SEARCH

SEARCH BY CITATION

Keywords:

  • Lake Geneva;
  • climate;
  • coupling;
  • lake model;
  • sensitivity study;
  • single column model

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. 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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. 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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. 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:

  • display math
  • display math
  • display math

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 (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 by McFarlane et al. [1992], the term Pu,v represents, in principle, the acceleration due to vertical and horizontal momentum flux divergence, essentially turbulent in nature. The heat energy term PT 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:

  • display math

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 inline image. Consequently, the mean contributions to the dynamics can be retrieved as follows:

  • display math

[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(ϕo, λo, η, t), v(ϕo, λo, η, t), T(ϕo, λo, η, t), and q(ϕo, λo, η, t)}, are a function of the altitudinal coordinate η, where ϕo and λo denote a fixed point of latitude and longitude, and are evolving with time as follows:

  • display math

[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 inline image 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:

  • display math

where the prescribed dynamics computed on the basis of GCMii archives in the column, inline image = (ϕo, λo, η, t), is superimposed on white noise, inline image, with inline image 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 inline image, 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 inline image 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 (ϕo, λo) is computed in FIZC schematically as follows:

  • display math

where time is evolving in a discrete manner as t = to + n Δt, with to as the initial time and Δt as the model time step and the vertical levels are labeled by inline image FIZC thus considers the following contributions to the tendencies: a prescribed dynamics inline image evaluated on the basis of (7) and then interpolated at each time step, as well as a recomputed physics in the atmospheric column inline image 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 Δt 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 Δt 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:

  • display math

where the values of ψm,ℓ at step m and at level inline image is a combination of computed FIZC and GCMii archived values controlled by Nψ,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 tA = m ΔtA, 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:

  • display math

where ps is the surface pressure, po is a specified reference pressure, and ηT 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) and the diagnostically determined vertical motion variable ( inline image), where d/dt represents the material derivative, is defined on the staggered levels (ηℓ+½) as shown in Table 1. The reference pressure po 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 (ϕo, λo).

Table 1. Position of the Unstaggered Layers in GCMii, and in the 10 Layer Version of FIZC
Layer ()ηηℓ+½
  0.005 (Top)
10.0120.020
20.0380.056
30.0880.120
40.1600.200
50.2650.330
60.4300.530
70.6330.736
80.8030.870
90.9150.960
100.9801.000

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:

  • display math

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.

3. Interfacing FIZC With a One-Dimensional Lake Model

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

[20] The one-way driven approach described by Perroud et al. [2009] is a necessary step toward developing a coupled climate-lake model. But this step does not guarantee 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 surface temperature and on the vertical structure of the atmosphere, including both “lake” and “no lake” experiments; (b) perform a sensitivity analysis of the atmospheric model parameters to the predicted Lake Geneva temperature 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 atmospheric model II. Thermal response of the deep Swiss Lake Geneva under a 2 × CO2 global climate change, submitted to Water Resources Research, 2012).

3.1. The k-ε Simstrat Lake Model

[21] The one-dimensional Simstrat lake model, a buoyancy-extended k-ε 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 ε). 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 bottom. Governing equations of the k-ε model and extensions included in Simstrat are fully described by Goudsmit et al. [2002]. This model takes into account the bathymetry, thus providing better parameterization of the seiche energy production. The influence of river inflows and outflows is, however, not taken into account, so that the lake water balance remains fixed. In addition, two adjustable parameters relevant for the simulation of the thermal evolution of lake waters are prescribed in the seiches parameterization, αseiche and qseiche. For the current application, no lake-ice module is used in conjunction with this lake model.

3.2. Coupling FIZC With Simstrat Lake Model

[22] The lake model is interacting with the lower atmosphere of FIZC through a coupling interface as shown schematically in Figure 1. The coupling is realized at each FIZC time step using the GCMii physics package to compute the incoming solar inline image and downward atmospheric infrared inline image 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, respectively inline image and inline image depend on the water albedo αw, the surface water temperature computed by the lake model Tsfc = inline image, and the water emissivity εw (fixed at 0.97), where z is the lake-depth vertical coordinate and σ is the Stefan-Boltzmann constant. The albedo αw that is used to compute the reflected solar flux at the surface accounts for the solar zenith angle [Bonan, 1996]:

  • display math

with μ 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 depth z is a function of the water transparency and is given by inline image, where the decay is controlled by an extinction coefficient a (m−1), a lake dependent value determined on the basis bimonthly values of the Secchi disk depth and interpolated at a daily interval.

image

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 τsfc, computed on the basis of the 10 m wind speed component [u, v]anem and of the surface drag cD, the downward solar radiation flux inline image as a function of the cloudiness C, the reflected solar radiation flux inline image as a function of the surface albedo αw, the solar radiation flux penetrating into the lake inline image as a function of the lake turbidity, the downward long-wave flux inline image as a function of the atmospheric temperature and specific humidity profiles, and cloud amount, the emitted long-wave flux inline image as a function of the lake surface temperature Tsfc, the sensible heat fluxes QH as a function of the difference in the surface air and water temperatures, the latent heat flux QE as 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.

