Score-based Diffusion Models for the Space-Time Interpolation of Sea Surface Turbidity

This study explores the application of score-based generative diffusion models for mapping sea surface Suspended Particulate Matter (SPM) of the Dutch Wadden Sea using satellite-derived images, focusing on their comparative efficacy against state of the art deterministic methods such as 4DVarNet, UNet, and DInEOF. Although deterministic deep learning approaches provide robust reconstructions, they often struggle with probabilistic uncertainty and extreme values of overly complex real-world scenarios. Our findings indicate that diffusion models, when conditioned with 4DVarNet and DInEOF, offer improved performance over DInEOF and UNet. Although slightly less accurate than 4DVarNet, this discrepancy is not a significant concern, as the primary goal extends beyond merely maintaining accurate reconstructions. Instead, our approach aims to provide a comprehensive view of the distribution through the samples. Our results show that diffusion models are able to generate the tail of the distribution, thereby capturing extreme values more effectively. And they assist in identifying areas of high uncertainty, particularly when the samples show inconsistencies. Furthermore, unlike typical 2D diffusion models, this study employs a 3D approach, incorporating 2D spatial and 1D temporal dimensions, allowing the model to capture dynamic physical changes over time and enhance the accuracy of probabilistic predictions of the image time series.