Modern Statistical Methods for Remote Sensing of the Environment

A growing constellation of Earth-observing satellites are providing new opportunities to monitor the planet's changing carbon cycle through global estimates of atmospheric greenhouse gases (GHGs), including carbon dioxide (CO₂). The satellite record provides comprehensive spatial coverage, enabling continental-scale partitioning of the natural carbon exchanges and perturbations due to anthropogenic sources. These carbon cycle science investigations are sensitive to uncertainty in the satellite CO₂ estimates, or retrievals. Satellite retrievals result from a Bayesian formulation that combines observed satellite spectra and prior information on the atmospheric composition with a physical forward model. This retrieval approach incorporates uncertainty in the prior state and measurement noise in the satellite spectra, but other physical parameters are estimated offline without accounting for their additional uncertainty. This presentation will highlight an alternative hierarchical model (HM) formulation that incorporates uncertainty in these parameters and illustrates the impact on the resulting uncertainty in atmospheric CO₂ using data from NASA's Orbiting Carbon Observatory-2 and -3 (OCO-2/3) missions. The comprehensive handling of parameter, geophysical state, and physical model uncertainty in the HM will be demonstrated for a range of geophysical conditions. 

An important use of remote sensing data is in data assimilation where satellite observations are used to constrain a large-scale dynamical system by solving an ultra-high-dimensional inverse problem. While point estimation in such settings is relatively well-established, uncertainty quantification in these problems has been a major open challenge. Here we present a new optimization-based uncertainty quantification framework for computing confidence intervals in large-scale data assimilation. We particularly focus on carbon flux inversion, the problem of inferring the net ecosystem exchange of CO2 by assimilating satellite observations into a global atmospheric transport model. We discuss the algorithmic and computational challenges of computing the confidence intervals in this setting and present custom-made optimizers for solving this problem efficiently. We use this approach to compute one-sided confidence intervals for the Continental US and Northern Hemisphere CO2 fluxes based on simulated GOSAT observations. To the best of our knowledge, these are the first statistically rigorous confidence intervals obtained in a realistic-scale data assimilation problem. 

We introduce a novel framework for scalable and flexible variational inference targeting the non-Gaussian posterior of a latent continuous function or field. For both the prior and variational family, we consider sparse autoregressive structures corresponding to nearest-neighbor directed acyclic graphs. Within the variational family, conditional distributions are modeled with highly flexible normalizing flows. We provide an algorithm for doubly stochastic variational optimization, achieving polylogarithmic time complexity per iteration. Empirical evaluations show that our method offers improved accuracy compared to existing techniques.