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Application of Stochastic Models to Annual Extreme Streamflow Data

Authors: Karim Hamidi Machekposhti, Hossein Sedghi


This study was designed to find the best stochastic model (using of time series analysis) for annual extreme streamflow (peak and maximum streamflow) of Karkheh River at Iran. The Auto-regressive Integrated Moving Average (ARIMA) model used to simulate these series and forecast those in future. For the analysis, annual extreme streamflow data of Jelogir Majin station (above of Karkheh dam reservoir) for the years 1958–2005 were used. A visual inspection of the time plot gives a little increasing trend; therefore, series is not stationary. The stationarity observed in Auto-Correlation Function (ACF) and Partial Auto-Correlation Function (PACF) plots of annual extreme streamflow was removed using first order differencing (d=1) in order to the development of the ARIMA model. Interestingly, the ARIMA(4,1,1) model developed was found to be most suitable for simulating annual extreme streamflow for Karkheh River. The model was found to be appropriate to forecast ten years of annual extreme streamflow and assist decision makers to establish priorities for water demand. The Statistical Analysis System (SAS) and Statistical Package for the Social Sciences (SPSS) codes were used to determinate of the best model for this series.

Keywords: Stochastic models, ARIMA, extreme streamflow, Karkheh River.

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[1] Box, G. E. P.; Jenkins, G. M. “Time Series Analysis: Forecasting and Control”, Holden Day, San Francisco, California, 1976.
[2] Can, I., Selim, S. “Stochastic modelling of mean monthly flows of Karasu River, in Turkey”, Water and Environment Journal, 2009.
[3] Hipel, K. W., McLeod, A. I. “Time series modeling of water resources and environmental systems”, Amsterdam, Elsevier, 1994.
[4] Huang, Y. F., Mirzaei M., Yap W. K. “Flood Analysis in Langat River Basin using Stochastic Model”, International Journal of GEOMATE, 2016, 11(27): 2796-2803.
[5] Modarres, R. “Streamflow Drought Time Series Forecasting”, Stoch Environ Res Risk Assess, 2007, 21: 223–233.
[6] Mohamed, T. M., Etuk, E. H. “Application of Linear Stochastic Models to Monthly Streamflow Data”, Journal of Scientific and Engineering Research, 2017, 4(4):322-326.
[7] Musa, J. J. “Stochastic Modelling of Shiroro River Stream flow Process”, American Journal of Engineering Research (AJER), 2013, 2(6): 49-54.
[8] Nigam, R., Nigam, S., Mittal, S.K. “The river runoff forecast based on the modeling of time series,” Russian Meteorology and Hydrology, 2014, 39(11), 750-761.
[9] O'Connel, P. E. “ARIMA model in synthetic hydrology: Mathematical model for surface hydrology”, John Wiley, NY, USA, 1977.
[10] Pisarenko, V. F., Lyubushin, A. A., Bolgov, M. V., Rukavishnikova, T. A., Kanyu, S., Kanevskii, M. F., Savel’eva, E. A., Dem’yanov, V. V., & Zalyapin, I. V. “Statistical methods for river runoff Prediction”, Water Resources, 2005, 32(2): 115–126.
[11] Shakeel, A.M.; Idrees, A.M.; Naeem, H.M.; Sarwar, B.M. “Time Series Modelling of Annual Maximum Flow of River Indus at Sukkur,” Pakistan. Journal of Agricultural Sciences, 1993, 30(1), 36-38.
[12] Srikanthan, R.; McMohan, T.A., Irish, J.L. “Time series analysis of annual flows of Australian streams”, J. Hydrology, 1983.
[13] Stojković, M.; Prohaska, S.; Plavšić, J. “Stochastic structure of annual discharges of large European rivers”, J. Hydrology and Hydromechanics, 2015, 63(1), 63–70.
[14] Tian, P., Zhao, G. J, Li, J., Tian, K. “Extreme Value Analysis of Stream flow Time Series in Poyang Lake Basin, China”, Water Science and Engineering, 2011, 4(2): 121-132.
[15] Thomas, H. A., Fiering, M. B. “Mathematic synthesis of streamflow sequences for analysis of river basins by simulation, in Design of Water Resources Systems”, edited by A. Mass, pp. 459 – 493, Harvard Univ. Press, Cambridge, Mass. 1962.
[16] Vijayakumar, N., Vennila, S. A. “comparative analysis of forecasting reservoir inflow using ARMA model and Holt winters exponential smoothening technique”, International Jour. of Innovation in Science and Mathematics, 2016, 4(2): 85-90.
[17] Yevjevich, V. “Stochastic Processes in Hydrology”, Water Resour. Publ., Highlands Ranch, Colo. 1972.
[18] Yurekli, K., Kurunc, K., Ozturk, F. “Application of linear Stochastic models to monthly flow data of Kelkit Stream”, Ecological Modeling, 2005, 183: 67–75.