1. Introduction
Lakes and other inland water bodies occupy approximately 4.6 × 106 km2, or 4%, of the land surface of the earth (Downing et al. 2006). Owing to their high heat capacity and low albedo, lakes as heat buffers have significant impacts on local and regional weather and climate (Hostetler et al. 1994; Bonan 1995; Lofgren 1997; Krinner 2003; Long et al. 2007; Samuelsson et al. 2010; Subin et al. 2012a). During early winter and late spring, storm formations are frequently enhanced in the areas downwind of midlatitude lakes under conditions of high surface evaporation and strong air instability (Zhao et al. 2012). Lakes are aerodynamically much smoother than land surfaces; this water–land discontinuity contributes to variations of the atmospheric flow over the landscape (Samuelsson and Tjernström 2001; Törnblom et al. 2007). In addition, lakes play an important role in the global carbon cycle, acting as sources of greenhouse gases through biogeochemical processes of carbon redistribution and mineralization (Cole et al. 2007; Battin et al. 2009; Downing et al. 2008; Tranvik et al. 2009).
Predictions of weather and climate in lake basins rely on lake models for surface heat, water, and momentum fluxes as the lower boundary conditions. In these models, the lake surface temperature is solved from the surface energy balance equation, and the fluxes of momentum and sensible and latent heat are calculated with bulk formulations (e.g., Oleson et al. 2004). Generally, these models assume that the horizontal gradients of temperature and salinity are substantially smaller than their vertical counterparts; thus, the state and flux variables are typically resolved only in the vertical direction. With respect to the parameterization of vertical mixing, a critical process affecting the redistribution of energy in the lake and between the lake and atmosphere aloft, lake models typically fall into two categories: the eddy diffusion type (e.g., Hostetler et al. 1994; Fang and Stefan 1998; Oleson et al. 2004; Subin et al. 2012b) and the turbulence-based type (e.g., Imberger et al. 1978; Goudsmit et al. 2002; Stepanenko and Lykosov 2005). The eddy diffusion type models consist of a prognostic equation for lake temperature in which vertical mixing is contributed by molecular and eddy diffusion, with the latter being two to three orders of magnitude larger than the former (e.g., Oleson et al. 2004). For eddy diffusivity, Henderson-Sellers (1985) proposed a parameterization based on surface wind speed and lake stratification. Despite the lack of a comprehensive evaluation against experimental data, the parameterization of Henderson-Sellers has been widely adopted in the eddy-diffusion-type models. In comparison, the turbulent-based type of models, also known as 
Like any other land surface schemes, offline evaluation of lake models against field observations is an important step before they are used for weather and climate predictions. Most of the evaluation studies have been performed at individual lakes (Hostetler and Bartlein 1990; Boyce et al. 1993; Peeters et al. 2002; Perroud et al. 2009; Voros et al. 2010). Recently, a more comprehensive evaluation, the Lake Model Intercomparison Project (LakeMIP), was carried out with the aim to compare eight one-dimensional lake models against observations, focusing, in the first phase, on temperate and boreal lakes (Stepanenko et al. 2010). For weather and climate studies, it is the performance of model-predicted surface fluxes that matters most because the planetary boundary layer (PBL) scheme is driven by these fluxes. So far, these evaluation studies have been restricted to comparison against observed seasonal and annual cycles of water temperature, with only a few exceptions that provide additional evaluation of model-predicted surface fluxes against indirect flux estimates (Hostetler and Bartlein 1990; Stepanenko et al. 2010; Martynov et al. 2010; Subin et al. 2012b). Indirect flux estimates are obtained using the mass transfer (e.g., Laird and Kristovich 2002) or the surface energy budget method (e.g., Lenters et al. 2005) and are subject to uncertainties in the parameters used and in how the energy flux components are partitioned. In comparison, direct field measurements using the eddy-covariance (EC) method are considered to provide more accurate and reliable flux data for model validation for dry-land ecosystems (e.g., Wood et al. 1998). However, because of logistical difficulty, in situ EC measurements on lakes, especially over seasonal and annual cycles, have been rare, except in recent years (e.g., Blanken et al. 2000; Vesala et al. 2006; Rouse et al. 2008; Liu et al. 2009; Blanken et al. 2011; Nordbo et al. 2011). To date, we are not aware of studies that evaluate lake model-predicted surface fluxes against in situ EC observations.
