An Assessment of the WKBJ Approximation to the Vertical Structure of Linear Mountain Waves: Implications for Gravity-Wave Drag Parameterization

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Abstract
The vertical structure of topographically induced, infinitesimal amplitude internal waves in atmospheres with varying wind and static stability profiles is studied with a numerical model. Despite its simplifications, this model nevertheless retains transient effects and internal reflections that may result from time and vertical variations of the index of refraction. It is shown that these two factors may lead to wave structures differing substantially from those obtained through the WKBJ approximation that neglects them. This is an important finding considering that the WKBJ approximation is always invoked in gravity-wave drag parameterization schemes implemented in virtually all large-scale models today to account for the composite effect of subgridscale topographic disturbances. Although our tests show no overall bias in the momentum flux estimated using the WKBJ approximation, the neglect of transience and internal reflections gives excessively weak or excessively strong WKBJ momentum fluxes ... Abstract The vertical structure of topographically induced, infinitesimal amplitude internal waves in atmospheres with varying wind and static stability profiles is studied with a numerical model. Despite its simplifications, this model nevertheless retains transient effects and internal reflections that may result from time and vertical variations of the index of refraction. It is shown that these two factors may lead to wave structures differing substantially from those obtained through the WKBJ approximation that neglects them. This is an important finding considering that the WKBJ approximation is always invoked in gravity-wave drag parameterization schemes implemented in virtually all large-scale models today to account for the composite effect of subgridscale topographic disturbances. Although our tests show no overall bias in the momentum flux estimated using the WKBJ approximation, the neglect of transience and internal reflections gives excessively weak or excessively strong WKBJ momentum fluxes ...

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