پیش بینی سری زمانی بارش سالانه ۱۲۵ ساله مشهد

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی آمار و ریاضی، دانشگاه پیام نور، مشهد، ایران

2 دانشیار، گروه آمار و ریاضی، عضو هیات علمی، دانشگاه پیام نور، شیراز، ایران

3 مربی، هیدرولوژی، دانشگاه آزاد اسلامی، مشهد، ایران

چکیده

سری‌های زمانی بارش در مقیاس سالانه دارای سه مولفه روند، تغییرات بلند مدت و نوسانات تصادفی است. دو مولفه روند و تغییرات بلندمدت با طول دوره آماری کمتر از ۱۰۰ سال در مناطق خشک و نیمه‌خشک بیان نمی‌شود. لذا الگوهای سری زمانی خطی، غیرخطی، ابتکاری یا فراابتکاری نمی‌تواند به خوبی این پدیده را تببین کنند. سری زمانی بارش سالانه و طولانی مدت ایستگاه مشهد با دوره آماری ۱۲۵ سال در این تحقیق بررسی شد. ابتدا معنی‌داری روند با بکارگیری دو آزمون ناپارامتری من-کندال و سن در سطح 95درصد ارزیابی شد. نتایج نشان داد بارش سالانه مشهد روند معنی‌دار در میانگین ندارد. اما روند در واریانس وجود دارد که با تبدیل باکس-کاکس تثبیت شد. بررسی تغییرات دوره‌ای با برازش چندجمله‌ای‌ها از درجه شش تا ۱۲ انجام و نتایج نشان داد که هیچکدام معنی‌دار نیستند. انتخاب بهینه تعداد پارامترهای الگو بر اساس توابع خودهمبستگی( ACF)، خودهمبستگی جزئی (PACF)، خوهمبستگی‌توسعه‌یافته ( EACF)، معیارهای آکائیک (AIC) و بیز‌ (BIC) انجام شد. عملکرد الگوها با معیارهایی مانند میانگین قدرمطلق خطا (MAE)، مجذور مربعات خطا (RMSE)، میانگین درصد قدرمطلق خطا (MAPE) و غیره بررسی شد. نتایج نشان داد الگوی IMA(1,1) دارای تعداد بهینه پارامتر در الگو، پارامترهای معنی‌دار و بهترین عملکرد است و مشاهدات نیز دارای داده پرت نیستند. نتایج تحلیل باقیمانده‌ها نیز نشان داد که باقیمانده‌ها نسبت به زمان پایا هستند، از توزیع نرمال پیروی می‌کنند و مستقل‌اند. بنابراین، سری زمانی بارش سالانه طولانی مدت مشهد از نوفه سفید پیروی می‌کند و بهترین پیش‌بینی مقدار بارش، میانگین داده‌ّها است.

کلیدواژه‌ها


عنوان مقاله [English]

Forecasting of 125 years annual precipitation time series in Mashhad

نویسندگان [English]

  • Nafiseh SeyyedNezhad Golkhatmi 1
  • Narges Abbasi 2
  • Hojat Rezaee-Pazhand 3
1 M.Sc. Student, Payame Noor University, Mashhad, Iran
2 Assistance Professor, Department of Statistics, Payame Noor University, I. R.Iran
3 Department of Civil Engineering, Faculty of Engineering, Islamic Azad University of Mashhad
چکیده [English]

Introduction

One of custom methods for forecasting climatic variables is time series approach. We used this method for long term precipitation in Mashhad synoptic station. The annual precipitation series has three components: trend, cyclic variations and random fluctuations. The two components of trend and cyclic are not showed in statistical period of less than 100 years in arid and semi-arid regions .Therefore, linear, nonlinear, heuristic, meta-heuristic methods of time series patterns cannot explain this phenomenon well. In this study, the annual and long-term precipitation time series of Mashhad station with a statistical duration of 125 years was considered. The trend in data, cyclic variation are considered. Box and Jenkins’s method (1976) for time series is fitted on data and optimal selection of parameters and best performance are studied. Also, test for outlier in data and diagnostic analysis for residual are done.

Material and Methods

In this research, the modeling of annual and long-term precipitation time series of Mashhad synoptic station with a statistical duration of 125 years (1894-2018) was investigated. At first, the trend of data in mean is tested using Mann-Kendall and Sen Approaches. Then, the variance of data was de-trended by box-cox transformation. Cyclic changes were considered by fitting polynomials from six to 12 degree. Optimal selection of the number of pattern parameters was based on Autocorrelation function (ACF), Partial Autocorrelation function (PACF), Extended Autocorrelation function (EACF) and Akaike (AIC) and Bayesian Criterion (BIC) criterions. Because ACF and PACF are good for distinguishing ARI (p, d) and IMA (d, q) patterns and if we have ARIMA(p, d, q) pattern we should use EACF. The patterns performance was evaluated by criterions such as the Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Percentage Error (MPE), Normalized Mean Squared Error (NMSE), Signed Mean Squared Error (SMSE) and U.





