Quantile-Conserving Ensemble Filters for All-Sky Infrared Radiance Assimilation

Abstract All-sky satellite radiance assimilation faces the challenge of non-Gaussian error distributions, which can be exacerbated by fine model resolutions with better-resolved physical processes. Compared to the ensemble adjustment Kalman filter (EAKF) that assumes Gaussian error distributions, the nonlinear rank histogram filter (RHF) uses a rank histogram distribution to represent the observation prior. The rank histogram filter with probit transform regression (QCF_RHF) further allows nonlinear regression updates by performing regression of observation increments onto state variables in a transformed space. The performance of the three ensemble filters is investigated in an observing system simulation experiment with noncycled assimilation of synthetic Geostationary Interferometric Infrared Sounder (GIIRS) all-sky infrared radiances, with model resolution increasing from 7.5 to 1.5 km and then to 300 m. Single observation assimilation experiments demonstrate the advantages of QCF_RHF over EAKF and RHF for both Gaussian and non-Gaussian error distributions, especially for the common all-sky situation with cloudy observations but mostly clear-sky ensemble priors. Consistent results are obtained for the analyses assimilating all synthetic observations from GIIRS channel 1025 and subsequent ensemble forecasts. For state variables of specific humidity, temperature, and wind speed, QCF_RHF produces improved analyses, better captures posterior distributions, and yields smaller forecast errors till 1-h lead time than EAKF and RHF. The advantages of QCF_RHF over EAKF and RHF become more prominent as the horizontal grid spacing decreases from 7.5 to 1.5 km and then to 300 m due to more non-Gaussian error distributions and nonlinear forward operators. Significance Statement All-sky radiance assimilation has shown great promise for improving numerical weather prediction. However, it faces significant challenges due to non-Gaussian error distributions and nonlinear error growth, which can be exacerbated with increased model resolutions and better-resolved nonlinear physical processes. Commonly used data assimilation methods for high-dimensional dynamical systems, such as the ensemble Kalman filter, often assume linear processes and Gaussian error distributions. To address these limitations, a nonlinear ensemble filter that does not assume Gaussian error distributions and enables nonlinear updates of state variables is investigated here. This nonlinear ensemble filter outperforms the widely used ensemble Kalman filter for both Gaussian and non-Gaussian error distributions.