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Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix.When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions. 

Abstract The ensemble forecast dominates the computational cost of many data assimilation methods, especially for high‐resolution and coupled models. In situations where the cost is prohibitive, one can either use a lower‐cost model or a lower‐cost data assimilation method, or both. Ensemble optimal interpolation (EnOI) is a classical example of a lower‐cost ensemble data assimilation method that replaces the ensemble forecast with a single forecast and then constructs an ensemble about this single forecast by adding perturbations drawn from climatology. This research develops lower‐cost ensemble data assimilation methods that add perturbations to a single forecast, where the perturbations are obtained from analogs of the single model forecast. These analogs can either be found from a catalog of model states, constructed using linear combinations of model states from a catalog, or constructed using generative machine‐learning methods. Four analog ensemble data assimilation methods, including two new ones, are compared with EnOI in the context of a coupled model of intermediate complexity: Q‐GCM. Depending on the method and on the physical variable, analog methods can be up to 40% more accurate than EnOI.