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Interfacing a one-dimensional lake model with a single-column atmospheric model: Application to the deep Lake Geneva,

Switzerland

GOYETTE, Stéphane, PERROUD, Marjorie

GOYETTE, Stéphane, PERROUD, Marjorie. Interfacing a one-dimensional lake model with a single-column atmospheric model: Application to the deep Lake Geneva, Switzerland. Water Resources Research , 2012, vol. 48, no. 4

DOI : 10.1029/2011WR011223

Available at:

http://archive-ouverte.unige.ch/unige:25496

Disclaimer: layout of this document may differ from the published version.

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Interfacing a one-dimensional lake model with a single-column atmospheric model : Application to the deep Lake Geneva, Switzerland

Ste´phane Goyette1and Marjorie Perroud1

Received 1 August 2011; revised 20 February 2012; accepted 21 February 2012; published 6 April 2012.

[1] A single column atmospheric model (SCM) coupled to a one-dimensional lake model devised for climate simulations is described in this paper. As a test case, this coupled model is applied to the deepest section of Lake Geneva in Switzerland. Both atmospheric and lake models require a minimal set of adjustable parameters to reproduce the local observations of temperature, moisture, and wind as well as those of the lake thermal profiles. A number of simulations have been performed to produce a sorted set of optimal model parameters that reproduces the mean and the variability of the seasonal evolution of the thermal profiles in the lake as well as those of the mean and the variability of the surface air temperature, moisture, and winds. The lake water temperature is reproduced realistically using the optimal calibration parameter values with a seasonal- and depth-averaged error of 0.41C in summer,0.15C in autumn, 0.01C in winter, and 0.27C in spring when compared to the lake observations. Also, the errors of the seasonally averaged simulated anemometer-level wind speed, screen-level air temperature, and specific humidity to the station-derived values are 0.04 m s1, 1.04C, and 0.74 g kg1, respectively. Results of this study contribute to the understanding of the air-lake interactions present over the deep Lake Geneva. In addition, the sensitivity experiments carried out in this paper serve as the basis for experiments aiming at studying the thermal response of the deep Swiss Lake Geneva under future global climate change conditions reported in a companion paper.

Citation: Goyette, S., and M. Perroud (2012), Interfacing a one-dimensional lake model with a single-column atmospheric model:

Application to the deep Lake Geneva, Switzerland,Water Resour. Res.,48, W04507, doi:10.1029/2011WR011223.

1. Introduction

[2] As the horizontal resolution of numerical models of weather and climate increases, more demands are being made for access to accurate lower boundary conditions of inland fresh water body temperatures. Lake parameteriza- tions for use in numerical weather prediction (NWP) and regional climate models (RCM) become an important issue when the surface computational grid includes a large num- ber of individual ‘‘inland water’’ grid points. Different approaches and modes have been used to resolve the lake thermal regimes. In the so-called ‘‘stand-alone mode,’’ i.e., when the forcing is provided by observations, one can afford a more detailed lake model to resolve the evolution of the water temperature profiles. However, efficiency becomes the major constraint for their use in the case of NWP and RCM models that exploit in practice the surface temperature only. Due to their finer horizontal grid spacing, thus allowing resolving a larger number of lakes, NWP models may use highly parameterized lake models using self-similarity of the temperature-depth profiles [Mironov,

2010]. On the other hand, RCMs employing a relatively coarse grid spacing, e.g., roughly 50 km in the case of the European Fifth Framework Programme EU FP5 PRU- DENCE [Christensen et al., 2002] and 25 km in the case of the Sixth Framework Programme EU FP6 ENSEMBLES [Hewitt and Griggs, 2004], may use either Lagrangian- based models [Swayne et al., 2005], eddy-diffusion models [Hostetler et al., 1993], or a mixed-layer model [Goyette et al., 2000]. More complex lake models, such as those based on turbulence kinetic energy production and dissipa- tion (e.g.,k-"), are not yet implemented routinely in NWP models, nor in RCMs, due to the high computational costs involved. However, one of them has been tested in a stand- alone mode [Peeters et al., 2002] over a number of annual cycles with a realistic reproduction of thermal profiles ; it was also noticed that simulations conducted with increased air temperatures produced an increase in lake water temper- atures at all depths. The turbulence-based model ‘‘Simstrat’’

[Goudsmit et al., 2002] has been tested with prescribed atmospheric forcing over Lake Geneva, Switzerland for a 10 year period, and results show a very good agreement with observed thermal profiles [Perroud et al., 2009].

Stand-alone forcing uses a prescribed atmosphere; therefore fluxes from the water surface cannot lead to changes in the atmosphere above. This technique proved useful in lake- model developments, but nonlinear effects between the atmosphere and the water body cannot be resolved, and

1Climatic Change and Climate Impacts, C3i, University of Geneva, Carouge, Switzerland.

Copyright 2012 by the American Geophysical Union 0043-1397/12/2011WR011223

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may thus produce misleading results, as is the case for land- surface schemes forced by observations [e.g., Koster and Eagleson, 1990].

[3] In order to circumvent this problem, in addition to avoiding the computational load of an RCM, the use of a single-column model (SCM) provides a practical and eco- nomical framework for assessing the sensitivity of water temperature profiles to current and perturbed climatic con- ditions. SCMs that encompass a variety of approaches and hypotheses have proven useful in the development of phys- ical parameterization of atmospheric processes, predomi- nantly for clouds and radiation ; for example convection in weather and climate models [Betts and Miller, 1986], as well as the atmospheric solar and infrared radiation trans- fers [Stephens, 1984]. Using an SCM,Stokes and Schwartz [1994] studied the processes that influence atmospheric radiation ; Randall et al.[1996] analyzed the parameteriza- tion of convection and of cloud amount ; Iacobellis et al.

[2003] andLee et al.[1997] used such an approach to study and validate interactions of clouds with radiation parame- terizations, and also to study nocturnal stratocumulus- topped marine boundary layers [Zhu et al., 2005] ; different cloud schemes have been compared within the framework of an SCM [Lohmann et al., 1999] ; Girard and Blanchet [2001] evaluated the impact of aerosol acidification on the lower ice crystal layer and humidity using an SCM. Other applications of SCMs include the sensitivity of a land sur- face scheme to the distribution of precipitation [Pitman et al., 1993], the development of a parameterization of rain- fall interception [Dolman and Gregory, 1992] ; Randall and Cripe [1999] proposed alternative methods for pre- scribing advective tendencies combined with a relaxation forcing that nudge the model’s temperature and humidity toward observed profiles within the framework of an SCM ; Ball and Plant[2008] compared different stochastic param- eterizations in a SCM. Then, owing to the possible interac- tions between the atmosphere and the surface which cannot be reproduced with stand-alone experiments,Pitman[1994]

assessed the sensitivity of a land-surface scheme to the parameter values using an SCM. A coupled atmosphere–

ocean SCM has also been developed for testing tropical atmosphere-ocean interactions in tropical areas of the Pacific [Clayson and Chen, 2002].

