Performance Evaluation of ARMA and CARMA Models in Modeling Annual Precipitation of Urmia Synoptic Station

Document Type : Research Paper

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Abstract

Due to the complexity of hydrological processes it seems that the multivariate models with more parameters can be used to improve the accuracy and results of the time series models. Indeed, with the involving other effective parameters in the multivariate models the results of description, modeling and forecasting of various parameters can be improved. In this research, the univariate ARMA models and multivariate contemporaneous autoregressive moving average (CARMA) models were evaluated to modeling the total annual precipitation of Urmia synoptic station. In order to use ARMA models total annual precipitation time series of Urmia station in the period of 1961-2010 was used. Furthermore, average of air temperature (°C), mean wind speed (Knot) and mean of precipitation time series in annual time scale of Urmia synoptic station were used in modeling by CARMA models. The results showed that by incorporation the mentioned time series, the accuracy of the models increased. As, for CARMA model in comparison with ARMA model, better results were obtained because of the higher correlation coefficient equal to 0.960 and lower root mean square error equal to 21.611 between the observed and modeled data. Also according to the obtained results, using the multivariate ARMA models caused to decrease model error up to 31 percentages.

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منابع مورداستفاده
ترابی س، 1380. بررسی و پیش­بینی تغییرات دما و بارش در ایران. دانشگاه تبریز، رساله دکتری جغرافیای طبیعی، 201 صفحه.
فیروزی ف، نگارش ح و خسروی م، 1391. مدل­سازی، پیش­بینی و بررسی روند بارش در ایستگاه­های منتخب استان فارس. فصل­نامه علمی – پژوهشی برنامه­ریزی منطقه­ای، جلد 2، شماره 7، صفحه­های 77 تا 91.
گلابی م، آخوندعلی ع­م، رادمنش ف و کاشفی­پور م، 1393. مقایسه دقت پیش­بینی مدل­های باکس – جنکینز در مدل­سازی بارندگی فصلی (مطالعه موردی: ایستگاه­های منتخب استان خوزستان). فصل­نامه تحقیقات جغرافیایی، جلد 29، شماره 3، صفحه­های 61 تا 72.
گودرزی ل و روزبهانی ع، 1393. مقایسه مدل­های سری زمانی خودهمبسته با میانگین متحرک و هالت وینترز در پیش بینی بارش. دومین همایش ملی بحران آب (تغییر اقلیم، آب و محیط زیست)، دانشگاه شهرکرد، 18 و 19 شهریور.
ناظری تهرودی م، احمدی ف، خلیلی ک و ناظری تهرودی ز، 1392. کاربرد نرم­افزار SAMS2007 در مدل­سازی اقلیم آینده استان کردستان جهت پیش بینی دما و بارندگی (مطالعه موردی: ایستگاه سینوپتیک). اولین کنفرانس هیدرولوژی مناطق خشک و نیمه خشک. 4 و 5 اردیبهشت. سنندج.
ویسی­پور ح، معصوم­پور سماکوش ج، صحنه ب و یوسفی ی، 1389. تحلیل پیش­بینی روند بارش و دما با استفاده از مدل­های سری زمانی آریما (نمونه موردی: شهرستان کرمانشاه)، فصل­نامه علمی پژوهشی جغرافیا، سال 3، شماره 12، صفحه­های 65 تا 80.
Box GE and Jenkins GM, 1976. Time series analysis. Forecasting and Control, San Francisco. Holden-Day.
Camacho F, 1984. Contemporaneous ARMA modeling with applications. Ph.D. Dissertation, Department of Statistical and Actuarial Sciences. The University of Western Ontario, London, Ontario, Canada.
Camacho F, McLeod AI and Hipel KW, 1985. Contemporaneous autoregressive - moving average (CARMA) modeling hydrology. Water Resources Bulletin 21:709-720
De Domenico M, Ghorbani MA, Makarynskyy O, Makarynska D and Asadi H, 2013. Chaos and reproduction in sea level. Applied Mathematical Modeling 37: 3687-3697.
Fiering MB, 1964. Multivariate techniques for synthetic hydrology. Journal of the Hydraulics Division 90(5): 43-60.
Kendall MG, 1938. A new measure of rank correlation. Biometrika 36: 81-93.
Khalili K, Nazeri Tahrudi M, Abbaszadeh Afshar M and Nazeri Tahrudi Z, 2014. Modeling monthly mean air temperature using SAMS2007 (Case Study: Urmia synoptic station). Journal of Middle East Applied Science and Technology 15: 578-583.
Khatibi R, Ghorbani MA, Naghipour L, Jothiprakash V, Fathima TA and Fazelifard MH, 2014. Inter-comparison of time series models of lake levels predicted by several modeling strategies. Journal of Hydrology 511:1-16.
Mann HB, 1945. Nonparametric test against trend. Econometrica 13: 245-259.
Matalas NC and Wallis JR, 1971. Statistical properties of multivariate fractional noise processes. Water Resource Research 7: 1460-1468.
Matalas NC, 1967. Mathematical assessment of synthetic hydrology. Water Resources Research 3(4): 937-945.
McLeod Al and Hipel KW, 1978. Simulation procedures for Box - Jenkins models. Water Resources Research 14(5): 969-975.
Mejia JM, 1971. On the generation of multivariate sequences exhibiting the Hurst phenomenon and some flood frequency analyses (Doctoral dissertation, Colorado State University).
Mendenhall W and Reinmuth J, 1982. Statistics for Management and Economics. Fourth Edition, Duxbury Press.
O'Connel PE, 1974. Stochastic modeling of long-term persistence in stream flow sequences. Ph.D, Thesis. Imperial College, University of London.
Pegram GGS and James W, 1972. Multilag multivariate autoregressive model for the generation of operational hydrology. Water Resources Research 8(4): 1074-1076.
Salas JD, Delleur JW, Yevjevich V and Lane WL, 1980. Applied Modeling of Hydrologic Time Series. Water resource Publications, P. O. Box 2841. Littleton, Colorado .80161, U.S.A. 484 P.  
Swinscow TDV and Campbell MJ, 2002. Statistics at Square One. London: BMJ Publication. 106 P.
Thomas HA and Fiering MB, 1962. Mathematical Synthesis of Stream flow Sequences for the Analysis of River basin by Simulation. Harward University Press, Cambrige, 751P.
Valencia D and Schaake JC, 1973. Disaggregation processes in stochastic hydrology. Water Resource Research 9(3): 580-585.
Wilcoxon F, 1945. Individual comparison by ranking methods. Biometrics 1(6): 80–83.
Yevjevich VM, 1963. Fluctuations of wet and dry years. Part 1. Research data assembly and mathematical models. Textit hydrology Paper 1, Colorado State University, Fort Collins, Colorado.
Young GD and Pisano WC, 1968. Operational hydrology using residuals. Journal of the Hydraulics Division 94(4): 909-924.       
Zou P, Jingsong Y, Jianrong F, Guangming L and Dongshun L, 2010. Artificial neural network and time series models for predicting soil salt and water content. Agricultural Water Management 97: 2009-2019.
Water and Soil Science
Volume 26, 2-1 - Serial Number 2
September 2016
Pages 13-28

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