Multivariate localization functions for strongly coupled data; assimilation in the bivariate Lorenz ’96 system | CU Experts

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 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 non-negative definite localization matrices, which are suitable for use in 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 analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiment the multivariate Gaspari-Cohn function leads to better performance than any of the other localization functions.;

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