A Bayesian approach for remote sensing of chlorophyll-a and associated retrieval uncertainty in oligotrophic and mesotrophic lakes

Satellite remote sensing of chlorophyll-a concentration (chla) in oligotrophic and mesotrophic lakes faces un-certainties from sources such as atmospheric correction, complex inherent optical property compositions, and imperfect algorithmic retrieval. To improve chla estimation in oligo-and mesotrophic lakes, we developed Bayesian probabilistic neural networks (BNNs) for the Sentinel-3 Ocean and Land Cover Instrument (OLCI) and Sentinel-2 MultiSpectral Imager (MSI). The BNNs were built using an in situ dataset of oligo-and mesotrophic water bodies (1755 observations from 178 systems; median chla: 5.11 mg m- 3, standard deviation: 10.76 mg m-3) and provide a per-pixel uncertainty percentage associated with retrieved chla. Shifts of oligo-and meso-trophic systems into the eutrophic regime, characterised by higher biomass levels, are widespread. To account for phytoplankton biomass fluctuation, a set of eutrophic lakes (167 observations from 31 systems) were included in this study (maximum chla 68 mg m-3). The BNNs were evaluated through five assessments including single day and time series match-ups with OLCI and MSI. OLCI BNN accuracy gains of >25% and MSI BNN accuracy gains of >15% were achieved in the assessments when compared to chla reference algorithms for oligotrophic waters (chla <= 8 mg m-3). In comparison to the reference algorithms, the accuracy gains of the BNNs decreased as chla and trophic levels increased. To measure the quality of the provided BNN uncertainty estimate, we calculated the prediction interval coverage probability (PICP), Sharpness and mean absolute calibration difference (MACD) metrics. The associated BNN chla uncertainty estimate included the reference in situ chla values for most ob-servations (PICP >= 75%) across the different performance assessments. Further analysis showed that the BNN chla uncertainty estimate was not constantly well-calibrated across different evaluation strategies (Sharpness 1.7-6, MACD 0.04-0.25). BNN uncertainties were used to test two chla improvement strategies: 1) identifying and filtering uncertain chla estimates using scene-specific thresholds, and 2) selecting the most accurate prior atmospheric correction algorithm per individual satellite observation to retain chla with the lowest BNN un-certainty. Both strategies increased the quality of the chla result and demonstrated the significance of uncertainty estimation. This study serves as research on Bayesian machine learning for the estimation and visualisation of chla and associated retrieval uncertainty to develop harmonised products across OLCI and MSI for small and large oligo-and mesotrophic lakes.

Automated summary

In this study, Bayesian probabilistic neural networks (BNNs) were developed for estimating chlorophyll-a concentration (chla) in oligotrophic and mesotrophic lakes. The BNNs provided per-pixel uncertainty percentages and were evaluated through various assessments. The results showed that the BNNs achieved higher accuracy in oligotrophic waters, but the accuracy decreased as nutrient levels increased. The study also demonstrated the importance of uncertainty estimation in improving the quality of the chla result.