A physically constrained inversion for high-resolution passive microwave retrieval of soil moisture and vegetation water content in L-band

Remote sensing of soil moisture and vegetation water content from space often requires inversion of a zeroth-order approximation of the forward radiative transfer equation in L-band, known as the τ-ω model. This paper shows that the least-squares inversion of the model is not strictly convex and the widely used unconstrained damped least-squares (DLS) can lead to biased retrievals, due to preferential descending paths. In particular, the numerical experiments show that for sparse (dense) vegetation with a low (high) opacity, the DLS tends to overestimate (underestimate) the soil moisture and vegetation water content when the soil is dry (wet). A new Constrained Multi-Channel Algorithm (CMCA) is proposed that confines the retrievals with a priori information about the soil type and vegetation density and accounts for slow temporal changes of the vegetation water content through a smoothing-norm regularization. It is demonstrated that depending on the resolution of the constraints, the algorithm can lead to high-resolution soil moisture retrievals beyond the radiometric spatial resolution. Controlled numerical experiments are conducted and the results are validated against ground-based gauge observations using the passive microwave observations by the Soil Moisture Active Passive (SMAP) Satellite.