[4] No SCM known to the authors has yet been coupled to lake models to simulate the long-term fresh water tem- perature profiles. An evaluation of the performance of such a coupled model is needed to assess the reliability of the coupling variables and fluxes at the model air-water inter- face of a number of lakes, such as the temperature and the wind speed, as well as of the various components of the energy budget.

[5] Although the experimental configurations and appli- cations of these SCMs have gained in complexity, most of them neglect or oversimplify the dynamical feedbacks of the atmospheric circulation. Such simplifications in SCMs reported in the literature, although making them computa- tionally efficient, have introduced errors that may have con- fused and compromised their atmospheric prognostics, especially in the long term. Nevertheless, these SCMs may be run over any part of the globe, principally if the parame- terization of the unresolved dynamical processes is not too restrictive.

[6] In this paper, a novel type of SCM, nicknamed FIZC, has been developed to include the contributions to the evo- lution of large-scale circulation dynamics in combination with diabatic contributions as parameterized in general cir- culation models (GCMs), thus allowing for a realistic time evolution of the prognostic atmospheric temperature, mois- ture and winds. ‘‘FIZ’’ is an acronym for ‘‘physics,’’ recall- ing that this SCM is physically based, and ‘‘C’’ stands for

‘‘column’’. FIZC is based on the second-generation Cana- dian GCM physical parameterization package (GCMii described by McFarlane et al. [1992]). This model also takes advantage of the detailed archives of GCMii to pre- scribe the boundary conditions in the atmospheric column.

In SCMs, the importance of large-scale dynamics has been demonstrated by Hack and Pedretti [2000]. When pre- scribed, these contributions of the dynamical tendencies drive the evolution of the prognostic variables toward a given solution. A specific procedure of prescribing the con- tributions to the dynamical tendencies makes FIZC locat- able over any surface of the globe.

[7] For this study, FIZC is coupled with the turbulence- based k-" lake model Simstrat [Goudsmit et al., 2002] to assess the potential for long term integrations of the current and future warming climate conditions of Lake Geneva in Switzerland. This lake model has not yet been coupled to any atmospheric models and this topic deserves much attention. The material presented in this paper may thus be considered as a follow-up study ofPerroud et al.[2009].

[8] In the following discussion, the coupled FIZC-Sim- strat model sensitivity experiments on the temperature pro- files of the deep Lake Geneva in Switzerland is investigated with respect to a number of adjustable parameters that con- trol the evolution of the ‘‘dynamics’’ ; these relaxing the ver- tical profiles of temperature, moisture, and wind speed components to the GCMii archives, as well as those lake pa- rameters controlling the evolution of the thermal profiles.

2. Methodology : The Concepts at the Base of the Atmospheric Model

[9] The numerical modeling approach—termed FIZ, where FIZ stands for physics—is based on the conceptual aspects of the physically based regional climate interpola- tor for off-line downscaling of GCM’s, nicknamed ‘‘FIZR’’

where ‘‘R’’ stands for ‘‘regional,’’ developed by Goyette and Laprise[1996]. It may be considered as a column ver- sion of the Canadian GCMii [McFarlane et al., 1992]

where, in the latter, atmospheric prognostic variables are evolving with time schematically as follows :

@u;v

@t ¼ Du;v þPu;v; (1)

@T

@t ¼ DT þPT; (2)

@q

@t ¼ Dq þPq; (3) including the momentum equation (1), the thermodynamic equation (2) and the vapor continuity equation (3) where [u, v] are the components of the horizontal wind vector,

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Tis the air temperature, andqis the specific humidity func- tion of space with’as the latitude,is the longitude, the altitude being a hybrid vertical coordinate, and time t.

GCMs are based on the primitive equations of motion (see, for example, Chap. 3 of Washington and Parkinson [1986]). In particular, the GCMii adiabatic formulation may be found by Boer et al. [1984]. The sum of the resolved large-scale circulation terms contributing to the local tendencies of atmospheric prognostic variables may be gathered into a single term called the ‘‘dynamics.’’

These adiabatic dynamical terms, operating essentially in the horizontal, are represented symbolically by ‘‘D’’ in each equation. They include contributions from the advec- tion due to horizontal motions, the horizontal pressure gra- dient and Coriolis forces, as well as the work done by compression or expansion of air masses.

[10] The atmospheric primitive equations also reveal that some of the contributions arising from ensemble effects of subgrid-scale Reynolds terms cannot be ignored. The sum of the physical sources-sinks and Reynolds terms evaluated in a parametric form is called the physics, represented sym- bolically by ‘‘P’’ in each equation. Physics depends on the atmospheric resolved flow variables as well as on a collec- tion of surface variables and parameters. The second mem- bers on the right-hand side of equations (1), (2), and (3) thus represent the physics contributions of momentum (Pu,v), of heat energy (PT), and of water vapor (Pq). These terms represent the contributions of processes which have important impacts on the larger resolved scales that cannot be neglected. These processes are operating essentially in the vertical. As explained byMcFarlane et al.[1992], the term Pu,v represents, in principle, the acceleration due to vertical and horizontal momentum flux divergence, essen- tially turbulent in nature. The heat energy termPTmay be generated by solar and infrared radiation processes, turbu- lent diffusion of heat, or by release of latent heat due to water vapor condensation. Turbulent diffusion of heat may result, in principle, in local heating due to vertical or hori- zontal flux divergence. Moisture in the form of water vapor can be redistributed by means of differential water vapor flux in the vertical or in the horizontal, and can be depleted by condensation. The vertical flux of moisture includes the effects of convection and other turbulent vertical fluxes.

