Bayesian calibration and uncertainty quantification for a large nutrient load impact model

Nutrient load simulators are large, deterministic, models that simulate the hydrodynamics and biogeochemical processes in aquatic ecosystems. They are central tools for planning cost-efficient actions to fight eutrophication since they allow scenario predictions on impacts of nutrient load reductions to, e.g., harmful algal biomass growth. Due to being computationally heavy, the uncertainties related to these predictions are typically not rigorously assessed though. In this work, we developed a novel Bayesian computational approach for estimating the uncertainties in predictions of the Finnish coastal nutrient load model FICOS. First, we constructed a likelihood function for the multivariate spatio-temporal outputs of the FICOS model. Then, we used Bayesian optimization to locate the posterior mode for the model parameters conditional on long term monitoring data. After that, we constructed a space-filling design for FICOS model runs around the posterior mode and used it to train a Gaussian process emulator for the (log) posterior density of the model parameters. We then integrated over this (approximate) parameter posterior to produce probabilistic predictions for algal biomass and chlorophyll a concentration under alternative nutrient load reduction scenarios. Our computational algorithm allowed for fast posterior inference and the Gaussian process emulator had good predictive accuracy within the highest posterior probability mass region. The posterior predictive scenarios showed that the probability to reach the EU’s Water Framework Directive objectives in the Finnish Archipelago Sea is generally low even under large load reductions. • We propose an algorithm for quantifying uncertainties in a large nutrient impact model. • Our algorithm implements Bayesian inference by using Gaussian process emulation. • We solve posterior distribution for biological parameters of a nutrient impact model. • We propagate parameter uncertainty into nutrient load reduction scenario predictions. • Probability to reach good environmental status in the Finnish Archipelago Sea is low.