پیش‌بینی تبخیر-تعرق مرجع ماهانه با استفاده از مدل سری‌های زمانی

نوع مقاله : مقالات پژوهشی

نویسندگان

دانشگاه بوعلی سینا

چکیده

تبخیر-تعرق از مؤلفه‌های مهم در مدیریت و برنامه‌ریزی آبیاری در کشاورزی است که پیش‌بینی آن می‌تواند نقش مهمی در برنامه‌های آتی داشته باشد. به‌منظور پیش‌بینی تبخیر-تعرق می‌توان از مدل‌های سری زمانی استفاده کرد و با کاربرد اصولی و صحیح این مدل‌ها، در عین سادگی، پیش‌بینی‌های کوتاه‌مدت خوبی را برآورد نمود. در این راستا، تبخیر-تعرق مرجع ماهانه در دوره‌ای 41 ساله، بین سال‌های 1965 تا 2005 میلادی، در ایستگاه‌های سینوپتیک اصفهان، سمنان، شیراز، کرمان و یزد از روش فائو پنمن– مانتیث محاسبه و سپس سری‌های زمانی آن تشکیل شدند. آزمون ریشه واحد برای بررسی مانایی سری‌های زمانی انجام شد و با توجه به روش باکس-جنکینز، مدل‌های ARIMA فصلی روی داده‌های نمونه برازش و مناسب‌ترین آن‌ها انتخاب شدند. سپس از مدل‌های ARIMA فصلی برای پیش‌بینی 12 ماهه استفاده شد که پیش‌بینی‌های خارج از نمونه خوبی به‌دست دادند، به‌طوری که در بین همه ایستگاه‌های مورد بررسی کمترین ضریب همبستگی پیرسون 988/0 و بیشترین جذر میانگین مربع خطا 515/0 میلی‌متر بر روز به‌دست آمد.

کلیدواژه‌ها


عنوان مقاله [English]

Forecasting the Reference Evapotranspiration Using Time Series Model

نویسندگان [English]

  • H. Zare Abyaneh
  • A. Afruzi
  • M. Mirzaei
  • H. Bagheri
Bu-Ali Sina University
چکیده [English]

Introduction: Reference evapotranspiration is one of the most important factors in irrigation timing and field management. Moreover, reference evapotranspiration forecasting can play a vital role in future developments. Therefore in this study, the seasonal autoregressive integrated moving average (ARIMA) model was used to forecast the reference evapotranspiration time series in the Esfahan, Semnan, Shiraz, Kerman, and Yazd synoptic stations.
Materials and Methods: In the present study in all stations (characteristics of the synoptic stations are given in Table 1), the meteorological data, including mean, maximum and minimum air temperature, relative humidity, dry-and wet-bulb temperature, dew-point temperature, wind speed, precipitation, air vapor pressure and sunshine hours were collected from the Islamic Republic of Iran Meteorological Organization (IRIMO) for the 41 years from 1965 to 2005. The FAO Penman-Monteith equation was used to calculate the monthly reference evapotranspiration in the five synoptic stations and the evapotranspiration time series were formed. The unit root test was used to identify whether the time series was stationary, then using the Box-Jenkins method, seasonal ARIMA models were applied to the sample data.

Table 1. The geographical location and climate conditions of the synoptic stations
Station Geographical location Altitude (m) Mean air temperature (°C) Mean precipitation (mm) Climate, according to the De Martonne index classification
Longitude (E) Latitude (N) Annual Min. and Max.
Esfahan 51° 40' 32° 37' 1550.4 16.36 9.4-23.3 122 Arid
Semnan 53° 33' 35° 35' 1130.8 18.0 12.4-23.8 140 Arid
Shiraz 52° 36' 29° 32' 1484 18.0 10.2-25.9 324 Semi-arid
Kerman 56° 58' 30° 15' 1753.8 15.6 6.7-24.6 142 Arid
Yazd 54° 17' 31° 54' 1237.2 19.2 11.8-26.0 61 Arid

