How to Observe the Gyre to Global-Scale Variability in Satellite Altimetry: Signal Attenuation by Orbit Error Removal

Abstract

It is well known that the orbit error removal procedure in satellite altimetry also attenuates the oceanic signal. With the aim of devising observational strategies for the large-scale oceanic variability and deciphering the signal contents of past results, we have analytically derived formulas analogous to the frequency response functions for commonly used filters in orbit error removal. These include the polynomial orbit error approximations (i.e., the bias-only, linear, and quadratic corrections) and the sinusoidal orbit error approximations (i.e., the purely sinusoidal correction, and the sinusoid-and-bias correction). These are not only useful for satellite altimetry, but for time series analysis as well, where linear or quadratic detrending of a time series before spectral analysis is a common occurrence. It is found that the frequency response function for a polynomial correction is a function of the ratio of wavelength/track length and to retain 90% or more of the signal at a certain wavelength, the ratio must be less than 0.65 (for the quadratic case), 0.90 (linear), and 1.54 (bias-only); whereas the counterpart for a sinusoidal correction is a function of the wavelength and track length separately (rather than their ratio). For wavelengths less than 20 000 km, the linear correction and the purely sinusoidal correction behave similarly, which also holds true for the quadratic and the sinusoid-and-bias corrections. We have also estimated the magnitudes and along-track scales (i.e., the scale sensed by the altimeter along track) of a variety of large-scale variations. For the gyre-scale variability, which can be annual (barotropic and topographic) or interannual [e.g., the 17.5 dyn cm change in 15 years in the North Atlantic observed by Levitus (1990)], the energy containing band is estimated to have an upper limit in along-track wavelength at 6700 km, leading to a strategy of using the quadratic correction with a track length of 10 000 km. For sea-level variations associated with El Niño, the typical along-track wavelength is estimated to be 6700 km or less. Thus perhaps the observational strategy for the gyre-scale variability would suffice here as well, but we recommend using longer tracks (perhaps with the help of the sinusoid-and-bias correction) to gain an extra safety margin. The seasonal cycle in global sea level (which is dominated by the density changes of the upper 200 m, and therefore, is important in the seasonal heat and water exchange) is the most difficult to preserve because of its global scales, which leave considerable energy in the neighborhood where the orbit error has its spectral peak?i.e., around 40 000 km. Nevertheless, one should strive to preserve this signal at wavelengths away from 40 000 km. It is recommended that the sinusoid-and-bias correction be used with a track length of 40 000 km for this purpose. Recent results are reviewed from the signal attenuation perspective, resulting in some interesting observations. In addition, we remark that a way may yet be found to take advantage of the large temporal scale separation between the oceanic signal and the orbit error to distinguish them from each other. With the advent of more and more precise satellite orbit (currently of the order of 50 cm), many interesting results regarding the large-scale sea-level variation may well be forthcoming in the near future.