Application of Time Series Modeling to Study River Water Quality

American Journal of Engineering and Applied Sciences Original Research Paper Application of Time Series Modeling to Study River Water Quality 1 Maryam Ghashghaie, 2Kaveh Ostad-Ali-Askari, 3Saeid Eslamian and 4Vijay P. Singh 1 Department of Water Resources Engineering, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, 6517833131, Iran 2 Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran 3 Department of Water Engineering, Isfahan University of Technology, Isfahan, Iran 4 Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A and M University, 321 Scoates Hall, 2117 TAMU, College Station, Texas 77843-2117, U.S.A Article history Received: 19-03-2018 Revised: 20-04-2018 Accepted: 24-04-2018 Corresponding Author: Kaveh Ostad-Ali-Askari Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Email: [email protected] Abstract: Water deficit problem originates from two factors: population increase and water pollution. However, studying and forecasting the quality of water are necessary to avoid serious problems in future through managerial works. In present study, using time series modeling, the quality of Madian Rood River is studied at Baraftab station using time series analysis. Nine parameters of water quality are studied such as: TDS, EC, HCO3-, Cl-, SO42+, Ca2+, Mg2+, Na+ and SAR. Investigation of observed time series shows that there is a common increasing trend for all parameters unless Na+ and SAR. The order of models for each parameter was determined using Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) of time series. The ARIMA model was used to generate and forecast the quality of stream flows. Akaike Information Criterion (AIC), Determination Coefficient (R2), Root Mean Square Error (RMSE) and (Volume Error in Percent (VE %) criteria were referred to evaluate the generation and validation results. The Results show that time series modeling is quite capable of water quality forecasting. For the majority of forecasts, the value of R2 was greater than 0.6 between predicted and observed values. Keywords: ARIMA, Time Series, Trend Elimination, Water Quality Introduction Water quality is a main subject of life due to its direct impact on human health. Water quality could be affected by geologic structure, salinity, overdraw of groundwater, urban and domestic wastewater entrance into surface streams as well as agricultural drainage and a wide range of chemical compounds (Tsakiris and Alexakis, 2012). Different methods and approaches are used to investigate and forecast the quality of water. Also the majority of water software such as SWAT, QUAL2K and MIKE-11 benefit from especial tools to assess the quality of streams. Time series analysis is one of the useful methods which are applied in water quality modeling and forecasting. Time series analyses is useful in understanding and analyzing the process of different phenomena. It is also helpful in generating past observations forecasting the future values based on the past memory. Time series is composed of a string of data over time with an equal interval between all data. The interval can be defined as daily, weekly, monthly as well as yearly time steps. Time series analyzing is used in decision making in many hydrological processes and operation systems. Time series analysis in hydrology has two main goals: 1. 2. Understand and model the stochastic mechanism of a hydrologic process and Forecast the future values for the process Applied Time-Series Analysis Main statistical characteristics of a hydrologic time series could be reproduced using ARIMA (autoregressive, integrated, moving average) models. ARIMA models have been used to examine runoff and river discharge (Kurunç et al., 2005;), water levels of lakes (Sheng and Chen 2011, Ghashghaie and Nozari, 2018), sediment yield © 2018 Maryam Ghashghaie, Kaveh Ostad-Ali-Askari, Saeid Eslamian and Vijay P. Singh. This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license. Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ studies on regional and localized groundwater quality all over the world including a few snapshots. Lee and Lee (2003) evaluated and quantified the potential of natural reduction of groundwater in an industrial area of Seoul, Korea. Different studies have focused on water temperature time series () Kim et al. (2005) applied time series analysis in a study through which the effect of tide on groundwater quality in a coastal area of Korea was investigated. Also temporal variability of turbidity, dissolved oxygen, conductivity, temperature and fluorescence in the lower Mekong River as investigated using time series analysis (Irvine et al., 2011).Water quality modeling plays an important role in water quality management and conservation (Singh et al., 2004; Chenini and Khemiri 2009; Fang et al., 2010; Su et al., 2011;; Prasad et al., 2014; Seth et al., 2013;Parmar and Bhardwaj, 2014). Application of time series analyzing in water resources demonstrates the efficiency and capability of this approach since it considers stochastic nature of hydrological processes. This study aims to use this methodology in water quality analyzing. In present study, water quality parameters of Madian Rood are investigated at Baraftab station. The methodology and the study area are presented at the following section. (Hanh et al., 2010) and water quality (Ahmad et al., 2001, Lehmann and Rode, 2001; Faruk, 2010; Hanh et al., 2010; Durdu, 2010; Khalil Arya and Zhang, 2015). Auto correlated models were used in some studies on stream analyzing (Thomas and Fiering, 1962). McKerchar and Delleur (1974) established the main step to apply time series in hydrology using Autoregressive Integrated Moving Average. They used seasonal modeling as well to analyze seasonal characteristics of stream parameters. Time series modeling is efficient in identifying and forecasting monthly stream pattern and integrated water resources management (Jalal Kamali, 2002). It has been widely used to forecast hydrologic variables such as rainfall and discharge as well as flood (Komornık et al., 2006; Damle and Yalcin, 2007). Many studies have focused on water quality parameters, a Brief reviews of which are mentioned as follow. Applied Time Series Analysis on Surface Water Quality Hirsch et al. (1982) used new methods to analyze monthly water quality data for monotonic trends. Also temporal changes in water quality parameters such as pH, Alkalinity, total Phosphorous and Nitrate concentrations have been studied using data series of Niagara (El-Shaarawi et al., 1983). Yu et al. (1993) analyzed surface water quality data of the Arkansas, Verdigris and Neosho as well as Walnut river basin to study trends in 17 major constituents using 4 different nonparametric methods. The trend of upland stream and water quality data from Plynlimon, mid wales were examined (Robson and Neal, 1996) applying the seasonal Kendall test. studied the time series of water quality parameters and the discharge of Strymon River in Greece from 1980 to 1997. Gangyan et al. (2002) investigated the temporal sediment load characteristics of the Yangtze River using the turning point test, Kendall’s rank correlation test. Jassby et al. (2003) developed a time series model for Secchi depth in Lake Tahoe, USA. Panda et al. (2011) studied the trends in sediment load of a tropical river basin in India. Materials and Methods The Study Area The study area is located in the west of Iran in Kuhdasht region. Figure 1 shows the study area in Iran. This station of the river is located at 47°48'E and 33°18'N. The area of basin is about 1108 Km2 which is located at Kashkan basin of Karkheh watershed. Time series of 9 water quality parameters such as TDS, EC, HCO3-, Cl-, SO42-, Ca2+, Mg2+, Na+ and SAR of Baraftab station at Madian Rood River were studied in this research. Methodology The theory and application of the ARIMA modeling have been conducted in different studies (Pankratz, 1983; Vandaele, 1983; Box and Jenkins, 1976). The background of this methodology is presented briefly. Autoregressive (AR) models estimate the values for the dependent variable, Zt, as regression function of previous values, Zt-1, Zt-2 ... Zt- n. An AR model of order 1 (i.e. an AR (1) model) is defined as Equation 1: Applied Time Series Analysis on Groundwater