Assessing the Equatorial Long- Wave Approximation: Asymptotics and Observational Data Analysis

Equatorial long- wave theory applies where a small horizontal aspect ratio between meridional and zonal length scales is assumed. In an idealized setting, the theory suggests that ( i) meridional wind is small, ( ii) geostrophic balance holds in the meridional direction, and ( iii) inertio- gravity waves are small in amplitude or `` filtered out.'' In this paper a spectral data analysis method is used to quantitatively assess the spatial and temporal scales on which each of these aspects of long- wave dynamics is observed in reanalysis data. Three different perspectives are used in this assessment: primitive variables, characteristic variables, and wave variables. To define each wave variable, the eigenvectors and theoretical wave structures of the equatorial shallow- water equations are used. Evidence is presented that the range of spatial and temporal scales on which long- wave dynamics holds depends on which aspect of the dynamics is considered. For example, while meridional winds are an order of magnitude smaller than zonal winds over only a very narrow range of spatial scales ( planetary wavenumber jkj& 1), an examination of meridional geostrophic balance and inertio- gravity waves indicates long- wave dynamics for a broader range of scales ( jkj& 4). Asimple prediction is also presented for this range of scales based on physical and mathematical reasoning.