Thermal regime and water-atmosphere Thermal regime and water-atmosphere interactions of interactions of

shallow mid-latitude lakes: shallow mid-latitude lakes: a case study within the framework of the a case study within the framework of the

Lake Model Intercomparison ProjectLake Model Intercomparison Project

Stepanenko, V.Stepanenko, V.11, A.Martynov, A.Martynov22, K.J, K.Jööhnkhnk33, ,

M.PerroudM.Perroud44, X.Fang, X.Fang55, Z.Subin, Z.Subin66, F.Beyrich, F.Beyrich77, , A.NordboA.Nordbo88, D.Mironov, D.Mironov99 and J.Huotari and J.Huotari1010

(1) Moscow State University, (1) Moscow State University, (2) Universite du Quebec a Montreal, (3) CSIRO Land and Water, Canberra, (2) Universite du Quebec a Montreal, (3) CSIRO Land and Water, Canberra,

(4) University of Michigan, (5) Auburn University, (4) University of Michigan, (5) Auburn University, (6) University of California, (7) Meteorologisches Observatorium(6) University of California, (7) Meteorologisches Observatorium

Lindenberg, (8) University of Helsinki, (9) DeutscherLindenberg, (8) University of Helsinki, (9) DeutscherWetterdienst, (10) Lammi Biological Station of University of HelsinkiWetterdienst, (10) Lammi Biological Station of University of Helsinki

EGU General Assembly 2011,

Session HS10.2/OS2.3 - Lakes and inland seas,8 April 2011

• Although numerous lake models exist, their validity range is rarely properly estimated by developers and by model users...

But: in regional and, especially, in global models simulation domains often cover different climatic and geomorphological zones with various types of lakes.

How can we be sure that lake models are valid in all these lakes?

LakeMIP: motivation

LakeMIP1 To assess the range of applicability of existing 1D model formulations, i.e. their capacities and limitations in reproducing lake-atmosphere interactions as well as internal lake thermodynamics. This includes the identification of the key physical processes to be taken into account in lake models in order to further improve their performance in lake-atmosphere interaction and in limnological studies.

LakeMIP2 To simulate the interaction mechanisms between lakes and the atmosphere in the framework of weather and climate models of different spatial domains, resolution and dimensionality.

• The LakeMIP web site: http://www.lakemip.net

LakeMIP goals

Kossenblatter Lake (Germany)Kossenblatter Lake (Germany)• Shallow (mean depth 2 m, max 5 m)

• Very turbid (extinction coef. ~7 m-1)

• Size 168 hectares

• Altitude 43 m ASL

• Observation data - Lindenberg Meteorological Observatory - Richard Aßmann Observatory, 2003

Observational dataVariables (sampling frequency/averaging interval)

• Conventional meteorological variables (1 Hz/10 min)

• Radiation (1 Hz/10 min)

• Turbulent heat and momentum fluxes (EC) (20 Hz/10 min)

• Water temperatureat 0, 0.02, 0.1, 0.2,0.5 and 1 m(1 Hz/10 min)

Physically-based quality controls

Mast 90 m

from shore

The set of 1D lake modelsThe set of 1D lake modelsLake model

The type of model

Soil scheme

Source

“Completely-mixed”

One-layer model No -

FLake Two-layer model Yes Mironov et al. 2010

Hostetler (CRCM)

Multilayer model No Hostetler et al., 1993

CLM-VRLS(Hostetler_CLM)

Multilayer model Yes Subin et al., submitted

MINLAKE96 Multilayer model Yes Fang and Stefan, 1996

LAKE Multilayer, K-ε model

Yes Stepanenko et al., 2011

Simstrat Multilayer, K-ε model

No Goudsmit et al., 2002

LAKEoneD Multilayer, K-ε model

No Jöhnk and Umlauf, 2001

Focus on effects on models' performanceof two features:

vertical mixing treatment (turbulence closure) heat exchage with bottom sediments

Setup of numerical experimentsSetup of numerical experiments

• warm season of 2003 (1 May–11 November)

• depth – mean lake depth (2m)

• extinction coefficient 7.08 m-1 (Secchi disk 0.24 m)

• timestep <10 min, MINLAKE96 – 24 h

• “native” surface turbulent flux schemes

• zero heat flux at the bottom or explicit

soil treatment if available

Reference experiment

Sensitivity experiments1) depth — local depth in point of measurements (1.2 m), maximal lake depth (5 m)2) model experiments with neglecting bottom sedimets

Two periodsTwo periods

• 1 – high temperature period (summer, stable stratification):

1 May – 10 August• 2 - temperature decrease period (late

summer, autumn, unstable stratification)

10 August – 10 November

1 — high T 2 — T decreases

Surface temperature errorsSurface temperature errorsfor temperature rise periodfor temperature rise period

K-ε models

During the period of stable stratification in a lake K-ε models have less errors. This does not depend on whether they includebottom sediments parameterization or assume zero bottom heat flux.

