Analysis and detection of functional outliers in water quality parameters from different automated monitoring stations in the Nalón River Basin (Northern Spain)

Abstract

The purposes and intent of the authorities in establishing water quality standards are to provide enhancement of water quality and prevention of pollution to protect the public health or welfare in accordance with the public interest for drinking water supplies, conservation of fish, wildlife and other beneficial aquatic life, and agricultural, industrial, recreational, and other reasonable and necessary uses as well as to maintain and improve the biological integrity of the waters. In this way, water quality controls involve a large number of variables and observations, often subject to some outliers. An outlier is an observation that is numerically distant from the rest of the data or that appears to deviate markedly from other members of the sample in which it occurs. An interesting analysis is to find those observations that produce measurements that are different from the pattern established in the sample. Therefore, identification of atypical observations is an important concern in water quality monitoring and a difficult task because of the multivariate nature of water quality data. Our study provides a new method for detecting outliers in water quality monitoring parameters, using turbidity, conductivity and ammonium ion as indicator variables. Until now, methods were based on considering the different parameters as a vector whose components were their concentration values. This innovative approach lies in considering water quality monitoring over time as continuous curves instead of discrete points, that is to say, the dataset of the problem are considered as a time-dependent function and not as a set of discrete values in different time instants. This new methodology, which is based on the concept of functional depth, was applied to the detection of outliers in water quality monitoring samples in the Nalón river basin with success. Results of this study were discussed here in terms of origin, causes, etc. Finally, the conclusions as well as advantages of the functional method are exposed.

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“…É um parâmetro importante para controlar e determinar o estado e a qualidade de água (Piñeiro Di Blasi et al, 2013). Existe uma correlação estatística entre a condutividade da água e a concentração de diversos elementos e íons (Tundisi e Matsumura-Tundisi, 2008).…”

A Functional Data Analysis for Assessing the Impact of a Retrofitting in the Energy Performance of a Building

“…If we assume that every curve in the data come from the same stochastic process, a curve would be considered such an outlier for two reasons: it is at a significant distance from the expected function of the stochastic process or its shape represents a very different behaviour from the other curves. Therefore, the curves with functional depth below a specific C value would be considered atypical and would be removed from the sample (see [23][24][25][26]). On the other hand, it would be convenient to choose a C that provides a controlled type I error level.…”

“…On the other hand, it would be convenient to choose a C that provides a controlled type I error level. It should be a value that, in absence of outliers, the probability of mislabelling a correct data as outlier would be approximately a 1% [23][24][25][26]:…”

“…In this context, Functional Data Analysis (FDA) can be useful because it is able to detect days that do not have individual outliers, but may be far from the mean behaviour [22][23][24][25][26]. A proof of its application is that FDA has expanded to a great number of scientific fields related with continuous-time monitoring processes such as the environment [24,[26][27][28][29], health and medical research [30,31], industrial processes [32,33], sensor technology [34,35] or even econometrics [36]. Moreover, it has also been applied with machine learning techniques in optimisation and classification problems [37,38].…”

Low-Cost Sensor Outlier Detection Framework For on-Line Monitoring of Particle Pollutants in Multiple Scenarios

“…series(Pineiro Di Blasi et al 2015;Sanchez-Lasheras et al 2020). Therefore, the characterization of data inconsistency and the boundary of outlier determination are crucial.…”