A harmonic projection and least–squares method for quantifying Kelvin wave activity

Abstract. A new method for isolating the equatorial and coastal Kelvin wave signal from alongtrack satellite altimetry data is presented and applied to sea level anomaly (SLA) observations in the tropical Indian Ocean. The method consists of sequential projections onto the SLA data, starting with meridional or cross-shore Kelvin wave profiles derived from shallow water theory (y-projections). Next, Fourier basis functions in x-t (along-waveguide distance and time respectively) space with the phase speed ranges of Kelvin and Rossby waves are projected onto the y-projections. After projections in all three dimensions have been carried out, least-squares methods are applied to optimize the non-orthogonal basis function coefficients and minimize the misfit of their along-waveguide forcing and dissipation. Lastly, the westward-propagating (Rossby wave-related) signals are removed, generating a Kelvin wave coefficient K that represents Kelvin wave activity. Along the Indian Ocean equatorial-coastal waveguide, Hovmöller diagrams of K show reduced high-wavenumber noise compared to analogous diagrams of pre-processed sea level anomaly. Results from a Monte Carlo simulation demonstrate that Kelvin wave signals generated a priori can be effectively recovered even when superimposed with strong Rossby waves; the signs of all but the weakest waves are diagnosed correctly in over 90 % of cases. When the method is applied to 21 years of satellite observations and the SLA signal associated with K is removed, the large residual in the equatorial SLA signal has a spatial distribution consistent with wind-forced Rossby waves. The equatorial SLA variability in the western part of the basin is poorly correlated with the SLA field associated with K, as the superimposed SLA profile of Rossby waves can distort the true origin locations of Kelvin waves in the raw SLA field. Therefore, this method offers improved tracking of Kelvin waves compared to the raw SLA dataset, and may provide the opportunity to study weakly nonlinear aspects of these waves by comparison with linear models.