### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Methodology: The Concepts at the Base of the Atmospheric Model
- 3. Interfacing FIZC With a One-Dimensional Lake Model
- 4. Data and Experimental Setup
- 5. Results
- 6. Discussion and Concluding Remarks
- Appendix A:: The Lake Versus No-Lake Experiments
- Acknowledgments
- References
- Supporting Information

[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 0.41°C in summer, −0.15°C in autumn, 0.01°C in winter, and 0.27°C 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 s^{−1}, 1.04°C, and 0.74 g kg^{−1}, 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.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Methodology: The Concepts at the Base of the Atmospheric Model
- 3. Interfacing FIZC With a One-Dimensional Lake Model
- 4. Data and Experimental Setup
- 5. Results
- 6. Discussion and Concluding Remarks
- Appendix A:: The Lake Versus No-Lake Experiments
- Acknowledgments
- References
- Supporting Information

[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 parameterizations for use in numerical weather prediction (NWP) and regional climate models (RCM) become an important issue when the surface computational grid includes a large number 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 PRUDENCE [*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 dissipation (e.g., *k*-*ε*), 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 temperatures 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 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 economical framework for assessing the sensitivity of water temperature profiles to current and perturbed climatic conditions. SCMs that encompass a variety of approaches and hypotheses have proven useful in the development of physical parameterization of atmospheric processes, predominantly 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 transfers [*Stephens*, 1984]. Using an SCM, *Stokes and Schwartz* [1994] studied the processes that influence atmospheric radiation; *Randall et al.* [1996] analyzed the parameterization of convection and of cloud amount; *Iacobellis et al.* [2003] and *Lee et al.* [1997] used such an approach to study and validate interactions of clouds with radiation parameterizations, 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 surface scheme to the distribution of precipitation [*Pitman et al.*, 1993], the development of a parameterization of rainfall interception [*Dolman and Gregory*, 1992]; *Randall and Cripe* [1999] proposed alternative methods for prescribing 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 parameterizations in a SCM. Then, owing to the possible interactions 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 temperature 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 interface 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 applications 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 computationally efficient, have introduced errors that may have confused 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 parameterization 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 evolution of large-scale circulation dynamics in combination with diabatic contributions as parameterized in general circulation models (GCMs), thus allowing for a realistic time evolution of the prognostic atmospheric temperature, moisture and winds. “FIZ” is an acronym for “physics,” recalling that this SCM is physically based, and “C” stands for “column”. FIZC is based on the second-generation Canadian GCM physical parameterization package (GCMii described by *McFarlane et al.* [1992]). This model also takes advantage of the detailed archives of GCMii to prescribe the boundary conditions in the atmospheric column. In SCMs, the importance of large-scale dynamics has been demonstrated by *Hack and Pedretti* [2000]. When prescribed, these contributions of the dynamical tendencies drive the evolution of the prognostic variables toward a given solution. A specific procedure of prescribing the contributions to the dynamical tendencies makes FIZC locatable over any surface of the globe.

[7] For this study, FIZC is coupled with the turbulence-based *k*-*ε* 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 of *Perroud et al.* [2009].

[8] In the following discussion, the coupled FIZC-Simstrat model sensitivity experiments on the temperature profiles of the deep Lake Geneva in Switzerland is investigated with respect to a number of adjustable parameters that control the evolution of the “dynamics”; these relaxing the vertical profiles of temperature, moisture, and wind speed components to the GCMii archives, as well as those lake parameters controlling the evolution of the thermal profiles.

