Data assimilation for nonlinear systems with a localized weighted ensemble transform Kalman filter

Abstract In the field of data assimilation in geosciences, ensemble Kalman filters are widely used. Although they exhibit significant stability when handling nonlinear systems, they are generally not considered optimal in such cases. An alternative method is the particle filter, which is fully suitable for nonlinear systems but is more complex to apply to high‐dimensional models. To combine the strengths of both filters, we introduce a new localized weighted ensemble transform Kalman filter (LWETKF). Specifically, the LWETKF extends the scalar weight of each particle into a spatially localized vector form, leverages adaptive Gaussian resampling to avoid filter collapse, and retains small‐ensemble stability even in strongly nonlinear regimes. By conducting numerical experiments using the nonlinear Lorenz 96 model, we show that the LWETKF can reduce analysis errors by up to about 23% compared with the local ensemble transform Kalman filter (LETKF) under nonlinearity and maintain robust performance with ensembles as small as 10 members. Comparisons among LWETKF, localized mixture coefficients particle filter (LMCPF), and LETKF demonstrate that the proposed method combines the advantages of the latter two in certain aspects and even provides better performance in some situations. In direct comparisons among LWETKF, LMCPF, and LETKF, the proposed LWETKF consistently achieves similar or better accuracy, especially under limited computational resources. For the Lorenz 96 model, at the same ensemble size, the new filter consistently achieves lower errors than LETKF under both weakly and strongly nonlinear conditions. It also significantly outperforms LMCPF and LETKF when the particle count is small, highlighting its suitability for resource‐constrained scenarios. By incorporating localization, the filter accommodates high‐dimensional models and maintains robustness against strong nonlinearity with limited ensemble sizes, offering promising application prospects in nonlinear data assimilation.