Quality Time series analysis has been applied on the groundwater quality modeling in different regions. Chang (1988) developed a modeling technique including the homogeneity test of data and the best model selection to fit the water loss series using a stochastic process. Wilson et al. (1992) determined groundwater quality changes as a result of anthropogenic activities using a time series analysis of well water quality data from 1964 to 1965. Loftis (1996) reviewed national assessments of agricultural and urban, point source and hazardous waste Z t = Φ1Z t −1 + α t (1) (1) where, Zt and Zt-1 show deviations from the mean, Φ1 is the first-order AR coefficient and describes the effect of a unit change in Zt-1 on Zt and αt is the white noise. ■■ Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ Fig. 1: The location of the study area The αt values are assumed normally distributed and independent with the mean value of 0 and a constant value of variance. The value of variance for a stationarity model of Zt is positive and finite (Vandaele, 1983) and |Φ1| must be less than 1 to meet these conditions. The Higher order of AR models are possible, similar to a multiple regression; for this case, the absolute value of each AR coefficient should be less than 1. Moving Average (MA) models incorporate the past random fluctuations to show the time series. An MA model of order 1 (i.e., an MA (1) model) can be expressed as Equation 2: Z t = α t − θ1α t −1 model can supply more flexibility to describe the results of interaction between the processes (Salas et al., 1980). The main goal of a time series analysis is to understand seasonal patterns and/or trends over time. Most of the time hydrologic time series show a regular seasonal pattern which can be removed by standardizing the data for the seasonal mean and standard. Also understanding and modeling the correlational structure in the time series is another goal of time series analysis. The basic stages in the ARIMA modeling are composed of: (1) Identifying the model, (2) estimating the orders of the model and (3) verifying the model using the standard tests. The results are presented in the following section. (2) Results and Discussion where, θ1 is the MA coefficient and the random shocks (white noise) (αt) are assumed normally distributed and independent with the mean value of 0 and a constant value of variance. The value of |θ1 | must be less than 1. The Values greater than 1 show that the observations further in the past have a greater effecton Zt than more recent observations which is not plausible in a hydrologic time series. Higher order of the MA models is possible. Similar to the AR model coefficients, the absolute value of each MA coefficient should be less than 1. Since the parsimony is important in a time series modeling it sometimes could be met using a mixed (ARMA) model instead of a pure AR or MA model. Also representing a time series with an ARMA (1,1) model is more parsimonious in comparison with an AR (3) model because the model requires fewer parameter estimation. Mixing models is possible because they could be theoretically denoted as pure AR or MA models of infinite order (Vandaele, 1983). A mixed In this study, nine water quality parameters were studied. Using one lag the data were transformed to make a yearly stationary time series. At the second stage MINITAB 14 was used in this study to analyze these 9 time series. The ACF and PACF of time series were plotted at the second stage. After identifying the ACF and PACF of each time series the order of model was determined at first. Then 4 criteria were used to compare the results of series generation through the suggested models and 35 datatime series were generated. Based on 4 criteria, the best model was selected for each time series of 35 data and these models were used to forecast 5 values of time series. These 4 criteria were R2, AIC, RMSE and VE % (Karamouz and Araghinejad, 2005). The value of AIC is estimated through Equation 3: ( AIC = n × Ln (σ 2 ) + 2 × ( p + q ) ■■ ) (3) Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ Fig. 8 demonstrates the standard series of Mg2+. The Fig.8 shows that the