An Uncertainty Quantification Framework for the Orbiting Carbon Observatory-2 Mission

A Bayesian approach to inference in atmospheric remote sensing, where the measurements are functions of the quantities of interest, uses the posterior distribution of the atmospheric state and includes the posterior covariance matrix as a measure of uncertainty. This optimal estimation paradigm is implemented in a number of remote sensing applications, including the Orbiting Carbon Observatory-2 (OCO-2) Level 2 (L2) retrieval algorithm. Each implementation of a retrieval algorithm requires numerous design choices, such as state vector configuration and prior distributions. These choices will impact the true uncertainty, which we define as the distribution of the retrieval error, and the adequacy of the retrieved posterior covariance as a measure of that true uncertainty.

We develop a surrogate forward model and retrieval to investigate the impact of these implementation choices on both the true and reported retrieval uncertainties. The surrogate model uses key aspects of the OCO-2 L2 forward model but is of reduced complexity to allow for fast computation and strict control over implementation choices. The surrogate model is embedded into a Monte Carlo framework that allows stochastic simulation from prescribed distributions of the true atmospheric state and of selected retrieval algorithm inputs. The bias and error covariance of the retrieved state estimate and functions of it, such as the profile-weighted average CO₂ mixing ratio, X_CO2, summarize the uncertainty and can be compared to the OCO-2 L2 retrieval’s reported posterior covariance. We illustrate these figures of merit in the presence of misspecification of various components of the atmospheric state vector.