Simulation and prediction of surface water quality using stochastic models

Abstract

In recent years, surface water quality has decreased due to the increasing demand for water and increasing the use of fertilizers, pesticides and the discharge of domestic and municipal wastewater to surface water. The purpose of this research is a comparison of the efficiency of different time-series models in modeling and prediction of monthly water quality performance in Harmaleh area of Khuzestan in the southwest of Iran. Water quality parameters including Ca, HCO3, SO4, Ec, pH, Mg, Cl, Na, and TDS for the period of 2001 to 2014 were evaluated. Five time-series models (AR, MA, ARMA, ARIMA, and SARIMA) with 12 different structures were assessed by R software. First, the data were normalized using Kolmogorov–Smirnov test. Also, the adequacy of data was tested by Hurst’s coefficient. The Hurst coefficient was > 0.5 for all investigated parameters, which indicated suitable length of the time series for the modeling. As the components of trend, jump, and seasonality are usually specific, modeling of them is not required, but modeling of stochastic components is of importance in water resources simulation and management. Therefore, using the R software, deterministic parts of the time series (e.g., trend, jump, and seasonality) were eliminated and non-deterministic component (e.g., randomness) was simulated (from 2011 to 2014), and finally, the data were predicted (from 2015 to 2018) based on the optimized models. The optimized models were selected based on auto-correlation function (ACF) and partial auto-correlation function (PACF) as well as the use of Akaike information criteria (AIC) and coefficient of determination. Results showed that in 66% of data ARMA [with the same rate of ARMA (1, 2), ARMA (2, 1), and ARMA (2, 2)], in 22% of data AR (1), and in 11% of data ARIMA (1, 1, 2) models presented the highest efficiency in monthly water quality simulation. Finally, each quality parameter was also predicted for the next 4 years (2015–2018) based on the selected optimized models. Results indicated that the values of SO4 and pH, respectively, showed the highest and lowest correlation with the related observations with a coefficient of determination of 0.54 and 0.19. Overall, modeling of water quality using stochastic models could save time and costs, especially when time series of parameters are long and adequate.