The impact of altimeter sampling patterns on estimates of background errors in a global wave model

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.