In this study, we aim at evaluating the Community Land Model version 4–Lake, Ice, Snow and Sediment Simulator (CLM4-LISSS) (Subin et al. 2012b) at Lake Taihu in Jiangsu Province, China—a shallow (2 m deep) and large (~2500 km2) freshwater lake where EC measurements of surface fluxes are available. CLM4-LISSS is an improved version of the lake model embedded in CLM4 (Oleson et al. 2004) and is well suited for a wide spectrum of weather and climate studies (Subin et al. 2012a). Our goal is threefold: 1) to quantify the sensitivity of the model performance to various intrinsic and external model parameters, 2) to evaluate the model-predicted fluxes of sensible and latent heat against the observed fluxes, and 3) to investigate the time evolution of the energy flux partitioning in response to solar radiation forcing. Our work complements the study by Subin et al. (2012a,b). In their study, CLM4-LISSS is optimized for application in global climate models, and its performance is evaluated at seasonal to multiyear time scales. The present study seeks to optimize the model parameter values at the diurnal time scale. This scale is relevant to local phenomena such as PBL growth, lake breeze circulations, and mixing of chemical constituents in the water. Although the study is restricted to CLM4-LISSS, the physical insights gained can be extended to other types of lake models.
Lake Taihu is chosen for three reasons. First, we are not aware of a detailed model evaluation study for a subtropical lake. When compared with other lakes in middle to high latitudes, Lake Taihu does not generate strong lake effect storms or lake–land breeze circulations. Second, a research emphasis in the past has been on evaluating modeled thermal structures in deep lakes (e.g., Lofgren 1997; Long et al. 2007). This emphasis is justified on the ground that lake processes are much more difficult to simulate than those of shallow lakes. Still, shallow lakes deserve attention because mixing regimes in these lakes tend to vary at finer time scales than in deep lakes. Third, the catchment of Lake Taihu represents only 0.4% of China’s land area but contributes nearly 12% of the national gross domestic product (An and Wang 2008). The intensive economic activities have created severe pollution stress on the lake system (e.g., Wang et al. 2011). A validated lake model may be a useful tool to aid the ongoing lake restoration efforts, such as for the calculations of lake water temperature for the prediction of algal outbreaks.
2. Methods
a. Site and data
The main experiment was conducted in Meiliangwan (MLW) Bay, which is situated in the north part of Lake Taihu (31°24′N, 120°13′E; Fig. 1). An eddy covariance system, consisting of a three-dimensional sonic anemometer/thermometer (model CSAT3, Campbell Scientific Inc., Logan, Utah, United States) and an open-path infrared gas analyzer (model LI7500, Li-Cor Inc., Lincoln, Nebraska, United States), was employed to measure the three-dimensional wind speed, air temperature, and atmospheric H2O and CO2 concentrations at 10 Hz. Fluxes of momentum (
Map showing the location of Lake Taihu and the two measurement sites.
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
A second measurement platform, the Dapuko (DPK) site (Fig. 1), is located on the west side of the lake. DPK is about 2 km from the shore and 30 km linear distance away from MLW. The measured variables included the four radiation components, wind speed, air temperature, and humidity. This site was much windier than MLW, with wind speed typically 100% greater than that at MLW. The annual mean air temperature at Lake Taihu is 16.3°C, and annual precipitation is 1360 mm. The lake is ice free throughout the year.
b. CLM4-LISSS and its calibrated version
CLM4-LISSS is an improved version of CLM4-Lake, developed by scientists at the National Center of Atmospheric Research and the Lawrence Berkeley National Laboratory (Oleson et al. 2004; Subin et al. 2012a,b). The core structure of the model can be traced to Hostetler et al. (1993, 1994), Bonan (1995), and Zeng et al. (2002). It consists of three component modules: namely, a surface module for flux estimation, a lake module for updating lake temperature, and a hydrology module for updating hydrological components. CLM4-LISSS is improved over CLM4-Lake by adopting more accurate representations of lake processes. For example, CLM4-LISSS takes into account the enhanced diffusion due to unresolved 3D processes and, thus, significantly improves the flux simulations for deep lakes. It is unclear, however, if the same enhancement is required for shallow lakes.
The eddy diffusivity 
Once the lake surface temperature is known, the surface fluxes 
c. Setup of model simulations
The model was forced by hourly air temperature, humidity, and wind speed observed at a height of 4.0 m above the water surface. Additional forcing variables were net shortwave radiation K* and incoming longwave radiation L↓. The vertical grid spacing was 0.2 m, and the time step of integration was 30 min. A spinup time of one year was used to remove the effect of the initial conditions and to bring the sediment layer into thermal equilibrium with the overlaying water. Model tests revealed that the simulated surface temperature became insensitive to the initial conditions after 10 days of integration.
