Forward model emulator for atmospheric radiative transfer using Gaussian processes and cross validation

Abstract. Remote sensing of atmospheric carbon dioxide (CO2) carried out by NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite mission and the related uncertainty quantification effort involve repeated evaluations of a state-of-the-art atmospheric physics model. The retrieval, or solving an inverse problem, requires substantial computational resources. In this work, we propose and implement a statistical emulator to speed up the computations in the OCO-2 physics model. Our approach is based on Gaussian process (GP) regression, leveraging recent research on kernel flows and cross validation to efficiently learn the kernel function in the GP. We demonstrate our method by replicating the behavior of OCO-2 forward model within measurement error precision and further show that in simulated cases, our method reproduces the CO2 retrieval performance of OCO-2 setup with computational time that is orders of magnitude faster. The underlying emulation problem is challenging because it is high-dimensional. It is related to operator learning in the sense that the function to be approximated maps high-dimensional vectors to high-dimensional vectors. Our proposed approach is not only fast but also highly accurate (its relative error is less than 1 %). In contrast with artificial neural network (ANN)-based methods, it is interpretable, and its efficiency is based on learning a kernel in an engineered and expressive family of kernels.