Super-resolution of satellite-derived SST data via Generative Adversarial Networks

TL;DR

The study tackles the ill-posed problem of super-resolving satellite-derived SST by framing it as learning the conditional distribution $p_{data}(m{x}|\hat{m{x}})$ and evaluating both an Autoencoder (AE) and a Conditional Generative Adversarial Network (C-GAN) with a residual generator. Training uses anomaly tiles from the Mediterranean and a tiling/merging strategy to cope with limited HR data, balancing adversarial realism with a conditioning loss via $\lambda$ in the objective. Results show that the AE improves large-scale agreement but cannot recover energetic subgrid variability, while the C-GAN restores small-scale statistics and maintains energy across scales at the cost of higher pointwise error and potential spatial-temporal inconsistencies. This demonstrates that conditional generative models can yield more physically realistic, gap-filled SST fields, with future work pointing toward temporally coherent, multi-image SR and diffusion-based methods for improved stability and realism.

Abstract

In this work, we address the super-resolution problem of satellite-derived sea surface temperature (SST) using deep generative models. Although standard gap-filling techniques are effective in producing spatially complete datasets, they inherently smooth out fine-scale features that may be critical for a better understanding of the ocean dynamics. We investigate the use of deep learning models as Autoencoders (AEs) and generative models as Conditional-Generative Adversarial Networks (C-GANs), to reconstruct small-scale structures lost during interpolation. Our supervised -- model free -- training is based on SST observations of the Mediterranean Sea, with a focus on learning the conditional distribution of high-resolution fields given their low-resolution counterparts. We apply a tiling and merging strategy to deal with limited observational coverage and to ensure spatial continuity. Quantitative evaluations based on mean squared error metrics, spectral analysis, and gradient statistics show that while the AE reduces reconstruction error, it fails to recover high-frequency variability. In contrast, the C-GAN effectively restores the statistical properties of the true SST field at the cost of increasing the pointwise discrepancy with the ground truth observation. Our results highlight the potential of deep generative models to enhance the physical and statistical realism of gap-filled satellite data in oceanographic applications.

Figures (12)

• Figure 1: SST fields over the Mediterranean Sea described by (a) L3S data obtained from the supercollection and processing of Sentinel 3A and 3B granules and (b) the Near Real Time gap-free L4 product provided by the Copernicus Marine Service at 1/16° spatial resolution and remapped over a 1/100° regular grid for the day 10/09/2021 (julian day = 253). The regional zooms show the SST gradients over the Levantine Sea to highlight the impact of the interpolation technique.
• Figure 2: The figure shows the model structure of the Conditional GAN (C-GAN) applied to the SST super-resolution problem. The generator network, represented by the parameters $\theta$, consists of a residual network split into an encoder-decoder architecture to map the LR input map, $\hat{\bm{x}}$, into a correction term that is added to the inputs themselves to obtain the HR reconstruction. The HR output, $\hat{\bm{x}}+\bm{f}_\theta(\hat{\bm{x}})$, is then compared to a ground truth data, $\bm{x}$, both in terms of its pointwise MSE and its statistical comparison provided by the discriminator classification prediction, $\bm{d}_\phi(\bullet)$, where $\bullet$ indicates that the discriminator can take in input either the ground-truth data, $\bm{x}$, or the generator reconstruction. The multi-objective adversarial loss functions used to identify the optimal parameters $\theta^*$ and $\phi^*$ of the two networks are defined as shown in panel (b). The Autoencoder (AE) network can be obtained from the same architecture of the Generator by optimizing on the loss function obtained with $\lambda=0$, hence without the discriminator's supervision.
• Figure 3: Probability distribution functions (PDFs) of tile-wise normalized mean squared error, $MSE^{(1)}_\bullet$ and $MSE^{(2)}_\bullet$ panels (a) and (c) computed on the SST field for each tile of the test data, comparing the low-resolution input ($SST_{LR}$, blue), Autoencoder reconstruction ($SST_{AE}$, red), and C-GAN reconstruction ($SST_{GAN}$, black). Panels (b) and (d) are the PDFs of the same two normalized mean squared errors, but computed for the SST gradient magnitude ($\nabla SST_{\bullet}$). The numbers between the brackets in the legend are the averages of the corresponding PDFs.
• Figure 4: Visual comparison of two representative tile reconstructions. Columns correspond to: the HR ground truth (first column), the model output (second column), MSE (third column), gradient field (fourth-fifth columns), and MSE for the SST gradients (sixth column). In each of the two panels, there are three rows, with the LR input data, the the AE, and the C-GAN reconstruction respectively.
• Figure 5: Spectral analysis of SST reconstructions. Panel (a) Power spectral density $E(k)$ of the high-resolution SST field ($E_{HR}$, green solid line) compared with the low-resolution input ($E_{LR}$, blue triangles), the AE reconstruction ($E_{AE}$, red circles), and the C-GAN reconstruction ($E_{GAN}$, black diamonds). Panel (b) Power spectra of the reconstruction errors, $E_{\Delta}(k)$ for all fields. Panel (c) Normalized error spectra, showing the relative deviation of each reconstruction method from the HR reference.