The internal parameters describe the intrinsic physical properties of the energy and momentum exchange processes. In CLM4-LISSS, the momentum roughness length (
3. Results and discussion
a. Parameter sensitivity
Unlike deep lakes where turnover occurs at the seasonal time scale, Lake Taihu experienced turnover at the diurnal scale as a result of its shallowness (Fig. 2a). During daytime, the upper part of the lake absorbed more solar radiation and was thus warmer than the lower part, resulting in stable stratification that limited the wind-induced vertical mixing (Fig. 3a). During our study period, water temperatures were mostly greater than 4°C, so the warmer upper layer has lower water density and is therefore associated with a stable water column. The stable stratification was eroded quickly when the lake surface cooled down after sunset. The lake thus turned into a neutral or slightly unstable condition during nighttime.
Time series for DOY 229–238 (2010) at the MLW site: (a) water temperature measurements [the number in the subscript denotes the measurement depth (cm)], (b) surface wind speed measured at 3.5 m above the water, and (c) depth-averaged (0–2 m) eddy diffusivity calculated as 2% of the value based on the parameterization of Henderson-Sellers (1985).
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
Temperature comparison for DOY 229–238 (2010): contour plot of (a) observed temperature, (b) predicted temperature with default 
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
The diurnal range of the surface temperature (
As shown in Fig. 3b, CLM4-LISSS with the default 
Our result regarding 
The adjusted 
Concerns were expressed as to whether the small 
Based on Fig. 3c, there is room for improvement on temperature profile simulations. In comparison with the observation, the simulated temperature gradient in the top 1-m water column was much too strong on DOYs 235–237. This problem, along with the fact that the scale factor is dependent on the choice of the target temperature for optimization, reveals limitations of the Henderson-Sellers (1985) eddy diffusivity model for simulating finescale temperature profiles in shallow lakes. We suspect that other lake models that do not have an explicit parameterization of the interfacial layer physics may also experience similar difficulty. In this regard, the scale factor may be interpreted as an empirical adjustment for the practical purpose of predicting Ts and the surface heat fluxes.
Figure 3d shows the 
In case d, a step change of 
The difference between cases c and e indicates the effect of roughness parameterization on the 
To further rule out computational artifacts, we carried out one additional simulation by using the default surface roughness, the default eddy diffusivity, and the standard 
b. Seasonal variations
It is not surprising that both the default and tuned version of CLM4-LISSS captured the seasonal variations of 
Surface temperature 
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
Frontal passages significantly increase the fluxes of sensible heat and water vapor from lakes to the atmosphere (Blanken et al. 2011; Liu et al. 2011). The flux enhancement is caused by the large water-to-air gradients in temperature and humidity during frontal events. Two frontal events are shown in the insets to Fig. 4. The Ts predicted with the default ke was delayed in reference to the observed time series in both events and did not reach the lowest observed temperature (insets to Fig. 4, top panel). These problems were largely overcome with the tuned version (insets to Fig. 4, bottom panel). The default model overestimated the latent heat flux by about 80 and 30 W m−2 during frontal events around DOY 240 and 300, respectively. Tuning reduced the model bias to less than 5 W m−2. (The downward-facing longwave radiation sensor failed during DOY 246–250. The surface temperature measurement during this period was gap filled with a regression equation using the observed air temperature, resulting in artificially large diurnal amplitudes.)
The results shown in Fig. 4 were obtained with the snow/ice module turned off. If the snow module was left active in the simulation, both versions of the model had high Ts biases during the winter period from DOY 350, 2010 to DOY 35, 2011. The bias error was around 5 K for the default version and 3 K for the calibration version. The reason for this may lie in the parameterizations of snow and ice formation, which were triggered whenever air temperature fell below the freezing point. During this time period, MLW recorded air temperature frequently below 0°C, but there was no ice formation and precipitation remained rain instead of snow.
c. Variations between sites
We now evaluate the performance of the calibrated CLM4-LISSS for a 40-day period in 2011 across the two measurement sites (Fig. 5), namely, the MLW site near the shoreline and the more offshore DPK site (Fig. 1). These two sites are about 30 km apart. They had similar water quality and water depth but markedly different wind speed. On average, wind speed at DPK was 84% greater than at MLW during this measurement period, so any differences between the sites can be used to gauge the effects of wind speed. The water surface temperature was nearly identical between the two sites, suggesting a low sensitivity to wind speed. If the model was driven by wind speeds at 50% of the observed values, the modeled surface temperature at DPK would increase by above 0.3 K, confirming the observed low wind sensitivity.
