An Ultrasimple Spectral Parameterization for Nonorographic Gravity Waves

This paper describes a new computationally efficient, ultrasimple nonorographic spectral gravity wave parameterization model. Its predictions compare favorably, though not perfectly, with a model of gravity wave propagation and breaking that computes the evolution with altitude of a full, frequency- and wavenumber-dependent gravity wave spectrum. The ultrasimple model depends on making the midfrequency (hydrostatic, nonrotating) approximation to the dispersion relation, as in Hines' parameterization. This allows the full frequency–wavenumber spectrum of pseudomomentum flux to be integrated with respect to frequency, and thus reduced to a spectrum that depends on vertical wavenumber m and azimuthal direction ϕ only. The ultrasimple model treats the m dependence as consisting of up to three analytically integrable segments, or "parts." This allows the total pseudomomentum flux to be evaluated by using analytical expressions for the areas under the parts rather than by performing numerical quadratures. The result is a much greater computational efficiency. The model performs significantly better than an earlier model that treated the m dependence as consisting of up to two parts. Numerical experiments show that similar models with more than three parts using the midfrequency approximation yield little further improvement. The limiting factor is the midfrequency approximation and not the number of parts.