[11] A simplified field equation for ¼(u,v,T,q) can therefore be written symbolically as follows :

@

@t ¼ D þ P : (4)

This partial differential equation allows for a forward inte- gration in time when appropriate initial and boundary condi- tions are provided. During the GCMii simulations, the atmospheric prognostics were archived at regular time intervals and the contribution to the physics tendencies were cumulated and archived at 24 h intervals, whose values are symbolized byP . Consequently, the mean contributions to the dynamics can be retrieved as follows:

D ¼ @

@t P : (5)

[12] That dynamics, also a function of space and time represented by 24 h average values, are prescribed to FIZC

(same procedure used in FIZR) and will serve to compute the atmospheric profiles as described next.

2.1. The FIZC Approach

[13] The SCM FIZC is a one-dimensional atmospheric model applicable anywhere over the Earth’s surface. The prognostic variables ¼ {u(’o, o, , t), v(’o, o, , t), T(’o,o,,t), andq(’o,o,,t)}, are a function of the altitu- dinal coordinate, where’oandodenote a fixed point of latitude and longitude, and are evolving with time as follows:

@

@t ¼ D þ P: (6)

[14] Owing to the small archival frequency and to the low spatial resolution of GCMii outputs that are used to compute the mean contributions to the dynamical tenden- cies as in equation (5), a stochastic component is intro- duced to parameterize the term D in equation (6). This component, based on the general ideas described byWilks [2008] is used to parameterize the contributions to the dy- namical tendencies as follows :

D ¼ R ; D ; (7)

where the prescribed dynamics computed on the basis of GCMii archives in the column,D ¼(’o,o,,t), is super- imposed on white noise,R ; ¼ S ; R, withS ; scaling parameters allowed to vary in the vertical for each prognos- tic variable andRis a random number ranging from1 to þ1. Consequently, the introduction of noise in the above parameterization is intended to reinject the unresolved vari- ability in the dynamical processes that is present in the real atmosphere (e.g., subdaily horizontal advection processes), but is lost in equation (5). This version allows a different scaling, i.e., a different intensity, to each of the contribu- tions to the dynamic tendencies, but the mean subdaily fre- quency variability is similar to all of these. Although a more sophisticated parameterization could be derived for D, the method used here is considered satisfactory because the flow fields computed by this SCM do not inter- act with adjacent atmospheric columns ; therefore no feed- backs on the GCMii dynamical tendencies are considered.

Work is currently underway to implement subdaily vari- ability for subgrid-scale dynamical processes based on other types of noise (e.g., red noise spectra) in order for the simulated flow fields to match the observed local atmos- pheric variability in the atmospheric column. In equation (6) the termP represents the contributions to the tenden- cies due to the physics computed at each time step through- out the atmospheric column on the basis of the GCMii physics package. As is the case for GCMii, the dynamics are contributions to the tendencies of processes operating essentially in the horizontal, whereas the physics are contri- butions to the tendencies of processes operating in the ver- tical. Therefore, the evolution of in an atmospheric column over a fixed point (’o, o) is computed in FIZC schematically as follows :

n; ‘ ¼ n1; ‘þ t D n1; ‘ þPn1; ‘

; (8)

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where time is evolving in a discrete manner as t¼toþn Dt, withtoas the initial time andDtas the model time step and the vertical levels are labeled by‘FIZC thus considers the following contributions to the tendencies : a prescribed dynamicsD evaluated on the basis of (7) and then interpo- lated at each time step, as well as a recomputed physics in the atmospheric column P using the standard GCMii physics package [McFarlane et al., 1992]. In addition to the simple forward-in-time marching scheme shown in (8), a model option may also allow for using a second-order centered method for time differencing combined with a weak time filter developed byAsselin[1972]. The time step Dt used in FIZC is kept the same as that used in GCMii although there is no upper bound for it due to the restriction regarding dynamical instabilities. No attempts are made in the present paper to increaseDtfurther.

[15] FIZC is then interfaced with the lake model via a coupling interface described below.

2.2. Nudging Interface

[16] An FIZC option allows nudging the vertical profiles of toward the GCMii archived profiles. ‘‘Nudging’’

means that the prognostic variables computed in FIZC from (8), such as temperature, moisture, and winds, are

‘‘relaxed’’ toward the GCMii values found in the archives in the column. The difficulty is to find a nudging coefficient suitable for preventing FIZC from drifting too far from the GCMii prognostics, but at the same time allowing it to de- velop its own structures and variabilities. The variability may turn out to be necessary to drive a lake model in a real- istic manner since GCMii prognostic variables have been resolved using a coarse spatial resolution, as well as surface conditions different to that of FIZC. Part of the variability is brought about by the prescribed contributions to the dy- namics tendencies (equation (7)), and the other by the con- tribution to the physics tendencies through processes such as the diurnal and seasonal cycles of the solar radiation, the atmospheric instabilities, which enable vertical diffusion of momentum, heat and moisture, etc.

[17] The nudging procedure is as follows :

m; ‘ ¼ N ; ‘ GCMii;m; ‘ þ ð1 N ;‘Þ FIZC;m; ‘; (9)

where the values of m,‘at stepmand at level‘is a combi- nation of computed FIZC and GCMii archived values con- trolled byN ,‘, the nudging parameter, whose value is 1 for a complete nudging to GCMii archives, and 0 for no nudg- ing ; m denotes the discrete time archival frequency tA ¼ m DtA, being 1 per 12 h. Variables are thus allowed to be nudged independently of each other at all levels at 12 h intervals.

2.3. Vertical Levels

[18] The vertical levels in FIZC are originally the same used by GCMii [McFarlane et al., 1992]. The hybrid coordinate system has been developed by Laprise and Girard[1990] and is a function of the local pressure pas follows :

p¼po þ ðps poÞ T 1 T

2

; (10)

wherepsis the surface pressure,pois a specified reference pressure, andTis the value of the upper boundary coordi- nate, chosen at a finite pressure of 5 hPa. The coordinate surfaces are terrain following in the lower troposphere, but become nearly coincident with isobaric surfaces as p decreases. In this scheme, is defined on full levels () and the diagnostically determined vertical motion variable (d=dt), where d/dt represents the material derivative, is defined on the staggered levels (‘þ1=2) as shown in Table 1.

The reference pressure pois 1013 hPa. In addition, the sur- face pressure may be hydrostatically adjusted according to the difference between the altitude of a station and that resolved by GCMii at the point (’o,o).

