A univariate model of river water nitrate time series

Abstract Four time series were taken from three catchments in the North and South of England. The sites chosen included two in predominantly agricultural catchments, one at the tidal limit and one downstream of a sewage treatment works. A time series model was constructed for each of these series as a means of decomposing the elements controlling river water nitrate concentrations and to assess whether this approach could provide a simple management tool for protecting water abstractions. Autoregressive (AR) modelling of the detrended and deseasoned time series showed a “memory effect”. This memory effect expressed itself as an increase in the winter–summer difference in nitrate levels that was dependent upon the nitrate concentration 12 or 6 months previously. Autoregressive moving average (ARMA) modelling showed that one of the series contained seasonal, non-stationary elements that appeared as an increasing trend in the winter–summer difference. The ARMA model was used to predict nitrate levels and predictions were tested against data held back from the model construction process – predictions gave average percentage errors of less than 10%. Empirical modelling can therefore provide a simple, efficient method for constructing management models for downstream water abstraction.