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

- Top of page
- Abstract
- 1. Introduction
- 2. Methodology: The Concepts at the Base of the Atmospheric Model
- 3. Interfacing FIZC With a One-Dimensional Lake Model
- 4. Data and Experimental Setup
- 5. Results
- 6. Discussion and Concluding Remarks
- Appendix A:: The Lake Versus No-Lake Experiments
- Acknowledgments
- References
- Supporting Information

[9] The numerical modeling approach—termed FIZ, where FIZ stands for physics—is based on the conceptual aspects of the physically based regional climate interpolator 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 version of the Canadian GCMii [*McFarlane et al.*, 1992] where, in the latter, atmospheric prognostic variables are evolving with time schematically as follows:

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, *T* is the air temperature, and *q* is the specific humidity function of space with *ϕ* as the latitude, *λ* is the longitude, the altitude *η* 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 advection due to horizontal motions, the horizontal pressure gradient 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 symbolically by “*P*” in each equation. Physics depends on the atmospheric resolved flow variables as well as on a collection of surface variables and parameters. The second members on the right-hand side of equations (1), (2), and (3) thus represent the physics contributions of momentum (*P*_{u,v}), of heat energy (*P*_{T}), and of water vapor (*P*_{q}). 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 by *McFarlane et al.* [1992], the term *P*_{u,v} represents, in principle, the acceleration due to vertical and horizontal momentum flux divergence, essentially turbulent in nature. The heat energy term *P*_{T} may be generated by solar and infrared radiation processes, turbulent 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 horizontal 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 *ψ* = (*u*, *v*, *T*, *q*) can therefore be written symbolically as follows:

This partial differential equation allows for a forward integration in time when appropriate initial and boundary conditions are provided. During the GCMii simulations, the atmospheric prognostics *ψ* 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 by . Consequently, the mean contributions to the dynamics can be retrieved as follows:

[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 *ψ* = {*u*(*ϕ*_{o}, *λ*_{o}, *η*, *t*), *v*(*ϕ*_{o}, *λ*_{o}, *η*, *t*), *T*(*ϕ*_{o}, *λ*_{o}, *η*, *t*), and *q*(*ϕ*_{o}, *λ*_{o}, *η*, *t*)}, are a function of the altitudinal coordinate *η*, where *ϕ*_{o} and *λ*_{o} denote a fixed point of latitude and longitude, and are evolving with time as follows:

[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 tendencies as in equation (5), a stochastic component is introduced to parameterize the term in equation (6). This component, based on the general ideas described by *Wilks* [2008] is used to parameterize the contributions to the dynamical tendencies as follows:

where the prescribed dynamics computed on the basis of GCMii archives in the column, = (*ϕ*_{o}, *λ*_{o}, *η*, *t*), is superimposed on white noise, , with scaling parameters allowed to vary in the vertical for each prognostic variable and *R** is a random number ranging from −1 to +1. Consequently, the introduction of noise in the above parameterization is intended to reinject the unresolved variability 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 contributions to the dynamic tendencies, but the mean subdaily frequency variability is similar to all of these. Although a more sophisticated parameterization could be derived for , the method used here is considered satisfactory because the flow fields computed by this SCM do not interact with adjacent atmospheric columns; therefore no feedbacks on the GCMii dynamical tendencies are considered. Work is currently underway to implement subdaily variability for subgrid-scale dynamical processes based on other types of noise (e.g., red noise spectra) in order for the simulated flow fields *ψ* to match the observed local atmospheric variability in the atmospheric column. In equation (6) the term represents the contributions to the tendencies due to the physics computed at each time step throughout 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 contributions to the tendencies of processes operating in the vertical. Therefore, the evolution of *ψ* in an atmospheric column over a fixed point (*ϕ*_{o}, *λ*_{o}) is computed in FIZC schematically as follows:

where time is evolving in a discrete manner as *t* = *t*_{o} + *n* Δ*t*, with *t*_{o} as the initial time and Δ*t* as the model time step and the vertical levels are labeled by FIZC thus considers the following contributions to the tendencies: a prescribed dynamics evaluated on the basis of (7) and then interpolated at each time step, as well as a recomputed physics in the atmospheric column 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 by *Asselin* [1972]. The time step Δ*t* 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 increase Δ*t* further.

