Multivariate functional data analysis and machine learning methods for anomaly detection in water quality sensor data

Aug 4, 2026

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Reliable anomaly detection is vital for water resources management, yet water quality sensor data are complex and often suffer from limited labeled examples. This study evaluates multivariate functional data analysis and benchmarks it against supervised machine learning approaches using 18 years of expert-annotated records from four monitoring stations along Spain’s Ebro River. A multivariate functional model is proposed with a new amplitude metric and a nonparametric outlier detector (MMSA). A Random Forest architecture with sliding windows and balancing yields the best average F1 of 93%.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Introduction

Anomaly detection in environmental sensor systems

Drivers of water quality changes in the Ebro River watershed

Expert-driven anomaly detection workflow

Methodological background

Time series analysis vs functional data analysis

Environmental Modelling and Software 190 (2025) 106443 | Multivariate functional data analysis and machine learning methods for anomaly detection in water quality sensor data
Xurxo Rigueira a,b ,∗, David Olivierib, Maria Araujo a, Angeles Saavedra c, Maria Pazo aa Department of Natural Resources and Environmental Engineering, University of Vigo, Vigo, 36310, Spain
b Department of Computer Science, University of Vigo, Ourense, 32004, Spain
c Department of Statistics and Operational Research, University of Vigo, Vigo, 36310, Spain | | | --- | --- | | A R T I C L E I N F O | A B S T R A C T | | Dataset link: [https://doi.org/10.5281/zenodo.1](https://doi.org/10.5281/zenodo.1) | Reliable anomaly detection is crucial for water resources management, but the complexity of environmental | | 4769545, [https://doi.org/10.5281/zenodo.147](https://doi.org/10.5281/zenodo.147) | sensor data presents challenges, especially with limited labeled data in water quality analysis. Functional data | | 69551 | has experienced significant growth in anomaly detection, but most applications focus on unlabeled datasets. | | Keywords: | This study assesses the performance of multivariate functional data analysis and compares it with current | | Water quality | machine learning models for detecting water quality anomalies on 18 years of expert-annotated data from | | Sensor data | four monitoring stations along Spain’s Ebro River. We propose and validate a multivariate functional model | | Functional data analysis
Supervised machine learning | incorporating a new amplitude metric and a nonparametric outlier detector (Multivariate Magnitude, Shape, and Amplitude–MMSA). Additionally, a Random Forest-based machine learning architecture was developed | | Anomaly detection | for the same purpose, employing sliding windows and data balancing techniques. The Random Forest model demonstrated the highest performance, achieving an average F1 score of 93%, while MMSA exhibited robustness in scenarios with limited anomalous data or labels. | 1. Introduction The widespread deployment of environmental sensors has resulted in large datasets containing valuable information, particularly for identifying anomalies that reveal underlying processes (Garces and Sbarbaro, 2011). Anomaly detection, which involves identifying deviations from historical data, is therefore of critical importance (Hodge and Austin, 2004). In water systems, anomalies can signify events affecting quality and safety, such as those caused by pollution, extreme weather conditions, tampering or equipment malfunctions. These occurrences underscore the importance of thoroughly investigating the origins of such anomalies. The Ebro River watershed is an environmentally diverse region significantly impacted by climate and land use changes, as well as intense economic and social transformations, which collectively affect the ecological quality of water bodies (Cooper et al., 2013; Skoulikidis et al., 2017). Climate projections for the Mediterranean indicate shifts in temperature and precipitation patterns, leading to more frequent extreme events such as heavy rainfall and droughts (CeballosBarbancho et al., 2008; Gonzalez-Hidalgo et al., 2010; López-Moreno et al., 2010). These changes are compounded by land-use transformations, such as the abandonment of agricultural areas, which has expanded forests, increasing evapotranspiration and reducing runoff (Gallart et al., 2011; Buendia et al., 2016). Additionally, irrigation schemes ∗ Corresponding author. E-mail address: [xurxo.rigueira@uvigo.gal](xurxo.rigueira@uvigo.gal) (X. Rigueira). disrupt river regimes by reversing seasonal hydrological patterns (Piqué et al., 2016). Furthermore, urban areas in this region further contribute to these changes, acting as point sources of pollution that elevate nutrient and contaminant concentrations in water (Han et al., 2009; Jeppesen et al., 2011; Brown et al., 2005). These factors collectively con

FAQs

Why is anomaly detection important in water quality management?

Anomalies indicate deviations from historical behavior that can reflect pollution events, extreme weather, tampering, or equipment malfunctions, which threaten water quality and safety.

What datasets and study setting are used to evaluate the methods?

The evaluation uses 18 years of expert-annotated water quality data from four monitoring stations along Spain’s Ebro River.

How do the proposed multivariate functional approach and Random Forest compare?

The Random Forest model achieves the highest average performance (average F1 of 93%), while MMSA remains robust when anomalous data or labels are limited.

Aug 4, 2026

Upload by Quinn