1. Deep ventilation in Lake Baikal: 1
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
PhD Candidate:
Sebastiano Piccolroaz
Supervisor:
Dr. Marco Toffolon
Trento, April 19th 2013 1

2. Outline 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
Part 2 – Back to the surface
A simple lumped model to convert Ta into surface Tw
Conclusions

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

4. Lake Baikal - Siberia (Озеро Байкал - Сибирь)
The lake of records
The oldest, deepest and most voluminous lake in the world 4

5. Lake Baikal in numbers Lake Baikal
Lake Baikal formed in an ancient rift valley
 tectonic origin
Divided into 3 sub-basins:
South Basin
Central Basin
North Basin
Main characteristics:
Volume: km3
Surface area: km2
Length: 636 km
Max. width: 79 km
Max .depth: m
Ave. Depth: 744 m
Shore Length:  km
Surf. Elevation: m
Age: 25 million years
Inflow rivers:  300
Outflow rivers: 1 (Angara River)
World Heritage Site in 1996
1461 m 5

6. Bathymetry Lake Baikal
An impressive bathymetry: maximum depth at 1642 m average depth at 744 m flat bottom steep sides
Source: The INTAS Project Team A new bathymetric map of Lake Baikal. Open-File Report on CD-Rom 6

7. 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)
ρparcel< ρlocal
1 bar  10 m water
depth  250 m
depth  1000 m
depth 2000 m
Density ρ [kg m-3]
Temperature T [°C]
ehc
strong
ew<ehc NO DEEP DOWNWELLING
ew>ehc DEEP DOWNWELLING ew
weak ew hc
external forcing
ehc
ρparcel > ρlocal

8. A simplified sketch Deep ventilation The main effects:
deep water renewal
a permanent, even if weak, stratified temperature profile
high oxygen concentration up to the bottom
deep ventilation at the shore
wind
sinking volume of water
Presence of aquatic life down to huge depths

9. The state of the art Deep ventilation 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)
Field measurement campaign
(photo credit: C. Tsimitri)
MIR: Deep Submergence Vehicle
Putin turns submariner at Lake Baikal
Walker and Watts, 1995
Estimates vary by one order of magnitude  non negligible uncertainties

10. A simplified 1D model The aims The site The input data
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
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
South Basin 10

11. Wind - based parameterization:
A simplified 1D numerical model
wind
downwelling
The model in three parts
simplified downwelling algorithm (wind energy input vs energy required to reach hc)
Available energy
(downwelling volume) →
T profile
Compensation depth - hc
Required energy →
ehc
ehc
Wind - based parameterization:
ehc
ew<ehc NO DEEP DOWNWELLING
ew>ehc DEEP DOWNWELLING
specific energy input ew
ew=ξCD0.5W
downwelling volume Vd
Vd=ηCDW2Δtw
ξ and η: main calibration parameters of the model
(mainly dependent on the geometry)

12. The model in three parts
A simplified 1D numerical model z
unstable
stable ρ
The model in three parts
Lagrangian vertical stabilization algorithm (re-arrange unstable regions, move the sinking volume) °C ρ
re-sorting starting form the pair of sub-volumes showing the higher instability
the mixing exchanges are accounted for at every switch
Tρmax z
where is the generic tracer and the mixing coeff.
Stable
Unstable

13. The model in three parts
A simplified 1D numerical model C z
flux
The model in three parts
vertical diffusion equation solver with source (reaction) terms (for temperature, oxygen and other solutes)
cooling
higher sat. conc. °C DO
the diffusion equation is solved for any tracer
given the BC at the surface
and R along the water column.
oxygen consumption
Tρmax
flux z
geothermal heat flux
source
geothermal heat flux
oxygen consumption

14. Thermobaric instability > Key factor driving deep ventilation
A simplified 1D numerical model
… 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
Thermobaric instability > Key factor driving deep ventilation
Parameterization of turbulent diffusivity remains a main issue in hydrodynamics modeling

15. Thanks to S. Somot and C. Dubois (Meteo France)
Calibration
Calibration
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 ( )  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
Thanks to S. Somot and C. Dubois (Meteo France) 15

16. Post-processing (downscaling) is necessary
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

17. Statistical downscaling
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 data
CDFo = cumulative distribution function of observations
[e.g. Minville et al.,2008; Diaz-Nieto and Wilby, 2005; Hay et al., 2000]
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

18. Quantile-mapping approach
Calibration
Quantile-mapping approach
From reanalysis (large scale) to observations (local scale)
Wind: seasonal CDFs
Temperature: daily CDFs Wr
Wr,adj
Ta,r
Tw,adj

