## 1 Introduction  
The vegetation canopy represents the most direct and dynamic interface between vegetation and the external environment, significantly influencing ecosystem material and energy exchanges as well as biodiversity [1]. In most natural vegetation canopies, leaves are not randomly distributed but exhibit varying degrees of aggregation at different levels, such as in tree clusters, crowns, branches, and leaf clusters [2]. The clumping index (CI) is a crucial structural parameter that quantifies the degree to which the leaf distribution deviates from randomness within the vegetation canopy [3, 4]. The CI is very important for the accurate inversion of other biophysical parameters, e.g., the leaf area index (LAI). According to [PERSON] and [PERSON], the CI is defined as the ratio of the effective leaf area index (LAIe) to the true leaf area index (LAI), represented by the formula CI = LAIe/LAI [5]. Thus, the CI can be utilized to improve the accuracy of leaf area index inversion [6]. When leaves are randomly distributed, the CI equals 1; when they are regularly distributed, the CI is greater than 1; and when they are clumped, the CI is less than 1. CI and LAI are fundamental for distinguishing between sunlit and shaded leaves within the canopy, making CI critical for improving the accuracy of terrestrial carbon cycle models [7]. For example, the CI can improve the accuracy of global gross primary productivity (GPP) estimates. When the LAI is used directly without considering clumping effects, the global GPP is overestimated by 12%, whereas using the LAIe without accounting for clumping effects results in a 9% underestimate of the global GPP [8]. The clumping effect also influences the interception and distribution of light and precipitation within the canopy, thereby affecting photosynthesis [9; 10; 11] and transpiration [12]. Additionally, the amount of radiative energy available for evapotranspiration in vegetation is directly influenced by the degree of canopy clumping [13]. Therefore, CI plays a crucial role in the study and modeling of ecological processes, including light propagation, surface hydrology, photosynthesis, and vegetation productivity, at both regional and global scales [14; 15; 16]. Numerous studies have demonstrated that multi-angle data provide substantial structural information about vegetation canopies [5; 17; 18; 19]. Consequently, many researchers have estimated the CI via multi-angle satellite data, including those from POLDER [20; 21; 22], MODIS [23; 24; 25; 26; 27], and the multiangle imaging spectroradiometer (MISR) [28]. [PERSON] et al. [20] developed a linear regression model linking the normalized difference hotspot and dark-spot index (NDHD) to CI based on a four-scale geometrical optical model under various conditions. Employing this model, a global CI product with a 6 km resolution was first generated, covering eight months of POLDER-1 data [20]. Building on these results, the terrain effects on CI inversion were corrected via POLDER-3 data [21]. However, because the operational MODIS algorithm underestimates the hotspot effect [26], [PERSON] et al. [24] refined the algorithm and generated a 500 m CI product for China. Similarly, the normalized difference vegetation index (NDVI) and solar zenith angle were applied to correct the MODIS hotspot reflectance, producing a global CI product for 2006 with a 500 m resolution, but only a single CI median value for the entire year was provided and released, posing challenges for time-sensitive models [23]. [PERSON] [28] subsequently applied the hotspot correction method proposed by [PERSON] et al. [23] to MISR data for CI inversion, but a global CI product was not provided because of the MISR multiangular acquisition mode and capability. [PERSON] et al. [27; 29] evaluated the impact of different BRDF model configurations and solar zenith angles on CI inversion and then produced a global CI product at a 500 mresolution for the years 2001-2017 based on MODIS BRDF products. [PERSON] et al.