Introduction: In irrigation science, accurate estimation of the water requirement of crops and horticultural products is one of the most basic pillars of design and engineering calculus (Islami and Qahreman, 2013).Observations on evaporation through the pans have not always been accompanied by precision. Also, the dense network of evapometry stations is not available and, on the other hand, the use of direct methods involves a lot of time and cost. Therefore, developing an alternative approach for estimating evaporation rates based on meteorological variables with the ability to measure and estimate more easily is necessary. In order to estimate reference evapotranspiration, using mathematical models with measurements of meteorological parameters as independent variables will be inevitable (Islami and Qahreman, 2013).Mohammad-Reza-Pour et al. (2015) presented modeling of monthly potential evapotranspiration using genetic programming in Sistan and Baluchestan Province. For this purpose, the reference evapotranspiration on a monthly scale using the Penman-Monteith method and based on meteorological data such as mean temperature, relative humidity, sunshine hours, wind speed and precipitation amount over a 40-year period at Zabol, Iranshahr, Chabahar and Zahedan stations was calculated and arranged in 16 separate time delay patterns. Then, modeling of monthly evapotranspiration values based on genetic programming using the GeneXproTools software was used to develop and implement genetic programming based models. The purpose of this study was to provide a simple, yet practical and accurate model for calculating potential evapotranspiration in order to calculate the evaporation rate from the surface using effective climatic elements in evaporation.

Materials and Methods: Kermanshah Province accounts for 1.5% of the total area of the country. This province is limited from north to Kurdistan Province, south to Ilam and Lorestan Provinces and east to Hamedan Province. In this study, due to the importance of growing season and water requirement for the growth and development of crops and pasture products, in order to estimate potential evapotranspiration at selected stations in the region, the sum of months of the year during the statistical period of 1995-2012 was considered. In this study, the GEP model was used to determine drought and evapotranspiration indices. The stations in the region were statistically surveyed and 5 stations in Kermanshah Province were selected. Then quantitative and qualitative data were analyzed by the run test in both Excel and SPSS. Then, the GEP model and software were used to determine the dry and semi-arid seasons and the seasons that were suitable for growing and cultivating. The accuracy of the estimated data was evaluated and finally, the zoning map of potential evapotranspiration of the province was prepared.

Results and Discussion: Important factors affecting the saturation deficit are temperature, wind, and relative humidity. Increasing the temperature and wind speed give rise to increasing the amount of the saturation deficit, thereby increasing the evaporation, and increasing the relative humidity, in contrast, decreases the saturation deficit, thereby decreasing the evaporation. Therefore, in this study, four factors of temperature, wind speed, relative humidity and saturation deficit as independent variables and the input of the model were used to estimate potential evaporation using the GEP model, and evaporation from the pan was also considered as a dependent variable in order to fit and evaluate the performance of the model. In examining the calculated values, it was observed that evaporation values estimated by the GEP model were close to the evaporation values measured through the evaporation pan and showed a very high correlation (r=0.98), which indicates the great efficiency of the GEP model to estimate the potential evapotranspiration in Kermanshah Province. In the present study, the IWD method was used for geostatistical interpolation, so that after calculating the potential evapotranspiration rate using the GEP model and generalizing the obtained values to the surface using the ArcGis software, the zoning map of evapotranspiration of Kermanshah Province based on the estimated and observed values was drawn. The survey of the zoning maps showed that there was very little difference between the results of the GEP model and the recorded rate of the evaporation pan and in the both cases, the highest evaporation was related to the western and southwest counties to near the center, and the least was related to the east and northeastern counties of the province.

Conclusion: In this study, the GEP model based on genetic algorithm was used to estimate the potential evapotranspiration. The results showed that there was a high correlation between the data obtained from the model and the evaporation pan. An absence of sufficient facilities such as the pan to record the potential evaporation rate and the incompleteness of existing statistics in most parts of the country reveal the importance of various methods and models in estimating the potential evapotranspiration based on the factors affecting it with a high coefficient of certainty. In this study, it was shown that the GEP model is an efficient model for estimating potential evapotranspiration in Kermanshah Province, and it can be used with high confidence to rebuild incomplete statistics and modify outlier data in the province. The analysis of the zoning maps of the potential evapotranspiration rate based on the measure of the evaporation pan and the GEP model showed that by moving from east to west and north to south, the evaporation rate was increased. The very important result obtained from the comparison of the annual rainfall of the province with evaporation was that from the beginning to the middle of the growing season, the plants of the eastern counties had a monthly precipitation more than evaporation, and this amount is reduced to the west, so that a little after the central areas (Islamabad), the amount of precipitation and evaporation is equal and then it decreases, and as we approach the end of the growing season, the situation is generalized to the whole of the province, that is more evaporation than rainfall, which indicates water scarcity and high water requirement of the plant, especially in the west to the provincial capital at the end of the growing season.