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

Abstract Analyzing retrieval accuracy and precision is an important element of space‐based CO2 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 CO2 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 CO2 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 Xco2 retrievals (with errors up to 0.17–0.28 ppm and 1.4–1.7 ppm, respectively, at SNR = 400). In situ measurements of CO2 are needed to further our understanding of this issue and related implications.