Redefining Uncertainty: A Complete Bayesian Workflow for Ocean Color Remote Sensing

Traditional satellite ocean color algorithms for chlorophyll-a and inherent optical property retrieval rely on deterministic regression models that typically produce single-point predictions without explicit uncertainty quantification. The absence of uncertainty awareness undermines in-situ/model match-ups, reduces predictive reliability, and ultimately erodes user confidence. In the present study, I address this limitation by demonstrating how to implement a complete Bayesian workflow applied to the foundational chlorophyll-a retrieval problem. To that end, I use a set of well-established Bayesian modeling tools and techniques to train and evaluate probabilistic models that approximate the underlying data-generating process and yield posterior distributions conditioned on both data and model structure. The posterior distribution is an information-rich construct that can be mined for diverse insights. I develop and compare models of increasing complexity, beginning with a baseline polynomial regression and culminating in a hierarchical partial pooling model with heteroscedasticity. Similar to classical machine learning, model complexity in a Bayesian setting must also be scrutinized for its potential to overfit. This is addressed through efficient cross-validation and uncertainty calibration that exploit the full posterior distribution. Within this framework, the most complex model performed best in terms of out-of-sample uncertainty calibration and generalizability. Persistent localized mismatches across models point to domains where predictive power remains limited. Taken together, these results show how placing uncertainty at the center of inference allows a Bayesian approach to produce transparent, interpretable, and reliable chlorophyll-a retrievals from satellite ocean color data, paving the way for the development of more robust marine ecosystem monitoring products.