A framework for quantifying uncertainties in remote sensing retrievals

The retrieval inverse problem is typically solved in one of two ways: least-squares fitting or Bayes' procedures. Least-squares estimates can be viewed as maximum likelihood, with an implied underlying Gaussian model on the state. This results in point estimates of the mean, and uncertainties are usually not reported although asymptotic estimates do exist in principle. The Bayesian approach has become more popular over the past two decades as a large segment of the remote sensing community has adopted optimal estimation (OE). Since the output of an OE retrieval characterizes a probability distribution, some argue that it automatically achieves uncertainty quantification. However, operational implementations and limited physical knowledge result in uncertainties that impact the reliability of retrieval output as estimates of the true quantities of interest (QOI's) they purport to represent.

Rigorous uncertainty quantification (UQ) for remote sensing demands a comprehensive approach that includes uncertainties due to lack of knowledge in physical models, uncertainties on input parameters, measurement errors on radiances, computational artifacts, and potentially other unknowns. Here we present a "top-down", simulation-based approach to uncertainty quantification for remote sensing retrievals. It is not necessary to enumerate individual sources of uncertainty, or to make strong assumptions such as Gaussianity. Instead, we use a simulation experiment to quantify the artifacts attributable to the retrieval algorithm through a nonparametric statistical model. Then, we infer the magnitude of the impact of such artifacts on actual retrieved estimates through a Gaussian mixture regression. The method is applicable to both least-squares and OE retrievals.