Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

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