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

arXiv: https://arxiv.org/abs/2601.15503 · HTML: https://mlsanity.com/paper/2601.15503/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 67 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizons](https://mlsanity.com/paper/2310.07446/) (2023)
- [Review of automated time series forecasting pipelines](https://mlsanity.com/paper/2202.01712/) (2022)
- [Long-Term Missing Value Imputation for Time Series Data Using Deep Neural Networks](https://mlsanity.com/paper/2202.12441/) (2022)
- [Recommending Training Set Sizes for Classification](https://mlsanity.com/paper/2102.09382/) (2021)
- [Sample size determination via learning-type curves](https://mlsanity.com/paper/2303.09575/) (2023)
- [Imputation of Missing Streamflow Data at Multiple Gauging Stations in Benin Republic](https://mlsanity.com/paper/2211.11576/) (2022)

## Abstract (arXiv)

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.