## 1 Introduction  
Reference crop evapotranspiration (ET\({}_{0}\)) is a predominant factor in hydrologic processes and a prerequisite for calculation of crop water requirements [1, 2]. In recent years, model estimation of ET\({}_{0}\) has been a major way to obtain ET\({}_{0}\) due to its low cost and acceptable accuracy [3]. With solar radiation and aerodynamic factors considered, FAO Penman-Monteith (PM) model has been a reference method for computing ET\({}_{0}\)[4]. However, access to full meteorological datasets (i.e., air temperature, solar radiation, sunshine hours, wind speed and vapor pressure etc.) is not always easy in numerous developing nations, making the practice of PM model limited in many countries [5]. Radiation and temperature data are the commonest meteorological data obtained by weather stations. Many studies also reported that radiation and temperature were the factors most correlated to ET\({}_{0}\)[6, 7]. How to efficiently obtain higher precision ET\({}_{0}\) estimation models using less data has been an urgent problem to be solved. ET\({}_{0}\) estimation models are divided into two main categories: empirical models and machine learning models. Empirical models are site-specific, needing modifications for different locations [8]. In this context, it is difficult to select a broadly adopted empirical model suitable everywhere [9]. Recently, machine learning models have been successfully implemented to predict the ET\({}_{0}\)[10]. Artificial neural network (ANN) uses the interconnected information processing units to turn meteorological inputs into ET\({}_{0}\) outputs and has been regarded as one of the best approaches to predict ET\({}_{0}\)[11]. For example, neural network models have been proposed to compute ET\({}_{0}\) in the Beas-Suttlej basin, India [12] and in the Peloponnese Peninsula, Greece [13], based on different combinations of input data and they concluded that neural network models showed good performance in ET\({}_{0}\) prediction. In the tropical climate of Brazil, neural networks performed better in ET\({}_{0}\) prediction with limited meteorological data than support vector machine (SVM) models [14]. In Victoria, Australia, only temperature and wind speed data were adopted to predict ET\({}_{0}\) using artificial and wavelet neural networks and it was reported that both models predicted ET\({}_{0}\) with good accuracy [15]. The back propagation network (BP) model is one of the most popularly adopted neural network models due to its simple structure and easy implementation. Several studies have been adopting BP neural networks to predict ET\({}_{0}\)[16; 17]. In Florida, USA, regional ET\({}_{0}\) was predicted using BP models in a continental climate and it had good consistency with the measured ET\({}_{0}\)[18]. In India, the accuracy of BP models was verified in a subtropical monsoon climate and was proved effective in ET\({}_{0}\) prediction [19]. However, the BP neural network has some drawbacks, which makes it easy to fall into local optimal solution [20]. Some scholars found that local extremum was easily produced by the BP neural network, yielding low applicability among various climatic locations [21; 22]. Several studies have reported that climatic types exerted significant effect on the performance of BP models. For example, the accuracy of BP models for ET\({}_{0}\) estimation was lower in the monsoon plateau than in subtropical climate due to its difference in sensitivity to radiation and temperature [23]. Furthermore, BP models were shown to have greater biases in ET\({}_{0}\) estimation in cold seasons than in warm seasons [24; 25]. The uncertainty in ET\({}_{0}\) estimation across different climatic zones was probably due to the fact that in tropical regions wind speed was really slow, especially in rainy months, while it was very high in mountain plateau areas [15]. In addition, in tropical regions relative humidity was very high, whereas in arid and semi-arid areas relative humidity was extremely low [4].