Knowledge-guided mixture density network for chlorophyll-a retrieval and associated pixel-by-pixel uncertainty assessment in optically variable inland waters

Machine learning has been increasingly used to retrieve chlorophyll -a (Chl-a) in optically variable waters. However, without the guidance of physical principles or expert knowledge, machine learning may produce biased mapping relationships, or waste considerable time searching for physically infeasible hyperparameter domains. In addition, most Chl-a retrieval models cannot evaluate retrieval uncertainty when ground observations are not available, and the retrieval uncertainty is crucial for understanding the model limitations and evaluating the reliability of retrieval results. In this study, we developed a novel knowledge -guided mixture density network to retrieve Chl-a in optically variable inland waters based on Sentinel -3 Ocean and Land Color Instrument (OLCI) imagery. The proposed method embedded prior knowledge derived from spectral shape classification into the mixture density network. Compared to another deterministic model, the knowledge -guided mixture density network outputted the conditional distribution of Chl-a given an input spectrum, enabling us to estimate the optimal retrieval and the associated uncertainty. The proposed method showed favorable correspondence with the field Chl-a, with root mean square error (RMSE) of 6.56 mu g/L, and mean absolute percentage error (MAPE) of 43.64 %. Calibrated against Sentinel -3 OLCI spectrum, the proposed method also performed well when applied to field spectrum (RMSE = 4.58 mu g/L, MAPE = 72.70 %), suggesting its effectiveness and good generalization. The proposed method provided the standard deviation of each estimated Chl-a, which enabled us to inspect the reliability of the estimated results and understand the model limitations. Overall, the proposed method improved the Chl-a retrieval in terms of model accuracy and uncertainty evaluation, providing a more comprehensive Chl-a observation of inland waters.