2.4. Wind Gust Parameterization

[19] Another FIZC option allows generation of random strong wind events between 1 November and 1 March of each simulated year as follows :

½u;vFIZC ¼ ½u;vs; (11)

where the horizontal wind components are fixed to a pre- scribed wind profile [u, v]s. Consequently, the simulated wind speed may be set to a profile determined on the basis of station observations during winter windstorms. This pro- cedure is done independently to the nudging procedure (section 2.2) in order to apply these profiles to consecutive time steps which is not possible to reproduce with a 12 h wind prescribed on the basis of the GCMii archives.

3. Interfacing FIZC With a One-Dimensional Lake Model

[20] The one-way driven approach described byPerroud et al. [2009] is a necessary step toward developing a coupled climate-lake model. But this step does not guaran- tee computational stability when a lake model is interfaced with an atmospheric model since lakes affect surface fluxes of heat, water vapor, and momentum and thus the structure of the atmospheric layer that are further feeding back into the lake model. Thus, our modeling approach for this study consists of the following steps : (a) carry out a preliminary test to assess the role of the underlying surface on the sur- face temperature and on the vertical structure of the atmos- phere, including both ‘‘lake’’ and ‘‘no lake’’ experiments ; (b) perform a sensitivity analysis of the atmospheric model parameters to the predicted Lake Geneva temperature

Table 1. Position of the Unstaggered Layers in GCMii, and in the 10 Layer Version of FIZC

Layer (‘) ‘þ1=2

0.005 (Top)

1 0.012 0.020

2 0.038 0.056

3 0.088 0.120

4 0.160 0.200

5 0.265 0.330

6 0.430 0.530

7 0.633 0.736

8 0.803 0.870

9 0.915 0.960

10 0.980 1.000

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profiles in order to devise an optimal parameter set ; and (c) study the thermal response of Lake Geneva under future climate change conditions ; this third step is presented in a companion paper (M. Perroud and S. Goyette, Interfacing a one-dimensional lake model with a single-column atmos- pheric model II. Thermal response of the deep Swiss Lake Geneva under a 2CO2global climate change, submitted toWater Resources Research, 2012).

3.1. Thek-eSimstrat Lake Model

[21] The one-dimensional Simstrat lake model, a buoy- ancy-extended k-" model described by Burchard et al.

[1998], has been updated to include the effects of internal seiches on the production of turbulent kinetic energy (TKE). Turbulent mixing is solved by two equations for the TKE (indicated by k) and for the dissipation of TKE

(indicated by"). The source of TKE is generated by shear stress from the wind and buoyancy production in case of unstable stratification. The seiching motion developed under the action of the wind increases the TKE in the interior of the lake due to loss of seiche energy by friction at the bot- tom. Governing equations of thek-"model and extensions included in Simstrat are fully described byGoudsmit et al.

[2002]. This model takes into account the bathymetry, thus providing better parameterization of the seiche energy pro- duction. The influence of river inflows and outflows is, how- ever, not taken into account, so that the lake water balance remains fixed. In addition, two adjustable parameters rele- vant for the simulation of the thermal evolution of lake waters are prescribed in the seiches parameterization,seiche andqseiche. For the current application, no lake-ice module is used in conjunction with this lake model.

Figure 1. Schematic diagram showing the coupling process taking place at the air-water interface in the lowest atmospheric model layer and the upper lake model layer. This involves a number of surface fluxes such as the momentum flux sfc, computed on the basis of the 10 m wind speed component [u,v]anemand of the surface dragcD, the downward solar radiation fluxR#S;sfcas a function of the cloudi- nessC, the reflected solar radiation fluxR"S;sfcas a function of the surface albedow, the solar radiation flux penetrating into the lakeR#S as a function of the lake turbidity, the downward long-wave fluxR#L;sfc as a function of the atmospheric temperature and specific humidity profiles, and cloud amount, the emit- ted long-wave fluxR"L;sfcas a function of the lake surface temperatureTsfc, the sensible heat fluxesQHas a function of the difference in the surface air and water temperatures, the latent heat fluxQEas a function of the surface water vapor deficit, as well as on the lake surface temperature. These are used to compute the net flux at the surface,QN,sfc.

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3.2. Coupling FIZC With Simstrat Lake Model [22] The lake model is interacting with the lower atmos- phere of FIZC through a coupling interface as shown sche- matically in Figure 1. The coupling is realized at each FIZC time step using the GCMii physics package to compute the incoming solar R#S;sfc and downward atmospheric infrared R#L;sfc at the surface. The formulation of these fluxes is described by McFarlane et al. [1992]. The reflected solar and emitted thermal infrared fluxes at the surface, respec- tivelyR"S;sfc ¼

wR#S;sfcandR"L;sfc ¼"wTsfc4 depend on the water albedow, the surface water temperature computed by the lake modelTsfc¼Tw ðz ¼ 0Þ, and the water emissivity

"w (fixed at 0.97), wherezis the lake-depth vertical coordi- nate andis the Stefan-Boltzmann constant. The albedow that is used to compute the reflected solar flux at the surface accounts for the solar zenith angle [Bonan, 1996]:

w ¼ 0:05ðþ 0:15Þ1 (12)

with being the cosine of the local solar zenith angle. In the lake model the exchanges occurring at the air-water interface are realized mainly through conduction and by the absorption of solar radiation in the water column. The solar flux reaching any depthzis a function of the water transpar- ency and is given by R#S ¼ R#S;sfcea z, where the decay is controlled by an extinction coefficient a(m1), a lake de- pendent value determined on the basis bimonthly values of the Secchi disk depth and interpolated at a daily interval.

[23] In addition, the GCMii physics package computes the subgrid-scale vertical component of the turbulent fluxes of sensible and latent heat, taking into account the surface drag coefficient as well as the differences of the air temperature and moisture in the vertical at the water-atmosphere inter- face. The vertical component of the turbulent flux of momen- tum prescribed at the lake surface is parameterized using the anemometer level wind speed [u, v]anem, computed in the GCMii physics package as follows [Goudsmit et al., 2002]:

sfc¼cDaðsuu2anem þ svv2anemÞ; (13)

wherearepresents the air density. The parameterssuand svare applied to the anemometer-level wind speeds to scale the simulated values in order to match those of the station observations. This can be done without altering the prog- nostic variables since the anemometer-level wind speed is a diagnostic quantity. The evolution of the lake thermal profiles is also dependent on the value of the surface drag coefficientcD.

