Forward Model Emulator for Atmospheric Radiative Transfer Using Gaussian Processes And Cross Validation

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 (UQ) effort involves 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 orders of magnitude faster computational time. 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 is mapping 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.

美国国家航空航天局（NASA）轨道碳观测站-2（Orbiting Carbon Observatory-2，OCO-2）卫星任务开展的大气二氧化碳（CO₂）遥感研究，及其相关的不确定性量化（Uncertainty Quantification，UQ）工作，需要对当前最先进的大气物理模型进行反复评估。大气CO₂反演（即求解逆问题）过程需消耗大量计算资源。本研究提出并实现了一种统计仿真器，用以加速OCO-2大气物理模型的计算流程。我们的方法基于高斯过程（Gaussian Process，GP）回归，借助近期在核流（Kernel Flows）与交叉验证（Cross Validation）领域的研究进展，高效学习高斯过程中的核函数。我们通过在测量误差精度范围内复现OCO-2正演模型（forward model）的行为验证了所提方法的有效性，并进一步在模拟场景中证明：本方法可在将计算时间缩短数个数量级的同时，准确复现OCO-2配置下的CO₂反演性能。该仿真问题具有较高挑战性，因其属于高维任务；且其与算子学习（operator learning）相关，因为待近似的函数是将高维向量映射至另一组高维向量的映射关系。我们提出的方法不仅计算速度快，同时具备极高的精度（相对误差小于1%）。与基于人工神经网络（Artificial Neural Network，ANN）的方法相比，本方法具有可解释性，其高效性源于在工程化且具备强表达能力的核函数族中学习得到核函数。