Idealized study of representing spatial and temporal variations in the error contribution of surface emissivity for assimilating surface‐sensitive microwave radiance observations over land

Abstract The assimilation of surface‐sensitive microwave radiance observations over land can improve numerical weather prediction accuracy at Environment and Climate Change Canada. However, the benefits of these observations are limited by large errors in surface emissivity and skin temperature, along with challenges accounting for these errors in the data assimilation system. Typically, the contribution of surface emissivity error is treated as a deficiency in the observation operator and represented by inflating a fixed observation error covariance matrix ( R ). However, this study demonstrates the error contributions of surface emissivity in observation space for each radiance observation profile can vary substantially due to variations in the surface emissivity Jacobians, even if the surface emissivity error covariances are fixed. An approach is introduced to account for this variability by representing the surface emissivity errors in the background error covariance matrix ( B ) and including surface emissivity as an additional analysis variable. Using an idealized one‐dimensional variational assimilation framework, the approach is compared with a reference experiment that uses a fixed R to represent the average error contribution of surface emissivity. The proposed approach results in up to 20% and 35% greater error reduction in the mid–lower tropospheric air temperature and skin temperature analyses, respectively, when compared to the reference experiment. Both methods would be mathematically equivalent in estimating air and skin temperatures if the variations in the error contribution of surface emissivity were fully represented within the R in the reference approach, which may require significant technical changes to the assimilation system. However, additional benefits of the proposed approach could potentially be realized in a 4D‐EnVar assimilation system by propagating the updated surface emissivity and within the outer loop of an incremental formulation. Additionally, it is demonstrated that well‐represented background error correlations between air and skin temperatures in B can further improve the error reductions.