4. Data and Experimental Setup

[24] The deep Lake Geneva is used for the numerical investigations during a 10 year period. This period is deemed sufficient for the lake-parameter validation proce- dure [Perroud et al., 2009]. This lake is a fresh water body of 580 km2surface area, shared by Switzerland to the north and France to the south at 372 m a.s.l. It is divided into two basins, the deep or ‘‘Grand Lac’’ (zmax ¼ 309 m) to the east, and the shallower ‘‘Petit Lac’’ to the west. It remains stratified most of the year and surface waters do not freeze.

It is considered as a warm monomictic lake for which com- plete turnover rarely occurs in the deep lake.

[25] The French National Institute for Agricultural Research (INRA) collects bimonthly samples of thermal profiles at the deepest point of the lake (Database INRA of Thonon-Les-Bains, data management by the Commission Internationale pour la Protection des Eaux du lac Le´man, CIPEL) at the SHL2 station. It is located between Lau- sanne, Switzerland (46.52N ; 6.63E), and Evian, France (46.38N ; 6.58E). Discrete temperature measurements have been made available since 1957 where samples are currently recorded atz¼0, 2.5, 5, 7.5, 10, 15, 20, 25, 30, 35, 50,100, 150, 200, 250, 275, 290, 300, 305, and 309 m depths. The penetration of solar radiation into the water col- umn is a function of the water transparency. The depth-de- pendent light extinction coefficient is not directly measured in the lake, but bimonthly values are deduced on the basis of the Secchi disk depth and interpolated through time in order to cover the period simulated by the lake model.

[26] Meteorological records of hourly mean temperature and wind speed of an inland meteorological station to the west of SHL2 (i.e., Changins, 46.38N; 6.22E) for compar- ison with simulated values are supplied by the Automatic Network (ANETZ) of the Federal Office of Meteorology and Climatology, Meteoswiss [Bantle, 1989] for a 10 year period centered on 1981. To simulate the effects of wind- storms, the wind speed is set to a prescribed wind profile determined on the basis of observations made at the Swiss Climatological Station Payerne (46.8N, 6.9E, 490 m a.s.l.); this station is the only one that routinely operates reg- ular upper air soundings in Switzerland. Surface air tempera- tures are adjusted owing to the station altitude differences compared to the water surface of the lake. In order to remove the bias of inland wind speed recordings, and to generate values over the lake open water at station SHL2, a correction factor applied to the observed winds has been developed [Perroud et al., 2009]. Unfortunately, no measurements are made and available for comparison with SHL2.

[27] For these investigations, the simulated GCMii cur- rent climate (1 CO2 case by Boer et al. [1992]) flow fields, as well as the contributions to the physics tenden- cies, are employed to provide the necessary information to drive the FIZC model ; these fields serve to compute the contributions to the dynamic tendencies (equation (5)) and to specify the flow fields required in the nudging procedure (equation (9)). FIZC is positioned over the location of sta- tion SHL2 of Lake Geneva. The computational time step of 20 min is the same for both models, and the altitude differ- ence between the observed lake altitude and the surface level diagnosed in GCMii is 16 m, so that surface pressure is hydrostatically adjusted in FIZC.

[28] FIZC and thek-"lake models contain numerical pa- rameters, and it is important to establish the sensitivity of the coupled model results to reasonable variations of these parameters. Sensitivity tests on the lake thermal water pro- files, as well as on the atmospheric temperature and wind speed statistics, involve the intensity and the number of vertical levels of the nudging of the air temperature, the moisture, and the horizontal component of the wind N ,‘

(equation (9)) toward GCMii archived values. Another pa- rameter, allowed to vary in the vertical to scale the contri- bution to the dynamics tendencies S ,‘is tested (equation

(8)

(7)). The parameterssuandsvintroduced to scale the simu- lated anemometer wind speed to fit the observed statistics are also tested. The wind gust parameterization can be acti- vated or not, thus impacting on the intensity of mixing dur- ing strong wind events. Additional runs investigate some of the lake calibration parameters, such as the surface drag coefficient cD, as well as those relevant for the seiches parameterization,seicheandqseiche. The vertical grid spac- ing of Simstrat is fixed at 0.75 m, so that 412 levels are needed for the simulation at the hydrological station SHL2.

[29] This coupled atmosphere-lake model is run over a 10 year period, starting 1 January. The initial lake tempera- ture profile is based on the mean December 1980 and Janu- ary 1981 observations. The greenhouse gas concentrations are fixed at current levels (i.e., 1CO2case). The archival frequencies are fixed at 12 h (0000 and 1200 UTC) for the simulated lake profile, and hourly for the mean screen-level temperature and humidity, as well as for the anemometer- level wind speed.

5. Results

[30] The goal of these modeling experiments is to repro- duce optimally the observed atmospheric surface conditions and the lake thermal profiles by adjusting parameter values within reasonable limits, and to analyze the sensitivity of the lake-water temperature profiles to the variation of these parameters. The sensitivity analysis is carried out by way of the comparison of seasonal means of a number of variables simulated using the optimal combination of parameter val- ues with a number of sets of experiments with modified pa- rameter values, as well as the number of vertical levels on which these are applied. The comparison is performed using

simulated and observed hourly-mean atmospheric screen- level temperature and anemometer winds as well as those of twice-daily water temperature profiles, seasonally averaged.

5.1. Preliminary Test : The ‘‘Lake’’ Versus

‘‘No-Lake’’ Experiments

[31] This preliminary test is designed to assess the role of the underlying surface on the surface temperature and on the vertical structure of the atmosphere, including both

‘‘lake’’ and ‘‘no-lake’’ experiments. Details about these experiments and results are found in the Appendix. Figure 2 shows the evolution of the surface temperatures when the lake model and the GCMii land-surface scheme are inter- faced separately with FIZC over a 1 year cycle for the same geographical location in Switzerland, and initialized with the same initial surface temperature. The moments in time when the lake surface temperature reaches the annual min- ima and maxima are delayed in the lake case due to the larger thermal inertia of the water compared to that of the solid ground surface. The daily and annual temperature amplitudes of the water are significantly reduced compared to the solid soil surface. The seasonality, in terms of the time it takes to reach these extremes, is also modified; there is a 2 month lag in the deep Lake Geneva compared to the soil case, even though the atmospheric dynamical forcing is similar in magnitude, thus emphasizing the role of the ther- mal characteristics of such a large body of water. As shown in Table 2, the different surface radiation and thermal char- acteristics (the lake has a lower albedo and a much larger heat capacity than the soil) have thus a strong impact on the surface radiation and heat flux components that changed completely the surface net heat budget. The lake absorbs a large quantity of heat during the spring and summer seasons

Figure 2. The time evolution of the simulated lake surface temperature using thek-"lake model (bold line) and that of the ground surface temperature using the land-surface energy budget scheme of GCMii [McFarlane et al., 1992] (dashed line) under a similar surface forcing. Both lake model and land-surface scheme are interfaced with FIZC over a 1 year cycle for the same geographical location (’o,o) in Swit- zerland. Lake surface temperatures displayed on the graph are archived at 12 h intervals, and the ground surface temperatures, also archived at 12 h intervals, are filtered with a 6 day running average in order to smooth out the diurnal cycles.

