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

Abstract:

Equatorial long-wave theory applies where a small horizontal aspect ratio

between meridional and zonal lengthscales 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 spatiotemporal scales (planetary wavenumber |k| < 2), an examination of

meridional geostrophic balance and inertio-gravity waves indicates long-wave

dynamics for a broader range of scales (|k| < 5). A simple prediction is also

presented for this range of scales based on physical and mathematical reasoning.