Download figure to PowerPoint

[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 interface. The vertical component of the turbulent flux of momentum 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]:

  • display math

where ρa represents the air density. The parameters su and sv are 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 prognostic 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 coefficient cD.

4. Data and Experimental Setup

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. 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 km2 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” (zmax = 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 × CO2 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 Nψ,ℓ (equation (9)) toward GCMii archived values. Another parameter, allowed to vary in the vertical to scale the contribution to the dynamics tendencies Sψ,ℓ is tested (equation (7)). The parameters su and sv 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 cD, as well as those relevant for the seiches parameterization, αseiche and qseiche. 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 × CO2 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.

5. Results

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

[30] The goal of these modeling experiments is to reproduce 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 values with a number of sets of experiments with modified parameter 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 interfaced 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 minima 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 thermal characteristics of such a large body of water. As shown in Table 2, the different surface radiation and thermal characteristics (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 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 archives 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 thermodynamical vertical structure of the atmosphere.

image

Figure 3b. (continued)

Download figure to PowerPoint

image

Figure 3a. Comparison of observed and computed atmospheric temperature, wind speed and specific humidity profiles. Vertical levels are labeled inline image × 1000, where p and ps are the pressure and the surface 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).

Download figure to PowerPoint

image

Figure 2. The time evolution of the simulated lake surface temperature using the k-ε 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 (ϕo, λo) in Switzerland. 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.

Download figure to PowerPoint

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
 MAMJJASONDJF
 No LakeLakeNo LakeLakeNo LakeLakeNo LakeLake
  • a

    Precipitation (pcp) is displayed in the units of mm d−1, cloudiness C, where the total cloud amount ranges from 0 (clear sky) to 1 (overcast), downward long-wave radiation flux at the surface inline image, absorbed long-wave radiation by the surface inline image, absorbed short-wave radiation by the atmosphere inline image, absorbed shortwave radiation at the surface inline image, latent and sensible heat flux, respectively, QE and QH, and the net energy at the surface, QN,sfc are in the units of W m−2, the momentum flux τsfc is in N m−2. The sign convention is positive downward for inline image, positive for net absorbed radiation for inline image, inline image, inline image, and QN,sfc. RiB is the bulk Richardson number (dimensionless). Surface temperature is computed by the GCMii land-surface module in the no-lake experiment, and the lake surface temperature (i.e. z = 0 m) in the lake experiment by the k-ε lake model.

inline image (W m−2)324.3314.3351.6337.4311.2329.8291.0312.5
inline image (W  m−2)−154.2−144.6−175.8−160.4−154.9−155.0−132.4−133.5
inline image (W  m−2)58.755.280.975.837.237.619.219.6
inline image (W  m−2)137.4154.3204.4234.395.696.048.046.1
τsfc (N  m−2)0.540.160.750.180.880.220.610.18
Tsfc (°C)8.98.716.216.510.113.64.08.3
QH (W m−2)17.27.923.516.4−3.213.2−16.52.2
QE W m−2)85.046.0136.678.949.871.422.844.4
pcp (mm  d−1)3.53.12.61.92.62.63.13.1
C0.580.560.460.430.460.460.550.57
QN,sfc (W  m−2)2.257.3−0.177.2−1.5−42.10.0−43.9
RiBNightDayNightDayNightDayNightDayNightDayNightDayNightDayNightDay
0.38−0.95−0.03−0.050.5−0.8−0.09−0.090.5−0.4−0.1−0.150.480.15−0.1−0.07

5.2. Coupled-Model Optimal Parameter Values

[32] To carry out these simulations with the coupled FIZC/k-ε lake model, an arbitrary combination of parameter values aiming at reproducing the observed water temperature profiles is used. A set of 50 simulations has been performed using the following combinations, Sψ = [1, 3, 5, 6, 7, 8, 9], su and sv = [0.5, 0.6, 0.7, 0.8, 1.0] and Nψ = [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).

