Nonlinear Growth Models for Modelling Time Series of Groundwater Nitrate Concentrations

In this paper, a novel approach of modelling time series of nitrate concentrations in drinking water by nonlinear growth functions is proposed. An almost constant increase in the average values of nitrate concentrations occurred at the Vinokov??ak wellfield in the county of Vara?din, Croatia, in the period between 1998 and 2013. Our hypothesis was that the time series would be well adjusted to the nonlinear growth function with asymptotic properties after smoothing performed by the moving average method. We used a general growth model which does not have asymptotic properties and the logistic, Gompertz and Richards functions which do have asymptotic properties. Last three growth functions were modified based on the knowledge of a constant presence of basic nitrate concentrations in the drinking water before growth. The fit of growth curves to experimental data was assessed using R ² and Aikake’s information criterion. The modified growth functions gave the best fit to the smoothed time series of nitrate concentrations with R ² ranging from 0.9960 to 0.9986.