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The composite-tendency Robert–Asselin–Williams (RAW) filter in semi-implicit integrations

Amezcua, J. and Williams, P. D. ORCID: (2015) The composite-tendency Robert–Asselin–Williams (RAW) filter in semi-implicit integrations. Quarterly Journal of the Royal Meteorological Society, 141 (688). pp. 764-773. ISSN 1477-870X

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To link to this item DOI: 10.1002/qj.2391


The 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 leapfrog integrations from first-order to fifth-order. This improvement is achieved by replacing the Robert--Asselin filter with the RAW filter and using a linear combination of the unfiltered and filtered states to compute the tendency term. The purpose of the present paper is to apply the composite-tendency RAW-filtered leapfrog 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 leapfrog scheme is suitable for use in semi-implicit integrations.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:36768
Publisher:Royal Meteorological Society


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