Title: A Physically Bounded Inversion Model for Improved Microwave Retrievals of Soil Moisture and Vegetation Water Content in L-band
Abstract: Passive microwave retrievals of soil moisture and vegetation water content often require underdetermined inversion of a zeroth-order approximation of the radiative transfer equation in L-band, known as the τ - ω model. This talk elaborates that the least-squares (LS) inversion of the τ - ω model is not a convex problem due to its saddle shape—which could lead to biased and physically unrealistic retrievals. In particular, we demonstrate that for sparse (dense) vegetation with a shallow (deep) optical depth, the classic unconstrained damped LS approaches tend to significantly overestimate (underestimate) the soil moisture and vegetation water content. To cope with the problem, this paper proposes a new inversion model that recasts the retrieval into an overdetermined LS problem using the Tikhonov regularization, which enables to obtain physically-bounded and unbiased a posteriori estimates of the soil moisture and vegetation water content from microwave L-band observations. Unlike the existing algorithms, which often assume that the vegetation water content remains constant over a window of time, this method formalizes a new way that can account for slowly varying dynamics of the vegetation water content, which could be of paramount importance for improved space-based soil moisture retrievals over croplands during the growing season. The results are validated for soil moisture gage data and examined using the data from the NASA’s Soil Moisture Active Passive Satellite.
