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A revaluation of lake-phosphorus loading models using a Bayesian hierarchical framework

机译：使用贝叶斯分级框架重新评估湖泊-磷负荷模型

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We revisit the phosphorus-retention and nutrient-loading models in limnology using a Bayesian hierarchical framework. This methodological tool relaxes a basic assumption of regression models fitted to data sets consisting of observations from multiple systems, i.e., the systems are assumed to be identical in behavior, and therefore the models have a single common set of parameters for all systems. Under the hierarchical structure, the models are dissected into levels (hierarchies) that explicitly account for the role of significant sources of variability (e.g., morphometry, mixing regime, geographical location, land-use patterns, trophic status), thereby allowing for intersystem parameter differences. Thus, the proposed approach is a compromise between site-specific (where limited local data is a problem) and globally common (where heterogeneous systems in wide geographical areas are assumed to be identical) parameter estimates. In this study, we used critical values of the mean lake depth (z = 10.3 m) and the hydraulic residence time (τ_w = 2.6 years) to specify the hierarchical levels of the models. Our analysis demonstrates that the hierarchical configuration led to an improvement of the performance of six out of the seven hypothesized relationships used to predict lake-phosphorus concentrations. We also highlight the differences in the posterior moments of the group-specific parameter distributions, although the inference regarding the importance of different predictors (e.g., inflow-weighted total phosphorusrninput concentration, and hydraulic retention time) of lake phosphorus or the relative predictability of the models examined are not markedly different from an earlier study by Brett and Benjamin. The best fit to the observed data was obtained by the model that considers the first-order rate coefficient for total phosphorus loss from the lake as an inverse function of the lake hydraulic retention time. Finally, our analysis also demonstrates how the Bayesian hierarchical framework can be used for assessing the exceedance frequency and confidence of compliance of water-quality standards. We conclude that the proposed methodological framework will be very useful in the policy-making process and can optimize environmental management actions in space and time.
机译：我们使用贝叶斯分级框架重新研究了石灰学中的磷保持和养分加载模型。这种方法论工具放宽了回归模型的基本假设，该模型适用于包含来自多个系统的观察值的数据集，即假设系统在行为上是相同的，因此对于所有系统而言，该模型具有一组相同的公共参数。在层次结构下，将模型分为多个层次（层次），这些层次明确说明了重要的可变性源（例如形态，混合方式，地理位置，土地利用模式，营养状态）的作用，从而考虑了系统间参数差异。因此，所提出的方法是在特定于站点（其中有限的本地数据是一个问题）和全局通用（其中在宽地理区域中的异构系统被假定为相同）参数估计之间的折衷方案。在这项研究中，我们使用平均湖泊深度（z = 10.3 m）和水力停留时间（τ_w= 2.6年）的临界值来指定模型的层次级别。我们的分析表明，层次结构导致用于预测湖磷浓度的七个假设关系中的六个改善了性能。我们还强调了特定组参数分布的后矩的差异，尽管有关湖磷的不同预测因素（例如，流入加权总磷输入浓度和水力停留时间）的重要性或湖磷的相对可预测性的推论所研究的模型与Brett和Benjamin的较早研究没有显着差异。该模型获得了与观测数据的最佳拟合，该模型将湖泊中总磷流失的一级速率系数视为湖泊水力停留时间的反函数。最后，我们的分析还证明了如何使用贝叶斯分级框架来评估超出频率和水质标准符合性的置信度。我们得出的结论是，所提出的方法框架将在决策过程中非常有用，并且可以优化时空环境管理措施。

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