Data-driven Lake Water Quality Forecasting for Time Series with Missing Data using Machine Learning

2026-01-21

AI Summary

This study addresses temporal gaps in volunteer-led lake monitoring caused by ice cover, weather, and human factors by leveraging three decades of in situ observations from 30 lakes in Maine. Missing values are handled via multiple imputation by chained equations (MICE), and a ridge regression model is developed to predict Secchi disk depth. The work innovatively introduces a joint feasibility function that simultaneously optimizes the length of recent historical data and feature selection. Remarkably, using only approximately 64 recent samples and a single predictor variable, the approach achieves 95% of the accuracy (measured by normalized mean absolute error, nMAE) of a full-history, full-feature model, substantially reducing monitoring costs. These findings demonstrate the viability of lightweight, highly efficient sampling strategies for early warning of harmful algal blooms.

Technology Category

• Machine Learning: Ensemble Methods
• Search and Optimization: Metareasoning and Metaheuristics
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Abstract

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.

Problem

• lake water quality forecasting
• missing data
• time series
• harmful algal blooms
• Secchi Disk Depth

Innovation

• Multiple Imputation by Chained Equations (MICE)
• normalized Mean Absolute Error (nMAE)
• minimal sample size
• feature selection
• joint feasibility function