大型营养盐负荷影响模型的贝叶斯校准与不确定性量化
Bayesian Calibration and Uncertainty Quantification for a Large Nutrient Load Impact Model
AI总结：
针对芬兰 FICOS 营养盐负荷模型计算昂贵、预测不确定性难评估的问题，提出结合贝叶斯优化与高斯过程仿真器的校准和概率预测方法，揭示大幅减排下群岛海达标概率仍低。
摘要：
营养盐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和生物地球化学过程。它们是规划具有成本效益的富营养化治理行动的核心工具，因为这些模型能够对营养盐负荷削减所产生的影响进行情景预测，例如对有害藻类生物量增长的影响。然而，由于计算量巨大，与这些预测相关的不确定性通常没有得到严格评估。在本研究中，我们开发了一种新颖的贝叶斯计算方法，用于估计芬兰沿海水域营养盐负荷模型 FICOS 预测中的不确定性。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，我们利用 Bayes optimization（贝叶斯优化），在长期监测数据的条件下定位模型参数的后验众数。之后，我们围绕后验众数为 FICOS 模型运行构建了空间填充设计，并利用其训练了一个 Gaussian process emulator（高斯过程仿真器），以逼近模型参数的（对数）后验密度。接着，我们对这一（近似）参数后验进行积分，从而在不同营养盐负荷削减情景下生成藻类生物量和叶绿素 a 浓度的概率预测。我们的计算算法支持快速后验推断，并且 Gaussian process emulator 在后验概率质量最高的区域内具有良好的预测精度。后验预测情景表明，即使在大幅削减负荷的情况下，芬兰群岛海达到欧盟《水框架指令》目标的概率总体上仍然较低。
英文摘要：
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.
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