## 5 Conclusions  
In this study, based on the collected datasets from the 14 national meteorological stations in China, BP and GABP models were developed to estimate daily ET\({}_{0}\) across  
Figure 8: Graphic showing GABP model performance for ET\({}_{0}\) estimation compared with BP models. Figure 7: Graphic showing climatic and seasonal effects on ET\({}_{0}\) estimation of models. different climatic zones and seasons. Correlation analysis between ET\({}_{0}\) and meteorological parameters helped determine the most commonly influencing variables applied to neural network models. U\({}_{2}\) had the least \(r^{2}\) with ET\({}_{0}\), followed by \(\Delta\)T. T\({}_{\text{max}}\) had the greatest \(r^{2}\) with ET\({}_{0}\), followed by T\({}_{\text{mean}}\), R\({}_{\text{a}}\) and T\({}_{\text{min}}\). Median and third quartile values of \(r^{2}\) = 0.50 and 0.70 were adopted as threshold values for the selection of input variables. The results showed that the GABP\({}_{0.5}\) model using radiation and temperature data had a better performance than the GABP\({}_{0.7}\) model in autumn and winter seasons and GABP models were superior to BP models in ET\({}_{0}\) estimation. Although GABP\({}_{0.7}\) model produced less accuracy than the GABP\({}_{0.5}\) model, it outperformed both the BP\({}_{0.5}\) and BP\({}_{0.7}\) models. When seasonal differences were taken into account, the GABP\({}_{0.5}\) model outperformed the GABP\({}_{0.7}\) model. Our study clearly addressed the hypothesis that GABP models significantly improved model performance in annual ET\({}_{0}\) estimation across various climatic zones and seasons. It was concluded that the GABP\({}_{0.5}\) model can be used for irrigation engineers and agricultural practitioners to estimate ET\({}_{0}\) for efficient crop water requirement calculation and can be a useful tool to be adopted in smart irrigation in different climatic zones in China. The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app122010689/s1](https://www.mdpi.com/article/10.3390/app122010689/s1)]([https://www.mdpi.com/article/10.3390/app122010689/s1](https://www.mdpi.com/article/10.3390/app122010689/s1)). Figure S1: Comparison of daily ET\({}_{0}\) estimates from BP\({}_{0.5}\) model in testing phase to ET\({}_{0}\) estimates from FAO PM equation; Figure S2: Comparison of daily ET\({}_{0}\) estimates from BP\({}_{0.7}\) model in testing phase to ET\({}_{0}\) estimates from FAO PM equation; Figure S3: Comparison of daily ET\({}_{0}\) estimates from GABP\({}_{0.5}\) model in testing phase to ET\({}_{0}\) estimates from FAO PM equation; Figure S4: Comparison of daily ET\({}_{0}\) estimates from GABP\({}_{0.7}\) model in testing phase to ET\({}_{0}\) estimates from FAO PM equation; Table S1: Statistical indices of root mean square error (RMSE), correlation coefficient (R), mean absolute error (MAE), and mean bias error (MBE) for BP and BPGA models across different climatic zones. Conceptualization, A.Q. ; methodology, Z.F. ; software, L.Z. ; validation, A.Q. ; formal analysis, A.Q. ; investigation, Z.F. ; resources, L.Z. ; data curation, L.Z. ; writing--original draft preparation, A.Q. ; writing--review and editing, Z.F. ; visualization, L.Z. ; supervision, A.Q. ; project administration, Z.F. ; funding acquisition, Z.F. All authors have read and agreed to the published version of the manuscript. This research was funded by State Key Laboratory of Aridland Crop Science, Gansu Agricultural University (grant number GSCS-2020-03) and the Central Public-Interest Scientific Institution Basal Research Fund, Institute of Farmland Irrigation of CAAS (grant number FIRI2022-09). The data that support the findings of this study are available from the corresponding authors upon reasonable request. The authors sincerely thank the anonymous reviewers who made valuable comments on this paper. The authors declare no conflict of interest.