Accounting for the three-dimensional nature of mountain waves: parametrizing partial critical level filtering

Gravity waves generated by mountains are multi-scale and three-dimensional. Current orographic gravity wave drag parametrization schemes assume that the waves are two-dimensional, varying only in the vertical and along one horizontal direction. These schemes, therefore, do not represent the process of partial critical level filtering, whereby a portion of the wave spectrum is saturated where the winds parallel to the wavevectors become small. This results in an unrealistic vertical distribution of the momentum flux and forcing of the waves on the mean flow. In this work, a method of accounting for partial critical level filtering in an orographic gravity wave drag parametrization using the full spectrum of realistic topography is presented. This is achieved through binning of the expression for linear hydrostatic surface stresses, computed using Fourier transforms of the subgrid orographic heights within model gridboxes, into wavevector directions. The parametrization is compared with idealised nonlinear simulations of flow over complex topography and is shown to perform well as the number of wavevector direction bins is increased. Implementation of the scheme into the Met Office Unified model is tested using short-range 5-day forecasts. As is found from idealised simulations, the binned scheme leads to less forcing in the troposphere and increased forcing in the stratosphere within the model. The binned scheme is shown to alleviate biases in the upper stratosphere, between 45 km and 65 km, as well as having significant local effects in the troposphere