Table 3. Comparison of the Station Observation Statistics (Annual Means ± Standard Deviations) With the Statistics of the Simulated Outputsa
 Wind Speed (m s−1)Temperature (°C)Specific Humidity (g kg−1)
  • a

    Variables are the anemometer-level wind speed, the screen-level air temperature, and the screen-level specific humidity as a function of the FIZC parameter values for the nudging technique Nψ, for the scaling of the contribution to the tendencies due to the dynamics inline image and for the scaling of the anemometer-level wind speed su and sv. Here ψ stand for all prognostic variables, T, q, u, and v, and for 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.

Observations at Changins (1981–1990)
 2.98 ± 1.9110.44 ± 7.76.46 ± 2.73
 
Optimization
Nψ = 0.5   
Sψ = 72.47 ± 1.6512.67 ± 5.867.99 ± 3.17
su,v = 0.5   
Nψ = 0.5   
Sψ = 82.54 ± 1.7512.50 ± 5.757.81 ± 3.09
su,v = 0.5   
Nψ = 0.5   
Sψ = 92.60 ± 1.8412.33 ± 5.637.64 ± 3.02
su,v = 0.5   
Nψ = 0.1   
Sψ = 72.89 ± 1.8211.31 ± 5.486.86 ± 2.69
su,v = 0.6   
 
Nudging
Nψ = 0.3   
Sψ = 72.87 ± 1.9112.56 ± 5.657.75 ± 3.03
su,v = 0.6   
Nψ = 0.5   
Sψ = 72.98 ± 1.9212.66 ± 5.617.91 ± 3.08
su,v = 0.6   
Nq,T = 0.5   
Nu,v = 0.12.76 ± 1.8912.76 ± 5.657.96 ± 3.11
Sψ = 7   
su,v = 0.6   
Nψ, =1 = 0.1   
Sψ = 73.08 ± 2.1412.56 ± 5.317.64 ± 2.97
su,v = 0.6   
Nψ, =3 = 0.1   
Sψ = 72.82 ± 1.8411.79 ± 5.447.13 ± 2.79
su,v = 0.6   
 
Scaling of the Contributions to the Dynamics Tendencies
Nψ, =10 = 0.1   
Su,v = 1   
ST = [1, 3, 7]1.83 ± 0.9412.75 ± 6.77.82 ± 3.4
Sq = [1, 3, 7]   
su,v = 0.6   
Nψ, =10 = 0.1   
Su,v = 7   
ST = [1, 3, 7]2.94 ± 1.811.35 ± 5.57.02 ± 2.7
Sq = [1, 3, 7]   
su,v = 0.6   
 
Scaling of the Anemometer-Level Wind Speed
Nψ = 0.1   
Sψ = 72.40 ± 1.5211.34 ± 5.826.92 ± 2.82
su,v = 0.5   
Nψ = 0.1   
Sψ = 73.85 ± 2.4511.26 ± 4.786.74 ± 2.41
su,v = 0.8   

[34] When Nψ = 0.5, three combinations reproduced realistic water temperature profiles with RMSEs ranging from 1.04 to 1.24°C in GD1, from 0.32 to 0.42°C in GD2, from 0.21 to 0.24°C in GD3, and from 0.5 to 0.53°C in GD4. For these, su and sv = 0.5, and Sψ = [7, 8, 9]; Sψ = 9 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, Sψ = 9 produces the smallest bias (Figure 4). Furthermore, for su and sv = 0.5, the bias diminishes with increasing Sψ (Table 3). The bias varies between 0.03 (winter) and 1.58°C (spring) at the surface, −0.08 (winter) and 0.84°C (summer) at 15 m, −0.41 (autumn) and 0.23°C (winter) at 50 m, and 0.03 (autumn) and 0.23°C (spring) at 100 m.

image

Figure 4. Observed lake-water temperature profiles compared with simulations using two different values for the nudging toward the GCMii archived values; ψ stands for T, q, u, and v, and inline image = 10. Profiles are seasonally averaged: (a) winter (DJF), (b) spring (MAM), (c) summer (JJA), and (d) autumn (SON).

Download figure to PowerPoint

[35] The same analysis has been performed using a smaller nudging parameter value Nψ = 0.1. The lowest RMSEs are reached for su and sv = 0.6 and Sψ = 7. The RMSEs are of the order of 0.75°C in GD1, 0.38°C in GD2, 0.24°C in GD3, and 0.15°C 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 seasonal 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 (−0.92°C), at 15 m in spring (+ 0.48°C), and at 50 and 100 m (−0.65 and 0.37°C) in autumn.

