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 spatiotemporal outputs of the FICOS model. Then, we used Bayes 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 EUs Water Framework Directive objectives in the Finnish Archipelago Sea is generally low even under large load reductions.

翻译：营养负荷模拟器是大型确定性模型，用于模拟水生生态系统中的水动力过程与生物地球化学过程。作为规划成本效益型富营养化治理措施的核心工具，此类模型能够对营养负荷削减（例如对有害藻类生物量增长）的影响进行情景预测。然而，由于计算量庞大，这些预测相关的不确定性通常未能得到严格评估。本研究针对芬兰海岸营养负荷模型FICOS的预测不确定性，提出了一种新颖的贝叶斯计算方法。首先，我们为FICOS模型的多变量时空输出构建了似然函数；随后，基于长期监测数据，采用贝叶斯优化方法定位模型参数的后验众数；接着，在后验众数附近构建FICOS模型运行的填充空间设计，并基于此训练高斯过程仿真器以逼近模型参数的（对数）后验密度；最后，通过对该（近似）参数后验进行积分，获得了不同营养负荷削减情景下藻类生物量与叶绿素a浓度的概率预测。本计算算法实现了快速后验推断，且高斯过程仿真器在高后验概率质量区域内具有良好的预测精度。后验预测情景表明，即使在较大负荷削减条件下，芬兰群岛海区域达到欧盟《水框架指令》目标的概率总体仍处于较低水平。