The Overamplification of Gravity Waves in Numerical Solutions to Flow over Topography

The tendency of high-resolution numerical weather prediction (NWP) models to overpredict the strength of vertically propagating mountain waves is explored. Discrete analytic mountain-wave solutions are presented for the classical problem of cross-mountain flow in an atmosphere with constant wind speed and stability. Time-dependent linear numerical solutions are also obtained for more realistic atmospheric structures. On one hand, using second-order-accurate finite differences on an Arakawa C grid to model nonhydrostatic flow over what might be supposed to be an adequately resolved 8 Delta x-wide mountain can lead to an overamplification of the standing mountain wave by 30%-40%. On the other hand, the same finite-difference scheme underestimates the wave amplitude in hydrostatic flow over an 8 Delta x-wide mountain. Increasing the accuracy of the advection scheme to the fourth order significantly reduces the numerical errors associated with both the hydrostatic and nonhydrostatic discrete solutions. The Coupled Ocean-Atmosphere Mesoscale Prediction System (COAMPS) model is used to generate two 70-member ensemble simulations of a mountain-wave event during the Terrain-Induced Rotor Experiment. It is shown that switching from second-order advection to fourth-order advection leads to as much as a 20 m s(-1) decrease in vertical velocity on the lee side of the Sierra Nevada, and that the weaker fourth-order solutions are more consistent with observations.