The Analysis of Seasonal Precipitation Time Series in Iran

Document Type : Full length article


1 Assistant professor of climatology, department of geography, Razi University, Kermanshah, Iran

2 Assistant professor of statistics, department of statistics, Razi University, Kermanshah, Iran

3 MSc in Climatology, Razi University, Kermanshah, Iran


Due to the increasing significance of water supply in Iran, the management of water resources is of a particular importance. Precipitation is regarded as the most considerable source of water that is faced with great temporal (daily, monthly, seasonal and yearly) and spatial changes among other climatic factors. Therefore, the studies, focusing extensively on this issue are really useful, for they would provide the ways for optimal use and water management in the temporal and spatial scales.
Generally, there are a lot of predictive methods trying to determine the relationship between dependent and independent variables. Moreover, different statistical models have been applied to predict climatic variables. In recent years, the analysis of time series has been extensively used in scientific issues.
As a matter of fact, the analysis of a time series provides the ways to determine its possible structure, recognize its components to analyze and predict the process and future values. Therefore, the investigation and prediction of precipitation in different temporal dimension (daily, monthly, seasonal, and yearly) for each region and watershed are considered as the most important climatic parameters for optimal use of water resources affecting temporal and spatial distribution of other climatic factors. Accordingly, it is necessary to recognize the seasonal pattern of precipitation, and spatial similarities and differences of this time pattern, especially when they are not the same for different regions of Iran. The present research aims at studying the seasonal precipitation of Iran. It turns out that the precipitation does not follow a distinct unique pattern in each part of Iran, so the recognition of seasonal precipitation, separating different region, would help the authorities for environmental planning and management. Moreover, it even can lead to more successful predictions.
Materials and methods
In the present study, seasonal precipitation time series of synoptic stations (during the statistical period of 1985- 2014) is modeled applying SARIMA model. The accuracy of the fitted models to the data series for each station is evaluated by the standardized residuals graph, autocorrelation graph of residuals models and Ljung-Box test (in the significance level of 0.05). Then, the appropriate model for seasonal precipitations is presented for each station (Table. 1) according to Akaik Information Criterion (AIC). Furthermore, seasonal and inter-seasonal autoregressive rate (P, p) and moving average rate (Q, q), which were found by fitted models, are studied to investigate the seasonal and interseasonal precipitation relationship in each station. At the end, the relationship of seasonal precipitation patterns is mapped by applying ArcGIS.
Moreover, all statistical tests and temporal series computations are conducted in the environment of R software. 
Results and discussion
Evaluating the adequacy of the fitted models has revealed that the model of correlation structure is able to describe the data for all stations in this study (except for Booshehr, Shahr-e-Kurd, Birjand, Omidiye Aghajari, and Rasht). This can analyze seasonal precipitations for the stations correctly. Therefore, it is adequate enough. Seasonal and interseasonal autoregressive rate (P. p) and moving average (Q, q) from the fitted models have been used to determine the relationship of seasonal and interseasonal precipitation for each station. Except for Kashan, Abali, Doushantape, Semnan and Shahroud stations, the other 62 studying stations (93%) follow the seasonal pattern showing seasonal behavior. Furthermore, the rate of seasonal part of the model (P) shows that there is a direct relationship between the precipitation of each season and the precipitations of that season in the previous years (1 to 2). The (Q) rate has revealed that random oscillation of seasonal precipitations of 1 to 2 years before is also indirectly effective for some stations. The rates of interseasonal difference (d) have been investigated to analyze the process of time series of precipitation for the studying stations. It has demonstrated that the stations of Maraghe, Sanandaj, Hamedan-Nouzhe, and Ferdos have a decreasing process in their data, while, in the other stations, seasonal precipitation does not follow a decreasing or increasing process. In fact, it follows a constant process having no static process.
Applying SARIMA model, the relationship of seasonal and interseasonal precipitations of Iran has been recognized.  Hence, first, the adequacy of SARIMA model has been evaluated. The findings prove that the aforesaid model can describe the correlation structure of the data for the studying stations (except for Booshehr, Shahr-e-Kurd, Birjand, Omidiye Aghajari and Rasht) well and it is adequate enough. This fact is in accordance with the findings of Alijani and Ramezani (2002), Golabi et al (2013), Chang et al (2012), Bari et al (2015) who used SARIMA model to predict drought and temporal series of precipitation to prove its adequacy.
The investigation of seasonal and interseasonal precipitation dependency and the analysis of temporal series process of seasonal precipitation in each station show that, according to seasonal autoregressive rate (P) in all studying stations (except for Kashan, Abali, Doushantape, Semnan and Shahroud), the precipitations of each season is directly dependent upon the precipitations of that seasons in the previous years (1 to 2). Besides, the random oscillation of seasonal precipitation of the previous years (1 to 2) also affects the seasonal precipitations on some stations. Therefore, it can be concluded that the precipitations of the stations (93%) follow the seasonal patterns showing seasonal behavior. Furthermore, the findings of interseasonal autoregressive rate (p) for all stations prove that the precipitations of each season have a direct relationship with the precipitations of the previous season for 19 stations (28%).
Analyzing the process of seasonal precipitations has indicated that, except for Maraghe, Sanandaj, Hamedan-Nouzhe and Ferdos stations,  time series of seasonal precipitation has no process (random or non-random) in the stations. This process has a decreasing process for these 4 stations, while it is static in the other stations.


