Weight structure of the Local Ensemble Transform Kalman Filter: A case with an intermediate atmospheric general circulation model

Abstract

AbstractThe Local Ensemble Transform Kalman Filter (LETKF) computes analysis by using a weighted average of the first‐guess ensemble with surrounding observations within a localization cut‐off radius. Since overlapped observations are assimilated at neighbouring grid points, the LETKF results in spatially smooth weights. This study explores the spatial structure of the weights with the intermediate atmospheric model SPEEDY (Simplified Parameterizations, Primitive Equation Dynamics). Based on the characteristics of the weight structure, we also aim to improve the weight interpolation (WI) method, which we use to compute the weights at coarser reference points and interpolate the weights into higher‐resolution model grid points. The results show that larger localization and sparser observations result in spatially smoother weights. WI is less detrimental when weight patterns are spatially smoother. An advanced WI method with observation‐density‐dependent reference points results in better forecasts than those with uniformly distributed reference points. This improvement may be due to the spatially inhomogeneous localization function realized by the WI method with observation‐density‐dependent reference points. The spatial distribution of the optimal localization scales shows that larger (smaller) localization is beneficial in sparsely (densely) observed regions. The WI method is computationally more efficient with larger ensembles since the additional computational cost for the WI is lower than that for the LETKF.