5.3. Sensitivity to the Nudging

[36] Sensitivity to the nudging is analyzed first by relaxing prognostic variables toward the GCMii archives with a set of values, i.e., Nψ = [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 Nψ = 0.1 and 0.5; in these experiments, the nudging is applied to all vertical levels.

[37] As shown in Figure 5the 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 0.58 and 0.6°C for the minima, and 0.84 and 1.5°C for the maxima when Nψ = 0.3. For a nudging of 0.5, the warming continues and the differences range respectively from 0.7 to 0.77°C and 0.98 to 1.63°C. The largest differences are observed from the surface down to 20 m. Even though the mean wind speed does not differ significantly from the reference 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 temperature profile.

image

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 tendencies (Sψ = 7) and of the anemometer wind speed (su, sv = 0.6), but varying values for the nudging Nψ, inline image,where inline image is the number of levels in the vertical above the surface on which these are applied.

Download figure to PowerPoint

[38] The screen-level atmospheric temperature and specific humidity are more sensitive to the large nudging values. 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 number of vertical levels. A nudging on inline image levels implies that Nψ of less than one is applied on the inline image 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 0.1°C. 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 average values of the screen-level temperature, specific humidity, 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 (−0.69°C), GD2 (−0.24°C), and GD3 (−0.23°C), but increases in GD4 (+0.53°C). Despite this, the bias between observed and simulated screen-level variables does not decrease further (Table 3). At the surface, the water temperature error lies between 0.01 (winter) and −0.43°C (autumn), at 15 m between 0.07 (winter) and 0.65°C (summer), at 50 m between 0.22 (winter) and −0.35°C (autumn), and at 100 m between 0.01 (autumn) and 0.21°C (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 Sψ,ℓ 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 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 bottom water temperatures are, and the steeper is the temperature gradient in the thermocline. The Su and Sv components 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, 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 = 7 agrees with that of the observation, whereas the bias in the atmospheric temperature and specific humidity averages is positive, whatever the values given to ST and Sq.

image

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 = 0.6) and for the nudging toward the GCMii archived values (Nψ = 0.1), but varying values are applied to the scaling of the contributions to the dynamics tendencies Sψ.

Download figure to PowerPoint

[42] Small variations in the screen-level variable averages are observed according to the combinations of values 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 1.80°C (Su and Sv = 1), 1.15 and 1.30°C (Su and Sv = 3), 0.7 and 0.76°C (Su and Sv = 7), for any given values of ST and Sq.

[43] The scaling parameters that produce the lowest RMSE with regard to the whole water column are as follow: Sq = 1, ST = 7, Su and Sv = 7. 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 0.49°C (spring) at the surface, −0.19 (winter) and 0.63°C (summer) at 15 m, −0.49 (autumn) and 0.01°C (winter) at 50 m, and −0.18 (autumn) and 0.03°C (spring) at 100 m.

image

Figure 7. Time-depth vertical cross section of simulated lake water temperature using the optimal parameter values: Nψ,ℓ = 0.1, Sψ,ℓ = 7, where ψ = {T, u, v}, Sψ,ℓ = 1 for ψ = q, inline image = 10; su, sv = 0.6, wind gust parameterization is not activated, αseiche = 0.01, qseiche = 0.9. Differences (°C) between observed and simulated temperatures are in dash-dotted lines.

Download figure to PowerPoint

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

[44] The effect of the intensity of the simulated anemometer-level wind speed on the thermal profile has been evaluated by varying its scaling around the value of the reference calibration. Therefore, the scaling su and sv is varied from 0.5 to 0.8.

[45] As shown in Figure 8, the reduction of su and sv produces a warming of the topmost 2.5 m of water in spring (difference of +0.11°C) and the first 7.5 m in summer (difference of +0.58°C), when compared to the reference profile. Below, the average cooling reaches −0.63°C at 50 m and −0.47°C at 100 m. Reverse effects are noticed when su and sv both increase. The higher these values are the colder the surface temperature, the warmer the bottom temperature and the smoother the temperature gradient are in the thermocline. For instance, a scaling of 0.8 produces a cooling of 1.19°C at the surface and a warming of 1.84°C at 15 m, 1.49°C at 50 m and 1.03°C 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.

image

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 tendencies (Sψ = 7) and of the nudging toward GCMii archived values (Nψ = 0.1), but varying values are applied to the scaling of the anemometer wind speed, su and sv.

