A split semi-implicit reformulation of the Bushby-Timpson 10–level model is described. The integration cycle is split into two main parts. Firstly, the dependent variables are advected by the wind using the explicit two-step Lax-Wendroff integration scheme with the grid staggered in time and space. Secondly, these advected values are adjusted to account for the terms that govern the motion of small amplitude inertio-gravity waves in the model, using a combination of an unconditionally stable implicit scheme and a conditionally stable explicit scheme. A novel feature of the scheme is the implicit treatment of only two of the model's ten gravity wave modes. This split semi-implicit scheme is more than four times as efficient as the original explicit scheme designed by Bushby and Timpson. The results of one semi-implicit integration to 36 hours are described and compared with an integration made with Bushby and Timpson's original explicit scheme.
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