[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 *ψ* 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 develop its own structures and variabilities. The variability may turn out to be necessary to drive a lake model in a realistic 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 dynamics tendencies (equation (7)), and the other by the contribution 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:

where the values of *ψ*_{m,ℓ} at step *m* and at level is a combination of computed FIZC and GCMii archived values controlled by *N*_{ψ,ℓ}, the nudging parameter, whose value is 1 for a complete nudging to GCMii archives, and 0 for no nudging; *m* denotes the discrete time archival frequency *t*_{A} = *m* Δ*t*_{A}, 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 *η* has been developed by *Laprise and Girard* [1990] and is a function of the local pressure *p* as follows:

where *p*_{s} is the surface pressure, *p*_{o} is a specified reference pressure, and *η*_{T} is the value of the upper boundary coordinate, 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, *ψ* is defined on full levels (*η*_{ℓ}) and the diagnostically determined vertical motion variable ( ), where *d/dt* represents the material derivative, is defined on the staggered levels (*η*_{ℓ+½}) as shown in Table 1. The reference pressure *p*_{o} is 1013 hPa. In addition, the surface pressure may be hydrostatically adjusted according to the difference between the altitude of a station and that resolved by GCMii at the point (*ϕ*_{o}, *λ*_{o}).

Table 1. Position of the Unstaggered Layers in GCMii, and in the 10 Layer Version of FIZCLayer (*ℓ*) | *η*_{ℓ} | *η*_{ℓ+½} |
---|

| | 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 |

#### 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:

where the horizontal wind components are fixed to a prescribed 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 procedure 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.

### 4. Data and Experimental Setup

- Top of page
- Abstract
- 1. Introduction
- 2. Methodology: The Concepts at the Base of the Atmospheric Model
- 3. Interfacing FIZC With a One-Dimensional Lake Model
- 4. Data and Experimental Setup
- 5. Results
- 6. Discussion and Concluding Remarks
- Appendix A:: The Lake Versus No-Lake Experiments
- Acknowledgments
- References
- Supporting Information

[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 procedure [*Perroud et al.*, 2009]. This lake is a fresh water body of 580 km^{2} surface 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” (*z*_{max} = 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 complete 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 Léman, CIPEL) at the SHL2 station. It is located between Lausanne, Switzerland (46.52°N; 6.63°E), and Evian, France (46.38°N; 6.58°E). Discrete temperature measurements have been made available since 1957 where samples are currently recorded at *z* = 0, 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 column is a function of the water transparency. The depth-dependent 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, 46.38°N; 6.22°E) for comparison 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 windstorms, the wind speed is set to a prescribed wind profile determined on the basis of observations made at the Swiss Climatological Station Payerne (46.8°N, 6.9°E, 490 m a.s.l.); this station is the only one that routinely operates regular upper air soundings in Switzerland. Surface air temperatures 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 current climate (1 × CO_{2} case by *Boer et al.* [1992]) flow fields, as well as the contributions to the physics tendencies, 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 station SHL2 of Lake Geneva. The computational time step of 20 min is the same for both models, and the altitude difference 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 the *k*-*ε* lake models contain numerical parameters, 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 profiles, 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*_{ψ,ℓ} (equation (9)) toward GCMii archived values. Another parameter, allowed to vary in the vertical to scale the contribution to the dynamics tendencies *S*_{ψ,ℓ} is tested (equation (7)). The parameters *s*_{u} and *s*_{v} introduced to scale the simulated anemometer wind speed to fit the observed statistics are also tested. The wind gust parameterization can be activated or not, thus impacting on the intensity of mixing during strong wind events. Additional runs investigate some of the lake calibration parameters, such as the surface drag coefficient *c*_{D}, as well as those relevant for the seiches parameterization, *α*_{seiche} and *q*_{seiche}. The vertical grid spacing 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 temperature profile is based on the mean December 1980 and January 1981 observations. The greenhouse gas concentrations are fixed at current levels (i.e., 1 × CO_{2} case). 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.

