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Published March 2017 | Published
Journal Article Open

Assessing accuracy and precision for space-based measurements of carbon dioxide: An associated statistical methodology revisited


Analyzing retrieval accuracy and precision is an important element of space‐based CO_2 retrievals. However, this error analysis is sometimes challenging to perform rigorously because of the subtlety of Multivariate Statistics. To help address this issue, we revisit some fundamentals of Multivariate Statistics that help reveal the statistical essence of the associated error analysis. We show that the related statistical methodology is useful for revealing the intrinsic discrepancy and relation between the retrieval error for a nonzero‐variate CO_2 state and that for a zero‐variate one. Our study suggests that the two scenarios essentially yield the same‐magnitude accuracy, while the latter scenario yields a better precision than the former. We also use this methodology to obtain a rigorous framework systematically and explore a broadly used approximate framework for analyzing CO_2 retrieval errors. The approximate framework introduces errors due to an essential, but often forgotten, fact that a priori climatology in reality is never equal to the true state. Due to the nature of the problem considered, realistic numerical simulations that produce synthetic spectra may be more appropriate than remote sensing data for our specific exploration. As highlighted in our retrieval simulations, utilizing the approximate framework may not be universally satisfactory in assessing the accuracy and precision of X_(co_2) retrievals (with errors up to 0.17–0.28 ppm and 1.4–1.7 ppm, respectively, at SNR = 400). In situ measurements of CO_2 are needed to further our understanding of this issue and related implications.

Additional Information

©2017. The Authors. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. Received 10 OCT 2016. Accepted 16 FEB 2017. Accepted article online 24 FEB 2017. Published online 29 MAR 2017. We gratefully acknowledge the helpful comments/suggestions from three anonymous reviewers and the Editor. We thank Paul O. Wennberg, John Worden, Vijay Natraj, Michael Line, King‐Fai Li for useful comments/discussions, and Le Kuai for providing the model used in this study. This research is supported in part by the Orbiting Carbon Observatory (OCO‐2) project, a NASA Earth System Science Pathfinder (ESSP) mission, and JPL P765982 grant to the California Institute of Technology.

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