Reduction of Spatially Structured Errors in Wide-Swath Altimetric Satellite Data Using Data Assimilation

Sparse Approximation of the Precision Matrices for the Wide-Swath Altimeters

The upcoming technology of wide-swath altimetry from space will deliver a large volume of data on the ocean surface at unprecedentedly high spatial resolution. These data are contaminated by errors caused by the uncertainties in the geometry and orientation of the on-board interferometer and environmental conditions, such as sea surface roughness and atmospheric state. Being highly correlated along and across the swath, these errors present a certain challenge for accurate processing in operational data assimilation centers. In particular, the error covariance matrix R of the Surface Water and Ocean Topography (SWOT) mission may contain trillions of elements for a transoceanic swath segment at kilometer resolution, and this makes its handling a computationally prohibitive task. Analysis presented here shows, however, that the SWOT precision matrix R−1 and its symmetric square root can be efficiently approximated by a sparse block-diagonal matrix within an accuracy of a few per cent. A series of observational system experiments with simulated data shows that such approximation comes at the expense of a relatively minor reduction in the assimilation accuracy, and, therefore, could be useful in operational systems targeted at the retrieval of submesoscale variability of the ocean surface.

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

Wide-swath satellite altimeter observations are contaminated by errors caused by the uncertainties in the geometry and orientation of the on-board interferometer. These errors are strongly correlated across the track, while also having similar error structures in the along-track direction. We describe a method for modifying the geometric component of the error covariance matrix which facilitates accuracy in the removal of the respective error modes from the signal and improves computational efficiency of the data assimilation schemes involving wide-swath altimeter observations. The method has been tested using the Surface Water and Ocean Topography simulator. We show substantial computer cost savings in the pseudo-inversion of the respective error covariance matrix. This efficiency improvement comes with a few per cent error in the approximation of the original covariance model simulating uncertainties in the geometry and orientation of the on-board interferometer.

Effects of Interferometric Radar Altimeter Errors on Marine Gravity Field Inversion

The traditional altimetry satellite, which is based on pulse-limited radar altimeter, only measures ocean surface heights along tracks; hence, leads to poorer accuracy in the east component of the vertical deflections compared to the north component, which in turn limits the final accuracy of the marine gravity field inversion. Wide-swath altimetry using radar interferometry can measure ocean surface heights in two dimensions and, thus, can be used to compute vertical deflections in an arbitrary direction with the same accuracy. This paper aims to investigate the impact of Interferometric Radar Altimeter (InRA) errors on gravity field inversion. The error propagation between gravity anomalies and InRA measurements is analyzed, and formulas of their relationship are given. By giving a group of possible InRA parameters, numerical simulations are conducted to analyze the accuracy of gravity anomaly inversion. The results show that the accuracy of the gravity anomalies is mainly influenced by the phase errors of InRA; and the errors of gravity anomalies have a linear approximation relationship with the phase errors. The results also show that the east component of the vertical deflections has almost the same accuracy as the north component.

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

In the near future, the Surface Water Ocean Topography (SWOT) mission will provide images of altimetric data at kilometric resolution. This unprecedented 2-dimensional data structure will allow the estimation of geostrophy-related quantities that are essential for studying the ocean surface dynamics and for data assimilation uses. To estimate these quantities, i.e., to compute spatial derivatives of the Sea Surface Height (SSH) measurements, the uncorrelated, small-scale noise and errors expected to affect the SWOT data must be smoothed out while minimizing the loss of relevant, physical SSH information. This paper introduces a new technique for de-noising the future SWOT SSH images. The de-noising model is formulated as a regularized least-square problem with a Tikhonov regularization based on the first-, second-, and third-order derivatives of SSH. The method is implemented and compared to other, convolution-based filtering methods with boxcar and Gaussian kernels. This is performed using a large set of pseudo-SWOT data generated in the western Mediterranean Sea from a 1/60 ∘ simulation and the SWOT simulator. Based on root mean square error and spectral diagnostics, our de-noising method shows a better performance than the convolution-based methods. We find the optimal parametrization to be when only the second-order SSH derivative is penalized. This de-noising reduces the spatial scale resolved by SWOT by a factor of 2, and at 10 km wavelengths, the noise level is reduced by factors of 10 4 and 10 3 for summer and winter, respectively. This is encouraging for the processing of the future SWOT data.