Main Subjects

آذرخشی، م.؛ فرزادمهر، ج.؛ اصلاح، م. و صحابی، ح. (1392). بررسی روند تغییرات سالانه و فصلی بارش و پارامترهای دما در مناطق مختلف آب و هوایی ایران، نشریة مرتع و آبخیزداری، 66(1): 1ـ16.
چتفیلد، ک. (1381). مقدمه‏ای بر تحلیل سری‏های زمانی، ترجمة حسینعلی نیرومند و ابوالقاسم بزرگ‏نیا، چ2، مشهد: انتشارات دانشگاه فردوسی مشهد.
حسینعلی‏زاده، م.؛ حسنعلی‏زاده، ن.؛ بابانژاد، م. و رضانژاد، م. (1393). پیش‏بینی بارش ماهانه با استفاده از بسته‏های تخصصی سری‏های زمانی در محیط، نرم‏افزار ) R مطالعة موردی: ایستگاه ارازکوسة استان گلستان(، نشریة حفاظتوبهره‏برداریازمنابعطبیعی، 2(2): 1ـ12.
داداشی رودباری، ع.ع. و کیخسروی کیانی، م. (1395). واکاوی مکانی و زمانی روند بارش سالانة ایران طی سال‏های 1329 تا 1386، مجلة محیط زیست و منابع آب، 2(2): 111ـ121.
دودانگه، ا.؛ عابدی کوپایی، ج. و گوهری، س.ع. (1391). کاربرد مدل‏های سری‏ زمانی به منظور تعیین روند پارامترهای اقلیمی در آینده در راستای مدیریت منابع آب، علوم آب و خاک (علوم و فنون کشاورزی و منابع طبیعی)، 16(59): 59ـ74.

رضیئی، ط.؛ دانش کارآراسته، پ. و ثقفیان، ب. (1384). بررسی روند بارندگی سالانه در مناطق خشک و نیمه‏خشک مرکزی و شرقی ایران، دوماهنامة آب و فاضلاب، 16(2): 73ـ81.

