Functional forecasting of dissolved oxygen in high-frequency vertical lake profiles

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.