## 3 Results
### Correlation between FVC Variation and Climate and Topographical Factors  
From a single-factor interpretation perspective, the climate factors of PRE, SUN, and TEM were dominant driving factors of FVC variation in Shaanxi Province with \(q\) values of 0.7197, 0.5812, and 0.5667 (Figure 8a), respectively. The topographical factors contributed less to FVC variation in Shaanxi Province than did climate factors, RIF and SLO received q values of 0.3698 and 0.2844, respectively, and few contributions were attributed to ALT and ASP. Climate factors of PRE, TEM, and SUN were dominant driving factors of FVC variation in the LOP area, with q values of 0.6556, 0.4525, and 0.4127 (Figure 8b), respectively. RIF and SUN were the dominant contributors of FVC variation in the GZP area, with q values of 0.1309 and 0.1062, respectively (Figure 8c). Topographic factors of RIF, ALT, and SLO were dominant driving factors of FVC variation in the QBM area, with q values of 0.1309, 0.1189, and 0.0797 (Figure 8d), respectively. Figure 7: Time-lag duration of FVC variation with climate factors in Shaanxi Province. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Topographic** & **Classification** & **Significant** & **Non-** & **Non-** & **Significant** & **Significant** & **Topographic** & **Classification** & **Significant** & **Non-** & **Significant** & **Significant** \\
**Factor** & **Classification** & **Degradation** & **Inverse** & **Inverse** & **Factor** & **Classification** & **Degradation** & **Inverse** & **Inverse** & **Inverse** & **Inverse** \\ \hline \multirow{4}{*}{ALT} & Low ALT & 1.58 & 5.62 & 0.49 & 0.22 & \multirow{4}{*}{ASP} & Northward & 0.97 & 1.08 & 0.99 & 1.01 \\  & Low ALT & 0.99 & 1.08 & 0.98 & 1.01 & \multirow{4}{*}{ASP} & Eastward & 1.01 & 0.93 & 1.00 & 1.01 \\  & Middle ALT & 0.69 & 0.27 & 1.03 & 1.30 & & Southwest & 1.04 & 1.20 & 0.97 & 0.97 \\  & High ALT & 1.99 & 0.81 & 1.24 & 0.44 & & Westward & 0.96 & 0.77 & 1.04 & 1.03 \\  & Higher ALT & 2.50 & 2.44 & 0.85 & 0.02 & \multirow{4}{*}{REF} & Plain & 1.21 & 3.50 & 0.85 & 0.27 \\ \hline \multirow{4}{*}{SLO} & Low SID & 1.09 & 2.57 & 0.86 & 0.75 & \multirow{4}{*}{REF} & Plateau & 1.13 & 1.63 & 0.85 & 0.91 \\  & Low SID & 0.85 & 0.52 & 0.87 & 1.34 & & Hill & 0.78 & 0.43 & 0.85 & 1.43 \\ \cline{1-1}  & Middle SID & 1.03 & 0.84 & 1.18 & 0.90 & Small muddling mountain & 1.11 & 0.46 & 1.26 & 0.74 \\ \cline{1-1}  & High SID & 1.25 & 0.87 & 1.32 & 0.58 & Medium muddling mountain & 1.40 & 0.69 & 1.31 & 0.68 \\ \cline{1-1}  & Higher SID & 1.37 & 0.65 & 1.34 & 0.47 & & Ringged mountain & 0.91 & 0.00 & 1.65 & 0.50 \\ \hline \end{tabular} Note: low ALT (\(<\)500 m), lower ALT (500-1000 m), middle ALT (1000-1500 m), high ALT (1500-2000 m), higher ALT (2000 m), low SLO (\(\leq\)2)’, lower SLO (2\({}^{-}\)6)’, middle SID (6\({}^{-}\)35)’, high SLO (15\({}^{-}\)25), higher SLO (15\({}^{-}\)25)’.  
\end{table} 
Table 2: Change trends of FVC under different topographic factors. We used the ridge regression method to calculate and establish regression models between environmental factors with significant contribution values, and FVC were developed for Shaanxi Province as well as three subregions (Equations (8)-(11)). The explanation rates of the four models were 60.14%, 64.59%, 16.49%, and 51.51%, respectively, all of which reached a highly significant level (\(p<0.01\)). \[\text{FVC}_{\text{Shaanxi}}=0.023+0.077\text{RIF}+0.009\text{TEM}+0.001\text{PRE }+0.005\text{SLO} \tag{8}\]  
\[\text{FVC}_{\text{LOP}}=-1.181+0.039\text{RIF}+0.035\text{TEM}+0.002\text{PRE }+0.003\text{SLO} \tag{9}\]  
\[\text{FVC}_{\text{GZP}}=0.097+0.002\text{RIF}-0.002\text{TEM}+0.001\text{PRE }+0.004\text{SLO} \tag{10}\]  
\[\text{FVC}_{\text{QBM}}=0.512+0.083\text{RIF}-0.010\text{TEM}+0.001\text{SLO} \tag{11}\]  
The geodetector tests indicated nonlinear and two-factor enhancement relationships between FVC changes and the climatic and geographical factors. Coupled interactions of any two factors were greater than those of single factors (Figure 9).