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and releases a larger quantity during the autumn and winter seasons. The sign and intensity of surface latent and sensible heat fluxes changed markedly in the lake case. Figure 3 shows the seasonally averaged temperature, horizontal wind speed, and specific humidity profiles simulated by FIZC for the lake and the no-lake experiments, these from GCMii ar- chives as well as those from observations for comparison.

The strong coupling between the lake surface and the atmosphere has an impact on the dynamical and thermody- namical vertical structure of the atmosphere.

5.2. Coupled-Model Optimal Parameter Values [32] To carry out these simulations with the coupled FIZC/k-"lake model, an arbitrary combination of parame- ter values aiming at reproducing the observed water tem- perature profiles is used. A set of 50 simulations has been performed using the following combinations,S ¼[1, 3, 5, 6, 7, 8, 9], suand sv ¼[0.5, 0.6, 0.7, 0.8, 1.0] and N ¼ [0.1, 0.5]. The wind gust parameterization is not activated.

[33] The comparison between simulated and observed mean seasonal water temperature, evaluated through the root mean square errors (RMSEs) for four groups of depths (GD1 : 0–10 m, GD2 : 15–50 m, GD3 : 100–200 m, GD4 : 275–309 m), serve to devise the calibration that produce the smallest bias. Annual means of hourly atmospheric temperature and screen level specific humidity are also compared with the station observations (Table 3).

[34] WhenN ¼0.5, three combinations reproduced re- alistic water temperature profiles with RMSEs ranging from 1.04 to 1.24C in GD1, from 0.32 to 0.42C in GD2, from 0.21 to 0.24C in GD3, and from 0.5 to 0.53C in GD4. For these,suandsv¼0.5, andS ¼[7, 8, 9] ;S ¼9 performed the best in GD1 and GD2, but the worst was in GD3 and GD4. Since the variability of the RMSEs is larger in the first 100 m below the surface, the latter is more

appropriate. For all these simulations, the bias between simulated and observed mean screen air temperature and specific humidity is positive. However, S ¼ 9 produces the smallest bias (Figure 4). Furthermore, for suand sv ¼ 0.5, the bias diminishes with increasing S (Table 3). The bias varies between 0.03 (winter) and 1.58C (spring) at the surface, 0.08 (winter) and 0.84C (summer) at 15 m, 0.41 (autumn) and 0.23C (winter) at 50 m, and 0.03 (autumn) and 0.23C (spring) at 100 m.

[35] The same analysis has been performed using a smaller nudging parameter value N ¼ 0.1. The lowest RMSEs are reached for su andsv¼ 0.6 andS ¼7. The RMSEs are of the order of 0.75C in GD1, 0.38C in GD2, 0.24C in GD3, and 0.15C in GD4. The nudging can thus be reduced to values as low as 0.1. The bias between observed and simulated atmospheric variables is reduced (Table 3). The latter combination will serve as a reference for the sensitivity analysis, thus producing realistic sea- sonal water temperature profiles as shown in Figure 4. The seasonal water temperature profiles show generally a small negative bias. At the surface, the error is maximal in autumn (0.92C), at 15 m in spring (þ0.48C), and at 50 and 100 m (0.65 and 0.37C) in autumn.

5.3. Sensitivity to the Nudging

[36] Sensitivity to the nudging is analyzed first by relax- ing prognostic variables toward the GCMii archives with a set of values, i.e., N ¼[0.1, 0.3, 0.5], and then by fixing one value to a given variable and relaxing independently the three others with values of N ¼0.1 and 0.5 ; in these experiments, the nudging is applied to all vertical levels.

[37] As shown in Figure 5 the water temperature profiles warm throughout the column as the intensity of the nudging toward the GCMii archived values increases. The seasonal differences with the reference simulation vary between Table 2. Comparison of Seasonal Averages of Selected Variables and Fluxes Between the Lake and No-Lake Experiments Over One Annual Cycle ; Averages Are Computed Over the Mar, Apr, May (MAM), Jun, Jul, Aug (JJA), Sept, Oct, Nov (SON), and Dec, Jan, Feb (DJF) Monthsa

MAM JJA SON DJF

No Lake Lake No Lake Lake No Lake Lake No Lake Lake

R#L;sfc(W m2) 324.3 314.3 351.6 337.4 311.2 329.8 291.0 312.5

RL;sfc(W m2) 154.2 144.6 175.8 160.4 154.9 155.0 132.4 133.5

RS;atm(W m2) 58.7 55.2 80.9 75.8 37.2 37.6 19.2 19.6

RS;sfc(W m2) 137.4 154.3 204.4 234.3 95.6 96.0 48.0 46.1

sfc(N m2) 0.54 0.16 0.75 0.18 0.88 0.22 0.61 0.18

Tsfc(C) 8.9 8.7 16.2 16.5 10.1 13.6 4.0 8.3

QH(W m2) 17.2 7.9 23.5 16.4 3.2 13.2 16.5 2.2

QEW m2) 85.0 46.0 136.6 78.9 49.8 71.4 22.8 44.4

pcp(mm d1) 3.5 3.1 2.6 1.9 2.6 2.6 3.1 3.1

C 0.58 0.56 0.46 0.43 0.46 0.46 0.55 0.57

QN,sfc(W m2) 2.2 57.3 0.1 77.2 1.5 42.1 0.0 43.9

RiB Night Day Night Day Night Day Night Day Night Day Night Day Night Day Night Day

0.38 0.95 0.03 0.05 0.5 0.8 0.09 0.09 0.5 0.4 0.1 0.15 0.48 0.15 0.1 0.07

aPrecipitation (pcp) is displayed in the units of mm d1, cloudinessC, where the total cloud amount ranges from 0 (clear sky) to 1 (overcast), downward long-wave radiation flux at the surface R#L;sfc, absorbed long-wave radiation by the surface RL;sfc, absorbed short-wave radiation by the atmosphere RS;atm, absorbed shortwave radiation at the surfaceRS;sfc, latent and sensible heat flux, respectively,QEandQH, and the net energy at the surface,QN,sfc

are in the units of W m2, the momentum fluxsfcis in N m2. The sign convention is positive downward forR#L;sfc, positive for net absorbed radiation forRL;sfc,RS;atm,RS;sfc, andQN,sfc.RiBis the bulk Richardson number (dimensionless). Surface temperature is computed by the GCMii land-surface mod- ule in the no-lake experiment, and the lake surface temperature (i.e.z¼0 m) in the lake experiment by thek-"lake model.

