## 3 Results
### Dominant Climate Factors of \(ET_{0}\) Change  
In order to identify the dominant climate factors affecting \(ET_{0}\), the contribution rate of each climatic factor was calculated using Equation (11). Comparing the \(ET_{0}\) trends caused by the four climate factors (\(C\_ET_{0}\)) and the \(ET_{0}\) trends calculated by P-M model (\(LR\_ET_{0}\)), the relative errors were 12.79%, 4.70% and 7.93% during 1970-1996, 1997-2018 and 1970-2018, respectively (Table 2). Therefore, equation (11) was a reasonable method to estimate the contribution rates of the four climatic factors to \(ET_{0}\).  
Table 2 shows the contribution rate of the four climate factors to \(ET_{0}\) in different periods. During 1970-1996, \(U_{2}\) was the dominant factor influencing \(ET_{0}\), followed by \(RH\), \(T_{mean}\) and \(RS\). The decrease of \(U_{2}\) and increase of \(RH\) caused a \(-4.41\%\) and \(-2.43\%\) decrease to \(ET_{0}\), respectively. However, the increases in \(T_{mean}\) and \(RS\) led to a 0.80% and 0.10% increase to \(ET_{0}\), respectively. The comprehensive effect of climate factors finally led to a \(-6.7\%\) decline to \(ET_{0}\). During 1997-2018, the decrease of \(RH\) was the main reason causing the increase in \(ET_{0}\) by 3.33%. In addition, the rise of \(U_{2}\) and \(T_{mean}\) also aggravated the increase of \(ET_{0}\) to a certain degree, resulting in the increase of \(ET_{0}\) of 2.34% and 1.58%, respectively. The decrease of \(RS\) led to a variation in \(ET_{0}\) of \(-0.96\%\). The effects of the climatic condition eventually caused the increase of \(ET_{0}\) by 6.29%. In a word, the decrease of \(ET_{0}\) during 1970 and 1996 was mainly due to the decrease of \(U_{2}\), while the increase of \(ET_{0}\) during 1997 and 2018 was mainly due to the decrease of \(RH\).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Period** & \(CR_{RS}\) & \(CR_{RH}\) & \(CR_{Tmean}\) & \(CR_{U2}\) & \(C\_(ET_{0})\) & \(LR\_(ET_{0})\) & \(\epsilon\) \\ \hline
1970–1996 & 0.10 & \(-\)2.43 & 0.80 & \(-\)4.41 & \(-\)5.94 & \(-\)6.70 & 12.79 \\
1997–2018 & \(-\)0.96 & 3.33 & 1.58 & 2.34 & 6.29 & 6.60 & 4.70 \\
1970–2018 & \(-\)0.67 & 1.04 & 3.05 & \(-\)4.29 & \(-\)0.87 & \(-\)0.94 & 7.93 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The contribution rate of climate factors to \(ET_{0}\) in different periods (%).  
Figure 7: Spatial distribution of sensitivity coefficient on the TP during 1970–2018. (**a**) \(S_{RS}\); (**b**) \(S_{RH}\); (**c**) \(S_{Tmean}\); (**b**) \(S_{U2}\).  
Figure 8 gives the spatial distribution of contribution rates of four climatic factors to \(ET_{0}\) during 1970-1996 and 1997-2018. From 1970 to 1996, the contribution rate of \(RS\) (\(CR_{RS}\)) was positive in the southeast and western TP, and the negative \(CR_{RS}\) was found in eastern and central parts of TP. From 1997 to 2018, \(CR_{RS}\) was mainly positive and the negative contribution distributed in the northern and central sporadic areas. The contribution rate of \(RH\) (\(CR_{RH}\)) was negative in most parts of TP and the positive \(CR_{RH}\) was only distributed partly in northwest and east before 1997; while, most regions on the TP exhibited a positive \(CR_{RH}\), except some areas of eastern TP after 1997. The distribution of contribution rate of \(U_{2}\) (\(CR_{U2}\)) was similar to that of \(RH\). The contribution rate of \(T_{mem}\) (\(\mathrm{CRT}_{mem}\)) was positive in most parts of TP during both periods.  
Figure 8: Spatial distribution of contribution rates of four climatic factors to \(ET_{0}\) during 1970–1996 (**a–d**) and 1997–2018 (**e–h**) (%); (**a,e**) \(CR_{RS}\); (**b,f**) \(CR_{RH}\); (**c,g**) \(\mathrm{CRT}_{mem}\); (**d,h**) \(CR_{U2}\).