A mesoscale semi‐implicit numerical model

A three‐dimensional semi‐implicit mesoscale numerical model based on the Navier‐Stokes equations is described and tested. Numerical techniques for achieving numerical stability with long time steps are discussed. In simulating flow over mountains the model accurately reproduces the results of an explicit model. Low vertical resolution causes moderate damping of the orographically forced responses, but adjustment rates are not seriously affected. the model is stable with time steps six times those of a similar explicit model and its computational efficiency is about three times greater. A cross‐section version is used to examine the response characteristics. With four layers in the vertical, the phase speeds of external gravity waves with wavelengths 8 Δx to 30 Δx are slowed to 50% to 85% of the analytic phase speeds, respectively. Even so, simulations with eight and sixteen layers show that the semi‐implicit model reproduces the features of simulations with the explicit model and has comparable mass and energy conservation characteristics. Adjustment rates of the mass and momentum fields towards a steady state are studied for mountain wave and jet stream circulations. Despite the reduced gravity wave phase speeds, root‐mean‐square error calculations show very little difference between the semi‐implicit and explicit models. This is attributed to the fact that most of the adjustment is effected by relatively slow internal modes which are not greatly slowed in the semi‐implicit model. the verification that the semi‐implicit model produces adjustments between mass and momentum fields about as well as an explicit model is an important step in ensuring that the semi‐implicit technique can be successfully applied to mesoscale forecasting.