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0.58 and 0.6C for the minima, and 0.84 and 1.5C for the maxima whenN ¼0.3. For a nudging of 0.5, the warming continues and the differences range respectively from 0.7 to 0.77C and 0.98 to 1.63C. The largest differences are observed from the surface down to 20 m. Even though the mean wind speed does not differ significantly from the ref- erence simulation, a stronger nudging has an impact on warming the mean screen-level air temperature and increasing the screen-level specific humidity (Table 3), and

thus serves to explain the warm shift of the water tempera- ture profile.

[38] The screen-level atmospheric temperature and spe- cific humidity are more sensitive to the large nudging val- ues. The increase of the screen-level temperature and specific humidity is thus similar to mean values defined for a nudging of 0.5.

[39] The nudging has also been tested on a reduced num- ber of vertical levels. A nudging on‘levels implies thatN Figure 3. Comparison of observed and computed atmospheric temperature, wind speed and specific humidity profiles. Vertical levels are labeledp=ps 1000, wherepandpsare the pressure and the sur- face pressure, respectively ; the surface is located at vertical level 1000 and values are decreasing upward. The simulated profiles are produced by GCMii, and by FIZC interfaced with the lake model (SIM_LAKE) and land-surface energy budget approach (SIM_NO LAKE). The observed profiles (OBS) are measurements collected from radio soundings made at Payerne in Switzerland at 0000 and 1200 UTC aggregated onto FIZC vertical levels. Profiles are seasonally averaged : (a) spring (MAM), (b) summer (JJA), (c) autumn (SON), and (d) winter (DJF).

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of less than one is applied on the‘layers above the surface (equation (9)), whereas a value of one is applied otherwise.

Nudging the prognostic variables from 4 to 10 levels above the surface does not significantly impact on the surface conditions. The screen- and anemometer-level variables remain essentially unchanged and the water temperature profiles vary within 0.1C. The effects are significant when nudging three levels and less. Screen-level temperature and specific humidity increase, whereas mean wind speed remains essentially unchanged, except when only one level is considered. From a nudging on 10 to 1 levels, the aver- age values of the screen-level temperature, specific humid- ity, and anemometer-level wind speed increase (Table 3) ; this warms the water column and temperature RMSEs increase in all groups of depths. However, it turns out that the increase in the mean of these atmospheric variables by

a nudging of 0.1 on three levels reduces the RMSE in GD1 (0.69C), GD2 (0.24C), and GD3 (0.23C), but increases in GD4 (þ0.53C). Despite this, the bias between observed and simulated screen-level variables does not decrease further (Table 3). At the surface, the water tempera- ture error lies between 0.01 (winter) and0.43C (autumn), at 15 m between 0.07 (winter) and 0.65C (summer), at 50 m between 0.22 (winter) and 0.35C (autumn), and at 100 m between 0.01 (autumn) and 0.21C (winter).

5.4. Sensitivity to the Scaling of the Contributions to the Dynamics Tendencies

[40] The analysis has been done by allowing the scaling parameters S ,‘to vary independently to the contributions to the dynamics tendencies (equation (7)). The optimal ad hoc scaling was found to be 7, so this value is fixed for at Figure 3. (continued)

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least one variable, whereas for the other variables it takes the values of 1 and 3, thus producing 19 simulations.

[41] The seasonal water temperature profiles simulated using the various scaling values all behave differently, while the location of the thermocline and water temperature produce three groups of profiles as shown in Figure 6. The analysis of the water temperature profiles shows that the

scaling of the contributions to the wind dynamics is the most important. The smaller the scaling, the colder the bot- tom water temperatures are, and the steeper is the tempera- ture gradient in the thermocline. TheSuandSvcomponents explain 99% of wind variance, 95% of temperature variance, and 81% of specific humidity variability. Their increase raises the mean wind speed and its standard deviation, Table 3. Comparison of the Station Observation Statistics (Annual Means6Standard Deviations) With the Statistics of the Simulated Outputsa

Wind Speed (m s1) Temperature (C) Specific Humidity (g kg1)

Observations at Changins (1981–1990)

2.9861.91 10.4467.7 6.4662.73

Optimization N ¼0.5

S ¼7 2.4761.65 12.6765.86 7.9963.17

su,v¼0.5 N ¼0.5

S ¼8 2.5461.75 12.5065.75 7.8163.09

su,v¼0.5 N ¼0.5

S ¼9 2.6061.84 12.3365.63 7.6463.02

su,v¼0.5 N ¼0.1

S ¼7 2.8961.82 11.3165.48 6.8662.69

su,v¼0.6

Nudging N ¼0.3

S ¼7 2.8761.91 12.5665.65 7.7563.03

su,v¼0.6 N ¼0.5

S ¼7 2.9861.92 12.6665.61 7.9163.08

su,v¼0.6 Nq,T¼0.5

Nu,v¼0.1 2.7661.89 12.7665.65 7.9663.11

S ¼7 su,v¼0.6 N ,‘¼1¼0.1

S ¼7 3.0862.14 12.5665.31 7.6462.97

su,v¼0.6 N ,‘¼3¼0.1

S ¼7 2.8261.84 11.7965.44 7.1362.79

su,v¼0.6

Scaling of the Contributions to the Dynamics Tendencies N ,‘¼10¼0.1

Su,v¼1

ST¼[1, 3, 7] 1.8360.94 12.7566.7 7.8263.4

Sq¼[1, 3, 7]

su,v¼0.6 N ,‘¼10¼0.1 Su,v¼7

ST¼[1, 3, 7] 2.9461.8 11.3565.5 7.0262.7

Sq¼[1, 3, 7]

su,v¼0.6

Scaling of the Anemometer-Level Wind Speed N ¼0.1

S ¼7 2.4061.52 11.3465.82 6.9262.82

su,v¼0.5 N ¼0.1

S ¼7 3.8562.45 11.2664.78 6.7462.41

su,v¼0.8

aVariables are the anemometer-level wind speed, the screen-level air temperature, and the screen-level specific humidity as a function of the FIZC pa- rameter values for the nudging techniqueN ,for the scaling of the contribution to the tendencies due to the dynamicsS ;‘and for the scaling of the ane- mometer-level wind speedsuandsv.Here stand for all prognostic variables,T,q,u, andv, andfor the number of vertical levels above the surface on which the nudging and the scaling of the contributions to the dynamics are applied. This comparison is partitioned into the optimization phase, as well as into different sensitivity experiments involving the nudging and scaling intensities to the screen-level temperature and anemometer-level wind speed.

