Accurate Global Atmospheric State Analysis Using Objective Error Statistics Including Observation Error Dependence on Water Substance Field

Abstract Atmospheric state analysis is a difficult scientific problem but essential for atmospheric sciences. Data assimilation can generate accurate analyses by integrating information on the atmospheric state using probability density functions (PDFs), where the Gaussian approximation is typically used and PDFs are described by error covariance matrices (ECMs). However, ECMs have been estimated empirically, and dependency of the ECMs on meteorological conditions (flow) is only partially represented. These limit atmospheric state analysis accuracy. This is especially problematic for water substance‐sensitive microwave radiances (WS‐MWRs) because of their strong flow dependence. We objectively estimated ECMs of all data including flow‐dependence of the ECMs of WS‐MWRs. Since the ECM of each data is a component of one ECM representing one joint PDF as a whole, it is theoretically better to objectively estimate ECMs of all data, not just a particular data. For WS‐MWRs, we categorized flow into four using water substance amount and estimating an ECM for each category. Numerical experiments using the new ECMs on an operational global numerical weather prediction system show the followings. The new error standard deviations are generally smaller than those of empirical. Standard deviations and interchannel correlations of observation errors of WS‐MWRs increase with water substance amount. The effects of WS‐MWRs on analysis were approximately doubled. The analysis fields differ systematically such as increase of low‐level clouds over cold oceans. The forecast accuracy improved with 95% statistical significance up to 9%. Both the flow dependence of correlation and variance of WS‐MWRs contributed to the improvement of forecast accuracy.