### 6. Discussion and Concluding Remarks

- Top of page
- Abstract
- 1. Introduction
- 2. Methodology: The Concepts at the Base of the Atmospheric Model
- 3. Interfacing FIZC With a One-Dimensional Lake Model
- 4. Data and Experimental Setup
- 5. Results
- 6. Discussion and Concluding Remarks
- Appendix A:: The Lake Versus No-Lake Experiments
- Acknowledgments
- References
- Supporting Information

[50] The results from the lake versus no-lake experiments showed that a change from a land to a lake surface in FIZC led to consistent modifications in the atmospheric profiles, as well as in the surface variables and fluxes, despite similar atmospheric dynamical forcing. The minimum and maximum values of the lake surface temperatures are delayed and the daily temperature amplitude is significantly reduced compared to the land surface. Thus, these modifications emphasize the role played by the surface conditions accounted for in the lake model and these of the vertical exchanges in the atmospheric column accounted for in the contributions to the physics tendencies.

[51] Then, ensuing results indicated that the model's adjustable parameters have an impact on the simulated water temperature profiles, on the anemometer-level wind speed, screen-level temperature, and humidity. However, devising an optimal combination is challenging because of the nonlinear effects generated by the coupling technique. These parameters modulate the surface turbulent and radiation fluxes that couple the lower atmosphere to the lake, drive the surface water temperature, and then feedback on the atmospheric boundary layer that modulates the values of surface atmospheric variables. The differences between observed and simulated downward solar and infrared fluxes at the surface are generally from 3 to 74 W m^{−2} for the solar flux, and from −4 to 28 W m^{−2} for the infrared flux, respectively, where the clouds are the major factors explaining these differences. Yet, a combination of these parameter values has been found to produce seasonal water temperature profiles and surface atmospheric variables in a realistic manner.

[52] While nudging the atmospheric variable toward the GCM profiles tends to increase the mean screen-level atmospheric temperature and specific humidity, a higher scaling of the contributions to the dynamics tendencies reduce their values. However, their individual effects on the water temperature profiles are similar. In both cases, a warming is observed throughout the whole water column. While the mean anemometer-level wind speed is not significantly affected by a stronger nudging, higher scaling values increase the mean and variability. This increase in the momentum flux toward the water surface, and thus more energy is available to transfer heat with depth and the effects of colder air temperature, does not impact on the water column. To cool the water temperature, it is thus necessary to modify the parameter that scales the anemometer-level wind speed without significantly modifying the other variables. This is achieved by scaling down the anemometer-level wind speed, together with increasing the scaling of the contributions to the dynamics tendencies. This shows that the effects of a reduction of the nudging toward the GCMii profiles can be compensated by varying the scaling of the contribution to the dynamics tendencies and the anemometer-level wind speed.

[53] Parameters optimization using a weak nudging toward the GCMii archived values (*N*_{ψ,ℓ} = 0.1) can realistically reproduce the observed water temperature profiles as well as the atmospheric screen variables. A constant value for the scaling of the contributions to the dynamics tendencies (*S*_{ψ,ℓ} = 7) and an adequate value for the scaling of the anemometer-level wind speed (*s*_{u}, *s*_{v} = 0.6) generate RMSEs of 0.75°C in GD1, 0.38°C in GD2, 0.24°C in GD3, and 0.15°C in GD4. Despite a small negative bias in the seasonal water temperature profiles, the mean error of the screen-level air temperature, specific humidity, and anemometer-level wind speed are, respectively, 0.09 m s^{−1}, −0.87°C, and −0.4 g kg^{−1}. However, the sensitivity analysis revealed that the water temperature profiles can more closely approximate to seasonal observations. Even though the scaling of the contributions to the dynamics tendencies was proven to impact mainly on the anemometer-level wind speed, a different scaling of the temperature and specific humidity may slightly shift the temperature profiles. Therefore, the most accurate results were found when *S*_{q} was lowered to 0.1. The RMSEs was reduced to 0.73°C in GD1, to 0.25°C in GD2, to 0.15°C in GD3, but increased to 0.34°C in GD4. The mean value of the anemometer-level wind speed is reduced (0.04 m s^{−1}), but the mean values of temperature and specific humidity are increased, 1.04°C and 0.74 g kg^{−1}, respectively.

