The accuracy of linear theory for predicting mountain-wave drag: Implications for parametrization schemes

This study focuses on the accuracy of simple methods used in parametrization schemes for predicting the drag due to orographically excited gravity waves (mountain waves). Linear and nonlinear model simulations of flow over a long, low two-dimensional ridge are used to evaluate the importance of internal wave reflection and nonlinearity. A long ridge with a small non-dimensional mountain height and a gentle slope is used so that, in the absence of vertical variations in the background profile of wind and stability, the mountain-wave drag is accurately predicted by linear theory. Simulations conducted for simple idealised profiles in which the background stability has a two-layer (troposphere stratosphere) structure show that whilst the drag is accurately predicted by linear solutions, interference effects due to partial wave reflection can alter the drag significantly. Estimates of the drag which are based solely on low-level measurements of wind and stability, such as those in current operational mountain-wave parametrizations, cannot account for this effect. Results from simulations based on more complex realistic profiles, obtained from both radiosondes and a forecast model, show that the linear and nonlinear drag predictions can differ significantly. This implies that linear solutions can be inaccurate even when they are calculated for the full atmospheric profile (rather than being based on low-level average quantities). It is hypothesised that, in this case, the nonlinearity is due to resonant triad interactions which occur when there are oscillations in the Scorer parameter with a wavelength half that of the dominant vertically propagating mountain wave. The implications of the results for mountain-wave drag parametrization are discussed. (C) Crown Copyright 2010. Published by John Wiley & Sons, Ltd.