## 3 Results
### The Relationship and Correlation between NDVI and WUE  
In this paper, the changes of NDVI and WUE from 2001 to 2010 and 2011 to 2020 were superimposed. It was found that the area where NDVI and WUE increased at the same time accounted for the largest proportion, and the area of the Loess Plateau from 2001 to 2010 accounted for the largest proportion, increasing from 6.845% to 7.464% in 2011-2020 (Table 4). This shows that the restoration of vegetation on the Loess Plateau has played a certain role in promoting vegetation WUE. The area where NDVI increased and WUE decreased was reduced from 13.08% of the Loess Plateau to 8.81% from 2001 to 2010, mainly reflected in Linhe, Inner Mongolia, and Yulin, Shaanxi (Figure 5a). The area where NDVI decreased but WUE increased rose by 2.98% in the two time periods, mainly reflected in some areas such as Yan'an and Weinan in Shaanxi Province. The area where NDVI and WUE decreased at the same time accounted for 10.12% of the Loess Plateau from 2001 to 2010, but only 5.28% of the total area from 2011 to 2020 (Figure 5b), indicating that both NDVI and WUE of the Loess Plateau have been reduced to a certain extent.  
To learn more about the Loess Plateau's NDVI's process for influencing WUE, the correlation coefficients of NDVI with WUE, GPP, and ET in 2001-2010 and 2011-2020 were calculated. It can be seen from the results (Figure 6) that the correlation of NDVI with GPP was higher than with ET, and NDVI mainly led to a change in the WUE by affecting GPP. Different correlations were observed in different regions. The correlation between NDVI and WUE in the same change region was also higher than others. The sensitivity coefficient of NDVI to WUE was 0.59 (Figure 6c), the sensitivity coefficient of NDVI to GPP was 0.68 (Figure 6f), and the sensitivity coefficient of NDVI to ET was 0.32 (Figure 6i). NDVI was positively correlated with WUE, GPP, and ET as a whole; however, in 2011-2020, in the area  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Period** & **NDVI** & **WUE** & **Area Change Ratio (\%)** \\ \hline \multirow{4}{*}{2001–2010} & – & – & 10.12 \\  & – & + & 8.34 \\  & + & – & 13.08 \\  & + & + & 64.45 \\ \hline \multirow{4}{*}{2011–2020} & – & – & 5.28 \\  & – & + & 11.28 \\ \cline{1-1}  & + & – & 8.81 \\ \cline{1-1}  & + & + & 74.63 \\ \hline \hline \end{tabular} Note: + means increase, – means decrease.  
\end{table}
Table 4: The changes of NDVI and WUE.  
Figure 4: (**a**) Trend of WUE of Loess Plateau 2001–2010. (**b**) Trend of WUE of Loess Plateau 2011–2020.  
where NDVI increased and WUE decreased, NDVI and ET showed a negative correlation with a correlation factor of \(-0.02\).  
Figure 5: (**a**) Distribution map of NDVI and WUE area change from 2001 to 2010. (**b**) Spatial distribution map of NDVI and WUE from 2011 to 2020.  
Figure 6: Spatial distribution and statistical images of correlation between NDVI and WUE (**a–c**), NDVI and GPP (**d–f**), and NDVI and ET (**g–i**). (**a**,**d**,**g**) are correlations for 2001–2010, (**b**,**e**,**f**) are  
correlations for 2011-2020; the upper right corner is the image without excluding significant \(p>0.05\) elements (**c**,**f**,**i**). Correlation statistics of NDVI with GPP, ET, and WUE.