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```Deep ventilation in Lake Baikal:
a simplified model for a complex natural phenomenon
Department of Civil,
Environmental and
Mechanical Engineering
University of Trento
PhD Candidate:
Sebastiano Piccolroaz
Supervisor:
Dr. Marco Toffolon
Group of Environmental
Hydraulics and
Morphodynamics, Trento
Trento, April 19th 2013
Modelling deep ventilation of Lake Baikal
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Outline
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
Modelling deep ventilation of Lake Baikal
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Part 1
A plunge into the abyss of the world's deepest lake
Modelling deep ventilation of Lake Baikal
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Lake Baikal
Lake Baikal - Siberia
(Озеро Байкал - Сибирь)
The lake of records
The oldest, deepest and most voluminous lake in the world
Modelling deep ventilation of Lake Baikal
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Lake Baikal
Lake Baikal in numbers
Lake Baikal formed in an ancient rift valley
 tectonic origin
Main characteristics:
Volume: 23 600 km3
Surface area: 31 700 km2
Length: 636 km
Max. width: 79 km
Max .depth: 1 642 m
Ave. Depth: 744 m
Shore Length:  2 100 km
Surf. Elevation: 455.5 m
Age: 25 million years
Inflow rivers:  300
Outflow rivers: 1 (Angara River)
World Heritage Site in 1996
Modelling deep ventilation of Lake Baikal
Divided into 3 sub-basins:
South Basin
Central Basin
North Basin
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Lake Baikal
Bathymetry
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
Modelling deep ventilation of Lake Baikal
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Deep ventilation
Deep ventilation
The physical phenomenon
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
Density ρ [kg m-3]
depth 2000 m
http://www.engineeringtoolbox.com
Temperature T [°C]
Modelling deep ventilation of Lake Baikal
depth  250 m
ehc
depth  1000 m
w
ρparcel > ρlocal
ew
strong
weak
external forcing
hc
ew>ehc DEEP DOWNWELLING
1 bar  10 m water
eew<ehc NO DEEP DOWNWELLING
ρparcel< ρlocal
7/40
Deep ventilation
A simplified sketch
The main effects:
deep ventilation at the shore
wind
sinking
volume
of water
Modelling deep ventilation of Lake Baikal
− 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
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Deep ventilation
The state of the art
− 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:
Putin
Field
measurement
campaign
at Lake
Baikal
MIR:turns
Deepsubmariner
Submergence
Vehicle
(photo credit: C. Tsimitri)
Akitomo, 1995; Walker and Watts, 1995; Killworth et al., 1996; Tsvetova, 1999; Peeters et al., 2000; Botte
and Kay, 2002; Lawrence et al., 2002
Walker and Watts, 1995
− 2D or 3D numerical models
− Simplified geometries or partial domains
− Main aim: understand the phenomenon
(triggering factors/conditions)
Modelling deep ventilation of Lake Baikal
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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)
• Courtesy of Prof. A. Wüest and his research team (EAWAG)
• ERA-40 reanalysis dataset, thanks to Clotilde Dubois and Samuel
Somot (Meteo France)
─ wind speed and duration (observations + reanalysis)
• Rzheplinsky and Sorokina, 1977
• ERA-40 reanalysis dataset, thanks to Clotilde Dubois and Samuel
Somot (Meteo France)
Modelling deep ventilation of Lake Baikal
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downwelling
A simplified 1D numerical model
The model in three parts
1. simplified downwelling algorithm
(wind energy input vs energy required to reach hc)
Available energy
→
T profile
→
wind
Required energy
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)
Modelling deep ventilation of Lake Baikal
ehc
Compensation depth - hc
ehc
ew>ehc DEEP DOWNWELLING
Wind - based parameterization:
ew<ehc NO DEEP DOWNWELLING
(downwelling volume)
11/40
A simplified 1D numerical model
ρ
The model in three parts
z
Lagrangian vertical stabilization algorithm
2.
unstable
(re-arrange unstable regions, move the sinking volume)
°C
stable
ρ
− re-sorting starting form the
pair of sub-volumes showing
the higher instability
z
− the mixing exchanges are
accounted for at every switch
Stable
Unstable
Modelling deep ventilation of Lake Baikal
where
and
is the generic tracer
the mixing coeff.
12/40
A simplified 1D numerical model
C
The model in three parts
vertical diffusion equation solver with source (reaction) terms
3.
