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Diana J. M. Greenslade
Ian R. Young


One of the main limitations to current wave data assimilation systems is the lack of an accurate representation of the structure of the background errors. One method that may be used to determine background errors is the observational method of Hollingsworth and Lönnberg. The observational method considers correlations of the differences between observations and the background. For the case of significant wave height (SWH), potential observations come from satellite altimeters. In this work, the effect of the irregular sampling pattern of the satellite on estimates of background errors is examined. This is achieved by using anomalies from a 3-month mean as a proxy for model errors. A set of anomaly correlations is constructed from modeled wave fields. The isotropic length scales of the anomaly correlations are found to vary considerably over the globe. In addition, the anomaly correlations are found to be significantly anisotropic. The modeled wave fields are then sampled at simulated altimeter observation locations, and the anomaly correlations are recalculated from the simulated altimeter data. The results are compared to the original anomaly correlations. It is found that, in general, the simulated altimeter data can capture most of the geographic and seasonal variability in the isotropic anomaly correlation length scale. The best estimates of the isotropic length scales come from a method in which correlations are calculated between pairs of observations from prior and subsequent ground tracks, in addition to along-track pairs of observations. This method was found to underestimate the isotropic anomaly correlation length scale by approximately 10%. The simulated altimeter data were not so successful in producing realistic anisotropic correlation functions. This is because of the lack of information in the zonal direction in the simulated altimeter data. However, examination of correlations along ascending and descending ground tracks separately can provide some indication of the areas on the globe for which the anomaly correlations are more anisotropic than others.

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Diana J. M. Greenslade
Dudley B. Chelton
, and
Michael G. Schlax


A formalism recently developed for determining the effects of sampling errors on objectively smoothed fields constructed from an irregularly sampled dataset is applied to investigate the relative merits of single and multiple satellite altimeter missions. For small smoothing parameters, the expected squared error of smoothed fields of sea surface height (SSH) varies geographically at any particular time and temporally at any particular location. The philosophy proposed here for determining the resolution capability of SSH fields constructed from altimeter data is to identify smoothing parameters that are sufficiently large to satisfy two criteria: 1) the expected squared errors of the estimates of smoothed SSH over the space–time estimation grid must be either spatially and temporally homogeneous to within some a priori specified degree of tolerance or smaller than some a priori specified threshold, and 2) the space–time estimation grid on which smoothed SSH estimates are constructed must satisfy the Nyquist criteria for the wavenumbers and frequencies included in the smoothed fields.

The method is illustrated here by adopting a specified tolerance of 10% variability and a nominal expected squared error threshold of 1 cm2 to determine the resolution capabilities of SSH fields constructed from 10 single and multiple combinations of altimeter measurements by TOPEX/Poseidon, the ERS Earth Resource Satellites, and Geosat. Because of the lack of coordination of the orbit configurations of these satellites (different repeat periods and different orbit inclinations), the mapping resolution capabilities of the combined datasets are not significantly better than those of fields constructed from TOPEX/Poseidon data alone. The benefits of coordinated multiple missions are demonstrated by consideration of several multiple combinations of 10-, 17-, and 35-day orbit configurations.

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