# The Contributions of Climate and Human Activities to Water Use Efficiency in China's Drylands
## 2 Materials and Method
### Method
#### Geographical Detector  
Various factors, including topography, climate, and land cover changes, subject WUE to multiple influences. The interactions among these factors further compound their impact [26]. This study employed a geographic detector to quantify the impacts of individual factors and unravel the driving forces behind the spatial variations in WUE. Specifically, 21 factors were selected to investigate the spatial driving forces of WUE within China's drylands. These factors were Tem, Prec, Solra, PET, VPD, SWC, ET, GPP, Relah, AI, LAI, NDVI, Soil, Veget, Elev, Slope, Aspect, Geomt, Lanct, GDP, and POP. The factor detector measured the contribution level of each factor to the spatial diversity in WUE, shedding light on their ability to explain spatial variations in WUE. Initially, a grid system was established over the study area, comprising a total of n grids. In every grid, an overlay analysis was performed to calculate the WUE and the explanatory strength q (ranging from 0 to 1) of the chosen factor, assessing its influence on the spatial variability of WUE throughout China's drylands. As \(q\) approached 1, it indicated a stronger influence of the individual factor on WUE. A \(q\) value of 0 signified no relation between the factor and the spatial variations in WUE.  
\[q=1-\frac{\sum_{h=1}^{3}n_{xih}\text{Var}\text{x}_{kh}}{n\text{Var}_{X}} \tag{7}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  &
\begin{tabular}{c} **Driving Force** \\ **Partition** \\ \end{tabular} & \multicolumn{4}{c}{**Contribution of Driving Forces/\%**} \\ \hline \(Slope_{WUEobs}\) & \(Slope_{WUEcli}\) & \(Slope_{WUEres}\) & **Climate Change** & **Human Activities** \\ \hline  & \(>\)0 & \(>\)0 & \(Slope_{NPpli}\)/\(Slope_{iucobs}\) & \(Slope_{iucobs}\) \\ \(>\)0 & \(>\)0 & \(<\)0 & 100 & 0 \\  & \(<\)0 & \(>\)0 & 0 & 100 \\  & \(<\)0 & \(<\)0 & \(-slope_{iucobs}\)/\(slope_{iucobs}\) & \(-Slope_{iucobs}\)/\(slope_{iucobs}\) \\ \(<\)0 & \(>\)0 & \(>\)0 & \(-100\) & 0 \\  & \(>\)0 & \(<\)0 & 0 & \(-100\) \\ \hline \hline \end{tabular} Note: \(slope_{WUEobs}\) represents the slope of the true value of WUE; \(slope_{WUEcli}\) represents the slope of simulated values of WUE under the control climatic factors; \(Slope_{NPpres}\) represents the slope of WUE residuals values, i.e., the slope in WUE under the control of human activities.  
\end{table}
Table 3: Approach for determining the proportional impact of climate variability and human actions on WUE alterations.  
where \(n_{Xh}\) denotes the number of subregions influenced by factor X, and Var\({}_{X}\) represents the variance of factor X across these subregions.  
The Interaction Detector was utilized to compute the q value representing the interplay between the spatial driving factors X\({}_{1}\) and X\({}_{2}\), both of which influence WUE. Following this calculation, the resulting value was compared to the combined sum of the q values associated with X\({}_{1}\) and X\({}_{2}\) when considered independently [26]. The purpose of this comparison was to ascertain if the interaction between X\({}_{1}\) and X\({}_{2}\) amplified or mitigated their joint impact on WUE in China's drylands, or if their effects were independent (Table 4). Examining how the interaction q value compares to the combined independent q values provided insights into whether X\({}_{1}\) and X\({}_{2}\)'s interaction had a synergistic effect on WUE or if their impacts were distinct. This method offered a nuanced understanding of the complex interactions among various factors that shape the spatial patterns of WUE within China's drylands. The results from the above methods were all at the 99% confidence level.