Accurate modeling and estimation of water and energy fluxes at the land surface is significant for climate and weather modeling, for predicting the impact of land use changes, and for agricultural and water resource planning [French et al., 2005]. The relative magnitudes of the turbulent latent and sensible fluxes, which are largely determined by the land surface moisture and temperature states, impact the development of the boundary layer and the dynamics of the lower troposphere [Fisher et al., 2008; Caparrini et al., 2004a].
 Recently, seasonal field experiments and permanent observation networks have been used to study these fluxes and their variability over diurnal, seasonal, and interannual time scales. Examples include experiments at First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) [Kanemasu et al., 1992], the Boreal Ecosystem-Atmosphere Study (BOREAS) [Sellers et al., 1997], the Northern Hemisphere Climate Processes Land Surface Experiment (NOPEX) [Halldin et al., 1998, 1999], and the FLUXNET [Baldocchi et al., 2001] network. These direct observations, either using eddy covariance systems, Bowen ratio methods, sap flow measurements, or other methods, are necessary for understanding the system and creating and validating models [e.g., Chen et al., 1997]. However, they are costly and not necessarily representative of landscape-scale fluxes because of the complex heterogeneity of the land surface [Stannard et al., 1994]. Research into scaling observations and models for land surface-atmospheric fluxes, including developing methods that can use satellite observations to improve spatial coverage, has been ongoing for years [e.g., Sellers, 1991; Wood and Lakshmi, 1993; Molod et al., 2004, Fisher et al., 2008].
 Accurate spatially distributed estimates of surface fluxes require physically based models driven by accurate field or remote sensing observations of surface variables [French et al., 2005]. Some models for estimating fluxes use remotely sensed data to take characteristics of surface heterogeneity into account. Examples include the Two-Source Energy Balance model (TSEB) [Norman et al., 1995], disaggregated atmosphere land exchange inverse model (DisALEXI) [Norman et al., 2003], the Surface Energy Balance Algorithm for Land (SEBAL) [Bastiaanssen et al., 1998], and the Surface Energy Balance System (SEBS) [Su, 2002].
 Regardless of their specific model structure, all of these models and methods require parameters to be specified, and there is a rich history of literature on methods of parameter estimation [e.g., Sellers et al., 1989; Franks and Beven, 1997]. Recently, a multicriteria parameter optimization method has been adopted by Gupta et al.  to estimate the optimal parameter values in the Biosphere-Atmosphere Transfer Scheme (BATS) and thus improve model performance over the use of standard look-up tables based on biomes. Xia et al.  used the same multicriteria calibration method on six modes of the Chameleon Surface Model (CHASM) and again found improvement of model performance. However, most parameter optimization methods require measurements of the fluxes (e.g., latent heat), limiting application to areas where such data exist (e.g., at AmeriFlux sites and in intensive field campaigns such as FIFE). The methods derived here are distinct in that they do not require measured fluxes for calibration, but rather infer parameters from the degree to which modeled tendency terms (the rate of change of water and energy storage) are stationary.
 The approach we propose is also distinct from data assimilation techniques [e.g., Reichle et al., 2001; Crow, 2003], which acknowledge errors in measured states, such as soil moisture and temperature, and optimally adjust the state variables using model forecasts. Most related to our work is that of Pan and Wood , who developed a constrained ensemble Kalman filter (CEnKF) that allows the merging of land surface state and flux observations assimilated into a land surface model while maintaining closure of the water budget (which can be considered a stationarity constraint). The quality of inferred fluxes from data assimilation depends on both the underlying model and the parameters specified in that model. The methods presented here for parameter estimation could be followed by data assimilation, but we have not attempted to do that here.
 Other strategies combine parameter estimation and surface temperature assimilation to estimate surface heat fluxes and energy partitioning [e.g., Castelli et al., 1999; Boni et al., 2001; Caparrini et al., 2004b]. Recently, Sini et al.  extended these efforts by introducing a simplified soil wetness model into a data assimilation scheme and thus enhanced the estimation of surface energy balance partitioning. The governing parameters estimated in these studies are evaporative fraction and bulk transfer coefficient, making the cost function relative easy and feasible to compute. However, evaporative fraction, which represents the surface control on latent heat flux, can only be assumed to be approximately constant for near-peak radiation hours on days without precipitation [Crago and Brutsaert, 1996], which imposes restrictions on the applicability of the method.
 Salvucci  developed a method to extract information about the soil moisture dependence of surface hydrologic fluxes from soil moisture and precipitation data. The basis of the method is that under stationary conditions, the expected value of the change in soil moisture storage over an interval of time, conditioned on the storage during that interval, is zero. In conjunction with the water balance equation, the disappearance of the storage change term implies that precipitation measurements over an interval time, conditionally averaged according to the soil moisture storage, can be used as a surrogate measure of moisture-dependent total outflow (evapotranspiration plus runoff and drainage). Under these constraints, model parameters can be estimated by matching the soil moisture conditional expectation of modeled fluxes to the soil moisture conditional expectation of precipitation. The novelty of the approach is that parameters controlling evaporation and drainage are estimated without measurements of evaporation and drainage. Instead, the parameters are estimated on the basis of the information provided by the covariance of precipitation and soil moisture, as expressed in the conditionally averaged precipitation . A further strength of this method is that the required data (precipitation and soil moisture) do not need to be measured continuously in time. However, while the method robustly estimates the combined sensitivity of evapotranspiration and drainage to soil moisture, it has difficulty distinguishing evaporation from drainage and runoff, particularly for relative dry surface soils when the root zone can draw moisture up from deeper stores to satisfy evaporative demand [Salvucci, 2001].
 To address this weakness, we take the energy balance into account and apply a similar conditional averaging approach to net radiation with conditioning on surface temperature. Because the water and energy balance are linked through evapotranspiration, more robust parameter estimation and flux partitioning can be expected.
 We describe the conditional averaging methodology and a simplified coupled water and energy balance model in section 2. Then we present and discuss results of applying the proposed parameter estimation technique at a synthetic case in Charlotte, North Carolina, in section 3 and two AmeriFlux sites (Vaira Ranch in California and Kendall Grassland in Arizona) in section 4. The results are contrasted with a traditional parameter estimation on the basis of matching the observed and modeled fluxes. This allows discrepancies between the estimated and measured fluxes to be attributed both to weaknesses of the underlying model and to uncertainties introduced by the proposed parameter estimation strategy.