1. Modelling deep ventilation of Lake Baikal:1
Modelling deep ventilation of Lake Baikal:
a plunge into the abyss of the world's deepest lake
PhD Candidate:
Sebastiano Piccolroaz
Supervisor:
Dr. Marco Toffolon
Department of Civil and Environmental Engineering
University of Trento - Italy
Swiss Federal Institute of Aquatic Science and Technology
Kastanienbaum - Switzerland
Group of Environmental Hydraulics and Morphodynamics, Trento
Kastanienbaum, Switzerland, October 17th 2011 1

2. Lake Baikal - Siberia (Озеро Байкал - Сибирь)
Lake Baikal - introduction
Lake Baikal - Siberia (Озеро Байкал - Сибирь)
The lake of records
The oldest, deepest and most voluminous lake in the world 2

3. Lake Baikal in numbers Lake Baikal - introduction
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 3

4. Some curiosities Lake Baikal - introduction
The largest freshwater basin in the world:
 20% of the world’s total unfrozen fresh water reserve
Great Lakes are almost 8 times more extended than Lake Baikal
but
taken all together, have the same volume of water!
Freezes annually:
Jan - May in the South Basin
Dec - June in the North Basin
Surface area: km2
Surface area: km2 4

5. The Pearl of Siberia 1/2 Lake Baikal - introduction
Singular, sometimes extreme, environmental conditions:
enormous depth
several months of ice cover
high oxygen concentration
low nutrient concentration
gave rise to a unique ecosystem:
 more than 1000 endemic species
(diatoms, sponges, salmonid fish and the Baikal freshwater seal)
An amphipod regards a diver from a sponge forest in Lake Baikal. It has been estimated that the biomass of crustaceans in the lake exceeds 1,800,000 tons
Baikal oilfish (Golomyanka): a translucent abyssal fish famous for decomposing almost instantly to fat and bones when exposed to the sun
Baikal seal or Nerpa (Pusa sibirica): the only exclusively freshwater pinniped species 5

6. The bathymetry Lake Baikal - introduction
An impressive bathymetry: average depth at 744 m flat bottom steep sides 6

7. Strong external forcing
Deep ventilation
Deep ventilation
The physical mechanism
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)
Temperature [°C]
Depth [m] 1 2 3 4
500
1000
1500
Tρmax
Strong external forcing
Weak external forcing
Temperature profile
ρparcel< ρlocal
ρparcel = ρlocal
Reference parcel
ρparcel > ρlocal
Compensation depth - hc

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; Killworth et al., 1996; Peeters et al., 1997, 2000; Wüest et al., 2005; Schmid et al., 2008
Downwelling periods (May – June and December – January)
Downwelling temperature (3 ÷ 3.3 °C)
Downwelling volumes estimations (10 ÷ 100 per year)
Numerical simulations:
Akitomo, 1995; Walker and Watts, 1995; Tsvetova, 1999; 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)
Walker and Watts, 1995

10. A simplified 1D model The aims The model in three parts
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 model in three parts
simplified downwelling mechanism (wind energy input vs energy required to reach hc)
lagrangian vertical stabilization algorithm (looking for unstable regions)
vertical diffusion equation solver with source terms (for temperature, oxygen and other solutes) 10

11. Constant-volume discretization scheme
A simplified 1D numerical model
The downwelling mechanism
Constant-volume discretization scheme
Temperature [°C]
Volume [km3]
Depth [m]
Hypsometric curve
Procedural steps:
assign Vd and ew
compute Td
calculate hc
compute the energy required to move Vd
move the Vd until zd
Two cases:
Shallow downwelling
Deep downwelling 3 Td
3.5 4 1 Vi
Vi+1
Vi-1
dT/dz|ad
200 hc
Depth [m]
Tρmax
1500
Vi = 5 km3
1272 sub-volumes

12. The lagrangian vertical stabilization algorithm
A simplified 1D numerical model
The lagrangian vertical stabilization algorithm
The profile is unstable:
 the sinking Vd is heavier (lighter) than the surrounding water
Temperature [°C] 3
3.5
dT/dz|ad
200 hc
We need to stabilize the temperature profile
mixing factor included to take into account the exchanges occurring during the sinking of Vd
Depth [m]
Tρmax
Remark: the stabilization is computed on the temperature profile, but all the other tracers follow the same re-arrangement!
1500

13. The vertical diffusion equation solver
A simplified 1D numerical model
The vertical diffusion equation solver
The diffusion equation is solved for any tracer C
Temperature [°C] 3
cooling
3.5
200
given the boundary conditions at the surface:
surface water temperature
oxygen saturation concentration
evolution of the CFC concentration
and along the shores:
geothermal heat flux
oxygen consumption rate
Depth [m]
geothermal heat flux
Tρmax
1500
geothermal heat flux

14. specific energy input ew
The input data
The input data
The main input data of the model
seasonal cycle of surface water temperature - Tsurf
energy input from the external forcing - ew
sinking water volume - Vd
The wind forcing
wind parameters
unknowns
equations
wind speed W
specific energy input ew
ew=ξCD0.5W
wind duration Δtw
downwelling volume Vd
Vd=ηCDW2Δtw
Thanks to: Chrysanthi Tsimitri prof. Alfred Wüest dr. Martin Schmid
 CD is the drag coefficient
ξ and η are the calibration parameters
(mainly dependent on the geometry) 14

15. Stochastic reconstruction of wind forcing
The input data
Stochastic reconstruction of wind forcing
Poor wind data seasonal probabilistic curves of W and Δtw
1st random extraction
2nd random extraction
0.945
0.454
0.231
0.586
0.571
0.646
0.785
0.154
0.945
0.454
0.829
0.645
0.785
0.586
0.154
0.662
0.829
8-12 h
0.571
summer IV-IX
Δtw
winter X-III
Δtw W 7
from: Rzheplinsky and Sorokina, 1997
Atlas of wave and wind action in Lake Baikal (in Russian)
(Атлас волнения и ветра озера Байкал) 15

