Trend analysis of water quality series based on regression models with correlated errors

This work proposes a methodology for characterizing the time evolution of water quality time series taking into consideration the inherent problems that often appear in this type of data such as non-linear trends, series having missing data, outliers, irregular measurement patterns, seasonal behavior, and serial correlation. The suggested approach, based on regression models with a Gaussian autoregressive moving average (ARMA) error, provides a framework where those problems can be dealt with simultaneously. Also the model takes into account the effect of influential factors, such as river flows, water temperature, and rainfall. The proposed approach is general and can be applied to different types of water quality series. We applied the modeling framework to four monthly conductivity series recorded at the Ebro river basin (Spain). The results show that the model fits the data reasonably well, that time evolution of the conductivity series is non-homogeneous over the year and, in some cases, non-monotonic. In addition, the results compared favorably over those obtained using simple linear regression, pre-whitening, and trend-free-pre-whitening techniques.