Statistical modeling of monthly streamflow using time series and artificial neural network models: Hindiya Barrage as a case study

Streamflow is an important issue in the design, operation, and control of many vital projects in the water resources and sanitary/environmental engineering specialities; examples are reservoir storage capacity, water treatment plants (WTPs), and wastewater treatment plants (WWTPs). For this reason, recorded data of streamflow (hourly, daily, weekly, monthly, and yearly) are required for the optimum design, operation, and control of these vital projects. Kawamura (2000) showed that during the preliminary studies to design a (WTP), the project engineer must evaluate the potential sources of water; one of the elements of this evaluation is the quantity of water required, which is directly related to the streamflow of the nearby river (delivering raw water). The importance of streamflow in the design, operation, and control of a WWTP is best illustrated by the direct relation between the self-purification of rivers to the river streamflow (as shown in the Streeter-Phelps equation) and the direct effect of the dilution factor (Metcalf et al. 1979). Monthly streamflow of the Sefidrood river, Iran, and Sangeen river, Canada, were studied and modeled by applying autoregressive (AR), moving average (MA) models and compared with two artificial intelligence (AI) approaches, namely, multivariate adaptive regression splines (MARS) and gene expression programming (GEP). Results indicate that AI models outperformed the conventional AR and MA models (Mehdizadeh et al. 2019). Frausto-Solis et al. (2008) compared ARIMA versus ANN in forecasting streamflow. Their results indicate that ARIMA has a higher forecast accuracy than ANN methodology. Moeeni et al. (2017) compared the Seasonal Autoregressive Integrated Moving Average (SARIMA) with the Artificial Neural Network-Genetic Algorithm (ANN-GA) method in forecasting the monthly streamflow. Their results confirm that the SARIMA model have much more accuracy than the ANN-GA model in short-term and long-term forecasting. Joodavi et al. (2020) presented a methodology based on the combination of numerical groundwater flow simulations and reservoir operation optimization models to develop an optimization model for the management of the off-stream Bar-Reservoir operation (Iran), taking into account the lake bed seepage and the random inflow to the reservoir, the planned objective was to satisfy water demand for a total amount of 12 million m³/year for drinking and industrial purposes. A two-stage time series model for the monthly flows of the Lim River basin in South-Eastern Europe for the period 1950–2012 was carried out by Stojković et al. (2020). The model took into consideration climate change and consisted of several components (trend, long-term periodicity, seasonality, and the stochastic component). It was designed to estimate future water availability. Water demand of any city varies according to the variation of climatic variables (Zubaidi et al. 2020a, 2020b, 2020c), such as rainfall, temperature, humidity, and evaporation (Zubaidi et al. 2019a, 2019b, 2020d, 2020e). Feng & Niu (2021) proposed a hybrid artificial neural network model enhanced by the addition of a cooperation search algorithm for nonlinear river stream flow time series forecasting. Mohammadi et al. (2020) developed novel robust models to improve the accuracy of daily streamflow time series modeling. Niu & Feng (2021) evaluated the performance of five artificial intelligence models in forecasting the daily streamflow time series. Adnan et al. (2020) evaluated the abilities of three models to predict monthly streamflow; they are Group Method of Data Handling-Neural Networks (GMDH-NN), Dynamic Evolving Neural-Fuzzy Inference System (DENFIS), and Multivariate Adaptive Regression Spline (MARS) methods. Peng et al. (2020) developed a monthly streamflow prediction model based on the Random Forest Algorithm and Phase Space Reconstruction Theory. Khazaei et al. (2020) simulated daily runoff correlated to weather generators utilizing the LARS-WG model. Avand & Moradi (2020) used machine learning models (including LARS-WG), remote sensing, and GIS to study the effects of changing climatic variables and land uses on flood probability.

To the best of the authors’ knowledge, this is the first time that statistical modeling models were built for monthly streamflow at the Euphrates River (Hindiya Barrage) in Iraq. Generally, this paper aims to firstly investigate the monthly streamflow at downstream of the Euphrates River (Hindiya Barrage) /Iraq for the period of January 2000 to December 2018. Secondly, building a Box-Jenkins ARIMA forecasting model for the data recorded during the above period, checking its adequacy and proving its goodness of fit. Then, performing a one-step-ahead forecast during the year 2019 (12 months). Thirdly, train, test and validate the above-recorded data using the multi-layer perceptron (MLP) and feed-forward neural network (FNN). Then performing a one-step-ahead forecast during the year 2019 (12 months). Finally, compare the forecast accuracy for the two methods relying on the root mean squared error (RMSE) and the coefficient of determination (⁠⁠. Average monthly streamflow data at the downstream of the Euphrates River (Hindiya Barrage), Iraq for the period January 2000 to December 2019 were selected as a case study (these data were obtained from the Ministry of Water Resources/Al-Mussaib Water Resources Directorate, Iraq). The data for the period 2000–2018 was adopted in model building and that during 2019 were adopted for calculating model forecast accuracy.

Figure 1 is an aerial view (Google Earth) of the study area with Latitude 32°43′01″N, Longitude 44°16′01″E.

