Ensemble reconstruction of missing satellite data using a denoising diffusion model: application to chlorophyll a concentration in the Black Sea

Satellite observations provide a global or near-global coverage of the World Ocean. They are however affected by clouds (among others), which severely reduce their spatial coverage. Different methods have been proposed in the literature to reconstruct missing data in satellite observations. For many applications of satellite observations, it has been increasingly important to accurately reflect the underlying uncertainty of the reconstructed observations. In this paper, we investigate the use of a denoising diffusion model to reconstruct missing observations. Such methods can naturally provide an ensemble of reconstructions where each member is spatially coherent with the scales of variability and with the available data. Rather than providing a single reconstruction, an ensemble of possible reconstructions can be computed, and the ensemble spread reflects the underlying uncertainty. We show how this method can be trained from a collection of satellite data without requiring a prior interpolation of missing data and without resorting to data from a numerical model. The reconstruction method is tested with chlorophyll a concentration from the Ocean and Land Colour Instrument (OLCI) sensor (aboard the satellites Sentinel-3A and Sentinel-3B) on a small area of the Black Sea and compared with the neural network DINCAE (Data-INterpolating Convolutional Auto-Encoder). The spatial scales of the reconstructed data are assessed via a variogram, and the accuracy and statistical validity of the reconstructed ensemble are quantified using the continuous ranked probability score and its decomposition into reliability, resolution, and uncertainty.