Download figure to PowerPoint

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 consecutive time steps upon which the parameterization is applied influences the sensitivity test on the water temperature profiles. 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 (equation (11)). The increase of the mean anemometer-level wind speed caused by the activation of the parameterization over 3 days is of the order of 0.03 m s−1, causing maximum differences with the reference profile of 0.04°C.

5.7. Sensitivity to the Surface Drag and the Seiches Parameterization

[47] The two lake-model specific parameters used to calibrate the production/dissipation of TKE due to seiches have been tested; αseiche = 0.006 instead of 0.01, and qseiche = 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 αseiche, as this value serves to calibrate the amount of mixing in the interior of the lake due to the energy transfer from the wind to seiche motions. Therefore, its reduction causes less heat to penetrate deeper into the lake. As a result, from 10 m down to the bottom, the cooling of the water temperature is systematic. Below 100 m the decrease is on average 0.3°C, whereas it ranges between 0.26 (spring) and 0.69°C (summer) at 15 m and between 0.31 (winter) and 0.56°C (autumn) at 50 m, due to the stronger temperature gradient simulated in the thermocline. At the surface, seasonal temperature differences are weak compared to the annual variability (<0.3°C). Screen- and anemometer-level variables are not significantly affected by the lake calibration.

[48] Finally, a new parameterization of the surface drag coefficient cD that accounts for the wind speed is tested. Simulations included an empirical drag parameterization for low wind speeds (from 3 m s−1, cD increases as wind speed decreases [Wüest and Lorke 2003] and an extra parameterization for increasing wind speeds computed from field measurements obtained during the Lake Geneva campaign [Graf et al., 1984]).

[49] Since this parameterization increases the wind energy acting upon the surface, a more intense mixing smears out the temperature gradient in the thermocline and warms the column at all times of the year, with one exception in summer from the surface down to 7.5 m. As a result, the water temperature error is lower than 0.13°C from 50 m down to 150 m during the stratification periods, and the warming of the simulated water profiles decreased the RMSEs in GD1, GD2, and GD3. The temperature increase varies between 0.3 (winter) and 0.82°C (summer) at 15 m and between 0.35 (spring) and 0.7°C (autumn) at 50 m. From 100 m and below, the increase ranges between 0.27 and 0.38°C. Screen- and anemometer-level variables do not vary significantly either. Unlike the seiche parameterization, the varying surface drag coefficient produces a similar RMSE between simulated and the observed water temperature profile, except in the 100 m layer above the bottom.

6. Discussion and Concluding Remarks

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. 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 (Nψ,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 (Sψ,ℓ = 7) and an adequate value for the scaling of the anemometer-level wind speed (su, sv = 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 Sq 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., Nψ, inline image>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 Nψ = 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, Sq = 1, ST = 7, Su and Sv = 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 αseiche, qseiche, and to cD, mean screen-level atmospheric variables do not vary significantly. The temperature gradient in the thermocline is less accurately resolved by decreasing the value of αseiche. On the contrary, a varying surface drag coefficient improves the simulation of the thermocline. The variations of cD due to increasing wind speeds allow heat to penetrate deeper, reducing the RMSEs down to 150 m. However, compared to the calibration with varying Sψ, 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 inline image, or ultimately those of the dynamics inline image 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.

Appendix A:: The Lake Versus No-Lake Experiments

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

[58] For these experiments, a set of ad hoc parameters has been devised. These are Nψ = 0.1, Sψ = 6, ψ = (T, q, u, v), inline image = 10, su = sv = 0.6, and the wind gusts parameterization is not activated. The lake parameters are fixed at αseiche = 0.01, and qseiche = 0.9 [Perroud et al., 2009]. The ground surface characteristics, the land-use, and the force-restore approach of the no-lake case to compute the surface temperature are the same as those used in the GCMii [McFarlane et al., 1992]. The experiments, starting 1 August, used the same initial surface temperature of 20.8°C (Figure 2). The minimum surface water temperature is reached in early March at 5.2°C, whereas that of the soil is reached in early January at −23°C; the lake surface maximum temperature is reached in late August at 22.1°C, whereas the ground surface maximum is reached at 39°C in late June.