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whereas they reduce those for the atmospheric temperature and specific humidity at the screen level (Table 3). The mean anemometer-level wind speed with Su and Sv ¼ 7 agrees with that of the observation, whereas the bias in the

atmospheric temperature and specific humidity averages is positive, whatever the values given toSTandSq.

[42] Small variations in the screen-level variable aver- ages are observed according to the combinations of values Figure 4. Observed lake-water temperature profiles compared with simulations using two different val-

ues for the nudging toward the GCMii archived values ; stands forT,q,u, andv, and‘¼10. Profiles are seasonally averaged : (a) winter (DJF), (b) spring (MAM), (c) summer (JJA), and (d) autumn (SON).

Figure 5. Observed and simulated lake-water temperature profiles, seasonally averaged for (a) DJF, (b) MAM, (c) JJA, and (d) SON. Simulations use a fixed scaling of the contributions to the dynamics ten- dencies (S ¼7) and of the anemometer wind speed (su,sv¼0.6), but varying values for the nudging N ,‘,where‘is the number of levels in the vertical above the surface on which these are applied.

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taken by ST and Sq. For given Su, Sv, and ST values, it appears that mean atmospheric temperature and specific humidity decrease with increasing Sq. However, their effects on the water temperature profiles are small. For instance, the mean of the seasonal RMSEs in layers 0–10 m varies between 1.48 and 1.80C (SuandSv ¼1), 1.15 and 1.30C (SuandSv¼3), 0.7 and 0.76C (SuandSv¼7), for any given values ofSTandSq.

[43] The scaling parameters that produce the lowest RMSE with regard to the whole water column are as fol- low :Sq¼1,ST¼7,SuandSv¼7. The simulated water temperatures fit with lake observations at all depths and for all seasons as shown in Figure 7; the bias varies between 0.67 (autumn) and 0.49C (spring) at the surface,0.19 (winter) and 0.63C (summer) at 15 m, 0.49 (autumn) and 0.01C (winter) at 50 m, and 0.18 (autumn) and 0.03C (spring) at 100 m.

5.5. Sensitivity to the Scaling of the Anemometer-Level Wind Speed

[44] The effect of the intensity of the simulated anemom- eter-level wind speed on the thermal profile has been eval- uated by varying its scaling around the value of the reference calibration. Therefore, the scalingsuandsvis var- ied from 0.5 to 0.8.

[45] As shown in Figure 8, the reduction ofsuandsvpro- duces a warming of the topmost 2.5 m of water in spring (difference of þ0.11C) and the first 7.5 m in summer

(difference of þ0.58C), when compared to the reference profile. Below, the average cooling reaches 0.63C at 50 m and 0.47C at 100 m. Reverse effects are noticed whensuandsvboth increase. The higher these values are the colder the surface temperature, the warmer the bottom tem- perature and the smoother the temperature gradient are in the thermocline. For instance, a scaling of 0.8 produces a cooling of 1.19C at the surface and a warming of 1.84C at 15 m, 1.49C at 50 m and 1.03C at 100 m during summer.

Table 3 shows that the scaling of the anemometer-level wind speed produces large variations of the mean wind speed, but does not affect significantly the atmospheric temperature and specific humidity. As the mean wind speed attains higher values, the warming of deeper layers is explained by the increase of the mixing processes and by the loss of heat in the surface layer due to heat penetration to deeper layers.

5.6. Sensitivity to the Wind Gust Parameterization [46] Wind gust parameterization has been activated in order to produce high wind events. The number of consecu- tive time steps upon which the parameterization is applied influences the sensitivity test on the water temperature pro- files. The module is thus activated during 72 time steps (1 day), 144 time steps (2 days) and 216 time steps (3 days).

The mean seasonal water temperature profiles are rather insensitive to such short events of a given magnitude (equa- tion (11)). The increase of the mean anemometer-level wind speed caused by the activation of the parameterization Figure 6. Observed and simulated lake-water temperature profiles, seasonally averaged for (a) DJF,

(b) MAM, (c) JJA, and (d) SON. Simulations use a fixed scaling for the anemometer wind speed (su,sv

¼0.6) and for the nudging toward the GCMii archived values (N ¼0.1), but varying values are applied to the scaling of the contributions to the dynamics tendenciesS .

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over 3 days is of the order of 0.03 m s1, causing maximum differences with the reference profile of 0.04C.

5.7. Sensitivity to the Surface Drag and the Seiches Parameterization

[47] The two lake-model specific parameters used to cal- ibrate the production/dissipation of TKE due to seiches

have been tested ; seiche ¼ 0.006 instead of 0.01, and qseiche ¼ 0.6 instead of 0.9. Variations of qseiche do not modify significantly the lake water temperature, apart from a 2 m shift in the thermocline position. On the contrary, the lake profile is sensitive to the variations of seiche, as this value serves to calibrate the amount of mixing in the inte- rior of the lake due to the energy transfer from the wind to Figure 7. Time-depth vertical cross section of simulated lake water temperature using the optimal pa-

rameter values :N ,‘¼0.1,S ,‘¼7, where ¼{T,u,v},S ,‘¼1 for ¼q,‘¼10 ;su,sv¼0.6, wind gust parameterization is not activated,seiche¼0.01,qseiche ¼0.9. Differences (C) between observed and simulated temperatures are in dash-dotted lines.

Figure 8. Observed and simulated lake-water temperature profiles, seasonally averaged for (a) DJF, (b) MAM, (c) JJA, and (d) SON. Simulations use a fixed scaling of the contributions to the dynamics ten- dencies (S ¼7) and of the nudging toward GCMii archived values (N ¼0.1), but varying values are applied to the scaling of the anemometer wind speed,suandsv.

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