The composite-tendency RAW filter in semi-implicit integrations

1 The time discretization in weather and climate models introduces truncation errors that limit 2 the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude 3 errors in leapfrog integrations from first-order to fifth-order. This improvement is achieved by 4 replacing the Robert–Asselin filter with the RAW filter and using a linear combination of the 5 unfiltered and filtered states to compute the tendency term. The purpose of the present paper is 6 to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A 7 theoretical analysis shows that the stability and accuracy are unaffected by the introduction of 8 the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both 9 a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model, 10 ∗Corresponding author address: Javier Amezcua, Department of Meteorology, University of Reading, Earley Gate, Reading, RG6 6BB, UK E-mail: [email protected]