Deep ventilation in Lake Baikal: a simplified model for a complex natural phenomenon
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Transcript of 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
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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
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Part 1A plunge into the abyss of the world's deepest lake
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The lake of records
Lake Baikal - Siberia (Озеро Байкал - Сибирь)
The oldest, deepest and most voluminous lake in the world
Lake Baikal
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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
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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
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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
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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
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− 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
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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
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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)
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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
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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
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… 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
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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
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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
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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 = 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]
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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)
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15th of February 15th of September
Calibration
Temperature profiles
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CFC and dissolved oxygen profiles
Calibration
Mean annual
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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
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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∼
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15th of February
Validation
Temperature and dissolved oxygen profiles
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.
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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
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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
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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
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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.
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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
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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
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Temperature profiles
Climate change
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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
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Part 2Back to the surface
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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
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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
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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
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(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
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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
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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.
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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)