Tow type of outlier test, Additive Outlier and Innovational Outlier are done on all observation. Also, Diagnostic analysis is done on residuals to consider their behavior over time, normality and independent.

Results and Discussion

First, the significant trend was evaluated by using the non-parametric Man-Kendall and Sen Tests at a significant level of 95%. The results showed that the annual precipitation in Mashhad does not have a significant trend in mean. But, Data has trend in variance which stabilized by box-cox transformation. Cyclic changes by fitting polynomials from six to 12 degrees displayed that none of them were significant. But they can approximately show the wet and drought cycle in 1984-2018 years. Optimal selection of the number of pattern parameters was based on Autocorrelation function (ACF), Partial Autocorrelation function (PACF), Extended Autocorrelation function (EACF). Also, Akaike (AIC) and Bayesian Criterion (BIC) criterions are used. But result showed that IMA (1, 1), ARIMA (1,2,3) and IMA(1,3) have significant parameters. The patterns performance was evaluated by criterions such as the Mean Absolute Error (MAE), Mean Percentage Error (MPE), Normalized Mean Sauared Error(NMSE), Signed Mean Squared Error(SMSE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE) and U. The results presented that the IMA (1, 1) model has the optimal number of parameter in the model, significant parameter and the best performance. The observations do not have AO and IO outlier. The results of diagnostic analysis also demonstrated that residuals are stable over time, follow normal distribution and are independent. Therefore, the long-term annual precipitation sequence of Mashhad follows the white noise pattern and the best prediction of the amount of precipitation is the average of data.

Conclusion

The annual and long-term precipitation time series of Mashhad station with a statistical duration of 125 years was modeled by time series pattern. We found that data doesn’t have trend in mean but has trend in variance. There are not significant cyclic changes but using the long term data we can see wet and drought cycles better. IMA (1, 1), ARIMA (1,2,3) and IMA(1,3) have significant parameters. IMA (1, 1) model has the optimal number of parameter in the model, significant parameter and the best performance. The observations do not have any outlier and residuals are stable over time, follow normal distribution and are independent. The long-term annual precipitation time series of Mashhad synoptic station follows the white noise pattern.

کلیدواژه‌ها [English]

