Vol.:(0123456789) 1 3 Sustainable Water Resources Management (2020) 6:74 https://doi.org/10.1007/s40899-020-00430-7 ORIGINAL ARTICLE Simulation and prediction of surface water quality using stochastic models Mostafa Dastorani 1  · Mohammad Mirzavand 2  · Mohammad T. Dastorani 3  · Hassan Khosravi 4 Received: 1 July 2019 / Accepted: 8 July 2020 © Springer Nature Switzerland AG 2020 Abstract In recent years, surface water quality has decreased due to the increasing demand for water and increasing the use of fer- tilizers, pesticides and the discharge of domestic and municipal wastewater to surface water. The purpose of this research is a comparison of the efciency of diferent 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, HCO 3 , SO 4 , 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 diferent 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 coefcient. The Hurst coefcient 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 specifc, 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 fnally, 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 coefcient 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 efciency 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 SO 4 and pH, respectively, showed the highest and lowest correlation with the related observations with a coefcient 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. Keywords Water quality · Stochastic models · Simulation · Prediction Introduction There is water all around us. There are vast oceans, large lakes, big rivers, small ponds, and tiny streams. All of these matter to us and other creatures on this planet. Our river systems connect to make watersheds. Little streams feed large rivers, which can then feed lakes or oceans. The contamination of the smallest stream will afect everything downstream. We often get our drinking water from lakes and rivers. Although we treat our drinking water, we should protect it at its initial source: up to the tiniest stream. Lots of other animals and plants depend upon the watersheds which we inhabit. Cleaner water means a healthier food chain (from bugs to fsh, to birds, to people), and poor water quality * Mostafa Dastorani m.dastorani@hsu.ac.ir 1 Faculty of Geography and Environmental Sciences, Hakim Sabzevari University, Sabzevar, Iran 2 Natural Resources and Earth Sciences, University of Kashan, Kashan, Iran 3 Faculty of Natural Resources and Environment, Ferdowsi University of Mashhad, Mashhad, Iran 4 Department of Arid and Mountainous Regions Reclamation, Faculty of Natural Resources, University of Tehran, Tehran, Iran