[59] For comparison, a number of variables and fluxes are seasonally averaged for the lake and the no-lake cases. These fluxes are a function of the vertical gradient of specific humidity and temperature, and of the surface-layer bulk Richardson number, which relates vertical static stability and the vertical shear serving to compute drag coefficients as by McFarlane et al. [1992]. A Richardson number less than a critical value (RiB,c = 0 in this parameterization) implies a dynamically unstable surface layer that is likely to become or remain turbulent. The atmospheric conditions are unstable on average over the lake surface, whereas over the solid surface stability prevails on the average during the nights. This is due to the rapid warming/cooling of the soil surface, a consequence of the smaller thermal inertia compared to that of the lake. During this annual cycle, the mean energy budget of the soil surface is close to zero but that of the lake is in excess of 48 W m−2, meaning that the lake stored energy to warm up the water of about 1°C, on average in the column. The values of individual surface heat fluxes are also modified: the upward latent heat flux is less intense over the lake than over the soil in the spring (46 versus 85 W m−2) and summer (78.9 versus 136.6 W m−2) seasons, but more intense during the autumn (71.4 versus 49.8 W m−2) and winter (44.4 versus 22.8 W m−2) seasons; the sensible heat flux is less intense over the lake than over the soil in the spring (7.9 versus 17.2 W m−2) and summer (16.4 versus 23.5 W m−2) seasons, and even changes direction (i.e., upward instead of downward in the no-lake case) during the autumn (13.2 versus −3.2 W m−2) and winter (−16.5 versus 2.2 W m−2) seasons. The precipitations are similar for both cases during the autumn (2.55 versus 2.57 mm d−1) and winter (3.13 mm d−1 in both cases) seasons, but smaller over the lake surface during the spring (3.12 versus 3.46 mm d−1) and summer (1.99 versus 2.58 mm d−1) seasons. Also, cloudiness is not much modified during the autumn (0.46 in both cases), little during the winter (0.55 versus 0.57 for the no-lake and lake cases, respectively) and the spring (0.58 versus 0.56 for the no-lake and lake cases, respectively), and more during the summer (0.46 versus 0.43 for the no-lake and lake cases, respectively). These changes are also consistent with the absorbed short and long waves in the atmosphere where temperatures, but also clouds, are playing a role in the atmospheric column. Also, the momentum flux in the surface layer is reduced by more than 70% in the lake case compared to the no-lake case on the annual average meaning that less drag is exerted by the lake on the lower atmosphere compared to the solid surface.

[60] As shown in Figure 3, the seasonally averaged temperature, horizontal wind speed, and specific humidity profiles simulated by FIZC for the lake and the no-lake experiments can be compared to these of GCMii found in the original archive for the same column, as well as to the vertical soundings measured at the Payerne Climatological Station in Switzerland (up to 30–35 km high) and downloaded from the University of Wyoming, Department of Atmospheric Science web site (http://weather.uwyo.edu/upperair/sounding.html). One year in the 1980s has been arbitrarily chosen for this comparison. Seasonal averages are based on the 0000 and 1200 UTC profiles, and observed profiles are aggregated into the FIZC/GCMii vertical levels to ease the comparison. Unfortunately, the observed horizontal wind speed profiles are not displayed due to the lack of in-depth and continuous measurements that prevent us from producing meaningful seasonal averages throughout the atmospheric column. In these experiments, as the nudging parameter values are expected to be less than 1 (i.e., Nψ,ℓ = 0.1), the FIZC vertical profiles are generally not the same as these of GCMii. Moreover, a set of optimal parameters have been devised for the no-lake case to reproduce very closely the atmospheric structure, the surface variables, and the various fluxes found in the GCMii archives (not shown); however, these values are not necessarily suited for the lake case and are therefore not considered further. The seasonally-averaged wind profiles in the no-lake case are close to these computed using the GCMii archives. In the lake case, however, the horizontal winds are stronger than in the no-lake case in the column due to the smaller surface roughness height of the water surface compared to that of the solid surface. The seasonal temperature profiles match well those observed, despite a cold bias generally found above a level corresponding to a height of roughly 8 km above the surface. In the lake case during the summer season, the air above the surface up to an altitude of roughly 1500 m is generally colder compared with the no-lake case, in line with the reduced sensible heat and downward long-wave fluxes at the surface; during the winter season this is quite the opposite where the air is generally warmer and the sensible heat and downward long-wave fluxes at the surface are stronger than the no-lake case. The shape of seasonal specific humidity profiles match well those observed, despite a systematic moist bias found below roughly 5 km. In the lake case, during the spring and summer seasons, the specific humidity in the lower atmosphere is generally less than that in the no-lake case, in line with the reduced evaporation-evapotranspiration (or latent heat flux), with the increased downward solar radiation at the surface, as well as with the reduced cloudiness. The reverse occurs in the autumn and winter seasons for the lake case where the specific humidity is higher in the lowest atmospheric levels, in line with the increased evaporation, a decrease in the downward solar radiation at the surface, as well as with the increase (modest in autumn) in the cloudiness when compared to the no-lake case.

