Detection of outliers in water quality monitoring samples using functional data analysis in San Esteban estuary (Northern Spain).

Water quality controls involve 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 oxygen and turbidity as indicator variables. Until now, methods were based on considering the different parameters as a vector whose components were their concentration values. Our approach lies in considering water quality monitoring through time as curves instead of vectors, that is to say, the data set of the problem is considered as a time-dependent function and not as a set of discrete values in different time instants. The methodology, which is based on the concept of functional depth, was applied to the detection of outliers in water quality monitoring samples in San Esteban estuary. Results were discussed in terms of origin, causes, etc., and compared with those obtained using the conventional method based on vector comparison. Finally, the advantages of the functional method are exposed.