عنوان مقاله [English]
Introduction: Temperature is the most important climatic element and also one of the main factors in climatic zonation and classification and accordingly fluctuations and significant variations in the temperature of the globe or global warming have been considered as the most important phenomena of climate change in the present century. Therefore, prediction of climatic elements will necessary give planners more time to plan and provide necessary measures. To predict data series, stochastic statistical models have been used extensively in hydrological, weather and climate themes, including models such as Time Series or Box-Jenkins models. In this research, SARIMA seasonal stochastic model is used for modeling and forecasting the average monthly temperature of 5 synoptic stations from 4 different climates of Iran, to examine the model accuracy for estimating average monthly temperature of different climates.
Methodology: Five synoptic stations were selected in the cities Abadan, Isfahan, Anzali, Tabriz and Mashhad which were placed in 4 climatic classes; warm and super dry, cold and super dry, temperate and humid, cold and semi-arid, cold and semi-arid by De Martonne method’s evaluating and had long-term data on monthly temperature over the years 1951-2014.
The time series model, which is also called as the Box-Jenkins model, is a model commonly used to measure time-based data. This model which was introduced for the first time by Box and Jenkins in 1976, is intended for numerical simulation as well as prediction of the variables sorted by time that are recorded at the same time intervals. Among the time series models, the SARIMA model has been used in this research, which can be used to simulate the stochastic behavior of seasonal time series.
Autocorrelation function (ACF): This function is a very important function in the analysis of time series modeling, especially periodic time series. Among ACF’s usages, displaying and analyzing seasonal trends in data, and assessing return period of the series can be mentioned.
Model evaluation criteria: In order to ensure the accuracy of modeling and prediction, the outputs of the model should be compared with the same times’ actual values. For this, Schwarz Bayesian criterion, Root Mean Squared Error and coefficient of determination () have been used in this study.
Discussion: The temperature series were measured by ACF and a seasonal trend was confirmed with a 12 return period in each series and after 4 degrees of seasonal differencing, it was found that the best removing of the seasonal trend, is in the first degree in all series. Data were divided into two sections: 61 years old for calibration and 3 years old for validation that the first 61 years, by entering seasonal and non-seasonal autoregressive and moving average model from 0 to 3, in total 256 models for temperature series of each synoptic station were extracted, their outputs were measured by the evaluation criteria and the best models of each series were used to predict a long step in the next 3 years or 36 months. Best model for Abadan station was SARIMA(1,0,1)(1,1,1)12, Isfahan station was SARIMA(2,0,2)(3,1,1)12, Anzali station SARIMA(1,0,0)(1,1,1)12, Tabriz station SARIMA(1,0,2)(1,1,1)12 and Mashhad station was SARIMA(0,0,1)(0,1,1)12 and their errors was evaluated during 6, 12, 18, 24, 30 and 36 months forecasting horizons which expressed the remarkable accuracy of these models to forecast the monthly temperature time series.
Conclusion: During the evaluations, SARIMA model in order to accuracy, in Abadan synoptic station with modeling Root Mean Squared Error=1.23 and predicting Root Mean Squared Error =0.97 degrees of centigrade had the best performance among the 5 synoptic stations’ temperature series and after that the stations Anzali, Isfahan, Tabriz and Mashhad had the best results with the Root Mean Squared Error in order 1.36, 1.44, 1.81 and 1.90 degrees of centigrade for modeling, and 1.58, 1.06, 1.86, 1.46 degrees of centigrade for predicting. Estimating average monthly temperature during the similar statistical period, At these stations, the model shows that the model has the highest accuracy in estimating and predicting the temperature of hot and super dry climate of Khuzestan province, then in the temperate and humid climate of the north of the country, then in the cold and dry climate of Isfahan province, after that in the cold and semi-arid climate of the northwest and at last in the cold and semi-arid climate of Iran’s northwest.
10. Esfandiari Darabad, F., Hosseini, S., Azadi Mobaraki, M. and Hejazi Zadeh, Z., 2010, Monthly Average Temperature Forecast of Sanandaj Using MLP Artificial Neural Network model, Iranian Geographical Association, (8)27: 45-65.
11. Gautam, R. and Sinha, A. A., 2016, Time series analysis of reference crop evapotranspiration for Bokaro District, Jharkhand, India, Journal of Water and Land Development, 30(1): 51-56.
12. Ghavidel Rahimi, Y., 2012, Time Models Analysis and Forecasting of Low-Extreme Temperatures of Tehran, Journal of Geographical Space, 12(37): 141-157.
