Predicting dissolved oxygen (DO) in lakes is important for assessing environmental conditions as well as reducing water treatment costs. High levels of DO often precede toxic algal blooms, and low DO causes carcinogenic metals to precipitate during water treatment. Typically, DO is predicted from limited data sets using hydrodynamic modeling or data-driven approaches like neural networks. However, functional data analysis (FDA) is also an appropriate modeling paradigm for measurements of DO taken vertically through the water column. In this analysis, we build FDA models for a set of profiles measured every 2 hours and forecast the entire DO percent saturation profile from 2 to 24 hours ahead. Functional smoothing and functional principal component analysis are applied first, followed by a vector autoregressive model to forecast the empirical functional principal component (FPC) scores. Rolling training windows adapt to seasonality, and multiple combinations of window sizes, model variables, and parameter specifications are compared using both functional and direct root mean squared error metrics. The FPC method outperforms a suite of comparison models, and including functional pH, temperature, and conductivity variables improves the longer forecasts. Finally, the FDA approach is useful for identifying unusual observations.

中文翻译：

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高频垂直湖泊剖面中溶解氧的功能预报

预测湖泊中的溶解氧 (DO) 对于评估环境条件以及降低水处理成本非常重要。高水平的溶解氧通常先于有毒藻类大量繁殖，而低溶解氧会导致致癌金属在水处理过程中沉淀。通常，DO 是使用流体动力学建模或数据驱动方法（如神经网络）从有限的数据集中预测的。然而，功能数据分析 (FDA) 也是一种适当的建模范例，用于测量垂直穿过水柱的 DO。在此分析中，我们为每 2 小时测量一次的一组配置文件构建 FDA 模型，并预测提前 2 至 24 小时的整个 DO 百分比饱和度配置文件。首先应用函数平滑和函数主成分分析，然后是向量自回归模型来预测经验函数主成分 (FPC) 分数。滚动训练窗口适应季节性，并且使用函数和直接均方根误差指标比较窗口大小、模型变量和参数规范的多种组合。FPC 方法优于一套比较模型，包括功能性 pH 值、温度和电导率变量改进了更长的预测。最后，FDA 方法可用于识别异常观察结果。FPC 方法优于一套比较模型，包括功能性 pH 值、温度和电导率变量改进了更长的预测。最后，FDA 方法可用于识别异常观察结果。FPC 方法优于一套比较模型，包括功能性 pH 值、温度和电导率变量改进了更长的预测。最后，FDA 方法可用于识别异常观察结果。