The joint retrieval of surface reflectances and atmospheric parameters in VSWIR imaging spectroscopy is a computationally challenging high-dimensional problem. Using NASA's Surface Biology and Geology mission as the motivational context, the uncertainty associated with the retrievals is crucial for further application of the retrieved results for environmental applications. Although Markov chain Monte Carlo (MCMC) is a Bayesian method ideal for uncertainty quantification, the full-dimensional implementation of MCMC for the retrieval is computationally intractable. In this work, we developed a block Metropolis MCMC algorithm for the high-dimensional VSWIR surface reflectance retrieval that leverages the structure of the forward radiative transfer model to enable tractable fully Bayesian computation. We use the posterior distribution from this MCMC algorithm to assess the limitations of optimal estimation, the state-of-the-art Bayesian algorithm in operational retrievals which is more computationally efficient but uses a Gaussian approximation to characterize the posterior. Analyzing the differences in the posterior computed by each method, the MCMC algorithm was shown to give more physically sensible results and reveals the non-Gaussian structure of the posterior, specifically in the atmospheric aerosol optical depth parameter and the low-wavelength surface reflectances.

翻译：在VSWIR成像光谱中，地表反射率与大气参数的联合反演是一个计算复杂度极高的高维问题。以美国国家航空航天局（NASA）地表生物学与地质学任务为应用背景，反演结果的不确定性对于后续环境应用的可靠性至关重要。尽管马尔可夫链蒙特卡洛（MCMC）方法作为贝叶斯方法在不确定性量化方面具有理想特性，但全维度MCMC反演在计算上难以实现。本研究提出一种基于块状Metropolis的MCMC算法，用于高维VSWIR地表反射率反演。该算法利用前向辐射传输模型的结构特征，实现了可计算的完全贝叶斯推断。我们通过该MCMC算法获得的后验分布，评估了最优估计法的局限性——该方法是当前业务化反演中最先进的贝叶斯算法，虽具有更高计算效率，但其后验表征依赖于高斯近似。通过对两种算法所得后验分布的差异分析表明，MCMC算法能给出更具物理合理性的结果，并揭示了后验分布的非高斯结构，主要体现在大气气溶胶光学厚度参数和低波长地表反射率参数中。