Parameter estimation of coupled water and energy balance models based on stationarity constraints of soil moisture and temperature
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A new method is developed for estimating the parameters of land surface water and energy balance models through enforcement of stationary constraints on soil moisture and temperature. Through conditional averaging of the water balance equation with respect to soil moisture and the energy balance equation with respect to surface temperature, a measure of stationarity is derived that approximates the errors present in predicted fluxes (e.g. evaporation, runoff, sensible heat, ground conduction) in terms of measured model inputs (e.g. precipitation, radiation, soil moisture and temperature). Minimization of the approximated error yields estimates of model parameters. The approach is distinct from traditional model calibration because the minimized error term does not depend on measurements of the predicted fluxes. This proposed method is applied to a land surface water and energy balance model similar to those used in global climate models. The approach is tested at two Ameriflux sites with continuous in-situ measurements of soil moisture, temperature, radiation, and surface turbulent fluxes (evapotranspiration and sensible heat). Fluxes estimated with the proposed method match field measurements approximately as well as those estimated by traditional calibration. Replacing the in-situ land surface temperature and soil moisture with estimates retrieved from satellite leads to minimal degradation of model performance. Sensitivity analysis at these sites demonstrates that increasing model complexity does not improve performance. With promising results from testing the approach at these field sites, the method is applied to estimate evapotranspiration over the Southern Great Plains region of North America. In this test, archived meteorological data and remotely sensed moisture and temperature are used to force the model. The spatial pattern of estimated mean annual evapotranspiration is in good agreement (RMSE of 8 Wm-2 , R 2 of 0.75) with published estimates derived from measured precipitation and streamflow. Estimated parameters are reasonably distributed and consistent with climate and vegetation patterns over the region. Because there are so few sites on earth where surface turbulent fluxes are measured, the proposed approach is more widely applicable than traditional calibration methods, and thus could be used, with satellite data, to estimate maps of land surface parameters required by global climate models.
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