13. Ghorbani, M. A., Shiri, J. and Kazemi, H., 2010, Estimating Maximum Average and Minimum Air Temperature of Tabriz Using Artificial Intelligence Methods, Journal of Water and Soil Science, 1/20(3): 87-104.
14. Golabi, M. R., Akhondali, A. M. & Radmanesh, F., 2014, Anticipation of Comfortable Climate Traits in Abadan City with Using from Analysis of Time Series, Journal of Water & Soil, 27(6): 1235-1246.
15. Hayati, M. and Mohebi, Z., 2007, Temperature Forecasting Based on Neural Network Approach, World Applied Sciences Journal, 2(6): 613-620.
16. Kishore, V. and Pushpalatha, M., 2017, Forecasting Evapotranspiration for Irrigation Scheduling using Neural Networks and ARIMA, International Journal of Applied Engineering Research, 12(21): 10841-10847.
17. Landeras G., Ortiz-Barredo A. and Javier Lopez J. (2009). Forecasting weekly evapotranspiration with ARIMA and artificial neural network models. J. Irrig. Drain. Eng., 135(3): 323-334.
18. Mills, T. C, 2014, Time series modelling of temperatures: an example from Kefalonia, Meteorological Applications, 21: 578–584(2008).
19. Niroumand, H. A, and Bozorg Nia, A., 2011, Time Series, Payam Noor University Publications, Tehran.
20. Nuri, A. H., Hasan, K. and Jahir Bin Alam, Md., 2017, Comparative study of wavelet-ARIMA and wavelet-ANN models for temperature time series data in northeastern Bangladesh, Journal of King Saud University - Science, 29(1): 47-61.
21. Nury, A. H., Hasan, K. and Jahir Bin Alam, Md., 2017, Comparative study of wavelet-ARIMA and wavelet-ANN models for temperature time series data in northeastern Bangladesh, Journal of King Saud University - Science, 29(1): 47-61.
22. Patowary, A N., Goswami, K. and Hazarika, J., 2017, Monthly Temperature Prediction Based on ARIMA Model: A Case Study in Dibrugarh Station of Assam, India, International Journal of Advanced Research in Computer Science, 8(8): 292-298.
23. Rahimi, j., Ebrahimpour. M. and Khalili. A., 2013, Spatial changes of Extended De Martonne climatic zones affected by climate change in Iran, Theoretical and Applied Climatology, 112(3-4): 409-418.
24. Salas J. D. 1993. Analysis and modelling of hydrologic time series. In Handbook of hydrology, maidment, D. R. Chapter 19. McGraw-Hill. New York.
25. Salas J. D. 1993. Analysis and modelling of hydrologic time series. In Handbook of hydrology, maidment, D. R. Chapter 19. McGraw-Hill. New York.
26. Salas, J. D., Delleur, W., Yevjevich, V., Lane, W. L. 1988. Applied modeling of hydrologic time series. Water Resources Publications. Littleton, Colorado, U.S.A. Third prontonh. 484pp.
27. Shabani, B., Musavi Bayegi, M., Jabbari Nowghabi, M. and Ghahraman B., 2013, Modeling Monthly Maximum and Minimum Temperature of Mashhad Land Using Time Series Models, Journal of Water and Soil, 27(5): 896-906.
28. Ustaglu, B., Cigizoglu, H. K. and Karaca, M., Forecast of daily mean, maximum and minimum temperature time series by three artificial neural network methods, Meteorological Applications, 15: 431–445(2008).
29. Vahdat, S. F., Sarraf, A. P., Shamsnia, S. A. & Marashi, M., 2010, Relative Humidity and Mean Monthly Temperature forecasts and evaluation in Dezful station with ARIMA model in time series analysis, The First International Conference on Plant, Water, Soil & Weather Model, International Center for Science, High Technology & Environmental Sciences, Shahid Bahonar University of Kerman, 14-15 Nov, 2010, Kerman, Iran.
30. Veisipour, H., Masoumpour, J., Sahne, B. & Yousefi, Y., 2010, Analysis of rainfall and temperature trends using time series models (ARIMA) (Case study: Kermanshah), Journal of Geography, 4(12): 63-77.
31. Wang, W. C., Chau, K. W., Cheng, C. T. and Qiu, L., 2009, A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series, Journal of Hydrology, 374(3-4): 294-306.
32. Yakubo, M., 2014, Modeling an Average Monthly Temperature of Sokoto Metropolis Using Short Term Memory Models, International Journal of Academic Research in Business and Social Sciences, 4(7): 382-397.