Water Resources Management

, Volume 32, Issue 3, pp 1035–1052 | Cite as

Forecasting of Multi-Step Ahead Reference Evapotranspiration Using Wavelet- Gaussian Process Regression Model

  • Masoud KarbasiEmail author


Evapotranspiration is one of the most important components in the optimization of water use in agriculture and water resources management. In recent years, artificial intelligence methods and wavelet based hybrid model have been used for forecasting of hydrological parameters. In present study the application of the Gaussian Process Regression (GPR) and Wavelet-GPR models to forecast multi step ahead daily (1–30 days ahead) reference evapotranspiration at the synoptic station of Zanjan (Iran) were investigated. For this purpose a 10-year statistical period (2000–2009) was considered, 7 years (2000–2006) for training and the final three years (2007–2009) for testing the various models. Various combinations of input data (various lag times) and different kinds of mother wavelets were evaluated. Results showed that, compared to the GPR model, the hybrid model Wavelet-GPR had greater ability and accuracy in forecasting of daily evapotranspiration. Moreover, the use of yearly lag times in the GPR and wavelet-GPR model increased its accuracy. Investigation of various kinds of mother wavelets also indicated that the Meyer wavelet was the most suitable mother wavelet for forecasting of daily reference evapotranspiration. The results showed that by increasing the forecasting time period from 1 to 30 days, the accuracy of the models is reduced (RMSE = 0.068 mm/day for one day ahead and RMSE = 0.816 mm/day for 30 days ahead). Application of the proposed model to summer season showed that the performance of the model at summer season is better than its performance throughout the year.


Reference crop evapotranspiration Forecasting Time series Wavelet Gaussian Process regression 



The meteorological organization of the Iran is acknowledged due to providing meteorological data of Zanjan synoptic station.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Water Engineering Department, Faculty of AgricultureUniversity of ZanjanZanjanIran

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