  • Time series
  • cyclic variation
  • outlier
  • long-term precipitation
  • Mashhad
  1. Abdolahnezhad, K. 2015, Forecasting of Monthly Sum-raining by stochastic models in time Series, Geographical planning of space quarterly Journal, 5(17):15-25. (In Persian with English abstract).
  2. Adhikari, R., R. K. Agrawal, 2013, An Introductory Study on Time Series Modeling and Forecasting, LAP Lambert Academic Publishing, Germany.
  3. Asakereh, H., R. Khoshraftar, and F. Sotudeh 2012, Cycles Analysis of Time Discharge and Precipitation Series of Mashinekhaneh Station (Garakanrood of Talesh Catchment). Journal of Water and Soil, 1128-1139. (In Persian with English abstract).
  4. Belala, F., A. Hirche, D. Muller and et. al, 2018, Precipitation patterns of Algerian steppes and the impacts on natural vegetation in the 20th century, Journal of Arid Land, 10(4): 561–573.
  5. Box, G. E. P. and G.M. Jenkins, 1976, Times series analysis forecasting and control. Holden-Day, San Francisco.
  6. Box, G. E. P., G. M. Jenkins, and G. C. Reinsel, 2008, Time series analysis: forecasting and control, 4nd ed., Hoboken, New Jersey: John Wiley & Sons.
  7. Cryer, J. D. and K. S. Chan., 2008, Time Series Analysis with Applications in R (2nd). Springer.
  8. Edmond F. S., V. A. Koelzer, K. Mahmood, 1973, Floods and droughts, Water Resources Publications.
  9. Farzandi, M., H. Sanaeinejad, B. Ghahraman, M. Sarmad, 2019, Imputation of Missing Meteorological Data with Evolutionary and Machine Learning Methods, Case study: Long-term monthly Precipitation and temperature of Mashhad. (In Persian with English abstract).
  10. Fox, A.J. 1972, Outliers in Time Series. Journal of the Royal Statistical Society, Series B, 34: 350-363.
  11. Ghodoosi, M., S. Morid, M. Delavar, 2013, Comparison of detrending methods for the temperature and precipitations time series, Journal of Agricultural Meteorology, 1(2): 32-45. (In Persian with English abstract).
  12. Goodarzi, L. and A. Roozbahani, 2017, An Evaluation of ARIMA and Holt Winters Time Series Models for forecasting monthly precipitation and monthly temperature (Case study: Latian station), Irrigation Sciences and Engineering, 40(3):137-149. (In Persian with English abstract).
  13. Guerrero, V.M., 1993, Time-series analysis supported by power transformations, Journal of forecasting, 12: 37-48.
  14. Halabian, A.H., 2016, Assessment of Spatial- Temporal Changes of Precipitation in Iran. Desert Ecosystem Engineering Journal, 5(13): 101-116. (In Persian with English abstract).
  15. Hejabi, S. and Bazrafshan, J. 2013, Evaluation of several models in predicting standard precipitation index time series. Journal of water research in agriculture, 27(3): 429-444. (In Persian).
  16. Hosseinalizadeh, M., N. Hassanalizadeh, M. Babanezhad and M. Rezanezhad, 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, 2(2): 1-12. (In Persian with English abstract).
  17. D., D. W. Reed, A. J. Robson., 1999. Choosing a pooling group. Flood Estimation Handbook. 3nd. Institute of Hydrology, Wallingford, UK.
  18. Kaushik, I. and S.M. Singh, 2008, Seasonal ARIMA model for forecasting of monthly precipitation and temperature. Journal of environmental research and development, 3(2):506-514.
  19. Khazae, M. 2008, Introduction to time series analysis using S-plus software. Iran Statistics Center, Tehran. (In Persian).
  20. Mahsin, Md., Y. Akhter and M. Begun, 2012, modeling precipitation in Dhaka Division of Bangladesh using time series analysis. Journal of Mathematical Modeling and Application, 1(5): 67-73.
  21. Mckee, T. B., N. J. Doesken and Kleist, J, 1993, The relationship  of  drought  frequency  and  duration  to time  scales,  8th  Conference  of  Applied  Climatology, Anaheim, 179-184.  
  22. Mekanik, f., 2010, Precipitation time series modeling for a mountainous region in west Iran, Abstract of thesis presented to Senate of Universiti Putra Malaysia in fulfilment of the requirements for the degree of Master of Science.
  23. Mohamadi, B., 2012, Trend analysis of annual precipitation over Iran. Journal of Geography and environmental planning, 22(3): 95-106.
  24. Mondal, P., L. Shit and S. Goswami, 2014, Study of effectiveness of time series modeling (ARIMA) in forecasting stock prices. International Journal of Computer Science, Engineering and Applications, 4(2): 13.
  25. Nasrabadi, E. and Masoodian, S. A. 2013. Analysis gridded APHRODITE precipitation with half a century duration in Iran, Geographic Notion, 13: 88. (In Persian)
  26. Rasuli, A.A., 2002, modeling of climate parameters in north-west country. Forecasting monthly temperature of Tabriz city (Iran) by ARIMA model. Journal of Sociology Science, (8): 211-221. (In Persian with English abstract).
  27. , T., 2008, Investigation of annual precipitation trends in homogeneous precipitation sub-divisions of Western Iran, BALWOIS, Republic of Macedonia.
  28. Sampson, W., N. Suleman and A.Y. Gifty. 2013, Proposed seasonal autoregressive integrated moving average Model for Forecastiing precipitation pattern in the Navrongo Municipality, Ghana. Journal of Einvironment and Earth Scienc. 3(12): 80-85.
  29. Sen, P. K. 1968, asymptotically efficient tests by method of n rankings. Journal of the Royal Statistical Society, Series B. 30.
  30. Shamsnia, S. A., N. Shahidi, Liaghat, A. Sarraf, S. F. Vahdat, 2011, Modeling of Weather Parameters Using Stochastic Methods (ARIMA Model) (Case Study: Abadeh region, Iran). International Conference on Environment and Industrial Innovation, IPCBEE, 12.

 

  1. Sharifan, H., and B. Ghahraman, 2007, Evaluation of precipitation forecasting using SARIMA technique in Golestan province. Journal of Agricultural Sciences and Natural Resources, 14(3): 18-27. (In Persian with English abstract).
  2. Soltani-Gerdfaramarzi, S., A. Saberi, M. Gheisouri, 2017, Determination of the best time series model for forecasting annual precipitation of selected stations of Western Azerbaijan province. Researches in Geographical Sciences, 17(44): 87-105 (In Persian with English abstract).
  3. Tasy, R. S. and G. C. Tiao, 1984, Consistent estimates of autoregressive parameters and extended sample autocorrelation function for stationary and non-stationary ARMA Models. , Journal of the American Statistical Association, 79: 84-96.
  4. Wei, W. W. S. 2006, Time series analysis: Univariate and multivariate methods. Boston: Pearson Addison Wesley.