A filtered model of tropical wave motions

Large-scale tropical phenomena such as the Madden-Julian Oscillation (MJO) and El Niño-Southern Oscillation (ENSO) are often studied using the longwave approximation to equatorial β-plane theory. This involves the neglect of the ∂ν/∂t term in the meridional momentum equation. The approximation does not distort Kelvin waves, completely filters inertia-gravity waves, is reasonably accurate for long Rossby waves, but greatly distorts short Rossby waves. Here we present an improvement of the longwave model, based on an approximation of the ∂ν/∂t term rather than its complete neglect.

Writing the governing equations in terms of a single potential field (Ripa's potential) allows for this distinction between the complete or partial neglect of the ∂ν/∂t term. This potential field satisfies a single governing equation which can then be used to develop a new filtered system. The method of approximation presented yields a more realistic flow field than that obtained when the flow is divided into divergent/nondivergent, or geostrophic/ageostrophic pieces.

The new model is similar to the longwave model in the sense that it does not distort Kelvin waves and completely filters inertia-gravity waves. However, it differs from the longwave model in the sense that it accurately describes Rossby waves of all wavelengths, thus making it a useful tool for the study of a wider range of tropical phenomena than just the MJO and ENSO. Although most of the mathematical analysis performed here is in the context of equatorial β-plane theory, we briefly discuss how the ideas can be generalized to spherical geometry. This approach to developing filtered models significantly improves the accuracy and relevance of simple balanced models. -->