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Bayesian Monte Carlo and Maximum Likelihood Approach for Uncertainty Estimation and Risk Management: Application to Lake Oxygen Recovery Model

机译：贝叶斯蒙特卡洛法和最大似然法用于不确定性估计和风险管理：在湖氧回收模型中的应用

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Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficient for oxygen and wind speed and associated 95% confidence band, which are shown to be consistent with reported measured values at five different lakes. Finally, we illustrate the robustness of the BMCML to solve risk-based water quality management problems, showing that neglecting cross-correlations between parameters could lead to improper required BOD load reduction to achieve the compliance criteria of 5 mg/L.
机译：模型不确定性估计和风险评估对于环境管理和有关污染缓解策略的明智决策至关重要。在这项研究中，我们应用了一种概率方法，该方法结合了贝叶斯蒙特卡洛模拟和最大似然估计（BMCML）来校准湖泊氧气回收模型。我们首先导出控制湖泊平均氧气动力学随时间变化的风速的微分方程的解析解。然后，通过对分析溶液的贝叶斯条件调节，根据在上部状态纽约的富营养化湖泊的两个恢复期内从早期研究获得的每日风速和氧气浓度数据，得出模型参数和预测不确定性的统计推断。使用一年的氧气回收数据对模型进行校准，并使用一年的回收数据验证统计推断。与本质上分两步，回归和优化的方法相比，BMCML结果更全面，并且在预测湖中观测到的瞬时溶解氧水平（DO）方面表现相对更好。 BMCML还产生了与使用流行的马尔可夫链蒙特卡洛技术（MCMC）获得的校准和验证结果相当的结果，并且比MCMC在计算上更简单，更容易实现。接下来，使用校准的模型，我们得出氧气和风速的液膜传输系数与相关的95％置信带之间的最佳关系，这表明与五个不同湖泊的报告测量值一致。最后，我们说明了BMCML解决基于风险的水质管理问题的鲁棒性，表明忽略参数之间的互相关性可能会导致不适当的BOD负荷减少而无法达到5 mg / L的达标标准。

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