16. Calibration of the model
Calibration parameters and procedure
Parameters to be calibrated:
ξ (for the energy input)
η (for the downwelling volume)
vertical profile of the “effective” diffusivity
mixing factor
Calibration procedure:
 Medium term simulations in the period :
formation of the CFC profile ( )  no reactive, no decay rate
comparison of simulated temperature and oxygen profiles with measured data 16

17. Calibration of the model
Numerical solution and the probabilistic approach
The numerical solution depends on the random seed used for the stochastic reconstruction of winds and the definition of surface temperature
 Problems for the medium term simulations: we want to numerically reproduce a specific condition of the lake during a particular historical period (1980s- 1990s).
Possible solutions:
Set of simulations having different random seeds  average the solution over all the runs
Use re-analysis data for wind and surface temperature.
Past observations of the main meteorological variables are analyzed and interpolated onto a system of grids, giving the meteorological conditions really occurred.
Thanks to Samuel Somot (Meteo France)

18. to be suitably rescaled to the observed values
Calibration of the model
Re-analysis data 1/2
ERA-40 re-analysis dataset (53.375°N, °E)
 wind speed and air temperature every 6 hours from 1958 to 2002
Large interpolation grid:
the data are not representative of the real conditions at the lake surface
the data can give a good description of the historical sequence of events
to be suitably rescaled to the observed values 18

19. Calibration of the model
Re-analysis data 2/2
at every time step the wind speed value (occourred) is extracted from the series
Dec 1974
The probability associated to that wind speed is extracted from the reanalysis cdf
The adjusted wind speed is calculated through the observational-based cdf
0.91
0.91 6 14 19

20. Some results Some results
15th of February: average over the last 15 years simulation

21. Mean temperature after 150 years 3.36 °C
Some results
Validation of the model 1/2
Long term simulation (1000 years)
 same boundary conditions (wind, surface temperature, geothermal heat flux etc.)
 different initial condition of the temperature: T = const = 4°C
The aim:
validate the model comparing numerical solution with observations;
investigate the general behavior of Lake Baikal;
characterize deep ventilation (i.e.statistically estimate the typical downwelling volume and temperature).
Mean temperature after 150 years 3.36 °C

22. features of downwelling events
Some results
Validation of the model 2/2
features of downwelling events
VdM [km3]
TdM [°C]
Present model
60 ± 43
3.22 ± 0.08
Peeters et al. [2000]
110 -
Wüest et al., [2005]
10÷30
3.15÷3.27
Schmid et al., [2008]
50÷100 (winter season)
3.03÷3.28
VdM = mean annual sinking volume
TdM = typical downwelling temperature range
15th of February
15th of September

23. Between fall and winter
Current condition analysis
Temporal distribution of downwelling events
Between fall and winter
Late spring
15 April
15 June
15 August
15 December

24. Annual probability of downwelling
Current condition analysis
Energy demand
Annual probability of downwelling
Period
Prob. (>1300 m)
Winter
0.82
Summer
0.55
Energy increases for colder events
Energy demand is higher in winter

25. Climate change The scenarios Climate change scenarios
Simplified scenarios changing the main external forcing
Temperature trend: global warming +4°C in summer, +2°C in autumn (Hampton et al., 2008) reduction of ice-covered period (Magnuson et al., 2000)
 Wind: increasing/decreasing of the winds
Spring
Winter
ice
+4°C
+2°C
5 days
11 days

26. Current condition vs climate change 1/2
Climate change scenarios
TdM = 3.22 ± 0.08 °C
Current condition vs climate change 1/2
Current condition:
VdM = 60 ± 43 km3
Warming and strong wind
+4°C; +2°C
VdM = 83 ± 76 km3
TdM = 3.02 ± 0.06 °C
Warming
+4°C; +2°C
VdM = 59 ± 46 km3
TdM = 3.20 ± 0.09 °C
Strong wind
VdM = 83 ± 72 km3
TdM = 3.02 ± 0.06 °C
TdM = 3.34 ± 0.12 °C
VdM = 24 ± 22 km3
Calm wind

27. Current condition vs climate change 2/2
Climate change scenarios
Current condition vs climate change 2/2
The favorable periods are only shifted in time, not significantly modified in duration.
ice
+4°C
+2°C
5 days
11 days
Warming and strong windy
+4°C; +2°C
Warming
+4°C; +2°C

28. Conclusions Conclusions Modelling results:
simplified model suitable to simulate deep ventilation
analyse downwelling dynamics statistically
Physical results:
downwelling volume is estimated as 60 ± 43 km3/year
wind forcing and the duration of the favourable downwelling periods are the most important factors
surface temperature warming in summer does not strongly influence the downwelling mechanism
Further activities
construct more realistic/robust scenarios
use a 3D model to better investigate the initiation of thermobaric instability
investigate the periodical turnover of Lake Garda 28

29. Parallel works Conclusions
M. Toffolon, C. Carlin, S. Piccolroaz, G. Rizzi, Can turbulence anisotropy suppress horizontal circulation in lakes?, 7th International Symposium on Stratified Flows (ISSF), Roma (Italy), August 2011
A.Zorzin, S. Piccolroaz, M. Toffolon, M. Righetti, On the reduction of thermal destratification by a horizontal ciliate jet, 7th International Symposium on Stratified Flows (ISSF), Roma (Italy), August 2011
Altered colors 29

30. Thank you Conclusions sebastiano.piccolroaz@ing.unitn.it 30
Mysterious ice circles in the world’s deepest lake 30