شریفان، ح. و قهرمان، ب. (1386). ارزیابی پیش‏بینی باران با به‏کارگیری تکنیک ساریما در استان گلستان، علوم کشاورزی و منابع طبیعی، 3: 1ـ14.
شعبانی، ب.؛ موسوی بایگی، م.؛ جباری نوقابی، م. و قهرمان، ب. (1392). مدل‏سازی و پیش‏بینی دمای حداکثر و حداقل ماهانة دشت مشهد با استفاده از مد‏‏های سری ‏زمانی، نشریة آب و خاک (علوم و صنایع کشاورزی)، 27(5): 896ـ906.
شفیعی، م.؛ قهرمان، ب.؛ انصاری، ح. و شریفی، م.ب. (1390). شبیه‏سازی تصادفی شدت خشک‏سالی بر اساس شاخص پالمر، مدیریت آب و آبیاری، 1(1): 1ـ13.
صلاحی، ب. و ملکی مرشت، ر. (1394). پیش‏بینی و تحلیل تغییرات بارش‏های ماهانة شهرستان اردبیل با استفاده از مد‏ل‏های آریما، اتورگرسیو و وینترز، نشریة آب و خاک، 29(5): 1391ـ1405.
عبدالله‏نژاد، ک. (1394). مدل‏های تصادفی سری زمانی در پیش‏بینی بارندگی ماهانه (مطالعة موردی: ایستگاه هاشم‏آباد گرگان)، مجلة آمایشجغرافیاییفضا، 5(17): 15ـ25.
علیجانی، ب. و رمضانی، ن. (1381). پیش‏بینی خشک‏سالی‏ها و ترسالی‏های استان مازندران با استفاده از مدل باکس- جنکینز، پژوهش‏های جغرافیایی، یادنامة دکتر احمد مستوفی، ص155ـ 169.
فرج‏‏زاده، م. (۱۳۸۶). تکنیک‏های اقلیم‏شناسی، تهران: سمت.
گلابی، م.ر.؛ آخوندی، ع.م.؛ رادمنش، ف. و کاشفی‏پور، م. (1393). مقایسة دقت پیش‏بینی مدل‏های باکس- جنکینز در مدل‏سازی بارندگی فصلی (مطالعة موردی: ایستگاه‏های منتخب استان خوزستان)، تحقیقات جغرافیایی، 29(3): 61ـ72.
معروفی، ص.؛ ختار، ب.؛ صادقی‏فر، م.؛ پارسافر، ن. و ایلدورمی، ع.ر. (1393 الف). پیش‏بینی خشک‏سالی با استفاده از سری زمانی ساریما و شاخص SPI در ناحیة مرکزی استان همدان، نشریة پژوهشآبدرکشاورزی، 28(1): 213ـ 225.
معروفی، ص.؛ سقائی، ص.؛ ارشاد فتح، ف. و ختار، ب. (1393 ب). ارزیابی مدل‏های سری زمانی به منظور برآورد متوسط دمای ماهانه در ایستگاه‏های سینوپتیک قدیمی ایران طی دورة آماری 1977ـ2005، نشریة دانش آب و خاک، 24(4): 215-226.
موحدی، س.؛ عساکره، ح.؛ سبزی‏پرور، ع.ا.؛ مسعودیان، ا. و مریانجی، ز. (1392). بررسی تغییرات الگوی فصلی بارندگی در استان همدان، فصل‏نامة تحقیقات جغرافیایی، 28(2): 33ـ48.
ناظری تهرودی، م.؛ خلیلی، ک. و احمدی، ف. (1395). تحلیل روند تغییرات ایستگاهی و منطقه‏ای بارش نیم قرن اخیر کشور ایران، نشریة آب و خاک، 30(2): 643ـ654.
Abdolahnezhad, K. (2015). Forecasting of Monthly Sum-raining by Stochastic Models in Time Series, Geographical Planning of Space Quarterly Journal, 5(17): 15-25.
Abu Zafor, M.D.; Chakraborty, A.; Muniruzzaman, SH.M.D. and Mojumdar, S.R. (2016). Rainfall Forecasting in Northeastern part of BangladeshUsing Time Series ARIMA Model, Research Journal of Engineering Sciences, 5(3): 17-31.
Afrifa-Yamoah E.; Bashiru I.I.S. and Azumah, K. (2016). SARIMA Modelling and Forecasting of Monthly Rainfall in the Brong Ahafo Region of Ghana, World Environment, 6(1):1-9.
Alijani, B. and Ramezani, N. (2002). The Predicted droughts and Wet Periods of Mazandaran province using the Box-Jenkins, Geography Research (Reminder doctor Ahmed Mostofi), 155-169.
Azarakhshi, M.; Farzadmehr, J.; Eslah, M. and Sahabi, H. (2103). An Investigation on Trends of Annual and Seasonal Rainfall and Temperature in Different Climatologically Regions of Iran, Journal of Range and Watershed Management, 66(1): 1-16.
Bari, S.H.; Rahman, M.T.; Hussain, M.M. and Ray, S. (2015). Forecasting Monthly Precipitation in Sylhet City Using ARIMA Model, Civil and Environmental Research, 7(1): 69-77.
Box, G.E.P. and Jenkins, G.M. (1976).Time Series Analysis: Forecasting and Control, Third Edition, holden-day.
Bozorgnia, A. and Niromand, H.A. (1993). Time Series Analysis, Ferdowsi University Press.
Chang, X.; Gao, M.; Wang, Y. and Hou, X. (2012). Seasonal Autoregressive Integratedmoving average model for Precipitation time series, Journal of Mathematics and Statistics, 8(4): 500-505.
Chetfild, K. (2002). Introduction to Time Series Analysis, Translated by Niromand, H.A and Bozorgnia, A., Ferdowsi University Press.
Chiew, F.H.S.; Stewardson, M.J. and McMahon, T.A. (1993). Comparison of six rainfall-runoff modeling approaches, Journal of Hydrology, 147: 1-36.
Chowdhury, S. and Biswas, A. (2016). Development of a Monthly Rainfall Prediction Model Using Arima Techniques in Krishnanagar Sub-Division, Nadia District, West Bengal, International journal of Engineering Studies and Technical Approach, 2(2):18-26.
Dadashi Roudbari, A.A. and Keykhosravi Kiani, M. (2016). Analysis of the Spatial and Temporal Trend of Annual Rainfall in Iran during 1950-2007, Journal of Environment and Water Engineering, 2(2): 111-207.