Acknowledgments

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

[61] Douglas Cripe (GEOS) made helpful comments on an early draft of this manuscript. We would also like to thank Warren Lee of the Canadian Centre for Climate modeling and analysis (CCCma) for providing the second version General Circulation Model (GCMii) simulated archives needed to run the FIZC atmospheric model.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. Supporting Information
  • Asselin, R. A. (1972), Frequency filter for time integrations, Mon. Weather Rev., 100, 487490.
  • Ball, M. A., and R. S.Plant (2008), Comparison of stochastic parametrization approaches in a single-column model, Philos. Trans. R. Soc. Sect. A, 366, 26032621, doi:10.1098/rsta.2008.0050.
  • Bantle, H. (1989), Programmdokumentation Klima-Datenbank am RZ-ETH Zürich [in German], MeteoSwiss, Zürich.
  • Betts, A. K., and M. J.Miller (1986), A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets, Q. J. R. Meteorol. Soc., 112, 693709.
  • Boer, G. J., N. A.McFarlane, R.Laprise, J. D.Henderson, and J.-P.Blanchet (1984), The Canadian climate centre spectral atmospheric general circulation model, Atmos. Ocean, 22, 397429.
  • Boer, G. J., N. A.McFarlane, and M.Lazare (1992), Greenhouse gas-induced climate change simulated with the CCC second-generation general circulation model, J. Clim., 5, 10451077.
  • Bonan, G. D. (1996), A Land Surface Model (LSM Version 1.0) for Ecological, Hydrological, and Atmospheric Studies, Technical description and user's guide, NCAR Technical Note NCAR/TN-417+STR, National Center for Atmospheric Research, Boulder, CO.
  • Burchard, H., O.Petersen, and T. P.Rippeth (1998), Comparing the performance of the Mellor-Yamada and the κ-ε two-equation turbulence models, J. Geophys. Res., 103(C5), 10,54310,554, doi:10.1029/98JC00261.
  • Christensen, J. H., T.Carter, and F.Giorgi (2002), PRUDENCE employs new methods to assess European, Clim. Change, EOS, 83, 147.
  • Clayson, C. A., and A.Chen (2002), Sensitivity of a coupled single-column model in the tropics to treatment of the interfacial parameterizations, J. Clim., 15, 18051831.
  • Dolman, A. J. and D.Gregory (1992), A parameterization of rainfall interception in GCMs, Q. J. R. Meteorol. Soc., 118, 455467.
  • Girard, E., and J.-P.Blanchet (2001), Simulation of arctic diamond dust and ice fog and thin stratus using an explicit aerosol-cloud-radiation model, J. Atmos. Sci., 58, 11991221.
  • Goudsmit, G.-H., H.Burchard, F.Peeters, and A.Wüest (2002), Application of k-ε turbulence models to enclosed basins: The role of internal seiches, J. Geophys. Res., 107(C12), 3230, doi:10.1029/2001JC000954.
  • Goyette, S., and R.Laprise (1996), Numerical investigation with a physically based regional interpolator for off-line downscaling of GCMs: FIZR, J. Clim., 9, 34643495.
  • Goyette, S., N. A.McFarlane, and G. M.Flato (2000), Application of the Canadian Regional Climate Model to the Laurentian Great Lakes region: Implementation of a lake model, Atmos. Ocean, 38, 481503.
  • Graf, W. H., N.Merzi, and C.Perrinjaquet (1984), Aerodynamic drag: Measured at a nearshore platform on Lake Geneva, Arch. Meteor. Geophys. Bioclim., 33, 151173.
  • Hack, J. J., and J. A.Pedretti (2000), Assessment of solution uncertainties in single-column modeling frameworks, J. Clim., 13, 352365.
  • Hewitt, C. D. and D. J.Griggs (2004), Ensembles-based predictions of climate changes and their impacts, EOS, 85, 566.
    Direct Link:
  • Hostetler, S. W., G. T.Bates, and F.Giorgi (1993), Interactive coupling of a lake thermal model with a regional climate model, J. Geophys. Res., 98(D3), 50455057, doi:10.1029/92JD02843.
  • Iacobellis, S. F., G. M.McFarquhar, D. L.Mitchell, and R. C. J.Somerville (2003), The sensitivity of radiative fluxes to parameterized cloud microphysics, J. Clim., 16, 29792996.
  • Koster, R. D., and P. S.Eagleson (1990), A one-dimensional interactive soil-atmosphere model for testing formulations of surface hydrology, J. Clim., 3, 593606.
