## 1 Introduction  
Naturally, vegetation leaves are not randomly distributed; they are organized to different degrees according to vegetation structures, such as the distribution of vegetation landscapes and the configuration of crowns, branches, and leaves. The clumping index (CI) quantifies the relative degree of leaf grouping compared with a random distribution [1]. The clumping of leaves impacts the interaction between radiation and vegetation [2, 3, 4], which in turn affects vegetation growth and its carbon and water cycles [5, 6, 7]. For remote sensing applications, the CI reflects additional information on vegetation structure for mono-angle observations, which is the most extensive data acquisition mode to date. It not only influences the estimation of the leaf area index (LAI) by using mono-observed gap fraction information [8, 9, 10, 11], but also affects the separation of sunlit and shadowed leaves [12], which play important roles in the interpretation and estimation of vegetation photosynthesis and evapotranspiration [6, 13, 14]. The CI is also very useful for ecological and meteorological models [15, 16]. The multiangle capability of remote sensing instruments provides a means to obtain surface anisotropic reflectance that embeds structural information of vegetation sur faces [12; 17; 18]. To explore the relationship between the CI and reflectance anisotropy, three main steps must be taken. First, multiangle surface reflectance data are acquired. The anisotropic reflectance of surface scattering is usually described by the bidirectional reflectance distribution function (BRDF) [19], which is determined by surface characteristics and the illumination and viewing positions [20]. Multiangle satellite observations can be coupled with semiempirical models to retrieve the BRDF of a locality [21]. Second, the surface anisotropic reflectance is characterized by fewer feature parameters. Several angular vegetation indexes were proposed by using BRDF models to capture anisotropic surface features, e.g., the anisotropic flat index (AFX) calculated by normalizing the net scattering magnitude with isotropic scattering describes the dome-bowl BRDF patterns of the surface [22], and the normalized difference between hotspots and dark spots (NDHD) highlights the mutual shadow information in forward scattering [23]. Third, establishing the relationship between the angular index and the CI. As the hotspot and dark spot are sensitive to the mutual shadowing of vegetation, the NDHD has been successfully related to the CI under the circumstances of both model simulations and field measurements [12; 23]. This relationship is essential to retrieve the CI from remote sensing observations and has been applied to obtain CI maps at global and regional scales [24; 25; 26; 27; 28; 29; 30]. Additionally, the AFX has also been related to the CI for the dome-bowl BRDF shape information contained in this index, which is used as a backup algorithm for CI-NDHD equations [26]. The Moderate-Resolution Imaging Spectroradiometer (MODIS) BRDF/Albedo product (MCD43) is produced at a 500 m spatial resolution by inverting multidate, multi-angular, cloud-free, atmospherically corrected, surface reflectance observations acquired by MODIS instruments onboard the Terra and Aqua satellites over a 16-day period [21; 31]. The product is derived using a kernel-driven semiempirical BRDF model consisting of isotropic scattering, volumetric scattering, and geometric-optical (GO) scattering components [32; 33; 34]. When the multiangle observations are sufficient to invert model parameters, a high-quality full inversion can be conducted; otherwise, a low-quality magnitude inversion is performed by using available observations and a priori BRDFs based on recent high-quality MODIS retrievals at the same location [35]. The MCD43 product has been produced since the launch of Terra in 2000 and has been updated in several versions.