The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations
Amezcua, J. and Williams, P. (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
To link to this article DOI: 10.1002/qj.2391
Timediscretization in weatherandclimate modelsintroduces 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 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 leap-frog scheme is suitable for use in semi-implicit integrations.