Recently, numerous studies have focused on the estimation of surface energy flux components, based on the assimilation of land surface temperature (LST) within a variatiol data assimilation (VDA) framework. Unlike the previous investigations based on the force-restore equation, in this study, the full heat diffusion equation is employed in the VDA scheme as an adjoint (constraint). In addition, a model error term is added to the surface energy balance (SEB) equation and the VDA scheme to include the model uncertainty. Both VDA schemes (with and without the model uncertainty) are tested over the First Intertiol Satellite Land Surface Climatology Project Field Experiment (FIFE) site. The comprehensive comparisons between the present model (with heat diffusion equation) and previous model (with the force-restore equation) demonstrate that the present model will decrease the phase error associated with the ground heat flux diurl cycle, and improve the evaporative fraction and heat fluxes estimation. The numerical examples also conclude that the errors caused by model structures and noisy data in the SEB equation can be detected and quantified in the present model (with model uncertainty).
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