Comparison between observed and model-predicted 
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
The predicted 
Across this large lake there exist spatial heterogeneities in water properties (e.g., turbidity) (Wang et al. 2011) and meteorological conditions (e.g., wind speed). An open question is whether a large lake like Lake Taihu can be represented with one grid cell in climate models or if these spatial heterogeneities can create large enough changes in the surface fluxes (Spence et al. 2011) to warrant the use of multiple grid cells. The lack of sensitivity of Ts to turbidity (Fig. 3d) and to wind (Fig. 5) suggests that spatial variations in sensible and latent heat fluxes may be small across Lake Taihu.
d. Surface heat fluxes
The half-hourly 
Comparison between the observed and the model-predicted surface fluxes 
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
The multiday mean sensible and latent heat fluxes were less sensitive to the choice of parameterization scheme than the half-hourly values. The observed mean 
The diurnal composite fluxes of radiation and energy reveal the dynamic adjustment of various energy transfer processes in response to solar radiation forcing (Fig. 7, top). Averaged over the year, roughly 30% of the net shortwave radiation was transmitted below the surface layer [term 
Diurnal composite of radiation and energy balance components over one full annual cycle, DOY 183 (2010) to DOY 183 (2011): (top) tuned 
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
Over the annual time scale, the calibrated version improved the estimation of half-hourly 
Model-predicted surface fluxes 
Citation: Journal of Hydrometeorology 14, 2; 10.1175/JHM-D-12-067.1
Sensitivity analysis on annual (DOY 183, 2010 to DOY 183, 2011) mean radiation and energy balance components. In all three cases, K* (=131.3 W m−2) and L↓ (=338.7 W m−2) are forcing variables from the observations.
Changes in water quality, as measured with the light extinction coefficient 
4. Conclusions
The main purpose of this study is to calibrate the CLM4 lake model at the diurnal time scale using the direct flux observations at Lake Taihu. The most notable result is the amount of adjustment required of the eddy diffusivity ke parameterization in order to improve the model performance at the diurnal time scale. The modeled lake surface temperature Ts is insensitive to turbidity and shows moderate sensitivity to a surface roughness parameterization. Because surface roughness was constrained by observations, we are left with ke as the tunable model parameter. By reducing ke to 2% of the value calculated with the parameterization of Henderson-Sellers (1985), CLM4-LISSS was able to reproduce the observed vertical thermal stratification and diurnal variations in Ts and to improve the Ts prediction during frontal disturbances. (Forcing agreement of the model with the observed temperature at the 20-cm depth requires a slightly larger scale factor of 0.08 for ke.) We hypothesize that the drag force of the sediment layer in this large (~2500 km2 size) and shallow (2-m depth) lake may have been strong enough to prevent unresolved vertical motions and to suppress wind-induced turbulence.
At this shallow lake, convective overturning occurred frequently at the time when the lake water switched from being stable during the day to becoming unstable shortly after sunset. Associated with the overturning was a one to two orders of magnitude increase in the eddy diffusivity. Even though it made little difference in the predicted seasonal and annual mean QH and QE, tuning of ke brought improvement to the hourly fluxes. The calibrated model explained 87% and 89% of the observed variations in QH and QE, respectively.
Unlike deep lakes where heat storage in the water modulates the local climate at the seasonal time scale, near this shallow lake the modulation occurred at the diurnal time scale. A large fraction of the solar radiation energy was stored in the water during the daytime. The stored energy was then diffused up to the surface at night to sustain sensible and latent heat fluxes to the atmosphere. In the scenario of improved water quality, more solar radiation could be transmitted into the lower water layer, which was offset by a nearly identical enhancement of upward heat diffusion, resulting in little change in the surface sensible and latent heat fluxes.
Two issues are worth further investigation. First, it remains an open question as to how much improvement the calibrated lake model can bring to predictions of lake–land breeze circulations and the PBL dynamics near the shoreline. Work is underway to fully couple the lake model with the operational Weather Research and Forecasting model for the lake catchment. Second, both the observations and the model simulations show that eddy mixing should vary strongly over the diurnal course in shallow lakes. Inclusion of this time-varying characteristic in parameterizations for the gas transfer coefficient (e.g., Cole and Caraco 1998) may improve calculations of the lake–air fluxes of trace gases.
Acknowledgments
This research was supported by the Ministry of Education of China (Grant PCSIRT), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PARD), and the Natural Science Foundation of Jiangsu Province (Grant BK2011830).
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