| Summary: | Carbon dioxide (CO2) and methane (CH4) are two most significant anthropogenic greenhouse gases contributing to climate change and global warming. Indirect remote sensing measurements of atmospheric concentrations of these gases are crucial for monitoring man-made emissions and understanding their effects and related atmospheric processes. The reliability of these studies depends largely on robust uncertainty quantification of the measurements, which provides rigorous error estimates and confidence intervals for all results. The main goal of this work is to develop and implement rigorous, robust and computationally efficient means of uncertainty quantification for atmospheric remote sensing of greenhouse gases. We consider both CO2 measurements by NASA’s Orbiting Carbon Observatory 2 (OCO-2) and CH4 measurements by Sodankylä Arctic Space Center’s Fourier Transform Spectrometer (FTS), the latter being studied from the perspectives of both individual measurements, and the entire time series from 2009-2018. Our approach leverages recent mathematical results on dimension reduction to produce novel algorithms that are a step towards thorough and efficient operational uncertainty quantification in the field of atmospheric remote sensing. Mathematically, the process of inferring gas concentrations from indirect measurements is an ill-posed inverse problem, meaning that a well-defined solution doesn't exist without proper regularization. Bayesian approach utilizes probability theory to provide a regularized solution to the inverse problem as a posterior probability distribution. The posterior distribution is conventionally approximated using a Gaussian distribution, and results are reported as the mean of the distribution as a point estimate, and the corresponding variance as a measure of uncertainty. In reality, due to non-linear physics models used in the computations, the posterior is not well approximated by a Gaussian distribution, and ignoring its actual shape can lead to unpredictable errors and inaccuracies in ...
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