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Abstract:
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The steadily increasing amount of atmospheric carbon dioxide is having an unprecedented impact on the global climate system. In order to better understand the sources and sinks of CO2, NASA operates the Orbiting Carbon Observatory-2 & 3 instruments to monitor CO2 from space. These instruments measure the radiance of the sunlight reflected off the Earth's surface, which is then inverted to obtain CO2 estimates. In this work, we first analyze the current operational retrieval procedure, which uses a prior distribution to regularize the underlying ill-posed inverse problem, and demonstrate that the resulting uncertainties might be poorly calibrated both at individual locations and over a spatial region. To alleviate these issues, we propose a new method that uses known physical constraints and direct inversion of functionals of the CO2 profile to construct well-calibrated frequentist confidence intervals based on convex programming. Furthermore, we study the influence of individual nuisance variables on the length of the intervals and identify certain key variables that can greatly reduce the final uncertainty given additional deterministic or probabilistic constraints.
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