Results and Discussion: The monthly meteorological data were used as input for the Ref-ET software and monthly reference evapotranspiration were obtained. The mean values of evapotranspiration in the study period were 4.42, 3.93, 5.05, 5.49, and 5.60 mm day−1 in Esfahan, Semnan, Shiraz, Kerman, and Yazd, respectively. The Augmented Dickey-Fuller (ADF) test was performed to the time series. The results showed that in all stations except Shiraz, time series had unit root and were non-stationary. The non-stationary time series became stationary at 1st difference. Using the EViews 7 software, the seasonal ARIMA models were applied to the evapotranspiration time series and R2 coefficient of determination, Durbin–Watson statistic (DW), Hannan-Quinn (HQ), Schwarz (SC) and Akaike information criteria (AIC) were used to determine, the best models for the stations were selected. The selected models were listed in Table 2. Moreover, information criteria (AIC, SC, and HQ) were used to assess model parsimony. The independence assumption of the model residuals was confirmed by a sensitive diagnostic check. Furthermore, the homoscedasticity and normality assumptions were tested using other diagnostics tests.

Table 2- The selected time series models for the stations
Station Seasonal ARIMA model Information criteria R2 DW
SC HQ AIC
Esfahan ARIMA(1, 1, 1)×(1, 0, 1)12 1.2571 1.2840 1.2396 0.8800 1.9987
Semnan ARIMA(5, 1, 2)×(1, 0, 1)12 1.5665 1.5122 1.4770 0.8543 1.9911
Shiraz ARIMA(2, 0, 3)×(1, 0, 1)12 1.3312 1.2881 1.2601 0.9665 1.9873
Kerman ARIMA(5, 1, 1)×(1, 0, 1)12 1.8097 1.7608 1.8097 0.8557 2.0042
Yazd ARIMA(2, 1, 3)×(1, 1, 1)12 1.7472 1.7032 1.6746 0.5264 1.9943

The seasonal ARIMA models presented in Table 2, were used at the 12 months (2004-2005) forecasting horizon. The results showed that the models produce good out-of-sample forecasts, which in all the stations the lowest correlation coefficient and the highest root mean square error were obtained 0.988 and 0.515 mm day−1, respectively.
Conclusion: In the presented paper, reference evapotranspiration in the five synoptic stations, including Esfahan, Semnan, Shiraz, Kerman, and Yazd, were calculated using the FAO Penman-Monteith method for the 41 years, and the time series were formed. The selected models gave good out-of-sample forecasts of the monthly evapotranspiration for all the stations. The models can be used in the short-term prediction of monthly reference evapotranspiration. Note that, the use of models in long-term forecasting was not recommended. The time series model can be used in lost data. Even though more methods are available for model building, the use of time series models in water resources are advocated in modeling and forecasting. Time series can be used as a tool to find lost data.

کلیدواژه‌ها [English]

