baikal

Climate change

Climate change

Thanks to S. Somot and C. Dubois (Meteo France)

The aim─ investigate the future response of the limnic system to climate change

─ estimate the possible impact on deep ventilation

The scenarios

Constructed on the basis of the outputs from GCMs forced with different greenhouse gases (GHG) concentration projections (IPCC 2007)

CMIP5 datasets: wind speed (W) and air temperature (Ta) every 3 hours for the 3 different scenarios (rcp2.6, rcp 4.5 and rcp8.5) and the following periods 1960-2005, 2026-2046 and 2081-2101.

Page 29: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

29/40Modelling deep ventilation of Lake Baikal

Coarse resolution, global scale climate patterns

CMIP5 data: limitations

─ mismatch of spatial scales, simplification of natural phenomena, no information regarding Tw (as for re-analysis data)

─ due to their different derivation, CMIP5 data cannot be considered as the prosecution of the re-analysis series

Climate change

downscaling

compatibility

bias in the

ascending branch

Bias during the whole year

Page 30: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

30/40Modelling deep ventilation of Lake Baikal

Conversion… Air 2 Water

ΔTw

Climate change

Data processing: downscaling

Wind speed (W): a novel procedure has been developed, based on the quantile-mapping approach, but also accounts for potential modifications in both intensity and seasonality of wind speed.

Air temperature (Ta): a simple lumped model to convert Ta into surface Tw to assess the possible

impact on lake temperature (ΔTw) quantile-mapping approach, including ΔTw (delta method)

Ta,r Tw,adj ΔTw Tw,fut

Page 31: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

31/40Modelling deep ventilation of Lake Baikal

Temperature profiles

Climate change

15th of February 15th of September

Page 32: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

32/40Modelling deep ventilation of Lake Baikal

Oxygen profiles

Climate change

The main changes are expected for the RCP8.5 scenario: evident enhancement of deep water renewal (larger and colder downwelling volumes, strong oxygenation) the major impact is expected from modifications of the wind forcing (intensity and seasonality)

Mean annual

Page 33: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

33/40Modelling deep ventilation of Lake Baikal

Part 2Back to the surface

Page 34: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

34/40Modelling deep ventilation of Lake Baikal

Heat budget in the well-mixed surface layer

Main forcing factor: air temperature Ta

Main result: surface water temperature Tw

Ta Twphysical parameters

model

Air2Water

Air2Water

The modelA simple lumped model to convert air temperature (Ta) into surface water temperature (Tw) of lakes

The key equation

Page 35: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

35/40Modelling deep ventilation of Lake Baikal

seasonal forcing(hp. sinusoidal)

“gradient” withatmosphere

residual effect of Tw

effect of time-dependent stratification: dimensionless depth of the surface well-mixed layer(Tr is the deep temperature, for dimictic lakes =4°C)

residual

The heat budget

A simplified parameterization of the net heat exchange

Different versions of the model:─ 8-parameter (pi, i=1..8)─ 6-parameter (pi, i=1..6) simplified inverse stratification (winter)─ 4-parameter (pi, i=3..6) seasonal forcing included in the other periodic terms (p4, p5)

1

Air2Water

Page 36: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

36/40Modelling deep ventilation of Lake Baikal

Selection of parameters based on Nash efficiency index (108 Monte Carlo model realizations with uniform random sampling)

An application to Lake Superior (4 par. model)

calibration

validation

T air

T watermodel 4 par.

model 8 par

meas.

meas.

Air2Water

Page 37: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

37/40Modelling deep ventilation of Lake Baikal

(data: Great Lakes Environmental Research Laboratory, NOAA National Oceanic and Atmospheric Administration)

… using satellite data

T air

T watermodel 4 par.

model 8 par

meas.

meas.

Air2Water

− The model has been applied to other lakesBaikal (Russia), Great Lakes (USA-Canada), Garda (Italy) and Mara (Canada)

− The model is suitable to reproduce the evolution of Tw at long time scales seasonal, annual, inter-annual hysteresis cycle and inter-annual fluctuations

Page 38: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

38/40Modelling deep ventilation of Lake Baikal

ConclusionsMain results:

− a simplified numerical model has been developed to simulate deep ventilation in profound lakes (Lake Baikal)

−the model allows for a suitable description of seasonal lake dynamics and a proper evaluation of downwelling features (e.g. and )

−some preliminary evidence about the existence of significant feedback loops among the different physical processes has been found (e.g. ec vs )

−thanks to its simple structure (low computational cost) and suitable parameterization (necessary to investigate evolving systems) such a model is appropriate to predict long-term dynamics (i.e. climate change scenarios)

−a novel downscaling procedure and a simple physically-based model to convert air temperature into surface water temperature have been devised, which are suitable to be applied in climate change studies

Conclusions

Page 39: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

39/40Modelling deep ventilation of Lake Baikal

Light micrograph of diatom Amphorotia hispida discovered in Lake Baikal,

Diatoms viewed through the microscope. Image by Dr. G.T.

Taylor

Lake Garda (Italy)

Further activities:

−further research is expected to explore the coupling of physical and biological processes (e.g. plankton dynamics)

−further research is needed to better understand the complex network of interactions between the numerous physical processes that take place in the lake

−the model could be used to investigate the convective dynamics in the other very deep lakes in the world (e.g. Lake Tanganyika, Crater Lake) and possibly also is some deep alpine lakes (e.g.Lake Tahoe, Lake Como, Lake Geneva, Lake Garda)

−Air2Water is expected to be applied to lakes having different characteristic (e.g. geometry, climate, mixing regime) in order to assess the possible response of the lake to different climate conditions.

Page 40: Deep ventilation in Lake Baikal:  a simplified  model for a complex natural phenomenon

40/40Modelling deep ventilation of Lake Baikal

Thank you

Thank [email protected]

Mysterious ice circles in the southern basin of Lake Baikal (Nasa Earth Observatory, April 25, 2009; Balkhanov et al., TP 2010)