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 lengthscales is assumed. In this setting, idealized theories suggest 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". Here 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. 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 only over a very narrow range of spatiotemporal scales (planetary wavenumber |k|≤1), a spectral examination of meridional geostrophic balance and inertio-gravity waves indicates long-wave dynamics exist for a broader range of scales (|k|≤4). A brief comparison between each assessment method and a simple prediction based on physical and mathematical reasoning is also made.