LAUSR

Numerical simulations are carried out using the WRF model to explicitly calculate the ratio of orographic gravity wave drag (GWD) in the presence of a stable boundary layer (BL) to the inviscid drag in its absence, either obtained from inviscid WRF simulations or estimated using an analytical linear model. This ratio is represented as a function of three scaling variables defined as ratios of the BL depth to the orography width, height, and stability height scale of the atmosphere. All results suggest that the GWD affected by the stable BL, D_BL, is inversely proportional to the BL depth h_BL, roughly following D_BL ~ h_BL^(-2). The scaling relations are calibrated and tested using a multilinear regression applied to data from the WRF simulations, for idealised orography and inflow atmospheric profiles derived from reanalysis, representative of Antarctica in austral winter, where GWD is expected to be especially strong. These comparisons show that the scaling relations where the drag is normalised by the analytical inviscid estimate work best. This happens because stable BL effects reduce the amplitude of the waves above the BL, making their dynamics more linear. Knowledge of the BL depth and orography parameters is sufficient to obtain a reasonable correction to the inviscid drag without needing additional information about the wind and stability profiles. Since the drag currently available from numerical weather prediction model parametrizations comes from linear theory uncorrected for BL effects, the results reported here may be applied straightforwardly to improve those parametrizations.