No abstract

Numerical models of heat and moisture diffusion in the soil-vegetation-atmosphere continuum are linked through the moisture flux from the surface to the atmosphere. This mass flux represents a heat exchange as latent heat flux, coupling water, and energy balance equations. In this paper, a new approach for estimating key parameters governing moisture and heat diffusion equation and the closure function which links these equations, is introduced. Parameters of the system are estimated by developing objective functions that link atmospheric forcing, surface states, and unknown parameters. This approach is based on conditional averaging of heat and moisture diffusion equations on land surface temperature and moisture states, respectively. A single objective function is expressed that measures moisture and temperaturedependent errors solely in terms of observed forcings and surface states. This objective function is minimized with respect to the parameters to identify evaporation and drainage models and estimate water and energy balance flux components. The approach is calibration free (surface flux observations are not required), it is not hampered by missing data and does not require continuous records. Uncertainty of parameter estimates is obtained from the inverse of Hessian of the objective function, which is an approximation of the error covariance matrix. Uncertainty analysis and analysis of the covariance approximation, guides the formulation of a well-posed estimation problem. Accuracy of this method is examined through its application over three different field sites. This approach can be applied to diverse climates and land surface conditions with different spatial scales, using remotely sensed measurements.

[1] 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 E dS=dtj s  à and expectation E  dT s =dtj T s à ) 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.