Dodangeh, S.;  Abedi Koupai, J. and Gohari, S.A. (2012). Application of Time Series Modeling to Investigate Future Climatic Parameters Trend for Water Resources Management Purposes, Journal of Water and Soil Sciences (Science and Technology of Agriculture and Natural Resources), 16(59): 59-74.
Fallah Ghalhari, GH.A.; Bayatani, F. and Fahiminezhad, E. (2015). Comparing the Forecasting Accuracy of theBox–Jenkins Models in ModelingSeasonal Precipitation(Case Study: The South of Kerman Province, Iran), Journal of Applied Environmentaland Biological Sciences, 5(12): 64-78.
Fallah Ghalhari, GH.A.; Bayatani, F. and Fahiminezhad, E. (2015). Comparing the Forecasting Accuracy of theBox–Jenkins Models in ModelingSeasonal Precipitation(Case Study: The South of Kerman Province, Iran), Journal of Applied Environmentaland Biological Sciences, 5(12): 64-78.
Golabi, M.R.; Akhondali, A.M.; Radmanesh, F. and Kashefipoor, M. (2014). The Forecasting Accuracy Comparison of Box-Jenkins Models in Modeling the Seasonal Rainfall (Case study: Selected Stations in Khozestan Province), Geographical Research, 29(3): 61-72.
Hosseinalizadeh, M.; Hassanalizadeh, N.; Babanezhad, M. and Rezanezhad, M. (2014). Monthly Precipitation Forecast by Time Series Packages in R Environment (Case study: Arazkooseh station of Golestan province), Journal of Conservation and Utilization of Natural Resources, 3(2):  1-12.
Kaushik, I. and Singh, S.M. (2008). Seasonal ARIMA model for forecasting of monthly rainfall and temperature, Journal of Environmental Research and Development, 3(2): 2: 506 -514.
Kibunja, H.W.; Kihoro, J.M.; Orwa, G.O. and Yodah, W.O. (2014). Forecasting Precipitation Using SARIMA Model: A Case Study of Mt. Kenya Region, Mathematical Theory and Modeling, 4(11): 50-58.
Mahsin, M.d.; Akhter, Y. and Begum, M. (2012). Modeling rainfall in Dhaka division of bangladesh using time series analysis, Journal of Mathematical Modelling and Application, 1(5): 67-73.
Majid-Ali, S. (2013). Time Series Analysis of Baghdad Rainfall Using ARIMA Method, Iraqi Journal of Science, 54(4): 1136-1142.
Marofi, S.; Khatar, B.; Sadeghifar, M.; Parsafar, N. and Ildoromi, A.R. (2015). The Prediction of Drought Using the SARIMA time series and index SPI, In the Central Region of the Hamedan Province, Journal of Water Research in Agriculture, 28(1): 213-225.
Marofi, S.; Saghaei, S.; Ershadfath, F. and Khatar, B. (2014). Evaluating Time Series Models to Estimate Monthly Temperature of Iran’s Old Synoptic Stations During 1977-2005, Water and Soil Science, 24(4): 215-226.
Mishra, A.K. and Desai, V.R. (2005). Drought forecasting using stochastic models, Stochastic Environmental Research and Risk Assessment, 19(5): 326-339.
Mohamed, T.M. and Ibrahim, A.A. (2016). Time Series Analysis of Nyala Rainfall Using ARIMA Method, Journal of Science and Technology, 17(1): 5-11.
Movahedi, S.; Asakereh, H.; Sabziparvar, A.A.; Masodian, A. and Maryanaji, Z. (2013). Investigating the Changes of Seasonal Rainfall Pattern in Hamedan Province, Geographical Researches Quarterly Journal, 28(109): 33-48.
Naill, P.E. and Momani, M. (2009). Time series model for Rainfall data in Jordan: a case study for using time series, American Journal of Environmental Sciences, 5(5): 599-604.
Nazeri Tahrudi, M.; Khalili, K. and Ahmadi, F. (2016). Spatial and Regional Analysis of Precipitation Trend over Iran in the Last Half of Century, Journal of Water and Soil, 30(2): 643-654.
Raziei, T.; Daneshkar Arasteh, P. abd Saghafian, B. (2005). Annual Rainfall Trend Analysis in Arid and Semi-arid Regions of Central and Eastern Iran, Journal of Water and Wastewater, 16(2)(Serial number: 54): 73-81.
Shabani, B.; Mousavi Baygi, M.; Jabari Noghabi, M. and Ghareman, B. (2013). Modeling and Prediction of Monthly Max & MinTemperatures of Mashhad Plain Using Time Series Models, Journal of Water and Soil, 27(5): 896-906.
Shafiei, M.; Ghahraman, B.; Ansari, H. and Sharifi, M.B. (2011). Stochastic Simulation of Drought Severity Based on Palmer Index, Journal of Water and Irrigation Management, 1(1): 1-13.
Sharifan, H. and Ghahraman, B. (2007). Evaluation of rainfall forecasting in Golestan province using time series, Journal of Agricultural Sciences and Natural Resources, 14(3): 196-209.
Zakaria, S.; Al-Ansari, N.; Knutsson, S. and Al-Badrany, T. (2012). ARIMA Models for weekly rainfall in the semi-arid Sinjar District at Iraq, Journal of Earth Sciences and Geotechnical Engineering, 1(3): 25-55.