Applied Math Colloquium

Space-borne remote sensing instruments measure high-dimensional vectors of radiances for each ground footprint over which they observe. These observations are converted into estimates of geophysical quantities through complex processing algorithms called retrievals. Many instruments use \optimal estimation" (OE) methods based on Bayes' Rule to obtain the posterior distribution of the state given the radiances, and report the estimated posterior mean and variance as a shorthand description of this distribution.  However, numerous computational compromises and imperfect knowledge about other required inputs including the prior distribution, create uncertainties. Here we present a post-hoc methodology for assessing the biases and variances of individual estimates produced by OE. The method is based on simulations that characterize the performance of OE, under different geophysical conditions, as functions of measured radiances. The simulation results are used to t a nonlinear regression model that predicts bias and variance as a function of (dimension-reduced) radiance. We describe the methodology and its rationale, and illustrate using examples from NASA's Orbiting Carbon Observatory 2 (OCO-2) instrument.