Simulation-Based Uncertainty Quantification for Estimating Atmospheric CO$_2$ from Satellite Data

Abstract

Remote sensing of the atmosphere has provided a wealth of data for analyses and inferences in earth science. Satellite observations can provide information on the atmospheric state at fine spatial and temporal resolution while providing substantial coverage across the globe. For example, this capability can greatly enhance the understanding of the space-time variation of the greenhouse gas, carbon dioxide (CO2), since ground-based measurements are limited. NASA's Orbiting Carbon Observatory-2 (OCO-2) collects tens of thousands of observations of reflected sunlight daily, and the mission's retrieval algorithm processes these indirect measurements into estimates of atmospheric CO2. The retrieval is an inverse problem and consists of a physical forward model for the transfer of radiation through the atmosphere that includes absorption and scattering by gases, aerosols, and the surface. The model and other algorithm inputs introduce key sources of uncertainty into the retrieval problem. This article develops a computationally efficient surrogate model that is embedded in a simulation experiment for studying the impact of uncertain inputs on the distribution of the retrieval error. Abstract. Remote sensing of the atmosphere has provided a wealth of data for analyses and 5 inferences in Earth science. Satellite observations can provide information on the atmospheric state 6 at fine spatial and temporal resolution while providing substantial coverage across the globe. For 7 example, this capability can greatly enhance the understanding of the space-time variation of the 8 greenhouse gas, carbon dioxide (CO 2 ), since ground-based measurements are limited. NASA's Or-9 biting Carbon Observatory-2 (OCO-2) collects tens of thousands of observations of reflected sunlight 10 daily, and the mission's retrieval algorithm processes these indirect measurements into estimates of 11 atmospheric CO 2 . The retrieval is an inverse problem and consists of a physical forward model for 12 the transfer of radiation through the atmosphere that includes absorption and scattering by gases, 13 aerosols, and the surface. The model and other algorithm inputs introduce key sources of uncertainty 14 into the retrieval problem. This article develops a computationally efficient surrogate model that is 15 embedded in a simulation experiment for studying the impact of uncertain inputs on the distribution 16 of the retrieval error. 17

Flux towers in the sky: global ecology from space

“…To distinguish real phenomena, and combine observations from multiple sources in model statistical and data assimilation models, the uncertainty of each observation must be well quantified, to balance its influence against other sources of information (Fox et al ., ). Individual satellite observations often have complex sources of random and systematic errors (Hobbs et al ., ) therefore correctly computing the uncertainty becomes all the more complex when using multiple satellite observation records (Liu et al ., ; Fox et al ., ). At the same time, the extraordinary coverage and detail from satellite remote sensing data reduces sources of error that may dominate inference from in situ methods (Saatchi et al ., ; Schimel et al ., ).…”

Accelerated MCMC for Satellite-Based Measurements of Atmospheric CO2

“…While this is a comprehensive way to compute atmospheric radiative transfer, the model is computationally heavy to evaluate and hence is not suitable for Monte Carlo experiments. We ease this problem by following the approach in [16] and use the surrogate forward model by [17] to account for the major sources of error in the retrieval. A more comprehensive look can be found in Appendix A.2, but in short, the state vector used in the surrogate model can be split into four parts:…”

“…As a linear problem would have a unique minimum for the cost function, this suggests that the aerosol parametrization in the model causes problems in the retrieval that might significantly affect the accuracy of retrieved X CO 2 values. This is due to scattering by aerosols being a substantial source of non-linearity in the forward model (as was found for example by [17,20]), which might translate to a non-Gaussian posterior distribution.In addition to the potential effect of aerosol parametrization of the forward model, it was found in [16] that the MCMC on OCO-2 surrogate model has a very low acceptance ratio (number of accepted samples over number of computed samples), and that chains can often converge extremely slowly. These are symptoms of non-linearity, high dimensionality and strong correlations between the parameters in MCMC.…”

“…As a linear problem would have a unique minimum for the cost function, this suggests that the aerosol parametrization in the model causes problems in the retrieval that might significantly affect the accuracy of retrieved X CO 2 values. This is due to scattering by aerosols being a substantial source of non-linearity in the forward model (as was found for example by [17,20]), which might translate to a non-Gaussian posterior distribution.…”

“…where h ∈ R 20 is a pressure weighting function [23] assigning appropriate weights to the CO 2 profile. As noted in [17], the surrogate model does not include several elements of the operational retrieval's state vector, including a temperature profile offset, a water vapor profile scale factor, band-specific dispersion parameters for wavelength offsets, band-specific empirical orthogonal function scale factors, and solar-induced fluorescence (SIF) in the O 2 A-band. As such, the purpose of the surrogate model is to act as a computationally feasible means for quantifying the propagation of uncertainty in input arguments into the algorithm outputs.…”