## 1 Introduction  
The surface vegetation ecosystem, an important component of the earth's biosphere, is crucial for human survival and is closely related to human productivity. During interactionsbetween vegetation and the external environment, the vegetation canopy is the most direct and active contributor. Most natural vegetation is distributed in different ecosystems and subject to different climatic conditions and terrains. Therefore, the structure of the canopy is complex, and leaves are not randomly distributed but clump to different degrees. The clumping index (CI), as a parameter of vegetation structures, is used to quantify the non-random distribution of foliage [1]. CI was defined as the ratio of the effective leaf area index (LAI\({}_{\text{eff}}\)) to the true leaf area index (LAI\({}_{\text{true}}\)) [2]. When foliage distributions are clumped, random, and regular, the corresponding CI ranges are as follows: CI \(<\) 1, CI \(=\) 1, and CI \(>\) 1, respectively. CI can be determined through field measurements or retrieved based on remote sensing data, and the global CI values generally vary from 0.3 (foliage elements are very clumped) to 1.0 (foliage distributed randomly). Previous studies have shown that the LAI\({}_{\text{eff}}\) obtained through indirect optical methods during field measurements will be underestimated by at least 30% to 50% relative to LAI\({}_{\text{true}}\) without clumping correction [3; 4; 5; 6]. If LAI\({}_{\text{eff}}\) derived from remote sensing data is directly used to estimate forest evapotranspiration (ET) and gross primary productivity (GPP) without taking foliage CI into consideration, the former will be substantially underestimated [7], and the latter may be underestimated by up to 9% [8]. Furthermore, remote-sensing-based CI plays an important role in determining the radiation transfer and photosynthesis of the canopy [9; 10]. Therefore, remote-sensing-estimated CI values are crucial for land surface models in terms of hydrology, agriculture, ecology, and climate, as well as for the retrieval of other vegetation structures [11; 12]. The spatial distribution of vegetation foliage varies seasonally, and the CI exhibits certain characteristics of seasonal variation. Furthermore, climate change, land use variation, global warming, and other factors can lead to interannual variations of the CI. Moreover, the clumping effects of vegetation foliage vary from region to region, and the spatial distribution of CI is not the same. However, owing to the difficulties associated with obtaining CI, most existing ecological models and leaf area index (LAI) retrieval algorithms only considered the variation of CI with land cover types but did not consider its spatial and temporal variations [13; 14]. This assumption leads to significant uncertainties in model simulation and the retrieved LAI. Furthermore, previous studies on CI mainly focused on improving the relevant retrieval methods [15; 16; 17; 18; 19] and comparing different CI estimation methods [20; 21; 22]; there are relatively few studies that investigate the spatial and temporal variations in regional CI and quantify its driving forces. [PERSON] [23] has studied the sensitivity of global CI to climatic factors based on pixel-level correlation analysis; the results showed that CI was mainly negatively correlated to the temperature and precipitation. [PERSON] et al. [24] found that vegetation growth is closely related to topographic conditions, anthropogenic activities, and other factors; therefore, the spatial differentiation of CI is affected by the comprehensive effects of natural and anthropogenic factors. Theil\(-\)Sen trend analysis and the Mann\(-\)Kendall test have been increasingly applied to investigate variation trends and the significance of long time series data and are not affected by outliers. Moreover, the samples of long time series data do not need to follow a normal distribution.