Uncertainty Quantification of Soil Moisture Estimations Based on a Bayesian Probabilistic Inversion

Soil moisture (SM) inversions based on active microwave remote sensing have shown promising progress but do not easily meet expected application requirements because a number of inversion algorithms can only produce point estimates of SM and cannot quantify the uncertainty of SM inversions. Although previous studies have reported Bayesian maximum posterior estimations that are capable of retrieving SM within a probabilistic framework, they have primarily focused on the optimal estimators of SM and have typically ignored the uncertainty of SM inversions. This paper presents an SM probabilistic inversion (PI) algorithm based on Bayes' theorem and the Markov Chain Monte Carlo technique and capable of revealing the uncertainty of SM inversions and obtaining highly accurate SM estimates via maximum likelihood estimations (MLEs). The algorithm is implemented based on the advanced integral equation model, water cloud model simulations, and dual-polarized TerraSAR-X observations. The ground SM and vegetation water content (VWC) measurements from the Heihe watershed allied telemetry experimental research experiments are applied for validation. The results show that: 1) uncertainties in SM inversions, defined with respect to the measures of dispersion of SM posterior probability distribution, are approximately 0.1-0.12 m
³
/m
³
and 2) an acceptable inversion accuracy is obtained via MLEs, which present an SM Root Mean Square Error (RMSE) of 0.045 and 0.047 m
³
/m
³
for bare and vegetated soils, respectively, and a VWC RMSE of 0.45 kg/m
²
. The presented PI can quantify the uncertainty in SM inversions; therefore, it should be useful for improving active microwave remote sensing estimations of SM.