series follow an increasing trend. Modeling the Mg2+ series was done after trend elimination which is presented in this Figure as well. Table 7 shows that the selected model is capable of modeling the series well. where, σ is the standard error of residuals; n is the sample size; p and p show the order of AR and MA respectively. Also the value of VE % is calculated using (Equation 4): ∑ VE % = n t =1 yt − yˆ t yt n (4) where, yt and ŷt show the observed and estimated values respectively and n is the sample size. At the next stage forecasting the water quality parameters was accomplished. Results are shown in the following figs. Previously mentioned criteria (AIC, RMSE and VE %) were used at this stage for demonstrating the capability of each model to forecast the value of data. Figure 2 shows the standardized time series of water quality data for TDS parameter and the forecasted values of 5 successive years. Standard series of TDS show that this parameter has a positive trend, which was removed and modeled as it is demonstrated in Table 1. The Results show that the model is capable of modeling the time series well. However, there is an increasing trend for the observed values of 5 successive years which is not the same for forecasted one. For the second parameters, as it is clear from Fig. 3, EC time series follows an increasing trend which was removed at the second stage. Then using the best model, it was forecasted for 5 years. Also Table 2 shows the results for modeling and choosing the best fit. Figure 4 shows HCO3- time series and forecasted series for 5 years. The forecasted values for 5 successive years are shown in this Figure as well. Similar to the previous parameters HCO3- follows an increasing slope and, the modeling was accomplished after trend elimination. Table 3 shows the results of modeling for this parameter. Standardized time series of Cl- is presented in Fig. 5. Also the forecasted values of this parameter are shown in this Figure. The results show that the selected model, shown in Table 4, is capable of modeling the series well. Figure 6 demonstrates the standard series of SO42-. Modeling the SO42- series was done on the original series without trend elimination. The forecasted values for 5 years are shown in this Figure too. The results of generation and the best fit are shown in Table 5. Also the standard series of Ca2+ is presented in Fig. 7 and the forecasted values of this parameter are shown in this Figure. The results presented in Table 6 show that the selected model, shown in Table 6, is capable of modeling the series well. Table 1: The results of TDS generation, order (1,3) MODEL R R2 AIC RMSE (1,1,2) 0.81 0.66 -93.05 0.04 (1,1,3) 0.86 0.74 -98.83 0.03 (2,1,3) 0.86 0.74 -96.95 0.03 VE % 1.13 1.02 1.00 Table 2: The results of EC generation, order (1,1) MODEL R R2 AIC RMSE (1,1,1) 0.73 0.54 -76.97 0.05 (1,1,2) 0.81 0.66 -89.01 0.04 (2,1,1) 0.83 0.68 -90.36 0.04 (2,1,2) 0.83 0.69 -89.82 0.04 (1,1,3) 0.85 0.73 -94.32 0.04 (2,1,3) 0.86 0.73 -92.51 0.04 VE % 1.36 1.29 1.25 1.27 1.21 1.18 Table 3: The results of HCO3- generation, order (1,2) MODEL R R2 AIC RMSE (1,1,2) 0.79 0.62 -43.72 0.11 (2,1,2) 0.77 0.59 -39.39 0.12 (1,1,3) 0.80 0.64 -48.27 0.11 (2,1,3) 0.76 0.58 -39.17 0.12 VE % 2.66 3.74 2.39 4.68 Table 4: The results of Cl- generation,order (1,2) MODEL R R2 AIC RMSE (1,1,1) 0.84 0.70 -81.94 0.04 (1,1,2) 0.84 0.70 -77.96 0.04 (2,1,2) 0.84 0.70 -76.12 0.04 (1,1,3) 0.84 0.70 -75.97 0.04 (2,1,1) 0.82 0.67 -74.52 0.05 VE % 0.80 0.80 0.79 0.80 0.90 Table 5: The results of SO42- generation,order (1,1) MODEL R R2 AIC RMSE (1,0,1) 0.51 0.26 -27.71 0.11 (1,1,1) 0.46 0.21 -23.09 0.11 (1,1,2) 0.49 0.24 -21.10 0.11 (2,1,1) 0.56 0.31 -20.58 0.11 (2,1,2) 0.60 0.36 -21.25 0.11 (1,1,3) 0.55 0.30 -22.47 0.11 VE % 1.18 1.42 1.42 1.70 1.67 1.64 Table 6: The results of Ca2+ generation,order (1,1) MODEL R R2 AIC RMSE (1,0,1) 0.77 0.59 -61.39 0.06 (1,0,2) 0.82 0.67 -66.36 0.06 (2,0,1) … (2,0,2) … (1,1,1) 0.78 0.60 -61.90 0.06 (1,1,2) 0.84 0.70 -69.94 0.05 (2,1,1) 0.87 0.76 -76.41 0.05 (2,1,2) 0.87 0.76 -74.52 0.05 ■■ VE % 1.32 1.33 1.15 1.16 1.23 1.22 Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ TDS 