The recommended modeling procedure here, according to the published literature (Faraway & Chatfield 1998; Tealab et al. 2017), is the nonlinear autoregressive (NAR) or the autoregressive neural network (ARNN). It is of the kind of multi-layer perceptron (MLP), which comprises an input layer, hidden layer and an output layer. The input layer holds the target vector (time series), while the output layer computes the estimator vector (time series). The hidden and output layers are governed by an activation function, which may be defined by a (logistic, tanh, softmax…), and a weight function (uniform and Gaussian). Figure 2 is a schematic representation of a perceptron learning process.

Applying the Box-Jenkins modeling procedure to the recorded data, using IBM SPSS version 20 software referring to the route (Analyze/Forecasting/Create Models/Expert Modeler), the best-fit model relying on the RMSE criteria was: ARIMA (1,1,0) (0,1,1).

The original data suggested a natural logarithmic transformation to enhance the normality of residuals. The above model gave = 0.844, RMSE = 42.049 and Ljung-Box Q(18) = 21.906 with degrees of freedom (DF) = 16, also the significance of Q was 14.6% > 5%, indicating that residuals from the model were uncorrelated (random). Figure 3 depicts the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the residuals. Figure 4 depicts the normal probability paper of the residuals.

From the above figures, it is evident that the residuals are normally independently distributed. Figure 5 describes the predicted values of the streamflow time series together with the recorded values. It states that there was a clear, strong correlation between predicted and recorded values.

Figure 6 depicts the forecasted monthly streamflow for the 12 months during 2019, together with the recorded values. The calculated RMSE = 48.7 and the calculated = 0.801.

Applying the (ANN) modeling procedure to the above data using the STATISTICA version 12 software, referring to the route (Data Mining/Neural Networks/Time Series (Regression)), taking into consideration that the recorded data was considered as the Target, the input layer was taken as the Target with a lag of specified length, the input layer data were classified as (70% Training + 15% Test + 15% Validation) randomly. The results in the output layer will be compared with the target. Table 1 lists the statistics of the predicted ANN models for different lags between (1–12), noting that one cycle of seasonality = 12 months.

Table 1 reflects the fact that all predicted models are not strongly correlated with the Target, indicating a small coefficient of determination (⁠⁠). It is evident from Table 1 that the maximum (R) and the minimum SSE (validation stage) occurred at lag 1 (MLP 1-3-1); for this, it is selected as the best model. The notation (MLP 1-3-1), for example, refers to a multi-layer perceptron with 1 (number of inputs), 3 (number of hidden units), and 1 (number of outputs); also, the notation BFGS 4 refers to the Broyden-Fletcher-Goldfarb-Shanno training algorithm with 4 cycles of iteration. Figure 7 is a time-series graph that compares the prediction of the model at lag 1 (MLP 1-3-1) with the recorded data (Target). Figure 8 compares the (Target) streamflow Q (x-axis) with the output streamflow from the selected ANN model (y-axis). It is evident from Figures 7 and 8 that the predictions are not strongly correlated to the original (recorded) data, as prescribed in Table 1. The ANN time series model gave RMSE = 84.63 and = 0.365, indicating that it is less efficient than the Box-Jenkins time series model predicted above (which gave RMSE = 42.049 = 0.844). Figure 9 depicts the forecasted monthly streamflow for the 12 months during 2019 (by the ANN time series model), together with the recorded values. The calculated (RMSE = 93.4) and the calculated = 0.269). From this figure, it is evident that the ANN model does not simulate the seasonality of the recorded data. Figures 6 and 9 give an indication that Box-Jenkins models are competent in simulating seasonality, which is not the case for ANN models. Comparing the forecast accuracy (RMSE and ⁠) for the ANN model during 2019 with that resulted from the Box-Jenkins model, it is evident that the latter is more accurate. This result is in accordance with the results documented by other authors (Moeeni et al. 2017; Mehdizadeh et al. 2019). Figure 10 illustrates the future forecasts resulting from the Box-Jenkins model mentioned above by Equations (14) and (15) together with the recorded and fit monthly streamflow for the period 2000–2018. The long-term periodicity is clearly observed; this is in accordance with Stojković et al. (2020).

From the results of the study, it can be concluded that the Box-Jenkins model was more accurate than the ANN model in forecasting future monthly streamflow downstream of the Euphrates River (Hindiya Barrage)/Iraq for the period 2000–2019, that the ANN model was not able to simulate seasonality, which was not the case for the Box-Jenkins model. Future forecast of monthly streamflow by Box-Jenkins models indicates the existence of some long-period trend in the form of long-term periodicity, which already exists in the recorded data. It is advisable to study the monthly streamflow in terms of the climatic variables through multiple regression and apply the same modeling procedure; that is, the Box-Jenkins (transfer function models) and the ANN (regression models), also the Support Vector Regression and the Random Forest analysis may be adopted in the future studies.

The authors would like to express their appreciation and gratitude to the Ministry of Higher Education and Scientific Research, Al-Furat Al-Awsat Technical University, and the Ministry of Water Resources/Al-Mussaib Water Resources Directorate/Iraq for the facilities provided to complete this research. The authors are also grateful to the colleagues and the technician team who provided insight and expertise that greatly assisted the completion of the research.

Data cannot be made publicly available; readers should contact the corresponding author for details.