The over-amplification of gravity waves in numerical solutions to flow over topography

The real-time use of high-resolution numerical weather prediction

(NWP) models is now commonplace at operational centers around the

world. However, accurate forecasts of many mesoscale phenomenon remain

elusive. One example is the tendency of models to over-predict the

amplitude of mountain waves. In this talk we will examine how

numerical errors can result in mountain-wave over-amplification in NWP

model forecasts.

Discrete analytic mountain-wave solutions are presented for the

classical problem of cross-mountain flow in an atmosphere with

constant wind speed and stability. Using second-order-accurate finite

differences on an Arakawa "C grid" to model non-hydrostatic flow

over a supposedly well resolved 8Δx-wide mountain can lead to

an over-amplification of the standing mountain wave by as much

as 30%. On the other hand, the same finite-difference model

significantly underestimates the wave amplitude in hydrostatic flow

over an 8Δx-wide mountain. Increasing the accuracy of the

advection scheme to fourth-order significantly reduces the numerical

errors associated with both the hydrostatic and non-hydrostatic

discrete solutions.

We will also consider an example of mountain-wave over-amplification

in a full NWP simulation of TREX IOP 13. It is shown that switching

from second-order advection to fourth-order advection leads to as much

as a 20 m/s decrease in vertical velocity on the lee-side of the

Sierra-Nevada, and that the weaker 4th-order solutions are more

consistent with observations.