The impact of two-dimensional filtering on white noise spectra in SWOT along-track observations

TL;DR

This study demonstrates that two-dimensional filtering and aliasing of white noise can produce red spectra in SWOT along-track observations, affecting interpretation of ocean surface height variability.

Contribution

It introduces a synthetic noise model showing how measurement noise and filtering effects generate observed spectral slopes in SWOT data.

Findings

Red spectra can result from filtering of white noise.

Spectral slope depends on noise level and background signals.

Noise modeling is essential for accurate spectral analysis.

Abstract

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.