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The present study focuses on the interaction of gravity waves in theatmosphere with the tropopause. As the vertical extent of the latter is smallcompared to the density scale height, wave propagation is described by theTaylor-Goldstein equation as derived from the linearised Boussinesqapproximation. Of particular interest in the construction of gravity waveparameterisations for the upper atmosphere are the transmission and reflectionproperties of the tropopause as these determine the upward fluxes of energy andmomentum carried by internal waves.  A method is presented that decomposes internal waves explicitly into upwardand downward propagating contributions, thus giving direct access totransmission and reflection coefficients of finite regions of non-uniformstratification in a stationary atmosphere. The scheme utilizes a piecewiseconstant approximation for the background stratification and matches up- anddownward propagating plane wave solutions in each layer through physicallymeaningful coupling conditions. As a result, transmission and reflectioncoefficients follow immediately.

Reflection and transmission of gravity waves at non-uniform stratification layers