标题： 使用超统计方法和机器学习分析泰晤士河溶解氧的时空动力学 显示英文标题

标题： Analyzing Spatio-Temporal Dynamics of Dissolved Oxygen for the River Thames using Superstatistical Methods and Machine Learning

摘要： 通过采用超统计方法和机器学习，我们分析了泰晤士河水质指标的时间序列数据，特别关注溶解氧的动态变化。 去趋势后，溶解氧波动的概率密度函数表现出重尾特性，这些特性可通过$q$-高斯分布有效建模。 我们的研究结果表明，乘法经验模态分解方法在去趋势技术中表现最为出色，在几乎所有拟合中都获得了最高的对数似然值。 我们还观察到，$q$-高斯分布的最佳拟合宽度参数与距离海洋的距离呈负相关，突显了地理因素对水质动态的影响。 在同时期溶解氧预测的背景下，结合多种水质指标和时间特征的回归分析确定了Light Gradient Boosting Machine为最佳模型。 SHapley Additive exPlanations显示，温度、pH值和一年中的时间在预测中起着关键作用。 此外，我们使用Transformer来预测溶解氧浓度。 对于长期预测，Informer模型始终表现出优越的性能，使用我们使用的192个历史时间步长，实现了最低的MAE和SMAPE。 这种性能归因于Informer的ProbSparse自注意力机制，使其能够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。 它能够有效识别溶解氧的半衰期周期，特别是关注关键区间。 我们的研究结果为参与生态健康评估的政策制定者提供了有价值的见解，有助于准确预测河流水质和维护健康的水生生态系统。 显示英文摘要

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.