Objective frequentist uncertainty quantification for atmospheric CO$_2$ retrievals

TL;DR

This paper introduces a new frequentist-based CO$_2$ retrieval method from satellite data that produces well-calibrated confidence intervals, improving upon current probabilistic approaches in terms of coverage and uncertainty quantification.

Contribution

It develops a convex programming approach for atmospheric CO$_2$ retrieval that ensures accurate frequentist confidence intervals and incorporates physical constraints and nuisance variables.

Findings

Proposed intervals achieve desired frequentist coverage.

Operational uncertainties are poorly calibrated in current methods.

Key nuisance variables can significantly reduce uncertainty.

Abstract

The steadily increasing amount of atmospheric carbon dioxide (CO$_2$) is affecting the global climate system and threatening the long-term sustainability of Earth's ecosystem. In order to better understand the sources and sinks of CO$_2$, NASA operates the Orbiting Carbon Observatory-2 & 3 satellites to monitor CO$_2$ from space. These satellites make passive radiance measurements of the sunlight reflected off the Earth's surface in different spectral bands, which are then inverted in an ill-posed inverse problem to obtain estimates of the atmospheric CO$_2$ concentration. In this work, we propose a new CO$_2$ retrieval method that uses known physical constraints on the state variables and direct inversion of the target functional of interest to construct well-calibrated frequentist confidence intervals based on convex programming. We compare the method with the current operational retrieval procedure, which uses prior knowledge in the form of probability distributions to regularize the problem. We demonstrate that the proposed intervals consistently achieve the desired frequentist coverage, while the operational uncertainties are poorly calibrated in a frequentist sense both at individual locations and over a spatial region in a realistic simulation experiment. We also study the influence of specific nuisance state variables on the length of the proposed intervals and identify certain key variables that can greatly reduce the final uncertainty given additional deterministic or probabilistic constraints, and develop a principled framework to incorporate such information into our method.