Abstract
Gene Expression Programming (GEP) was used to develop new mathematical equations for estimating daily reference evapotranspiration (ETref) for the Kingdom of Saudi Arabia. The daily climatic variables were collected by 13 meteorological stations from 1980 to 2010. The GEP models were trained on 65% of the climatic data and tested using the remaining 35%. The generalised Penman-Monteith model was used as a reference target for evapotranspiration (ET) values, with h(c) varies from 5 to 105 cm with increment of a centimetre. Eight GEP models have been compared with four locally calibrated traditional models (Hargreaves-Samani, Irmak, Jensen-Haise and Kimberly-Penman). The results showed that the statistical performance criteria values such as determination coefficients (R-2) ranged from as low as 64.4% for GEP-MOD1, where the only parameters included (maximum, minimum, and mean temperature and crop height), to as high as 95.5% for GEP-MOD8 with which all climatic parameters included (maximum, minimum and mean temperature; maximum, minimum and mean humidity; solar radiation; wind speed; and crop height). Moreover, an interesting founded result is that the solar radiation has almost no effect on ETref under the hyper arid conditions. In contrast, the wind speed and plant height have a great positive impact in increasing the accuracy of calculating ETref. Furthermore, eight GEP models have obtained better results than the locally calibrated traditional ETref equations.