Evapotranspiration plays a pivotal role in the hydrological cycle. It is essential to develop an accurate computational model for predicting reference evapotranspiration (RET) for agricultural and hydrological applications, especially for the management of irrigation systems, allocation of water resources, assessments of utilization and demand and water use allocations in rural and urban areas. The limitation of climatic data to estimate RET restricted the use of standard Penman–Monteith method recommended by food and agriculture organization (FAO-PM56). Therefore, the current study used climatic data such as minimum, maximum and mean air temperature (T_max, T_min, T_mean), mean relative humidity (RH_mean), wind speed (U) and sunshine hours (N) to predict RET using gene expression programming (GEP) technique. In this study, a total of 17 different input meteorological combinations were used to develop RET models. The obtained results of each GEP model are compared with FAO-PM56 to evaluate its performance in both training and testing periods. The GEP-13 model (T_max, T_min, RH_mean, U) showed the lowest errors (RMSE, MAE) and highest efficiencies (R², NSE) in semi-arid (Faisalabad and Peshawar) and humid (Skardu) conditions while GEP-11 and GEP-12 perform best in arid (Multan, Jacobabad) conditions during training period. However, GEP-11 in Multan and Jacobabad, GEP-7 in Faisalabad, GEP-1 in Peshawar, GEP-13 in Islamabad and Skardu outperformed in testing period. In testing phase, the GEP models R² values reach 0.99, RMSE values ranged from 0.27 to 2.65, MAE values from 0.21 to 1.85 and NSE values from 0.18 to 0.99. The study findings indicate that GEP is effective in predicting RET when there are minimal climatic data. Additionally, the mean relative humidity was identified as the most relevant factor across all climatic conditions. The findings of this study may be used to the planning and management of water resources in practical situations, as they demonstrate the impact of input variables on the RET associated with different climatic conditions.

蒸散量在水文循环中起着关键作用。开发准确的计算模型来预测农业和水文应用的参考蒸散量（RET）至关重要，特别是对于灌溉系统的管理、水资源的分配、农村和城市地区的利用和需求评估以及用水分配。用于估计 RET 的气候数据的局限性限制了粮食及农业组织 (FAO-PM56) 推荐的标准 Penman-Monteith 方法的使用。因此，本研究使用的气候数据包括最低、最高和平均气温（T _max 、T _min 、T _mean ）、平均相对湿度（ RH _mean )、风速 (U) 和日照时数 (N)，使用基因表达编程 (GEP) 技术预测 RET。在这项研究中，总共使用了 17 种不同的输入气象组合来开发 RET 模型。将每个 GEP 模型获得的结果与FAO-PM56 进行比较，以评估其在训练和测试期间的性能。 GEP-13 模型（T _max 、T _min 、RH _mean 、U）显示出最低的误差（RMSE、MAE）和最高的效率（R < b7> ，NSE）在半干旱（费萨拉巴德和白沙瓦）和潮湿（斯卡杜）条件下，而 GEP-11 和 GEP-12 在训练期间在干旱（木尔坦，雅各布阿巴德）条件下表现最佳。然而，木尔坦和雅各布阿巴德的 GEP-11、费萨拉巴德的 GEP-7、白沙瓦的 GEP-1、伊斯兰堡和斯卡杜的 GEP-13 在测试期间表现出色。在测试阶段，GEP模型的R ² 值达到0.99，RMSE值范围为0.27至2.65，MAE值范围为0.21至1.85，NSE值范围为0.18至0.99。 研究结果表明，当气候数据最少时，GEP 可以有效预测 RET。此外，平均相对湿度被认为是所有气候条件下最相关的因素。这项研究的结果可用于实际情况下的水资源规划和管理，因为它们证明了输入变量对与不同气候条件相关的RET的影响。