Comparison of Monte Carlo Method and SARIMA Time Series Models in Forecasting Jamishan River Flow

Document Type : Research Paper

Authors

• Azar Darboei ¹
• Mohammad Taghi Sattari ²

¹ Department of Water Engineering Faculty of Agriculture, University of Tabriz,Tabriz, Iran.

² Department of Water Engineering Faculty of Agriculture, University of Tabriz, Tabriz, Iran.

Abstract

Keywords

• Discharge rate
• Jamishan
• Modeling
• Periodic pattern
• Seasonal autoregressive integrated moving average

Main Subjects

• آبیاری و زهکشی

Introduction

A crucial task in every water resource management is forecasting the discharge rates of river basins from various time horizons. Despite the prevalence of autoregressive integrated moving average models in the latter area, not much work has been done about the validation purposes of them in evaluating the monthly, seasonally and yearly discharge rates of river basins. Meanwhile, limited researches have been carried out into the performance of the Monte Carlo simulations of discharge rates observed with different time scales. Furthermore, multiple modelling with both autoregressive integrated moving average and Monte Carlo methods on time series has yet to be conducted. Hence, the present paper is aimed at filling this research gap by means of forecasting monthly, seasonally and yearly discharge rates of the Jamishan river, located in Kermanshah Province, Iran, with multiple models from autoregressive integrated moving average as well as Mone Carlo methods, thereby providing a more efficient and precise mechanism for forecasting this river’s water flow.

Method

Observations of the discharge rates of the Jamishan river throughout 31 years from 1989 to 2009 were collected. The observations were then converted into monthly, seasonally and yearly data in order to be simulated with Monte Carlo and time series methods. In the Monte Carlo approach, the most suitable distributions of the transformed time series were determined first, followed by performing simulations based on them. In the autoregressive integrated moving average method, after pre-processing data and fitting them with different model configurations, the optimal models were selected based on Akaike information criteria, Akaike information criteria corrected and Bayesian information criteria. Accordingly, the best models were determined under the assumptions of residuals’ normality, stationarity and independence.

Results

Forecasting the Jamsihan river’s discharge rates observed from different timeframes demonstrated the efficiency of both autoregressive integrated moving average and Monte Carlo methods. Particularly, the seasonal autoregressive integrated moving average models for monthly, seasonally and yearly observations were optimally configurated as ,  and , respectively. Assessing the performance diagnostics of the two methods suggest the seasonal autoregressive integrated moving average model with RMSE of 0.04, the Monte Carlo model with RMSE of 0.14 and the seasonal autoregressive integrated moving average with RMSE of 0.28 as the selected forecasting method for monthly, seasonally and yearly data, respectively. This study contributes to the current literate in the applied hydrology in various ways. Future research may extend this analysis by including other regional rivers neighboring the Jamishan river so as to compare the results and performance diagnostics from the geohydrologically similar rivers. Moreover, decisionmakers as well as practitioners in water resource management can be benefited from this study for the purpose of allocation optimization and the sustainable development of the region.

Conclusions

Water scarcity commingled with high demand in arid lands and semi-dry areas necessitate developing and devising an efficient approach for forecasting basins’ discharge rates when practicing water resource management. This study aimed to investigate the performance of two autoregressive integrated moving average and Monte Carlo methods in forecasting monthly, seasonally and yearly time series of the Jamishan river’s flow. Both methods achieved acceptable accuracy, where the seasonal autoregressive integrated moving average model of monthly data with , ,  and , Monte Carlo simulation of seasonally data with , ,  and , and the seasonal autoregressive integrated moving average model of yearly with , ,  and  indicated the best performance. In general, the findings suggest the suitability of both seasonal autoregressive integrated moving average and Monte Carlo methods for forecasting and simulating the discharge rates of river basins.

Author Contributions

Azar Darboei: software, validation, formal analysis, investigation, resources, data curation, writing—original draft preparation.

Mohammad Taghi Sattari: Conceptualization, methodology, writing—review and editing, supervision, project administration, funding acquisition, visualization. All authors have read and agreed to the published version of the manuscript.

 Data Availability Statement

Data is available on reasonable request from the authors.

Acknowledgements

The authors would like to thank The Regional Water Organization of Kermanshah for assistance in providing the information.

 Ethical considerations

The authors avoided data fabrication, falsification, plagiarism, and misconduct.

Conflict of interest

The author does not declare any conflicts of interest.