采用超统计方法与机器学习分析泰晤士河溶解氧的时空动态
Analyzing Spatio-Temporal Dynamics of Dissolved Oxygen for the River Thames using Superstatistical Methods and Machine Learning
AI总结：
本研究采用超统计方法与机器学习分析泰晤士河溶解氧动态，明确最优去趋势方法与预测模型，揭示地理及环境因子的影响，为河流水质预测与生态保护提供支撑。
摘要：
我们运用超统计方法与机器学习，对泰晤士河的水质指标时间序列数据展开分析，重点聚焦溶解氧的动态变化特征。经去趋势处理后，溶解氧波动的概率密度函数呈现出厚尾特性，可通过$q$-高斯分布进行有效建模。研究结果表明，乘法经验模态分解（multiplicative Empirical Mode Decomposition）方法是效果最优的去趋势技术，在几乎所有拟合中均取得了最高的对数似然值。我们还观察到，$q$-高斯分布最优拟合的宽度参数与到海洋的距离呈负相关，凸显了地理因素对水质动态的影响。在溶解氧同时预测场景下，结合各类水质指标与时间特征的回归分析显示，Light Gradient Boosting Machine（轻量梯度提升机）是性能最佳的模型。SHapley Additive exPlanations（沙普利可加性解释）方法揭示，温度、pH值和一年中的时段在预测中发挥着关键作用。此外，我们使用Transformer模型预测溶解氧浓度。在长期预测任务中，Informer模型始终表现出更优的性能，在我们使用的192个历史时间步长下，取得了最低的平均绝对误差（MAE）和对称平均绝对百分比误差（SMAPE）。这一性能表现得益于Informer的ProbSparse自注意力机制，该机制使其能比其他机器学习模型更有效地捕捉时间序列数据中的长程依赖关系，还能有效识别溶解氧的半衰期周期，尤其关注关键时间区间。本研究结果为参与生态健康评估的政策制定者提供了宝贵见解，有助于精准预测河流水质、维护健康的水生生态系统。
英文摘要：
By employing superstatistical methods and machine learning, we analyze time series data of water quality indicators for the River Thames, with a specific focus on the dynamics of dissolved oxygen. After detrending, the probability density functions of dissolved oxygen fluctuations exhibit heavy tails that are effectively modeled using $q$-Gaussian distributions. Our findings indicate that the multiplicative Empirical Mode Decomposition method stands out as the most effective detrending technique, yielding the highest log-likelihood in nearly all fittings. We also observe that the optimally fitted width parameter of the $q$-Gaussian shows a negative correlation with the distance to the sea, highlighting the influence of geographical factors on water quality dynamics. In the context of same-time prediction of dissolved oxygen, regression analysis incorporating various water quality indicators and temporal features identify the Light Gradient Boosting Machine as the best model. SHapley Additive exPlanations reveal that temperature, pH, and time of year play crucial roles in the predictions. Furthermore, we use the Transformer to forecast dissolved oxygen concentrations. For long-term forecasting, the Informer model consistently delivers superior performance, achieving the lowest MAE and SMAPE with the 192 historical time steps that we used. This performance is attributed to the Informer's ProbSparse self-attention mechanism, which allows it to capture long-range dependencies in time-series data more effectively than other machine learning models. It effectively recognizes the half-life cycle of dissolved oxygen, with particular attention to key intervals. Our findings provide valuable insights for policymakers involved in ecological health assessments, aiding in accurate predictions of river water quality and the maintenance of healthy aquatic ecosystems.
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