How to separate long-term trends from periodic variation in water quality monitoring

Modelling and multivariate analyses processed on multiple time series usually encounter some difficulties for three reasons: (1) sampling dates may be not equally spaced; (2) several values may be missing; and (3) the usual multivariate analyses may not succeed in separating long-term trends from regular periodic variations on an annual scale within the time series. To circumvent these difficulties, we propose a statistical approach based on the modelling of data by the non-parametric smoother Loess and the application of functional principal components analysis (FPCA). FPCA thereby facilitates the typology of variables based on their long-term trends and/or their periodic variation. We applied this approach to a long-term study over nine years (1983–1991) of the water quality of the Seine river (France) conducted downstream of a plant for wastewater treatment.