## 2 Materials and Methods
### Comparison of Statistical Indices of BP and GABP Models  
The statistical indices in testing phase for BP and GABP neural network models were presented in Figure 4. As indicated by RMSE, R, MAE and MBE, the accuracy for GABP estimation models was higher than that of BP models (Table S1). Mean values of RMSE, R, MAE and MBE were 0.755 mm d\({}^{-1}\), 0.724, 0.404 mm d\({}^{-1}\) and \(-\)0.023 mm d\({}^{-1}\), respectively, for BP models and were 0.434 mm d\({}^{-1}\), 0.894, 0.169 mm d\({}^{-1}\) and 0.053 mm d\({}^{-1}\), respectively, for GABP models. Generally, the performance of BP\({}_{0.5}\) and BP\({}_{0.7}\) models was best in tropical and subtropical monsoon zones, followed by the mountain plateau zone, and worst in temperate monsoon and temperate continental climates, respectively. However, GA significantly improved the performance of BP models for different climatic zones. For example, mean values of RMSE and MAE for GABP models were 0.434 and 0.169 mm d\({}^{-1}\), or a decrease of 42% and 58%, respectively, compared to BP models. Mean R values of GABP models were 0.894, or an increase of 23%, compared to BP models. As for MBE values, GABP models significantly decreased the values for tropical, subtropical monsoon and temperate continental zones, but significantly increased MBE values for temperate monsoon zone. It was a surprise that GA showed a contradictory effect on MBE among climatic types. Low mean MBE may be a result of an average of both positive and negative values, which may not indicate an approximation of true values. In this study, mean MBE value was low for BP\({}_{0.7}\) model but it was true that large difference existed in both negative and positive MBE values during different seasons for the BP\({}_{0.7}\) model. On the  
Figure 3: Coefficients of determination (r\({}^{2}\)) between ET\({}_{0}\) estimates (from FAO PM method) and models’ meteorological parameters from the 14 national meteorological stations. T\({}_{\max}\), T\({}_{\min}\) and T\({}_{\mean}\) represent maximum, minimum and mean temperature (°C); \(\Delta\)T is diurnal temperature range (°C), R\({}_{\rm a}\) stands for total solar radiation (M) m\({}^{-2}\) d\({}^{-1}\)), S, RH and U\({}_{2}\) mean actual sunshine duration (h), relative humidity (%) and wind speed at wind speed at 2 m height (m s\({}^{-1}\)).  
contrary, more neutral values of MBE for the GABP\({}_{0.5}\) model indicated a better estimation accuracy than did the BP\({}_{0.5}\), BP\({}_{0.7}\) and GABP\({}_{0.7}\) models. In this study, seasonal factor was considered in the comparison of statistical indices. Mean value of R was lowest (0.690) for winter season, whereas it was 0.812 to 0.877 for the other three seasons. Mean values of MAE were highest for winter (0.529 mm d\({}^{-1}\)), intermediate for autumn (0.309 mm d\({}^{-1}\)) and least for spring and summer seasons. RMSE values followed a similar order to MAE. However, GA significantly reduced RMSE and MAE across different seasons. For example, averaged RMSE and MAE values of GABP models for winter season were 0.292 mm d\({}^{-1}\) and 0.236 mm d\({}^{-1}\), or a decrease of 57% and 71%, compared to BP models, whereas the R value of GABP models was 0.841, or an increase of 56%, compared to BP models.