Parameter estimation of coupled water and energy balance models based on stationary constraints of surface states

Abstract

We use a conditional averaging approach to estimate the parameters of a land surface water and energy balance model and then use the estimated parameters to partition net radiation into latent, sensible, and ground heat fluxes and precipitation into evapotranspiration and drainage plus runoff. Through conditional averaging of the modeled fluxes with respect to soil moisture and temperature, we write an objective function that approximates the temperature‐ and moisture‐dependent errors of the modeled fluxes in terms of atmospheric forcing (e.g., precipitation and radiation), surface states (moisture ( S ) and temperature ( T s )), and model parameters. The novelty of the approach is that the error term is estimated without comparison to measured fluxes. Instead, it is inferred from the deviation of the conditionally averaged tendency terms (expectation and expectation ) from zero since each of these terms equals zero in stationary systems but diverges from zero in the presence of misspecified parameters. Minimization of the approximated error yields parameters for model applications. This strategy was previously studied for simple water balance models using soil moisture conditional averaging. Here we extend the idea to include energy balance fluxes and surface temperature conditioning. The method is tested at two AmeriFlux sites, Vaira Ranch (California) and Kendall Grassland (Arizona). The estimated fluxes (using only observed forcing and state variables) are in reasonable agreement with field measurements. Because this method is based on conditional averages, it can be applied to situations with subsampled or missing data; that is, continuous integration in time is not required.