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Mixture density networks (MDNs) have emerged as a powerful tool for estimating water-quality indicators, such as chlorophyll-a (Chl<inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula>) from multispectral imagery. This study validates the use of an uncertainty metric calculated directly from Chl<inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> estimates of the MDNs. We consider multispectral remote sensing reflectance spectra (<inline-formula> <tex-math notation="LaTeX">$R_{\text {rs}}$ </tex-math></inline-formula>) for three satellite sensors commonly used in aquatic remote sensing, namely, the ocean and land colour instrument (OLCI), multispectral instrument (MSI), and operational land imager (OLI). First, a study on a labeled database of colocated in situ Chl<inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$R_{\text {rs}}$ </tex-math></inline-formula> measurements clearly illustrates that the suggested uncertainty metric accurately captures the reduced confidence associated with test data, which is drawn for a different distribution than the training data. This change in distribution maybe due to: 1) random noise; 2) uncertainties in the atmospheric correction; and 3) novel (unseen) data. The experiments on the labeled in situ dataset show that the estimated uncertainty has a correlation with the expected predictive error and can be used as a bound on the predictive error for most samples. To illustrate the ability of the MDNs in generating consistent products from multiple sensors, per-pixel uncertainty maps for three near-coincident images of OLCI, MSI, and OLI are produced. The study also examines temporal trends in OLCI-derived Chl<inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> and the associated uncertainties at selected locations over a calendar year. Future work will include uncertainty estimation from MDNs with a multiparameter retrieval capability for hyperspectral and multispectral imagery.

Per-Pixel Uncertainty Quantification and Reporting for Satellite-Derived Chlorophyll-a Estimates via Mixture Density Networks