The Effect of Spatially Correlated Errors on Sea Surface Height Retrieval from SWOT Altimetry

Abstract

The upcoming technology of wide-swath altimetry from space will enable monitoring the ocean surface at 4–5 times better spatial resolution and 2–3 times better accuracy than traditional nadir altimeters. This development will provide a chance to directly observe submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. Taking full advantage of this opportunity requires correct treatment of the correlated SSH errors caused by uncertainties in environmental conditions beneath the satellite and in the geometry and orientation of the on-board interferometer. These observation errors are highly correlated both along and across the surface swath scanned by the satellite, and this presents a significant challenge for accurate processing. In particular, the SWOT precision matrix has off-diagonal elements that are too numerous to allow standard approaches to remain tractable. In this study, we explore the utility of a block-diagonal approximation to the SWOT precision matrix in order to reconstruct SSH variability in the region east of Greenland. An extensive set of 2dVar assimilation experiments demonstrates that the sparse approximation proposed for the precision matrix provides accurate SSH retrievals when the background-to-observation error ratio ν does not exceed 3 and significant wave height is below 2.5 m. We also quantify the range of ν and significant wave heights over which the retrieval accuracy of the exact spatially correlated SWOT error model will outperform the uncorrelated model. In particular, the estimated range is found to be substantially wider (ν<10 with significant wave heights below 8–10 m), indicating the potential benefits of further improving the accuracy of approximations for the SWOT precision matrix.

SWOT Level 2 Lake Single-Pass Product: The L2_HR_LakeSP Data Preliminary Analysis for Water Level Monitoring

“…At the time of writing, the L2_HR_LakeSP product v.1.1 included just the lake polygons retrieved from the SWOT data collected in April 2023 (Figure 1). These data were captured during the one-day repeat cycle of the CalVal phase of SWOT [18,32], which occurred from April to July 2023. Thus, the dataset is characterized by a high temporal resolution, including at least one observation per day for each lake considered in this research.…”

Block-Circulant Approximation of the Precision Matrix for Assimilating SWOT Altimetry Data

“…The respective SSH observation grid points will be enumerated by indices 1 ≤ i ≤ n x and 1 ≤ j ≤ n y . In contrast to our previous studies [25,28] focused on the approximation of the SWOT precision matrix at submesoscale wavelengths below 100 km, here we consider scale-independent approximations of R −1 and G based on their block-circulant representation. In addition, since the residual atmospheric error R a is several times smaller than R s in magnitude [29,30], in this study, we neglect its contribution to R.…”

“…In [25,28], it has been shown that R −1 and its symmetric square root R −1/2 could be well-approximated by sparse block-diagonal matrices if the target SSH features are at the submesoscale and are characterized by flat spectra at spatial frequencies above 0.01 km −1 . This approximation is suitable for use in multi-scale DA methods (e.g., [31,32]) at the second stage, after mesoscale features have already been assimilated.…”

“…The diagonal elements of K depend non-linearly on the distance of the SSH grid cell from nadir (i.e., across the swath) and on local SWH values, which can vary considerably along the swath (Figure 1, upper panel). However, the non-linearity of the SWH projection on the KaRIn noise error variance (Figure 5 of [8]) dumps spatial variations of diag(K) in such a way that even a transition from calm (SWH∼1 m) conditions to stormy (SWH∼5 m) conditions along the swath (Figure 1) results only in a moderate (10-20%) deviation of K from the block-diagonal pattern described by Equation (8) [28]. Furthermore, estimation of the BC deviation parameter from Equation (7),…”

“…Evaluation of BC performance was done via the OSSE technique similar to the one used in [28] for assessment of the block-diagonal approximation: ensembles of 2D variational (2DVAR) DA experiments have been made by randomly perturbing "true" SSH distributions to simulate background states and observations with prescribed perturbation statistics. Misfits between the "true" background states and those retrieved from the DA runs as well as the computational cost of the retrievals with BC approximation were then compared with the retrievals obtained using a simplified (uncorrelated) and exact observational error statistics.…”