Abstract Reference evapotranspiration (ET0) is one of the most important parameters, which is required in many fields such as hydrological, agricultural, and climatological studies. Therefore, its estimation via reliable and accurate techniques is a necessity. The present study aims to estimate the monthly ET0 time series of six stations located in Iran. To achieve this objective, gene expression programming (GEP) and support vector regression (SVR) were used as standalone models. A novel hybrid model was then introduced through coupling the classical SVR with an optimization algorithm, namely intelligent water drops (IWD) (i.e., SVR−IWD). Two various types of scenarios were considered, including the climatic data- and antecedent ET0 data-based patterns. In the climatic data-based models, the effective climatic parameters were recognized by using two pre-processing techniques consisting of τ Kendall and entropy. It is worthy to mention that developing the hybrid SVR-IWD model as well as utilizing the τ Kendall and entropy approaches to discern the most influential weather parameters on ET0 are the innovations of current research. The results illustrated that the applied pre-processing methods introduced different climatic inputs to feed the models. The overall results of present study revealed that the proposed hybrid SVR-IWD model outperformed the standalone SVR one under both the considered scenarios when estimating the monthly ET0. In addition to the mentioned models, two types of empirical equations were also used including the Hargreaves−Samani (H−S) and Priestley−Taylor (P−T) in their original and calibrated versions. It was concluded that the calibrated versions showed superior performances compared to their original ones.

中文翻译：

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智能水滴增强人工智能技术在月参考蒸发蒸腾估算中的应用

摘要 参考蒸发量（ET0）是最重要的参数之一，在水文、农业和气候研究等许多领域都需要它。因此，通过可靠和准确的技术对其进行估计是必要的。本研究旨在估计位于伊朗的六个站点的月度 ET0 时间序列。为了实现这一目标，基因表达编程 (GEP) 和支持向量回归 (SVR) 被用作独立模型。然后通过将经典 SVR 与优化算法相结合，即智能水滴 (IWD)（即 SVR-IWD）引入了一种新的混合模型。考虑了两种不同类型的情景，包括基于气候数据和前因 ET0 数据的模式。在基于气候数据的模型中，有效的气候参数是通过使用包括 τ Kendall 和熵的两种预处理技术来识别的。值得一提的是，开发混合 SVR-IWD 模型以及利用 τ Kendall 和熵方法来识别 ET0 上最有影响的天气参数是当前研究的创新。结果表明，应用的预处理方法引入了不同的气候输入来为模型提供数据。本研究的总体结果表明，在估算每月 ET0 时，所提出的混合 SVR-IWD 模型在两种考虑的情况下都优于独立的 SVR 模型。除了上述模型外，还使用了两种类型的经验方程，包括原始版本和校准版本的 Hargreaves-Samani (HS) 和 Priestley-Taylor (PT)。