Uncertainty Quantification in Land Surface Hydrologic Modeling: Toward an Integrated Variational Data Assimilation Framework

Variational data assimilation (VDA) is an effective technique for the estimation of land surface heat fluxes. In this method, sequences of remotely sensed land surface temperature measurements are assimilated into a dynamic surface energy balance model to estimate the key unknown parameters of the turbulent heat fluxes. Despite the advantages of the VDA technique in the retrieval of land surface heat fluxes, it suffers from a key limitation, which is its tendency to be ill posed. Moreover, unlike ensemble-based schemes, the VDA method itself does not provide estimates of the predictive uncertainty of estimated parameters and, thus, retrieved fluxes. This research addresses these shortcomings by proposing an uncertainty quantification (UQ) framework for the VDA technique. The proposed framework utilizes uncertainty analysis and analysis of error covariance approximation as a tool to quantify the uncertainty of estimated parameters and to guide the formulation of a well-posed estimation problem. It provides a calibration-free tool to assess the performance of the VDA technique in retrieving land surface heat fluxes over a range of land surfaces and climatic conditions. The UQ framework suggests that the VDA approach performs poorly over wet and highly vegetated land surface regions and when the difference between land surface and air temperature is low. Moreover, it reveals that characterizing the effect of vegetation dynamics on the bulk heat transfer coefficient reduces the correlation between unknown parameters and, hence, leads to a more robust estimation of parameters.