Optimal Estimation Versus MCMC for $$\mathrm{{CO}}_{2}$$ CO 2 Retrievals

Jenny Brynjarsdottir (), Jonathan Hobbs (), Amy Braverman () and Lukas Mandrake ()
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Jenny Brynjarsdottir: Case Western Reserve University
Jonathan Hobbs: California Institute of Technology
Amy Braverman: California Institute of Technology
Lukas Mandrake: California Institute of Technology

Journal of Agricultural, Biological and Environmental Statistics, 2018, vol. 23, issue 2, No 7, 297-316

Abstract: Abstract The Orbiting Carbon Observatory-2 (OCO-2) collects infrared spectra from which atmospheric properties are retrieved. OCO-2 operational data processing uses optimal estimation (OE), a state-of-the-art approach to inference of atmospheric properties from satellite measurements. One of the main advantages of the OE approach is computational efficiency, but it only characterizes the first two moments of the posterior distribution of interest. Here we obtain samples from the posterior using a Markov Chain Monte Carlo (MCMC) algorithm and compare this empirical estimate of the true posterior to the OE results. We focus on 600 simulated soundings that represent the variability of physical conditions encountered by OCO-2 between November 2014 and January 2016. We treat the two retrieval methods as ensemble and density probabilistic forecasts, where the MCMC yields an ensemble from the posterior and the OE retrieval result provide the first two moments of a normal distribution. To compare these methods, we apply both univariate and multivariate diagnostic tools and proper scoring rules. The general impression from our study is that when compared to MCMC, the OE retrieval performs reasonably well for the main quantity of interest, the column-averaged $$\mathrm{{CO}}_{2}$$ CO 2 concentration $$X_{\mathrm{{CO}}_{2}}$$ X CO 2 , but not for the full state vector $$\mathbf {X}$$ X which includes a profile of $$\mathrm{{CO}}_{2}$$ CO 2 concentrations over 20 pressure levels, as well as several other atmospheric properties.Supplementary materials accompanying this paper appear on-line.

Keywords: Orbiting Carbon Observatory; OCO-2; Remote sensing; Probabilistic forecast; Proper scoring rules; Carbon cycle science; Continuous ranked probability score; Energy score; PIT histogram; Average rank; Band depth rank; Kullback–Leibler divergence (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13253-018-0319-8

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