Lake stratificationLake stratification

Hostetler and Flake produce too strong stratification in summer

The 0 – 1 m depth temperature difference

Bottom temperatureBottom temperature

Hostetler and Flake produce almostconstant bottom temperature insummer, which is likely dueto very reduced turbulent mixing

Surface temperature errorsSurface temperature errorsfor temperature decrease periodfor temperature decrease period

there is no clear evidence whether turbulence closureor explicit soil parameterization play crucial role in models' performance k-ε models lacking soil parameterization produce negative mean difference

Models including soil/sediments block

K-ε models

Surface temperature in the fallSurface temperature in the fall

Underestimating the temperatureup to 4-5 °C

Modelsunderestimating temperature:two k-ε models (without soil),complete-mixed (without soil),MINLAKE96 (with soil!)

Time, days

Conclusions for Conclusions for Kossenblatter experimentKossenblatter experiment

• All models captured well diurnal and seasonal variability of lake surface temperature

• During most of summer correct parameterization of turbulent mixing is a major factor for simulating both surface and bottom temperatures

• During fall neglecting heat exchange with bottom sediments leads to systematic underestimation of surface temperature but the magnitude of this effect is model-dependent

Valkea-Kotinen lake (Finland)

Observation data gathered and processed by University of Helsinki

2 May — 31 December 2006 with hourly resolution meterorology radiation fluxes eddy covariance for heat and momentum fluxes water temperature at 13 levels from 0.2 m to 4 m

Depth:Maximal 6 mMean 3 mArea 4.1 hectares

First results of Valkea-Kotinen experiment

Small and relatively deep lake — beyond an applicability of 1D k-ε models?

LAKE (k-ε) model

Hostetler_CLM model

Conclusions• 3D lake modeling guidance is needed for

more physically-based determination of 1D models «applicability area»

• LakeMIP is open for new participants wishing to validate their lake models using

comprehensive observational datasets

““Completely-mixed” modelCompletely-mixed” model

ρc p∂T∂ t

=∂∂ zk T

∂T∂ z

−∂ S∂ z

ρc p∂ T∂ t

=−kT ∂ T

∂ t+S∣z=hz= 0

h=

1h F 0+S0− F b−S b

Assumes complete mixing in vertical, Fb = 0 additionally neglects heat flux through water-sediments interface

The influence of depth on The influence of depth on surface temperature errorsurface temperature error

Depths: local(1.2m), mean(2m) and maximal (5m)

Errors when using local and mean depths are close, but with 5 m they increase due the increase of lake heat capacity

Surface temperature errorsSurface temperature errorsfor the whole periodfor the whole period

K-ε models

Models including soil/sediments block

For the entire period models demonstrate comparable error values,with slightly lower RMSEs for K-ε models. The exception is complete-mixed model that produce significant underestimation of mean surface temperature.

Surface flux schemes testSurface flux schemes testSurface schemes areforced by

1) surface layermeteorology;

2) measuredwater surfacetemperature.

All meandifferencesare positive.

Heat fluxes at the lake surfaceHeat fluxes at the lake surfaceMeans:

SHF = 8 W/m2,

LHF = 67 W/m2

All meandifferencesarepositive.

The lake 1D heat balanceThe lake 1D heat balance

δ=ρc ph∂ T∂ t

−F 0+S0−Fb−S bNegligibledue to high water turbidity

Mean δ-24…-26 W/m2

depending onFb = 0 or Fb takenfrom LAKE model

Mean difference of computed total heat flux from observed:

Scheme d(mean), W/m2

FLake 9.48

Hostetler 15.1

LAKE 25.08

Simstrat 31.32

LAKEoneD 17.84

ConsistentwithValkea-KotinenLake (Finland),Nordbo et al., 2011

Errors of sensible and latent Errors of sensible and latent heat fluxesheat fluxes

The model Sensible heat flux Latent heat flux

D(MEAN) RMSE D(MEAN) RMSE

Coupled Decoupled Coupled Decoupled Coupled Decoupled

Coupled Decoupled

Flake_passive

5.70 3.46 13.95 9.34 15.96 6.02 42.52 35.99

Flake_active 6.16 3.46 14.06 9.34 16.96 6.02 43.09 35.99

Hostetler 5.82 5.04 12.75 10.22 15.99 10.60 44.04 41.15

MINLAKE96 6.75 0.02 - - 22.33 0.58 - -

LAKE 5.51 5.94 11.55 12.63 18.35 19.14 41.28 48.48

Simstrat 5.22 6.63 12.18 11.44 21.72 24.69 37.64 40.04

LAKEoneD 2.29 3.47 10.74 8.57 13.84 14.37 33.94 32.71