[54] Variations in the number of levels on which the nudging is applied also influenced the RMSEs in GD1, GD2, and GD3. When the strongest nudging toward the GCMii profiles is applied on more than six levels (i.e., *N*_{ψ,} >6 = 1), screen- and anemometer-level variables react to an increase in the value of the nudging, but more weakly. A nudging on 1 level (that is nine levels with *N*_{ψ} = 1) produces less variations than a nudging of 0.3 on 10 levels. Therefore a nudging on three levels was shown to improve the water temperature profile without negatively affecting the simulation of the atmospheric variables. However, this improvement is due to the negative bias of the simulated water temperature profile. Since the effects of the nudging of the atmospheric variables imply a warming of the water column, the simulated profile necessarily crosses the observation and may reduce the bias. By applying a nudging on three levels to the previous calibration obtained using the following scaling values, *S*_{q} = 1, *S*_{T} = 7, *S*_{u} and *S*_{v} = 7), the influence of the GCMii on the water profile is very strong and produces a positive bias. Since the wind gust function has a negligible effect on the atmospheric variables, the optimal calibration does not make use of it.

[55] The anemometer-level wind speed showed no significant changes following the application of the extreme winds parameterization, perhaps because we prescribed only the wind profiles regardless of the temperature and of the specific humidity profiles. Also, the nudging procedure should be modified during these extreme events.

[56] Even though the lake surface temperatures are sensitive to variations of lake-model parameters *α*_{seiche}, *q*_{seiche}, and to *c*_{D}, mean screen-level atmospheric variables do not vary significantly. The temperature gradient in the thermocline is less accurately resolved by decreasing the value of *α*_{seiche}. On the contrary, a varying surface drag coefficient improves the simulation of the thermocline. The variations of *c*_{D} due to increasing wind speeds allow heat to penetrate deeper, reducing the RMSEs down to 150 m. However, compared to the calibration with varying *S*_{ψ}, the RMSEs are higher.

[57] The optimal parameter values combination found in this study is applicable only for Lake Geneva. Other parameter values would presumably be required for other lakes. The coupled FIZC/*k*-*ε* is currently being tested on other lakes in order to cover a range from shallow to deep, nonfreezing to freezing, low altitude to high altitude, and crystal clear to turbid waters, but also other lake types, i.e., monomictic, dimictic, etc., such as that depicted in the Lake-MIP project (www.unige.ch/climate/lakemip/index.html). In addition, prior to coupling this lake model to other modules for investigations involving biological and/or chemical processes, thermal profiles must be adequately simulated. Consequently, this coupled model is further tested against a variety of configurations in order to adequately reproduce the atmosphere-water interactions and the lake thermal profiles. These include an increased number of vertical levels of FIZC to refine the vertical profiles, as well as to better represent the momentum and the energy fluxes in the boundary layer, but also other numerical time-marching schemes, etc. However, results from preliminary tests show that even with an increased number of vertical levels, as well as with using a more sophisticated physics package, the major conclusions drawn in this study are still valid. Other tests aim at reducing the number of vertical levels of the *k*-*ε* lake model to reduce the computational load that may be a limiting factor in regional climate simulation over a lake-rich region. The sensitivity experiments reported in this paper will thus help in the development and future implementation of coupled lake-atmosphere mesoscale model for Switzerland. Finally, if one plans to run a GCM or a RCM with the intention of outputting the contributions to the physics tendencies , or ultimately those of the dynamics in order to drive a column-model similar to FIZC, an archival frequency higher than 24 h would better represent the diurnal cycle of the large-scale circulation through their effects on the lateral advection of temperature, moisture and momentum.