Reconstruction of missing satellite data using a Probabilistic Denoising Diffusion Model applied to chlorophyll a concentration

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 study, 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 quality of the reconstruction is assessed using independent test data. 

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.

The diffusion method compared favorably against the U-Net DINCAE. The RMSE of the reconstructed data using the denoising diffusion model was smaller than the corresponding reconstruction of DINCAE. The main advantage of the diffusion model is, however, the ability to reproduce an ensemble of possible reconstructed conditions on the available data. Each of these reconstructions contains small-scale information comparable to the scales of variability in the original data, avoiding a common problem where the results of U-Net and autoencoders produce images that are too smooth, as the information on small scales can typically not be recovered under clouds with a certain extent. The overall conclusion is robust when applying this technique to other areas of the Black Sea.

The ensembles of reconstructed data generated by the diffusion model can be used, for example, in the detection of gradients and fronts in the satellite images or in the estimation of the error in derived quantities, where information on how the error is correlated in space is also needed.