## 1 Introduction  
Gross primary production (GPP) refers to the rate at which chemical energy is acquired by ecosystem producers over a given period of time and stored as biomass through photosynthesis [1]. GPP not only reflects vegetation growth, but also the carbon exchange process between terrestrial ecosystem and atmosphere, which is the key flux driving the terrestrial carbon cycle. Quantitative calculation of GPP and analysis of its temporal and spatial distribution are the focus of carbon cycle research [2].  
At present, the most widely used method to calculate GPP is to use the light energy utilization ratio (LUE) for inversion, where LUE is essentially used as the core of a physical model in GPP products around the world [3], e.g., the Carnegie-Ames-Stanford Approach (CASA) Model [4], Global Production Efficiency Model (GLOPEM) [5], Eddy Covariance-Light Use Efficiency (EC-LUE) [6], MOD17 algorithm [7], Vegetation yield Model (VPM) [8], C-Flux [9], etc.  
At present, the spatiotemporal analysis of GPP primarily focuses on the spatial distribution pattern of GPP and the inter-annual and intra-annual changes of GPP, e.g., spatiotemporal vegetation variations in the Greater Khingan Mountain on the basis of GPP products that were generated by the GLASS program from 1982 to 2015 [10]. The spatial pattern analysis of GPP can clarify the changes of GPP in different geographical environments [11]. Researchers use GPP trends to measure the influence of human factors and natural pressures on GPP. Additionally, the inter-annual variation of GPP can reflect the inter-annual variation driven by climate change [12]. Current research on GPP generally adopts the correlation coefficient method and trend analysis to analyze the spatial distribution and driving factors of GPP concentrated in the perspective of the dynamic changes, and correlation between all aspects of the spatial differentiation with the static study being lesser, especially as the quantitative attribution to the interaction between natural elements factor is relatively weak [13]. On the basis of traditional analysis methods, we use the Geodetector, which is a statistical tool to measure spatially stratified heterogeneity, to detect the explanatory power of single factors on GPP and the interaction between factors quantitatively [14]. For instance, the geodetector model was used to explore the dominant drivers of spatial variation in grassland NDVI, combined with 34 factors covering natural environmental changes and human disturbances over the same period [15]. In the past, when geographical detectors were used to analyze GPP in the Beijing-Tianjin-Hebei (BTH) region, the driving factors were generally natural factors. We added two human factors to the main natural factors for analysis [16].  
The BTH is the region which is the largest in economic scale and has the highest level of development in northern China [17]. It is a key ecological region in the North China Plain and plays an important role in the regional ecological security pattern. It is also an important heavy industry base in China, with carbon emissions of 1.085 billion tons in 2018, accounting for approximately one ninth of the country's carbon emissions.  
Due to the fragile ecological environment in the BTH, and with the acceleration of urbanization, urban carbon emissions show a continuous increasing trend [18]. In order to figure out the coordinated development of BTH and adhere to the principle of ecological priority, this study analyzed the spatiotemporal distribution pattern of GPP in BTH from 2000 to 2020 and analyzed the ecological development trend of this region. Through the analysis of temperature, precipitation, downward surface shortwave radiation, and other factors, the distribution of driving factors of GPP change in the BTH was obtained, so as to realize the control of ecological change in the BTH and provide a reference for the coordinated development of ecology, economy, and society.