1.0 0.5 0.0 -0.5 0 15 10 5 20 25 30 35 -1.0 -1.5 Year 1400 1200 TDS Observed 1000 TDS Forecasted mg/l 800 600 400 200 0 1968 1973 1978 1983 1988 1993 1998 2003 2008 Year Fig. 2: Standardized time series of TDS and the forecasted values for 5 years EC 1.0 0.5 0.0 0 5 -0.5 10 25 20 15 30 35 -1.0 -1.5 Year 1400 EC Observed µ Mhos/cm 1200 EC Forecasted 1000 500 0 1968 1973 1978 1983 1988 1993 1998 2003 Year Fig. 3: Standardized time series of EC and the forecasted values for 5 years ■■ 2008 Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ HCO3 3 2 1 0 0 10 5 20 15 25 30 35 -1 -2 Year 6 HCO3 Observed 5 HCO3 Forecasted 3 2 1 0 1968 1973 1978 1983 1988 Year 1998 1993 2008 2003 Fig. 4: Standardized time series of HCO3- and the forecasted values for 5 years Cl 1.5 Y = 0.0419x-1.05 1.0 0.5 0.0 0 5 10 20 15 25 30 35 -0.5 -1.0 Year 6 Cl observed 5 Cl forecasted 4 Mg/l Mg/ l 4 3 2 1 0 1968 1973 1978 1983 1988 Year 1993 1998 2003 Fig. 5: Standardized time series of Cl- and the forecasted values for 5 years ■■ 2008 Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ SO4 2 1 0 0 10 5 15 20 30 25 35 -1 -2 Year 10 SO4 Observed 8 SO4 Forecasted Mg/ l 6 4 2 0 1968 1978 1973 1983 1993 1988 1998 2003 2008 Year Fig. 6: Standardized time series of SO42- and the forecasted values for 5 years Ca 2.0 Y = 0.0471x-1.1339 1.0 0.0 0 10 5 20 15 25 30 35 -1.0 -2.0 Year 12 Ca Observed 10 Ca Forecasted Mg/ l 8 6 4 2 0 1968 1973 1978 1983 1988 1993 1998 2003 Year Fig. 7: Standardized time series of Ca2+ and the forecasted values for 5 years ■■ 2008 Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ Mg 3 y = 0.0601x-1.1129 2 1 0 0 10 20 30 -1 -2 Year 6.0 Mg observed 5.0 Mg forecasted Mg/ l 4.0 3.0 2.0 1.0 0.0 1968 1973 1978 1983 1993 1988 Year 1998 2003 2008 Fig. 8: Standardized time series of Mg2+ and the forecasted values for 5 years Na 2 1 0 -1 30 20 10 0 y = -0.0659x+1.1394 -2 Year 3.0 Na observed 2.5 Na forecasted Mg/ l 2.0 1.5 1.0 0.5 0.0 1968 1973 1978 1983 1988 1993 1998 2003 Year Fig. 9: Standardized time series of Na+ and the forecasted values for 5 years ■■ 2008 Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ SAR 2 1 0 0 5 10 20 15 30 25 35 -1 -2 -3 Year 1.6 1.4 Observed SAR Forecasted SAR Mg/ l 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1968 1973 1978 1983 1988 1993 1998 2008 2003 Year Fig. 10: Standardized time series of SAR and the forecasted values for 5 years SO4 CI Ca Mg Na SAR TDS EC HCO3 12 1800 1600 10 1400 Mg/ l 1200 1000 6 800 4 µ Mohs/cm 8 600 400 2 200 0 1968 1971 1974 1977 1981 1984 1987 1990 1993 1996 1999 2002 2005 0 2008 Fig. 11: Time series of forecasted values for the last 5 years of water quality parameters Figure 9 shows standard series of Na+. The Figure shows that series follow a decreasing trend. Modeling was done for Na+ series after trend elimination which is presented in this Figure as well. The results show that the selected model, shown in Table 8, is capable of modeling the series well. Finally, Fig. 10 demonstrates standard series of SAR. Modeling the SAR series was done after trend elimination which is presented in this Figure as well. Table 9 shows that the selected model is capable of modeling the series well. The Results of Forecasting Table 10 shows the results of forecasting for 9 parameters. Also time series of HCO3-, Cl-, SO42+, Ca+, Mg2+, Na+, SAR, TDS and EC are shown in Fig. 11. The last 5 years of time series demonstrate the forecasted values for parameters. ■■ Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ Table 7: The results of Mg2+ generation, order (1,1) MODEL R R2 AIC RMSE (1,0,1) 0.72 0.51 -19.21 0.11 (1,1,1) 0.69 0.48 -19.63 0.11 (1,0,2) 0.73 0.53 -22.28 0.10 (2,0,1) 0.67 0.45 -16.90 0.12 (2,0,2) 0.80 0.64 -29.81 0.09 (1,1,2) 0.79 0.62 -27.97 0.10 (2,1,1) 0.80 0.65 -29.72 0.09 (2,1,2) 0.80 0.65 -27.76 0.10 Table 8: The results of Na+ generation, order (1, 2) MODEL R R2 AIC RMSE (1,0,1) 0.87 0.75 -47.43 0.08 (1,1,1) 0.87 0.75 -46.73 0.08 (1,0,2) 0.87 0.75 -45.56 0.08 (2,0,1) … (2,0,2) 0.89 0.80 -50.54 0.07 (1,1,2) 0.89 0.78 -49.33 0.07 (2,1,1) 0.87 0.76 -45.04 0.08 (2,1,2) 0.89 0.78 -47.42 0.07 Table 9: The results of SAR generation, order (1,2) MODEL R R2 AIC