## Materials and Methods
### Methods  
(1) Spatial Heterogeneity  
Global autocorrelation can reflect the similarity degree among spatial neighborhood units. It is used to analyze the distribution pattern and trend of a certain attribute in the whole region. The calculation formula is as follows:  
\[I=\frac{\mathrm{n}(x_{i}-\overline{\mathrm{x}})\sum_{i=1}^{n}\sum_{j,j\
eq 1}^{n}w _{ij}(x_{i}-\overline{x})\big{(}x_{j}-\overline{x}\big{)}}{\sum_{i=1}^{n}(x_{i} -\overline{x})^{2}\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} \tag{1}\]  
Figure 1: Geographical location of the study area. In this equation, \(I\) is Moran's \(I\), \(n\) is the number of observed values, \(x_{i}\) and \(x_{j}\) are the attribute values of the observations of the regional units \(i\) and \(j\), \(\overline{x}\) is the average of the observations, and \(w_{ij}\) is the element of the space weight matrix. Local indicators of spatial association (LISA) is the expression coefficient of local Moran's \(I\), and the calculation formula is:  
\[I_{i}=\frac{n(x_{i}-\overline{x})\sum_{j,j\
eq 1}^{n}w_{ij}\Big{(}x_{j}- \overline{x}\Big{)}}{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}} \tag{2}\]  
where \(I_{i}\) is the local Moran's I of the ith county-level administrative unit: if \(I_{i}\) is a positive value, it indicates that the spatial unit is similar to adjacent units for an attribute; if \(I_{i}\) is a negative value, it indicates that the spatial unit is different from the adjacent units for an attribute. (2) Coefficient of Variation (CV)  
The coefficient of variation (CV) is a statistical value that measures the degree to which observed data are dispersed. In this study, the standard deviation in the coefficient of variation calculation reflects the dispersion degree of the annual mean NPP, and the difference in surface vegetation types can be eliminated by dividing by the annual mean. It can be used to not only judge the temporal stability of NPP over the years but also ensure the comparability of temporal stability at the pixel level. Therefore, the CV is a suitable method for analyzing the variation in geographical phenomena and is widely used for the stability analysis of an NPP time series [34]. The CV is a statistical parameter that reflects the degree of variation in NPP, namely, the ratio of the standard deviation to the mean:  
\[CV=\frac{SD_{NPP}}{\overline{ NPP}} \tag{3}\]  
where \(SD_{NPP}\) is the standard deviation of NPP, and \(\overline{ NPP}\) is the average value of NPP. The larger the value of the CV, the larger the fluctuation in NPP. In contrast, a small CV value reflects an NPP time series of vegetation that is relatively stable. (3) Trend analysis  
Unitary linear regression analysis can simulate the variation trend of each grid. In this method, the average annual slope of NPP is fitted by least squares pixel by pixel over a certain period to comprehensively reflect the spatial-temporal evolution characteristics of NPP [35]. \[\text{Slope}=\frac{n\times\sum_{i=1}^{n}i\times P_{i}-\sum_{i=1}^{n}i\sum_{i= 1}^{n}p_{i}}{n\times\sum_{i=1}^{n}i^{2}-\left(\sum_{i=1}^{n}i\right)^{2}} \tag{4}\]  
where Slope is the change in the trend, \(P_{i}\) is the NPP for the ith year, and \(n\) is the length of the time series. If Slope \(>\) 0, then NPP has an upward trend. Conversely, NPP has a downward trend if Slope \(<\) 0. The significance of the interannual change in NPP is determined by the F test:  
\[F=\frac{R^{2}}{1-R^{2}}\times\frac{t-k-1}{k} \tag{5}\]  
where \(R\) is the slope, \(t\) is the sample number, and \(k\) is the number of independent variables. The following formula is introduced in this study in order to evaluate the overall change in NPP over a long time series. It is expressed as the relative inter-annual rate of change (RARC\({}_{c}\)) in NPP and obtained by the following formula:  
\[RARC_{c}=\frac{Slope}{\overline{ NPP}}\times 100\% \tag{6}\](4) Second-order partial correlation method  
A geographical system is complex and composed of many variables. A change in any element within the system will inevitably affect other elements.