Data-driven Lake Water Quality Forecasting for Time Series with Missing Data using Machine Learning
This provides a practical, efficient rule for lake researchers to optimize monitoring efforts for water quality forecasting, though it is incremental as it builds on existing imputation and regression methods.
The paper tackled forecasting Secchi Disk Depth in lakes with irregular, missing data, showing that ridge regression achieved the best performance and that a minimal setup of about 64 recent samples and one predictor per lake could stay within 5% of full-history accuracy.
Volunteer-led lake monitoring yields irregular, seasonal time series with many gaps arising from ice cover, weather-related access constraints, and occasional human errors, complicating forecasting and early warning of harmful algal blooms. We study Secchi Disk Depth (SDD) forecasting on a 30-lake, data-rich subset drawn from three decades of in situ records collected across Maine lakes. Missingness is handled via Multiple Imputation by Chained Equations (MICE), and we evaluate performance with a normalized Mean Absolute Error (nMAE) metric for cross-lake comparability. Among six candidates, ridge regression provides the best mean test performance. Using ridge regression, we then quantify the minimal sample size, showing that under a backward, recent-history protocol, the model reaches within 5% of full-history accuracy with approximately 176 training samples per lake on average. We also identify a minimal feature set, where a compact four-feature subset matches the thirteen-feature baseline within the same 5% tolerance. Bringing these results together, we introduce a joint feasibility function that identifies the minimal training history and fewest predictors sufficient to achieve the target of staying within 5% of the complete-history, full-feature baseline. In our study, meeting the 5% accuracy target required about 64 recent samples and just one predictor per lake, highlighting the practicality of targeted monitoring. Hence, our joint feasibility strategy unifies recent-history length and feature choice under a fixed accuracy target, yielding a simple, efficient rule for setting sampling effort and measurement priorities for lake researchers.