RMSE (1,0,1) … (1,1,1) 0.91 0.83 -56.16 0.07 (1,0,2) 0.90 0.82 -52.50 0.07 (2,0,1) … (2,0,2) … (1,1,2) 0.91 0.83 -54.13 0.07 Based on the field studies (JCE, 2005), the high growth and relative density of population, increasing the consumption of artificial stocks, leaving urban wastewaters and majority of rural sewage in traditional method through rivers, inconvenient methods of burying litters, dispersion of rubbishes and litters in surface waters and streams which finally inflow through rivers are considered as the major reasons of water quality deterioration. Agricultural wastewaters and livestock are other reasons which make surface waters polluted. Also the danger of water quality aggravation is increasing as a result of high population growth in the region and efficient actions are necessary in the region to prevent more environmental destruction. VE % 1.02 1.03 1.05 1.12 0.84 0.84 0.94 0.95 VE % 1.06 0.93 1.07 Acknowledgement 0.95 0.91 0.94 0.91 We thanks Water Resources Engineering Department, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, 6517833131, Iran. Author’s Contributions VE % Maryam Ghashghaie, KavehOstad-Ali-Askari, Vijay P. Singh and Saeid Eslamian designed the study, collected data, wrote the manuscript and revised it. 0.83 1.03 Ethics 0.81 This study approved by Water Resources Engineering Department, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, 6517833131, Iran. Table 10: Results of forecasting the 5 years of parameters Parameter RMSE VE % R2 TDS 40.91 0.07 0.79 EC 60.33 0.08 0.65 HCO30.09 0.04 0.86 Cl0.12 0.07 0.95 SO420.62 0.44 0.73 Ca2+ 0.68 0.20 0.70 Mg2+ 0.56 0.26 0.88 Na+ 0.19 0.18 1.00 SAR 0.09 0.16 0.91 References Ahmad, S., I.H. Khan and B.P. Parida, 2001. Performance of stochastic approaches for forecasting river water quality. Water Res., 35: 4261-4266. DOI: 10.1016/S0043-1354(01)00167-1 Box, G.E.P. and G.M. Jenkins, 1976. Time Series Analysis, Forecasting and Control. 1st Edn., Holden-Day, Toronto. Chang, T.J., 1988. Stochastic forecast of water losses. J. Irrigat. Drainage Eng., 114: 558-558. DOI: 10.1061/(ASCE)0733-9437(1988)114:3(547) Chenini, I. and S. Khemiri, 2009. Evaluation of ground water quality using multiple linear regression and structural equation modeling. Int. J. Environ. Sci. Technol., 6: 509-519. Chow, V.T. and S.J. Kareliotis, 1970. Analysis of stochastic hydrologic systems. Water Resources Res., 16: 1569-1582. DOI: 10.1029/WR006i006p01569 Damle, C. and A. Yalcin, 2007. Flood prediction using time series data mining. J. Hydrol., 333: 305-316. DOI: 10.1016/j.jhydrol.2006.09.001 Conclusion In this study, nine water quality parameters of Madian Rood River were studied at Baraftab station. The ARIMA modeling process was found suitable in generating and forecasting the parameters. SO42-, Na+ and SAR show a decreasing trend in spite of other elements of water quality, which show an increasing trend. However, using one lag to eliminate the trend stationary time series were prepared to work on. Also investigation of observed time series shows that there is a common increasing trend for all parameters except forSO42-, Na+ and SAR. EC, Cl-, Ca2+, Mg2+ and HCO3- show an increasing trend which is a sign for deterioration of water quality in the region. ■■ Maryam Ghashghaie et al. / American Journal of Engineering and Applied Sciences 2018, ■ (■): ■■■.■■■ DOI: 10.3844/ajeassp.2018.■■■.■■■ Durdu, Ö.F., 2010. Stochastic approaches for time series forecasting of boron: A case study of Western Turkey. Environ. Monitor. Assessment, 169: 687-701. DOI: 10.1007/s10661-009-1208-y El-Shaarawi, A.H., S.R. Esterby and K.W. Kuntz, 1983. A statistical evaluation of trends in the water quality of the Niagara River. J. Great Lakes Res., 9: 234-240. DOI: 10.1016/S0380-1330(83)71892-7 Fang, H., X. Wang, L. Lou, Z. Zhou and J. Wu, 2010. Spatial variation and source apportionment of water pollution in Qiantang River (China) using statistical techniques. Water Res., 44: 1562-1572. DOI: 10.1016/j.watres.2009.11.003 Faruk, D.Ö., 2010. A hybrid neural network and ARIMA model for water quality time series prediction. Eng. Applic. 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