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

Rishit Chatterjee, Tahiya Chowdhury

TL;DR

The paper tackles forecasting lake water clarity (SDD) from irregular, citizen-generated time series by imputing missing covariates with MICE and evaluating multiple predictors, with ridge regression delivering the best performance. It introduces a backward-history sampling protocol to quantify the minimal data needed and a forward feature-selection procedure to identify a compact predictor set, culminating in a joint feasibility rule that prescribes the smallest training window and fewest predictors to stay within $5\%$ of a full-history baseline. The study finds that on average $176$ pre-test samples per lake suffice, and a four-feature subset (notably including OXIC) can match the full feature set, with many lakes achieving target accuracy using a single predictor. These results yield practical, field-deployable guidance for cost-effective lake monitoring and scalable forecasting across data-poor, climate-impacted inland lakes.

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.

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

TL;DR

The paper tackles forecasting lake water clarity (SDD) from irregular, citizen-generated time series by imputing missing covariates with MICE and evaluating multiple predictors, with ridge regression delivering the best performance. It introduces a backward-history sampling protocol to quantify the minimal data needed and a forward feature-selection procedure to identify a compact predictor set, culminating in a joint feasibility rule that prescribes the smallest training window and fewest predictors to stay within of a full-history baseline. The study finds that on average pre-test samples per lake suffice, and a four-feature subset (notably including OXIC) can match the full feature set, with many lakes achieving target accuracy using a single predictor. These results yield practical, field-deployable guidance for cost-effective lake monitoring and scalable forecasting across data-poor, climate-impacted inland lakes.

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.
Paper Structure (19 sections, 9 equations, 3 figures, 3 tables)

This paper contains 19 sections, 9 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Related Work
  4. Contribution
  5. Methods
  6. Data
  7. Time-series Imputation
  8. Minimal Sample Size with Backward Forecasting Strategy
  9. Evaluation Metric: Normalized MAE
  10. Feature Selection By Importance Ranking
  11. Joint selection of minimal observations--important feature
  12. Results
  13. What is the minimal number of training samples needed?
  14. How does nMAE enable depth-aware, cross-lake evaluation?
  15. Which features are most important?
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Cochnewagon Pond: observed and ridge-predicted SDD over the held-out last five years. The x-axis represents chronological sampling dates and the y-axis is the SDD (m). Observed values are shown as solid circles; ridge predictions (after MICE covariate imputation) are shown as dashed crosses, illustrating seasonal variability and agreement over the test period.
  • Figure 2: (a) Minimal samples and (b) features for forecasting water quality (based on the 30 lakes).
  • Figure 3: Bar height (y-axis) gives the percentage of lakes selecting each predictor (x-axis) when the joint rule returns a single-feature model ($\hat{k}_\ell=1$). Under the 5% tolerance, OXIC is selected for 90% of lakes and TPEC for 10%, indicating OXIC is the dominant lone predictor.