19. Calibration
Temperature profiles
15th of February
15th of September

20. CFC and dissolved oxygen profiles
Calibration
CFC and dissolved oxygen profiles
Mean annual

21. Sensitivity analysis Sensitivity analysis Sensitivity analysis
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
Sensitivity analysis
Aimed 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. 21

22. Validation Validation procedure Validation
Limited amount of available information
 a classical validation of this model with an independent set of data is not possible
adjustment phase
∼ 50 – 100 years
asymptotic equilibrium T ∼ 3.37°C
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 dataset
Limited amount of available information (used to obtain a reliable calibration):
if the model properly describes the fundamental processes, numerical results are expected to converge toward the actual observed conditions, after an adjustment phase depending on the IC.
Same 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. 22

23. Temperature and dissolved oxygen profiles
Validation
Temperature and dissolved oxygen profiles
15th of February
Mean annual

24. 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. 24

25. Seasonal cycle of temperature (mean year)
Main results
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

26. Main results
Downwelling properties  mean annual sinking volume ( ) and temperature ( )
Warm season: smaller and colder events
Cold season: larger and warmer events
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]
Statistical analysis of these parameters has been allowed thanks to the availability of the long-term series of simulation results

27. Wind-speed parameterization:
Main results
Downwelling properties  relationship between and the specific energy required to reach hc
Is this a contradictory result?
Warm season: smaller and colder events
Cold season: larger and warmer events
Wind is stronger during the cold season (Oct-Dec) 
Wind-speed parameterization:
is larger during this period …
specific energy input ew
ew=ξCD0.5W
downwelling volume Vd
Vd=ηCDW2Δtw
ec is higher in winter
… and is higher.
One would expect colder in winter than in summer
Seasonality of ec  due to the typical thermal structure of the epilimnion

28. Thanks to S. Somot and C. Dubois (Meteo France)
Climate change
Climate change
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 , and
Thanks to S. Somot and C. Dubois (Meteo France) 28

29. CMIP5 data: limitations
Climate change
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
downscaling
Coarse resolution, global scale climate patterns
compatibility
bias in the ascending branch
Bias during the whole year

30. Data processing: downscaling
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)
ΔTw
Conversion…
Air 2 Water
Ta,r
Tw,adj
ΔTw
Tw,fut

31. Temperature profiles Climate change 15th of February 15th of September
Risultati
Profili T DO
15th of February
15th of September

32. 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)
Risultati
Profili T DO
Mean annual

33. Part 2
Back to the surface

34. Air2Water Conversion Ta → Tw 1/2 The model The key equation
Tool: a simplified, physically-based multi-parametric model that solves the heat exchanges between lake and air
Air2Water
Air2Water
The model
A simple lumped model to convert air temperature (Ta) into surface water temperature (Tw) of lakes
model
Main forcing factor: air temperature Ta Ta Tw
physical parameters
Main result: surface water temperature Tw
The key equation
Heat budget in the
well-mixed surface layer
physically-based multi-parametric model that solves the heat exchanges between lake and air

35. 1 The heat budget Air2Water
A simplified parameterization of the net heat exchange
seasonal forcing
(hp. sinusoidal)
residual
“gradient” with
atmosphere
residual effect of Tw 1
effect of time-dependent stratification:
dimensionless depth of the surface well-mixed layer
(Tr is the deep temperature, for dimictic lakes =4°C)
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)

36. An application to Lake Superior (4 par. model)
Air2Water
An application to Lake Superior (4 par. model)
Selection of parameters based on Nash efficiency index
(108 Monte Carlo model realizations with uniform random sampling)
calibration
validation
T air
T water
model 4 par.
model 8 par
meas.

37. … using satellite data Air2Water
T air
meas.
T water
model 4 par.
model 8 par
meas.
(data: Great Lakes Environmental Research Laboratory,
NOAA National Oceanic and Atmospheric Administration)
The model has been applied to other lakes Baikal (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

38. a simplified numerical model has been developed to simulate deep ventilation and analyze downwelling dynamics in profound lakes (Lake Baikal)
Conclusions
Conclusions
Main 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
Tools 38

39. Diatoms viewed through the microscope. Image by Dr. G.T. Taylor
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.
Light micrograph of diatom Amphorotia hispida discovered in Lake Baikal,
Diatoms viewed through the microscope. Image by Dr. G.T. Taylor
Lake Garda (Italy)

40. Thank you Thank you sebastiano.piccolroaz@ing.unitn.it
Mysterious ice circles in the southern basin of Lake Baikal
(Nasa Earth Observatory, April 25, 2009; Balkhanov et al., TP 2010)