The impact of two-dimensional filtering on white noise spectra in SWOT along-track observations
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arXiv
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2026
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| author | Dù, Ryan Shìjié Hell, Momme Lenain, Luc Ardhuin, Fabrice Bôas, A. B. Villas |
| author_facet | Dù, Ryan Shìjié Hell, Momme Lenain, Luc Ardhuin, Fabrice Bôas, A. B. Villas |
| contents | The Surface Water and Ocean Topography (SWOT) mission provides two-dimensional observations of sea surface height (SSH) at unprecedented spatial resolution, enabling exploration of ocean variability down to scales of $O(10~\mathrm{ km})$. At these scales, however, interpreting SSH variability is challenging because ocean dynamical signals overlap with measurement noise, and their respective spectral signatures are not yet fully understood. Recent analyses of SWOT 2-km posting observations have shown that along-track spectra are red, with a power-law-like behavior at small scales and spectral slopes around or steeper than $-1$, with their magnitudes and slopes correlated with SWOT measurement noise. Here, we investigate the hypothesis that the red along-track spectra can arise from two-dimensional filtering and aliasing of spatially uncorrelated (white) noise. Using synthetic experiments, we show that the resulting one-dimensional along-track spectra exhibit red, power-law-like behavior at small scales, consistent with observations. The apparent spectral slope depends on the noise level, its cross-track variability, and the background ocean signal. This finding highlights the importance of carefully accounting for measurement noise and processing effects when interpreting SWOT spectra, and suggests that such a noise model should serve as a baseline null hypothesis for small-scale spectral analyses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14009 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The impact of two-dimensional filtering on white noise spectra in SWOT along-track observations Dù, Ryan Shìjié Hell, Momme Lenain, Luc Ardhuin, Fabrice Bôas, A. B. Villas Atmospheric and Oceanic Physics The Surface Water and Ocean Topography (SWOT) mission provides two-dimensional observations of sea surface height (SSH) at unprecedented spatial resolution, enabling exploration of ocean variability down to scales of $O(10~\mathrm{ km})$. At these scales, however, interpreting SSH variability is challenging because ocean dynamical signals overlap with measurement noise, and their respective spectral signatures are not yet fully understood. Recent analyses of SWOT 2-km posting observations have shown that along-track spectra are red, with a power-law-like behavior at small scales and spectral slopes around or steeper than $-1$, with their magnitudes and slopes correlated with SWOT measurement noise. Here, we investigate the hypothesis that the red along-track spectra can arise from two-dimensional filtering and aliasing of spatially uncorrelated (white) noise. Using synthetic experiments, we show that the resulting one-dimensional along-track spectra exhibit red, power-law-like behavior at small scales, consistent with observations. The apparent spectral slope depends on the noise level, its cross-track variability, and the background ocean signal. This finding highlights the importance of carefully accounting for measurement noise and processing effects when interpreting SWOT spectra, and suggests that such a noise model should serve as a baseline null hypothesis for small-scale spectral analyses. |
| title | The impact of two-dimensional filtering on white noise spectra in SWOT along-track observations |
| topic | Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2604.14009 |