Modelling wide-swath altimeter observation-error correlations with a regularised diffusion operator
Abstract
Unaccounted-for observation-error correlations have long been known to be detrimental to the quality of atmospheric and ocean analyses produced by data assimilation (DA) systems. While progress has been made over the past decade on modelling inter-channel error correlations, modelling spatial error correlations remains a challenge for large datasets. Common strategies for mitigating the harmful effects of spatial error correlations, such as variance inflation or data thinning, prevent the extraction of valuable small-scale information from the observations. With the emergence of new sources of high-resolution observations, such as those from the Surface Water and Ocean Topography (SWOT) wide-swath altimeter, the need to address this limitation of DA systems has become increasingly pressing.To do so, we consider a diffusion-based observation-error correlation operator, extending previous work on modelling correlated errors in conventional nadir altimeter data. When observation-error correlation length scales are large, the original method can suffer from an excessive sensitivity of the inverse correlation operator to small-scale perturbations. Since actual estimates of observation-error correlations from SWOT suggest the presence of large length scales, a more robust formulation of the method is required. We present a regularised formulation of the diffusion-based correlation operator that eliminates this excessive sensitivity while preserving computational efficiency. We describe the implementation of the operator for a mesh constructed from SWOT observation locations and demonstrate its application in a global ocean DA system. To validate the new formulation, we perform DA experiments with simulated SWOT observations. These experiments confirm that the regularised correlation operator provides an effective, robust and practical approach for representing wide-swath altimeter observation-error correlations in operational ocean DA systems.
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BibTeX
@misc{goux2026modelling,
title = {{Modelling wide-swath altimeter observation-error correlations with a regularised diffusion operator}},
author = {Olivier Goux and Anthony Weaver and Andrea Piacentini},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31409},
eprint = {2610.31409},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05830520v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Modelling wide-swath altimeter observation-error correlations with a regularised diffusion operator
AU - Olivier Goux
AU - Anthony Weaver
AU - Andrea Piacentini
PY - 2026
DA - 2026/10/21
PB - HAL
DO - 10.48550/arxiv.2610.31409
UR - https://hal.science/hal-05830520v1
AB - Unaccounted-for observation-error correlations have long been known to be detrimental to the quality of atmospheric and ocean analyses produced by data assimilation (DA) systems. While progress has been made over the past decade on modelling inter-channel error correlations, modelling spatial error correlations remains a challenge for large datasets. Common strategies for mitigating the harmful effects of spatial error correlations, such as variance inflation or data thinning, prevent the extraction of valuable small-scale information from the observations. With the emergence of new sources of high-resolution observations, such as those from the Surface Water and Ocean Topography (SWOT) wide-swath altimeter, the need to address this limitation of DA systems has become increasingly pressing.To do so, we consider a diffusion-based observation-error correlation operator, extending previous work on modelling correlated errors in conventional nadir altimeter data. When observation-error correlation length scales are large, the original method can suffer from an excessive sensitivity of the inverse correlation operator to small-scale perturbations. Since actual estimates of observation-error correlations from SWOT suggest the presence of large length scales, a more robust formulation of the method is required. We present a regularised formulation of the diffusion-based correlation operator that eliminates this excessive sensitivity while preserving computational efficiency. We describe the implementation of the operator for a mesh constructed from SWOT observation locations and demonstrate its application in a global ocean DA system. To validate the new formulation, we perform DA experiments with simulated SWOT observations. These experiments confirm that the regularised correlation operator provides an effective, robust and practical approach for representing wide-swath altimeter observation-error correlations in operational ocean DA systems.
ER -