A Variational Framework for Coupled Estimation of Evapotranspiration and Recharge Fluxes by Assimilating Land Surface Soil Moisture and Temperature

The evapotranspiration and recharge are the key fluxes that link the land's water and energy cycles. These fluxes have major impacts on agriculture, water supply system, water resources planning, climate, etc. Accurate mapping of these fluxes is limited due to lack of in-situ observation sites and errors in estimation from numerical models. The dynamics of land surface state observations, specifically land surface soil moisture (SM) and temperature (LST), have implicit information on the partitioning of evapotranspiration and recharge fluxes, which provides an opportunity for global mapping of these fluxes across a range of spatial and temporal scales. In this study, a variational data assimilation (VDA) framework is developed for coupled estimation of evapotranspiration and recharge fluxes by assimilating LST and SM observations into a coupled water and energy balance model. We modified LIDA framework (Abdolghafoorian and Farhadi, 2019) to calculate the effective soil hydraulic parameters required for estimating the recharge flux in addition to evaporative flux parameters. Two numerical experiments are conducted using synthetic dataset generated by Hydrus 1-D model to test the accuracy and feasibility of the proposed estimation framework. Second-order information is used to estimate the uncertainty of the estimated parameters and fluxes and guide toward a well-posed optimization problem. Results demonstrate the success of the VDA framework in estimating evaporative and recharge fluxes from implicit information contained in SM and LST data and feasibility test results show promise in extending the framework to large scale using remotely sensed observations.