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On the ensemble‐based linearization of numerical models
Author(s) -
Yaremchuk Max,
Nechaev Dmitri,
Frolov Sergey
Publication year - 2020
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3723
Subject(s) - linearization , computation , factorization , computer science , focus (optics) , sequence (biology) , mathematics , current (fluid) , algorithm , mathematical optimization , nonlinear system , physics , electrical engineering , quantum mechanics , biology , optics , genetics , engineering
Current parallelization trends in computer technology facilitates development of the algorithms that retrieve linear approximations of the model operators and their adjoints from ensembles of model simulations. In this study we address the problem of obtaining exact linearizations in the presence of semi‐implicit numerics of the parent model under realistic constraints on the ensemble size. The method is based on factorization of the model into a sequence of local and non‐local linear operators and employs prior information on the structure of the respective sparse matrices. The performance of the method is tested using 28 perturbed solutions of the shallow‐water equations with a moderate size ( 1 0 4 ) state vector. Numerical experiments have shown feasibility of the approach under relatively general constraints on the structure of the parent model. Because of the substantial expense of the ensemble‐based linearization, special focus is made on the assessment of the optimal frequency of such computations within the time intervals between data injections in typical operational systems.