The Sea Surface Height Spectrum of Internal Waves

Abstract Internal waves and geostrophic motions contribute to sea surface height (SSH) variability at scales order 100 km and smaller. Although geostrophic motions have a well‐defined contribution in SSH, the internal wave contribution is complex and small enough to be confounded with noise. This has impeded attempts to separate internal wave effects from geostrophic signals in SSH measurements. Shipboard acoustic doppler current profiler (ADCP) data combined with along‐track satellite altimetry are used to estimate the internal‐wave component of the SSH wavenumber spectrum in the southeast tropical Pacific. A modified wave‐vortex kinetic energy (KE) decomposition in combination with linear wave theory and the Garrett‐Munk model are used to convert the ADCP‐inferred wave KE spectrum into an SSH spectrum representative of the wave continuum. The continuum component explains the SSH spectral slope of this area. The full SSH spectrum is reconstructed as the sum of the contributions from the internal wave continuum, the geostrophically balanced (“vortex”) component, internal tides, and altimeter noise. The SSH spectra of internal tides and altimeter noise are derived from models. The reconstruction recovers 80% of the observed variance at large scales and 60% within the semidiurnal internal tide band. The residual between this reconstruction and the altimetry‐derived spectrum is interpreted as nonstationary internal tidal energy. The nonstationary tide is more energetic than suggested by previous altimeter‐based estimates, highlighting the challenge of extracting geostrophic signals from SSH.