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The composite‐tendency Robert–Asselin–Williams ( RAW ) filter in semi‐implicit integrations
Author(s) -
Amezcua Javier,
Williams Paul D.
Publication year - 2014
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.2391
Subject(s) - discretization , filter (signal processing) , stability (learning theory) , truncation (statistics) , nonlinear system , truncation error , limit (mathematics) , computer science , mathematics , algorithm , mathematical analysis , physics , statistics , quantum mechanics , machine learning , computer vision
Time discretization in weather and climate models introduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap‐frog integrations from first‐order to fifth‐order. This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams ( RAW ) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite‐tendency RAW ‐filtered leap‐frog scheme to semi‐implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi‐implicit numerical integrations in both a simple nonlinear stiff system and a medium‐complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite‐tendency RAW ‐filtered leap‐frog scheme is suitable for use in semi‐implicit integrations.