  • Box-Jenkins
  • FAO Penman-Monteith
  • SARIMA
1- Allen R.G. 2011. REF-ET: Reference evapotranspiration calculation software for FAO and ASCE standardized equations. Version 3.1. for Windows, University of Idaho.
2- Allen R.G., Pereira L.S., Raes D., and Smith M. 1998. Crop evapotranspiration: guidelines for computing crop water requirements. Rome: FAO Irrigation and Drainge Paper No. 56.
3- Asakereh H. 2009. ARIMA Modeling of annual mean temperature of Tabriz city. Geographical Research, (2-93):3-24. (in Persian)
4- Ashgar Toosi S., Alizadeh, A., and Shirmohamadi R. 2005. SARIMA modeling of seasonal rainfalls (case study: Khorasan Province, Iran). Iran-Water Resources Research 1(3):41-53. (in Persian with English abstract)
5- Azad Talatapeh N., Behmanesh, J., and Montaseri, M. 2013. Predicting potential evapotranspiration using time series models (case study: Urmia). Journal of Water and Soil, 27(1):213-223. (in Persian with English abstract)
6- Box G.E.P., and Jenkins G.M. 1976. Time Series Analysis: Forecasting and Control. Revised Edition, Oakland, CA: Holden-Day.
7- Box G.E.P., Jenkins G.M., and Reinsel G.C. 2008.Time Series Analysis: Forecasting and Control. Fourth Edition, Hoboken, NJ: John Wiley & Sons, Inc.
8- 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 Science and Technology of Agriculture and Natural Resources, Water and Soil Science, 16(59):59-74. (in Persian with English abstract)
9- Droogers P., and Allen R.G. 2002. Estimating reference evapotranspiration under inaccurate data conditions. Irrigation and Drainage Systems (16):33-45.
10- Fooladmand HR. 2010. Monthly prediction of reference crop evapotranspiration in Fars Province. Water and Soil Science, 1(20):157-169. (in Persian with English abstract)
11- Ghahreman N., and Gharekhani A. 2011. Evaluation of the stochastic time series models in the evaporation assessment of the pan (case study: Shiraz station). Journal of Water Research in Agriculture, 25(1):75-81. (in Persian)
12- Hipel K.W., McLeod A.I., and Lennox W.C. 1977. Advances in Box-Jenkins modeling 1. model construction. Water Resources Research, 13(1):567-575.
13- Jahanbakhsh S., and Babapour Baser A.A. 2003. Evaluation and forecasting mean monthly temperature of Tabriz using the ARIMA model. Geographical Research, 18(3):34-46. (in Persian)
14- Jahanbakhsh S., and Torabi S. 2004. Evaluation and forecasting temperature and rainfall fluctuations in Iran. Geographical Research, 19(3):104-125. (in Persian)
15- Jalali O., and Khanjar S. 2009. Evaluation of the temperature fluctuations using time series and probability distribution (case study: Kermanshah County). Journal of Geographic Space, 9(27):115-132. (in Persian)
16- Kheirabi J., Tavakoli A.R., Entesari, M.R., and Salamat, A.R. 1997. Theoretical and practical aspects of Penman-Monteith method. Iranian National Committee on Irrigation and Drainage (IRNCID), 165 pp. (in Persian)
17- Khorshiddoust A.M., Saniei R., and Ghavidel Rahimi Y. 2009. Forecasting Esfahan extremes temperature using time series. Journal of Geographic Space, 9(26):31-43. (in Persian)
18- Landeras G., Ortiz-Barredo A., and Lopez J. J. 2009. Forecasting weekly evapotranspiration with ARIMA and artificial neural network models. Journal of Irrigation and Drainage Engineering, 135(3):323-334.
19- Mosaedi A., Dehghani A.A., and Eivazi M. 2009. Investigation on the predictable drought durations by using time series. 1st International Conference on Water Resources: Emphasis on Regional Development, University of Shahrood, Shahrood, Iran. (in Persian with English abstract)
20- Psilovikos A., and Elhag M. 2013. Forecasting of remotely sensed daily evapotranspiration data over Nile Delta Region, Egypt. Water Resources Management, 27:4115–4130.
21- Shirvani A., and Honar T. 2011. Application of time series models for evapotranspiration forecasting in Bajgah station. Iranian Water Research Journal, (8):135-142. (in Persian with English abstract)
22- Souri A. 2012. Econometrics. Tehran: Farhang Shenadi Publishing and Noor-e Elm Publishing, 343 pp. (in Persian)
23- Valipour M. 2012. Ability of Box-Jenkins models to estimate of reference potential evapotranspiration (A case study: Mehrabad synoptic station, Tehran, Iran). IOSR Journal of Agriculture and Veterinary Science, 1(5):1-11.
CAPTCHA Image