Wide-Swath Altimetric Satellite Data Assimilation With Correlated-Error Reduction

Abstract

For decades now, satellite altimetric observations have been successfully integrated in numerical oceanographic models using data assimilation (DA). So far, sea surface height (SSH) data were provided by one-dimensional nadir altimeters. The next generation Surface Water and Ocean Topography (SWOT) satellite altimeter will provide two-dimensional wide-swath altimetric information with an unprecedented high resolution. This new type of SSH data is expected to strongly improve altimetric assimilation. However, the SWOT data is also expected to be affected by spatially correlated errors and, hence, can not be assimilated as easily as nadir altimeters. The present paper proposes to embed a state-of-the-art correlated-error reduction (CER) method for the SWOT data into an ensemble-based DA scheme. The DA with the new correlated-error reduced-data (CER-data) is implemented and tested in a simple SSH reconstruction problem using artificial SWOT data and a quasi-geostrophic model. The results show that, in an energetic large scale region, the DA with CER-data-in comparison to the classical DA-reduces the root-mean-square-error (RMSE) of the reconstruction in SSH by approximately 10%, in relative vorticity by 5% and in surface currents by 5-10%, and also slightly improves the noise-to-signal ratio and spectral coherence of the SSH signal at mesoscale (100-200 km) but with a small degradation on the large scales (>300 km). In a less energetic region, the DA with CER-data cuts down the RMSE in SSH by more than 50% on average therefore allowing a significantly more accurate reconstruction of SSH at mesoscale in terms of noise-to-signal ratio, spectral coherence, and power spectral density.

Facilitating Inversion of the Error Covariance Models for the Wide-Swath Altimeters

“…The presented effort sheds more light on the structure of P a and provides an opportunity to go beyond the simple assumptions used in [7,8] for filtering of the GOEs from innovations. It is necessary to note that the success of the filtering technique largely depends on the relative magnitudes of other types of errors (such as KaRIN noise, wet/dry atmosphere and model error) that contribute to the innovations.…”

“…where F y is the matrix of the along-track Fourier transform and S q are the positive-definite diagonal marices with the square roots of the LS GOE power spectra shown in Figure 1b. Similar to [7,8], we consider regional applications involving finite pieces of the satellite swath and, therefore, utilize the LS Fourier transform representation by the n y × n y unitary matrix F y .…”

“…This type of projection was used in [7,8] to remove GOEs from simulated SWOT observations under a rather restrictive assumption that the GOE field does not change along the track.…”

“…SSH errors caused by the uncertainties in the interferometer geometry and orientation (hereinafter referred to as geometric and orientation errors, GOEs) provide one of the two major contributions to the overall error budget. Recently, attempts have been made to remove these errors in data assimilation experiments using simulated SWOT data [7,8]. Success of the approach largely depends on the accuracy of the projection of the SSH innovations on the range of GOE covariance matrix as well as on the relative contribution of other types of errors to this projection.…”

Development of an Image De-Noising Method in Preparation for the Surface Water and Ocean Topography Satellite Mission

“…This is obviously due to the spatially correlated component of the errors (see Figure 2), which is not filtered out by any of the methods used here. Other approaches must be used to remove the correlated errors in order to obtain more accurate estimates [33,34].…”