An enhanced ensemble‐based method for computing CNOPs using an efficient localization implementation scheme and a two‐step optimization strategy: formulation and preliminary tests

Abstract

The ensemble‐based methods for computing conditional nonlinear optimal perturbations (CNOPs) often contain a localization implementation scheme; its computer implementation is very expensive because of huge memory usage or costly repeated calculations. As a result, the lack of efficient algorithms limits the applications of CNOP. To address this issue, an efficient new localization implementation scheme is proposed in this article. The main ideas are to utilize the correlation matrix and to approximate it by a set of selected Gaussian random samples. An enhanced ensemble‐based method is then proposed using the new localization scheme and a newly proposed two‐step optimization strategy. The proposed approach results in a significant speed‐up for overall optimization algorithms for computing the CNOPs and can be applied to complicated nonlinear models. Numerical experiments with a nonlinear model of the viscous Burgers equation show that the proposed new method produces comparable solutions against an existing ensemble‐based method and an adjoint‐based one for computing the CNOPs. In terms of the net growth ratio of norm square, the proposed method slightly outperforms these two existing methods. On the other hand, our numerical experiments show that the proposed method has an advantage on the memory usage and computational cost, which particularly demonstrates its high potential in predictability or sensitivity studies of operational prediction models. Another group of assimilation experiments conducted using the T21L3 quasi‐geostrophic (QG) model further demonstrates its potential for broader applications.