## 2 Materials and Methods
### Methods
#### 2.3.3 Geodetector  
Geodetector is a group of statistical methods that detect spatial variability and reveal the driving factors [32]. The geodetector consists of four parts: risk detector, factor detector, ecological detector, and interaction detector [15].  
Factor detector: Factor detector detects the spatial stratified heterogeneity (SSH) of the dependent variable y (GPP value) and the explanation degree of the independent variable x (natural factor and human factor) to the SSH of y value. The expression is as follows:  
\[\mathrm{q}=1-\frac{\sum\
olimits_{h=1}^{L}\mathrm{N_{h}}\mathrm{\sigma_{h}^{2 }}}{\mathrm{N_{g}}\mathrm{\sigma^{2}}} \tag{7}\]where L is the stratification of the dependent variable GPP or influence factor X, N and N\({}_{\text{h}}\) are the number of sample units in strata h and the total region, respectively. \(\sigma_{\text{h}}^{2}\) and \(\sigma^{2}\) are the variance in the h strata and the variance in the region. The larger the value, the stronger the explanatory power of each factor. In this paper, q value indicates the degree of explanation of different drivers.  
Interaction detector: Interaction detector identifies the interaction between the different risk factors X, i.e., whether the meteorological variables X\({}_{1}\) and X\({}_{2}\) work together to increase or decrease the explanatory power of the dependent variable Y, or whether the effects of these factors on Y are independent of each other. Interactions can be classified into five types, as shown in Table 1.  
Risk detector: Risk detection is used to determine whether there is a significant difference in the mean value of attributes between two sub-regions. On the strength of this, we can search the suitable region of factors affecting the dependent variable GPP.  
Ecological detector: Ecological detector determines whether there is a significant difference between two factors (X\({}_{1}\) and X\({}_{2}\)) in terms of their influence on the spatial pattern of GPP change, which is examined by F statistic:  
\[\text{F}=\frac{N_{X_{1}}\big{(}N_{X_{2}}-1\big{)}SSW_{X_{1}}}{N_{X_{2}}\big{(} N_{X_{1}}-1\big{)}SSW_{X_{2}}} \tag{8}\]  
\[SSW_{X_{1}}=\frac{\sum_{h=1}^{L_{1}}N_{h}{\sigma_{h}}^{2}}{N\sigma^{2}}\,\ SSW_{X_{1}}=\frac{\sum_{h=1}^{L_{1}}N_{h}{\sigma_{h}}^{2}}{N\sigma^{2}} \tag{9}\]  
where \(N_{X_{1}}\) and \(N_{X_{2}}\) represent the sample number of two factors (X\({}_{1}\) and X\({}_{2}\)), respectively. \(SSW_{X_{1}}\) and \(SSW_{X_{1}}\) represent the sum of variance of each class formed by two factors (X\({}_{1}\) and X\({}_{2}\)), respectively. X\({}_{1}\) and X\({}_{2}\) represent the number of classes for variable X\({}_{1}\) and X\({}_{2}\), respectively. F-test was used to determine the significance level of F statistic.  
Generally, natural and human factors are the main factors affecting GPP. Therefore, this paper selected three natural and two human activity factors to form the influencing factors of GPP. GPP, precipitation, and downward surface shortwave radiation were calculated as multi-year accumulated values, whereas temperature and nighttime light data were calculated as multi-year average values. All data need to be discretized. The natural breaks (jenks) method in ArcGIS is used for discretization (LST and PR are 6 levels, SRAD and LIGHT are 8 levels, LUCC is 7 levels.), and classification results are applied to create a fishing net tool and generated a grid of 5 \(\times\) 5 km. A total of 8600 center points were used as sampling points to extract the corresponding attribute values of the GPP and impact factors. Quantitative relationships between GPP and impact factors can be obtained by the Geodetector in BTH.