Urmia lake water level forecasting using Box-Jenkins model and system dynamics approach

Water is one of the largest challenges in the current century and can be a source of negative and positive changes in the world. In fact, nowadays challenge of water resource is a problem of many countries in the Middle East. Also, lake’s Water level variations are highly sensitive to many environmental forcing such as atmospheric pressure and wind forcing, as well as many other dynamic, presumably nonlinear and interconnected, physical variables. It is a complex phenomenon affected by the natural water exchange between the lake and its watershed, and thus the level reflects the climatic changes within the region. Urmia Lake is the largest inland lake in Iran and the second largest saline lake in the world. Understanding and forecasting water level fluctuations in the Lake is important for a variety of water resource management operations. Because the water level of the lake decreased and its water salinity increased by the decrease of precipitation, droughts, overuse of surface water resources and dams construction. Therefore, forecasting water levels of the Lake has started to attract the attention of the researchers in the country. This paper represents the evaluation of different stochastic methods for simulation and forecasting the lake’s water level.
This study utilizes two model approaches to predict water levels in the Urmia Lake in Iran: a time series forecasting (Seasonal Autoregressive Integrated Moving Average, SARIMA) model, and a combined SARIMA and system dynamics approach model. System dynamics is one of the most effective methods to evaluate complex systems. It is a computer-aided approach to policy analysis and design. It applies to dynamic problems arising in complex social, managerial, economic, or ecological systems-literally any dynamic systems characterized by interdependence, mutual interaction, information feedback, and circular causality. Mathematically, the basic structure of a formal system dynamics computer simulation model is a system of coupled, nonlinear, first-order differential (or integral) equations. Simulation of such systems is easily accomplished by partitioning simulated time into discrete intervals of length dt and stepping the system through time one dt at a time. A systems dynamics model consists of stocks and flows. A stock is an accumulation of material that has built up in a system over time. The model indicates system status and decisions, so the activities of the system are based on them. A flow is a material that enters or leaves a stock over a period of time. In this study, Vensim system dynamics software was used, as it provides a fully integrated simulation system to conceptualize, simulate, and analyze models of dynamic systems. This modeling tool allows the creation of complex models with greater ease than conventional methods. Also, monthly water level data (a total of 396 observations) was collected for model calibration and validation. The measured data from January 1, 1976, to December 31, 2007 (a total of 372 data sets), was used for calibration, while the data from January 1, 2008, to December 31, 2009 (a total of 24 data sets), was adopted for validation. To evaluate the performances of these models, two different criteria were used to compare the predicted results with the observed data: root mean square error (RMSE) and coefficient of correlation (𝑅). Additionally, The Akaike information criterion (AIC) was used to determined best model fit for the data. Data were analyzed using MINITAB statistical software.
For time series forecasting, ARIMA (1,1,3) (0,1,2), ARIMA (1,1,4) (0,1,1), ARIMA (1,1,2)(0,1,1) and ARIMA (1,1,3) (0,1,1) were used. According to the performance assessment, it could be found that ARIMA (1,1,2)(0,1,1) yields the best water level prediction with RMSE, 𝑅2, and AIC equal to 0.24 m, 0.74 and -2066.69, respectively. To improve the water level prediction quality, a system dynamics model was utilized to improve the prediction results from Autoregressive Integrated Moving Average model. The results showed that the proposed approach gave the best performance assessment with RMSE and 𝑅2 equal to 0.17 m and 0.75. Therefore, the proposed model was capable of simulating and predicting the lake’s water level. This approach used computer simulation to model a dynamic system that could help to develop scenarios to consider water level fluctuations. Its merits include the increased speed of model development, ease of model improvement, inherent flexibility and more reliable than the conventional methods.