A Filtered Model of Tropical Wave Motions

Abstract

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 approximation involves the neglect of the (∂ v /∂ 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 long wave model, based on an approximation of the (∂ v /∂ t ) term rather than its complete neglect. 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 long wave 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.