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Estimation of Land Surface Turbulent Heat and Evaporative Fluxes by Assimilating Remotely Sensed Land Surface Temperature and Moisture Open Access

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Land surface heat and evaporative fluxes exchanged between the land surface and the atmospheric boundary layer play an important role in the climate system. In situ measurements of these fluxes are expensive and available only over a limited number of field experiment sites. At present, the only way to achieve the goal of mapping land surface fluxes at regional scales is to use remote sensing technology that can provide various spatial and temporal imageries covering large areas. Current remote sensing technologies can directly detect the land surface states (e.g., soil moisture, surface temperature, and vegetation), but not land surface fluxes. Therefore, there is a need for developing numerical methods to estimate fluxes using available remotely sensed state data. Recently several studies have focused on the estimation of surface turbulent heat fluxes by assimilating land surface temperature (LST) via a variational data assimilation (VDA) scheme. The goal of these studies is to estimate key parameters of land surface fluxes, i.e., neutral bulk heat transfer coefficient (CHN) and evaporative fraction (EF).The goal of this study is to enhance the current VDA schemes for the estimation of turbulent heat and evaporative fluxes in three major ways: (1) characterizing the effect of vegetation dynamics on CHN, (2) coupling water and energy balance equations, assimilating soil moisture (SM) data in addition to LST, and constraining the VDA estimates by the moisture diffusion equation in addition to the heat diffusion equation; and (3) analyzing the second-order information that guides toward a well-posed estimation problem and provides uncertainty of parameters. The existing VDA algorithms assume that vegetation dynamics over the period of one month are negligible, and thus take CHN as a monthly constant parameter. However, bare soil may turn into a fully vegetated surface in only a few weeks during the growing season, undermining the assumption of constant monthly CHN. In this research, the VDA algorithm is advanced by taking CHN as Leaf Area Index (LAI). This improves the performance of the VDA scheme, especially at sites in which temporal variation of vegetation phenology is significant. The current VDA schemes retrieve surface fluxes by assimilating LST into an energy balance model and have not considered the inherent coupling between water (moisture) and energy (heat) in the soil-plant-atmosphere continuum. In this research, this issue is addressed by coupling the water and dual-source energy balance models through the flux of evapotranspiration and jointly assimilating SM and LST to improve the performance of VDA in the energy-limited regimes.The VDA scheme suffers from the following issues: (1) it does not explicitly compute the error covariance matrix of parameter estimates, (2) it tends to be ill-posed, and (3) it is a high-dimensional non-linear minimization problem and therefore, the optimization may reach a saddle point instead of a local minimum. This research addresses these shortcomings and enhances the performance of the VDA scheme through computing the Hessian matrix via the Lagrangian method and the analysis of second-order information at the critical point.The proposed modifications to the VDA scheme for estimation of turbulent heat and evaporative fluxes are tested at the point scale (through a set of synthetic and field site experiments) and at the large scale (over an area of 21780 km2 in the U.S. Southern Great Plains). The results show that simultaneous assimilation of land surface temperature and soil moisture data improves the robustness of land surface flux estimates obtained via VDA. Results also demonstrate the effectiveness of analysis of second-order information, obtained from the Hessian matrix, at the point of optima in quantifying the uncertainty of parameters, hence fluxes, and in guiding toward a well-posed estimation.

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