## 1 Introduction  
The radial growth and canopy dynamics of trees are important processes in forest carbon sequestration and determine the carbon sink potential of forests [1]. Forests fix carbon dioxide through the canopy and distribute it to various tree organs for growth [2], among which the trunk is the primary site of carbon sequestration. Therefore, trunk growth is partially influenced by tree canopy activity. The study of the relationship between tree trunks and the canopy is to reveal the physiological mechanism of tree carbon sequestration and provide a theoretical basis for increasing forest carbon sequestration. Recent studies on the relationship between radial tree growth and canopy dynamics have mainly centered on the relationship between tree rings and canopy phenology and between tree rings and the normalized difference vegetation index (NDVI) [3, 4, 5]. Several studies have discovered that there is a significant correlation between the radial growth of several coniferous species and NDVI during the tree growing season. Studies in the Bayinbuluke region of Xinjiang have found a significant positive correlation between radial growth of spruce and NDVI from June to August [6]. In the source area of the Yangtze River, studies have found the most significant correlation between radial growth of trees and NDVI in July and August [7]. Studies in the Qilian Mountains have found high consistency between spruce ring width index and NDVI in this region [8]. Similar findings were reported in the southwestern United States; studies have found that the radial growth of _Pinus edulis_, _Pinus Ponderosa_ and _Pseudoltsuga menziesii_ is most closely correlated with NDVI from June to August in the southwestern United States [9]. Furthermore, studies in the northern subtropical region have found that the ring width of _Pinus massoniana_ is highly consistent with NDVI in September [10]. However, NDVI is calculated based on the absorption and reflection of light at different wavelengths by chlorophyll in vegetation, which characterizes the surface vegetation cover [11] and does not directly respond to the activity of the canopy, making NDVI uncertain in response to conifers and bringing uncertainty to the correlation results. Compared to NDVI, gross primary productivity (GPP) is the amount of organic carbon fixed by photosynthesis in green plants per unit of time [12], which is an important indicator of the photosynthetic capacity of vegetation and is more representative of vegetation canopy activity [13]. Thus, studying the relationship between tree rings and GPP can directly reveal the relationship between radial growth and crown carbon sequestration. With the development of remote sensing technology, GPP inversion has made a lot of progress. In the last few years, some researchers have used several methods to calculate GPP based on remote sensing data and meteorological data from flux sites [14] and have obtained several GPP products. For example, the revised EC-LUE model is generated by integrating the regulation of several major environmental variables such as atmospheric CO\({}_{2}\) concentration, radiation components (i.e., direct and diffuse radiation), and atmospheric water vapor pressure difference (VPD). The revised EC-LUE can better simulate the spatial, seasonal, and interannual changes of global GPP. Especially at the site level and global scale, it has unique advantages in reproducing the interannual changes of GPP. Another GPP product, the GLASS GPP collection, currently consists of eight internationally and widely used light energy utilization models: CASA, CFix, CFlux, EC-LUE, MODIS, VPM, VPRM, and Two-leaf. The algorithm development and verification use remote sensing and meteorological data simultaneously based on the global vortex-related flux site data. The number of sites is 155, including 9 types of terrestrial ecosystems: evergreen broad-leaved forest, evergreen coniferous forest, deciduous broad-leaved forest, mixed forest, temperate grassland, tropical savanna, shrubs, farmland, and tundra.