  • Laprise, R. and C.Girard (1990), A spectral general circulation model using a piecewise-constant finite element representation on a hybrid vertical coordinate system, J. Clim., 3, 3252.
  • Lee, W. H., S. F.Iacobellis, and R. C. J.Somerville (1997), Cloud radiation forcings and feedbacks: General circulation model tests and observational validation, J. Clim., 10, 24792496.
  • Lohmann, U., N.McFarlane, L.Levkov, K.Abdella, and F.Albers (1999), Comparing different cloud schemes of a single column model by using mesoscale forcing and nudging technique, J. Clim., 12, 438461.
  • McFarlane, N. A., G. J.Boer, J.-P.Blanchet, and M.Lazare (1992), The Canadian climate centre second generation general circulation model and its equilibrium climate, J. Clim., 5, 10131044.
  • Mironov, D., E.Heise, E.Kourzeneva, B.Ritter, N.Schneider, and A.Terzhevik (2010), Implementation of the lake parameterization scheme FLake into the numerical weather prediction model COSMO, Boreal Environ. Res., 15, 218230.
  • Peeters, F., D. M.Livingstone, G.Goudsmit, R.Kipfer, and R.Forster (2002), Modeling 50 years of historical temperature profiles in a large central European lake, Limnol. Oceanogr., 47, 186197.
  • Perroud, M., S.Goyette, A.Martynov, M.Beniston, and O.Anneville (2009), Simulation of multiannual thermal profiles in deep Lake Geneva: A comparison of one-dimensional lake models, Limnol. Oceanogr., 54, 15741594.
  • Pitman, A. J. (1994), Assessing the sensitivity of a land-surface scheme to the parameter values using a single column model, J. Clim., 7, 18561869.
  • Pitman, A. J., Yang, Z.-L., and A.Henderson-Sellers (1993), Sub-grid scale precipitation in AGCMS: Re-assessing the land surface sensitivity using a single column model, Clim. Dyn., 9, 3341.
  • Randall, D. A., and D. G.Cripe (1999), Alternative methods for specification of observed forcing in single-column models and cloud system models, J. Geophys. Res., 104(D20), 24,52724,545.
  • Randall, D. A., K.-M.Xu, R. J. C.Somerville, and S.Iacobellis (1996), Single column models and cloud ensemble models as links between observations and climate models, J. Clim., 9, 16831697.
  • Swayne, D., D.Lam, M.MacKay, W.Rouse, and W.Schertzer (2005), Assessment of the interaction between the Canadian Regional Climate Model and lake thermal-hydrodynamic models, Environ. Mod. Software, 20, 15051513.
  • Stephens, G. L. (1984), The parameterization of radiation for numerical weather prediction and climate models, Mon. Weather Rev., 112, 826867.
  • Stokes, G. M., and S. E.Schwartz (1994), The atmospheric radiation measurement (ARM) program: Programmatic background and design of the cloud and radiation test bed, Bull. Am. Meteorol. Soc., 75, 12021221.
  • Washington, W. M., and C. L.Parkinson (1986), An Introduction to Three-Dimensional Climate Modeling, 422 pp., Univ. Sci. Books, Mill Valley, Calif.
  • Wilks, D. S. (2008), Effects of stochastic parametrization on conceptual climate models, Philos. Trans. R. Soc. Sect. A, 366, 24752488, doi:10.1098/rsta.2008.0005.
  • Wüest, A., and A.Lorke (2003), Small-scale hydrodynamics in lakes, Annu. Rev. Fluid Mech., 35, 373412.
  • Zhu, P., et al. (2005), Intercomparison and interpretation of Single-Column Model simulations of a nocturnal stratocumulus-topped marine boundary layer, Mon. Weather Rev., 133, 27412758.

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Methodology: The Concepts at the Base of the Atmospheric Model
  5. 3. Interfacing FIZC With a One-Dimensional Lake Model
  6. 4. Data and Experimental Setup
  7. 5. Results
  8. 6. Discussion and Concluding Remarks
  9. Appendix A:: The Lake Versus No-Lake Experiments
  10. Acknowledgments
  11. References
  12. Supporting Information
FilenameFormatSizeDescription
wrcr13329-sup-0001-t01.txtplain text document0KTab-delimited Table 1
wrcr13329-sup-0002-t02.txtplain text document3KTab-delimited Table 2
wrcr13329-sup-0003-t03.txtplain text document3KTab-delimited Table 3

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.