Passive microwave sensors use a radiative transfer model (RTM) to retrieve soil moisture (SM) using brightness temperatures (TB) at low microwave frequencies. Vegetation optical depth (VOD) is a key input to the RTM. Retrieval algorithms can analytically invert the RTM using dual-polarized TB measurements to retrieve the VOD and SM concurrently. Algorithms in this regard typically use the τ-ω types of models, which consist of two third-order polynomial equations and, thus, can have multiple solutions. Through this work, we find that uncertainty occurs due to the structural indeterminacy that is inherent in all τ-ω types of models in passive microwave SM retrieval algorithms. In the process, a new analytical solution for concurrent VOD and SM retrieval is presented, along with two widely used existing analytical solutions. All three solutions are applied to a fixed framework of RTM to retrieve VOD and SM on a global scale, using X-band Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) TB data. Results indicate that, with structural uncertainty, there ensues a noticeable impact on the VOD and SM retrievals. In an era where the sensitivity of retrieval algorithms is still being researched, we believe the structural indeterminacy of RTM identified here would contribute to uncertainty in the soil moisture retrievals.
Keywords: AMSR-E; VOD; equifinality; passive microwave; radiative transfer model; retrieval algorithm; soil moisture; uncertainty.