Frequency and wavenumber spectra of global sea surface height variability from satellite and in situ data

Frequency and wavenumber spectra of basic variables in geophysical fluid dynamics have been the subject of many outstanding theoretical works but, until recently, observations have been of relatively limited scope. Most famous theoretical results derive log-log wavenumber spectral slopes of -5/3 or -3 for kinetic energy. Satellite records of surface ocean variability have now reached the length of about two decades and can provide the ultimate test of existing theories as well as material for the derivation of spectral forms from observations. In this work, variability of sea surface height is characterized using fifteen years of altimetric data from the Topex/Poseidon, ERS-1/2, Jason and Envisat missions. Multi-taper frequency and wavenumber spectra are calculated for sea surface heights from mono-mission along-track data and merged gridded products. Comparisons are made with frequency spectra from the global tide gauge network to estimate variability at frequencies unsampled by altimetry and to verify energy levels at common frequencies. Geographic regions of common spectral shape are identified, including broad regions of roughly ω- 2 decay probably associated with high eddy energy. An immediate practical application of this work is in modeling effective observational error for ocean data assimilation schemes.