A Spatially Constrained Multichannel Algorithm for Inversion of a First-Order Microwave Emission Model at L-Band

Abstract

Understanding and reducing the uncertainties in the inversion of the first-order radiative transfer models at the L-band are important for the improved spaceborne retrievals of soil moisture (SM) and vegetation optical depth (VOD) over dense canopy. This article quantifies and compares the sensitivity of dual-channel inversion of the two-stream (2S) and $\tau $ – $\omega $ models and proposes a new inversion approach for simultaneous retrievals of SM, VOD, and vegetation-scattering albedo ( $\omega $ ) from a single satellite overpass. In particular, the inversion algorithm incorporates the information of the nearby spatial observations, assuming that the values of VOD and $\omega $ remain locally invariant, and constrains its solutions to high-resolution a priori physical/climatological knowledge of the retrieval variables. The results demonstrate that the uncertainty in the inversion of 2S model is slightly higher than the $\tau $ – $\omega $ model under noisy observations and remains homoscedastic for SM and $\omega $ , while grows heteroscedastically for higher VOD values due to the shape of the cost function. The results are validated using the SMAP data, the dense Mesonet SM network, the in situ measurements from the International SM Network (ISMN), and the derived VOD from the Moderate Resolution Imaging Spectroradiometer (MODIS)-normalized difference vegetation index (NDVI) over the state of Oklahoma in the United States. It is shown that the new approach can recover simultaneously high-resolution features of SM, VOD, and $\omega $ only from a single Soil Moisture Active Passive (SMAP) overpass, where the unbiased root-mean-squared error (ubRMSE) of SM and VOD is reduced by 30% and 70%, respectively, when compared with an unconstrained time-windowed inversion approach.