## 2 Materials and Methods
### Methods  
Most of the research is based on one partition, and few studies are based on different partitions. This study focuses on these differences, which are of great significance to protecting ecosystems according to local conditions. In addition, against the backdrop of global climate change, the dominant factors in the change process of vegetation NPP have also changed. It is not clear how the evolution mechanisms of vegetation NPP varied across different periods and ecological sub-regions. The related research is mostly based on the driving mechanisms of temperature, precipitation, population, and other factors [24; 25; 28; 29]. Based on the research status, most relevant research has selected these data; in the size of the influence of the driving factors, these factors can well explain the reasons for the change. A series of ecological and environmental problems caused by climate change, such as air pollution and dust storms, are not only troubled. People's lives have also had a negative impact on industrial production, which has hindered the sustainable development of the social economy to a certain extent. Therefore, it is of scientific significance to understand and understand the impact of climate change on vegetation. Therefore, this study selects two climatic factors (temperature and precipitation), two social factors (population density and Gross Domestic Product), and two geographical factors (altitude and slope).  
Moreover, previous studies mostly applied second-order partial correlation to explore the effects of different climatic factors on vegetation NPP but ignored the comprehensive and interactive effects of regional multi-type climatic factors. In the past, partial correlation analysis was mostly based on single factor and double factors. In this paper, third-order partial correlation analysis is used as an innovation point, which allows for comprehensively considering the complex effects of three factors on the evolution of vegetation, thereby more truly reflecting ecological processes.  
Geodetectors detect the spatial stratification heterogeneity of elements and reveal the driving forces behind them [30], thus making it advantageous for exploring driving mechanisms across different partitions. In this study, we utilized a Geodetector, third-order partial correlation analysis, and a gravity center model to analyze the change process of vegetation NPP in China from the perspective of partitions. The relative role of climate-human interactions during different historical periods was quantitatively distinguished, and the dominant factors of changes in vegetation NPP across different sub-regions and historical periods were revealed. The effects of global change on Chinese vegetation NPP response mechanisms were clarified, which provides support for important decisions regarding the restoration of regional vegetation ecosystems.  
The process was mainly divided into three parts: The first part was data preprocessing. The NPP, climate, land (land use, soil type), and socioeconomic (GDP, population density) datasets were preprocessed via kriging interpolation (Co-Kriging), re-projection, and clipping. The second part was the analysis of the spatio-temporal change process. Spatial distribution analysis was carried out from the perspective of mean distribution, different levels of vegetation NPP transfer scenarios, and mean comparative analysis. The analysis of temporal evolution was conducted from the perspective of gravity center migration. The  
Figure 3: Driving factor line chart. (**a**) Annual precipitation; (**b**) Annual average temperature.  
third part was the analysis of the driving mechanisms. The driving factors were explored using a geographic detector. A flow chart of this study is presented in Figure 4.