## 2 Materials and Methods
### Comparison of Seasonal ET\({}_{0}\) Estimates from FAO PM Equation, BP and GABP Models  
During model training and testing phase, ET\({}_{0}\) was estimated at a daily time step. Figures S1-S4 show the results of the daily ET\({}_{0}\) trends of FAO PM equation vs. trends of BP and GABP models during testing phase. These daily estimated ET\({}_{0}\) data were accumulated as seasonal ET\({}_{0}\) data for comparison. Based on FAO PM equation, annual ET\({}_{0}\) was greatest for TPM zone (1088 mm yr\({}^{-1}\)), intermediate for TC zone (1014 mm yr\({}^{-1}\)) and MP zone (1012 mm yr\({}^{-1}\)) and least for TM zone (984 mm yr\({}^{-1}\)) and STM zone (930 mm yr\({}^{-1}\))  
Figure 4: ET\({}_{0}\) estimation performance in testing phase as indicated by (**A**) root mean square error (RMSE), (**B**) correlation coefficient (R), (**C**) mean absolute error (MAE) and (**D**) mean bias error (MBE) of BP\({}_{0.5}\), BP\({}_{0.7}\), GABP\({}_{0.5}\), GABP\({}_{0.7}\) models for the 14 national meteorological stations.  
(Table 3). Model performance in seasonal ET\({}_{0}\) estimates varied markedly across various seasons (Figure 5). BP and GABP models underestimated seasonal ET\({}_{0}\) in spring by \(-2.27\%\) to \(-5.07\%\), overestimated ET\({}_{0}\) in autumn by \(6.05\%\) to \(10.1\%\) and well estimated ET\({}_{0}\) in summer (\(-1.50\%\) to \(-0.66\%\)). In winter season, BP\({}_{0.5}\) model underestimated ET\({}_{0}\) by \(-6.38\%\) while GABP\({}_{0.7}\) models overestimated ET\({}_{0}\) by \(6.69\%\). In contrast, GABP\({}_{0.5}\) model well estimated seasonal ET\({}_{0}\) in spring, summer and winter seasons (\(-0.55\%\) to \(-1.27\%\)). The greatest ET\({}_{0}\) overestimation (by \(10.1\%\)) was observed in autumn for BP models, while GABP\({}_{0.5}\) model appreciably decreased the overestimation to \(6.05\%\) in autumn. BP\({}_{0.5}\) and BP\({}_{0.7}\) models overestimated seasonal ET\({}_{0}\) in autumn by \(14.2\%\) to \(33.5\%\) in TC zone, which was unacceptable. Through comparison, GABP\({}_{0.5}\) model had the best model performance in seasonal ET\({}_{0}\) estimation, especially for autumn and winter seasons, with large discrepancy for other models.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Season**} & **Climatic** & \multirow{2}{*}{**FAO PM**} & \multirow{2}{*}{**BP\({}_{0.5}\)**} & \multirow{2}{*}{**BP\({}_{0.7}\)**} & \multirow{2}{*}{**GABP\({}_{0.5}\)**} & \multirow{2}{*}{**GABP\({}_{0.7}\)**} \\  & **Zone** & & & & & \\ \hline \multirow{8}{*}{Spring} & TC 1 & 330.8 & 306.6 & 310.6 & 323.4 & 319.0 \\  & TM 2 & 327.1 & 314.5 & 285.6 & 303.1 & 289.6 \\  & MP 3 & 292.1 & 283.8 & 258.1 & 284.0 & 275.0 \\  & STM 4 & 244.2 & 248.8 & 259.5 & 247.6 & 248.6 \\  & TPM 5 & 288.4 & 297.7 & 295.9 & 290.5 & 302.1 \\  & TC & 449.7 & 449.4 & 438.2 & 459.4 & 452.5 \\  & TM & 383.4 & 388.1 & 391.1 & 387.3 & 390.9 \\ Summer & MP & 360.9 & 352.9 & 373.9 & 360.3 & 362.4 \\  & STM & 356.9 & 348.6 & 336.6 & 347.7 & 335.0 \\  & TPM & 363.9 & 353.9 & 347.2 & 347.6 & 343.9 \\  & TC & 182.4 & 236.4 & 225.7 & 201.2 & 211.3 \\  & TM & 190.3 & 197.6 & 240.6 & 202.4 & 230.6 \\ Autumn & MP & 216.6 & 250.2 & 239.7 & 238.1 & 238.8 \\  & STM & 207.2 & 212.9 & 210.7 & 217.8 & 207.2 \\  & TPM & 245.3 & 247.5 & 227.1 & 243.4 & 235.2 \\  & TC & 51.1 & 23.7 & 32.8 & 49.9 & 60.1 \\  & TM & 82.8 & 74.7 & 65.8 & 79.7 & 83.5 \\ Winter & MP & 142.2 & 133.2 & 160.5 & 146.1 & 157.0 \\  & STM & 121.7 & 125.5 & 134.1 & 121.3 & 133.1 \\  & TPM & 190.4 & 195.2 & 209.1 & 189.8 & 195.8 \\ \hline \end{tabular} Note: 1 TC, temperate continental zone; 2 TM, temperate monsoon zone; 3 MP, mountain plateau zone; 4 STM, subtropical monsoon zone; 5 TPM, tropical monsoon zone.  
\end{table}
Table 3: Mean seasonal ET\({}_{0}\) (mm) in testing phase estimated from BP and GABP models for different climatic zones in China.