(for temperature, oxygen and other solutes)
cooling
flux
z
higher sat. conc. DO
°C
oxygen consumption
geothermal heat flux
z
− the diffusion equation is
solved for any tracer
flux
source
given the BC at the surface
and R along the water column.
geothermal heat flux
oxygen consumption
Modelling deep ventilation of Lake Baikal
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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
Modelling deep ventilation of Lake Baikal
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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 (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
Thanks to S. Somot and C. Dubois (Meteo France)
Modelling deep ventilation of Lake Baikal
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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
Modelling deep ventilation of Lake Baikal
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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
CDFr
CDFo
= generic climatic variable of re-analysis (W, Ta)
= cumulative distribution function of re-analysis data
= 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
Modelling deep ventilation of Lake Baikal
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Calibration
Quantile-mapping approach
From reanalysis (large scale) to observations (local scale)
Wind: seasonal CDFs
Wr
Modelling deep ventilation of Lake Baikal
Temperature: daily CDFs
Ta,r
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Calibration
Temperature profiles
15th of February
Modelling deep ventilation of Lake Baikal
15th of September
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Calibration
CFC and dissolved oxygen profiles
Mean annual
Modelling deep ventilation of Lake Baikal
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Sensitivity analysis
Sensitivity analysis
Results:
─ an
evident deviation
Sensitivity
analysisfrom measurements and calibrated solution
 suggesting that a proper calibration has been achieved
Aimed at evaluating the robustness of the calibration and the role played by each of the
parameters
of the
─main
no dramatic
changes
aremodel.
observed in the behavior of the limnic system
 indicating the suitability and robustness of the fundamental algorithms
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.
Modelling deep ventilation of Lake Baikal
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Validation
Validation
Validation procedure
Limited amount of available information
 a classical
validation
phaseof this model with an independent set of data is not possible
∼ 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
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.
Modelling deep ventilation of Lake Baikal
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Validation
Temperature and dissolved oxygen profiles
15th of February
Modelling deep ventilation of Lake Baikal
Mean annual
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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.
Modelling deep ventilation of Lake Baikal
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Main results
Seasonal cycle of temperature (mean year)
RMSE ∼ 0.07°C
MAE ∼ 0.03°C
MaxAE ∼ 0.78°C
Simulation
Measurements
(data courtesy of Prof. A. Wüest, unpublished
data)
Map
of residuals
(1000-year simulation, mean year)
(modeled - measured temperature profiles).
Modelling deep ventilation of Lake Baikal
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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]
Modelling deep ventilation of Lake Baikal
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Main results
Downwelling properties
 relationship between
and the specific energy required to reach hc
Warm season: smaller and colder events
Cold season: larger and warmer events
Wind is stronger during
the cold season (Oct-Dec)

is larger during this period …
ec is higher
in winter
Wind-speed parameterization:
specific energy input ew
ew=ξCD0.5W
downwelling volume Vd
Vd=ηCDW2Δtw
… and
is higher.
One would expect colder
winter than in summer
in
Seasonality of ec  due to the typical thermal structure of the epilimnion
Modelling deep ventilation of Lake Baikal
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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 1960-2005,
2026-2046 and 2081-2101.
Thanks to S. Somot and C. Dubois (Meteo France)
Modelling deep ventilation of Lake Baikal
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Climate change
CMIP5 data: limitations
─ mismatch of spatial scales, simplification of natural
phenomena, no information regarding Tw (as for re-analysis data)
downscaling
─ due to their different derivation, CMIP5 data cannot be
considered as the prosecution of the re-analysis series
compatibility
Bias during the whole year
Coarse resolution, global scale climate patterns
Modelling deep ventilation of Lake Baikal
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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
Modelling deep ventilation of Lake Baikal
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Climate change
Temperature profiles
15th of February
Modelling deep ventilation of Lake Baikal
15th of September
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Climate change
Oxygen profiles
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
Modelling deep ventilation of Lake Baikal
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Part 2
Back to the surface
Modelling deep ventilation of Lake Baikal
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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
Main result: surface water temperature Tw
Ta
physical parameters
Tw
The key equation
Heat budget in the
well-mixed surface layer
Modelling deep ventilation of Lake Baikal
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Air2Water
The heat budget
A simplified parameterization of the net heat exchange
seasonal forcing
(hp. sinusoidal)
atmosphere effect of Tw
effect 1
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)
Modelling deep ventilation of Lake Baikal
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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
meas.
T water
model 4 par.
model 8 par
meas.
Modelling deep ventilation of Lake Baikal
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Air2Water
… using satellite data
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
− The model is suitable to reproduce the evolution of Tw at long time scales
seasonal, annual, inter-annual  hysteresis cycle and inter-annual fluctuations
Modelling deep ventilation of Lake Baikal
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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
Modelling deep ventilation of Lake Baikal
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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)
viewed to
through
of diatom
Amphorotiacharacteristic
hispida
− Air2Water isDiatoms
expected
be the
appliedLight
tomicrograph
lakes having
different
(e.g.
microscope. Image by Dr. G.T. Taylor
discovered in Lake Baikal,
geometry, climate, mixing regime) in order to assess the possible response of the lake
to different climate conditions.
Lake Garda (Italy)
Modelling deep ventilation of Lake Baikal
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Thank you
[email protected]
Thank you
Mysterious ice circles in the southern basin of Lake Baikal
(Nasa Earth Observatory, April 25, 2009; Balkhanov et al., TP 2010)
Modelling deep ventilation of Lake Baikal
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```
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