## 1 Introduction  
Vegetation is an important component of the global ecosystem that can ameliorate climate change and maintain the global carbon cycle [1]. Remote sensing technology is suited for investigating vegetation distribution and studying its biological characteristics frequently and inexpensively [2]. However, coniferous forests have complex canopy structures through which sunlight can be refracted and reflected repeatedly, causing shadows in remote sensing images [3, 4]. Vegetation shadows are caused generally by sunlight being blocked by topographic relief or canopy obscuration,causing energy loss and the darkening of vision in remotely sensed images [5; 6]. Shadows reduce the spectral information of vegetation and interfere with tree species classification, biomass calculation, and quantitative algorithm construction [7; 8; 9]. Also, the amount of leaves exposed to sunlight is closely related to the intensity of photosynthesis, which is an important pathway for energy exchange and atmosphere adjustment [10; 11; 12]. The vegetation spectral shape affected by sunlight reflectance ranges mainly from the visible to the near-infrared bands, causing large differences in spectral curves of the same vegetation species [13; 14]. With the development of spectroscopy technology, the image quality and spatial resolution of sensors are improving constantly [15; 16]. The ability for images to display the details of the target has been improved, while the shadow details have been enhanced as well. For this reason, the interference of shadows on image pixels is also increasing with finer spatial resolutions [17]. How to effectively detect and quantify the shadow proportion in satellite imagery has become a subject of much research. Shadows have been found to have considerable negative effects on remotely sensed images [18]. To prevent the adverse effects of shadows on images, most of the research concerned shadow monitoring, shadow recognition and removal [19]. In [20] by [PERSON], the vegetation canopy was considered into sunlit or shaded leaves to propose the simplified soil-plant-atmosphere model, and photosynthesis was calculated. The related model has been continuously developed and modified, for example, by [PERSON] and [PERSON] [21; 22]. [PERSON] modified the JULES land-surface scheme and took into account variations in direct and diffuse radiation on sunlit and shaded canopy photosynthesis. [PERSON] modeled gross primary productivity using two-leaf (separating the canopy into sunlit and shaded parts) and big-leaf upscaling approaches. A model of bidirectional reflectance for forests was proposed by [PERSON] [23] in a comprehensive consideration of sunlit canopy, shaded canopy, sunlit background, and shaded background. Two simple physical models of vegetation reflectance have been derived to correct satellite imagery for bidirectional and topographic effects by [PERSON] [24]. [PERSON] has developed a stepwise masking system to separate sunlit and shaded image-objects of tree canopies to aid in forest species mapping [25]. Researchers have studied the influence of shadows on vegetation and have proposed models for quantitative retrieval of fractional vegetation cover [26; 27; 28; 29]. Four-Scale geometric optical modeling was promoted by [PERSON] based on Li-Strahler and describes the aggregation effect between canopies or among the leaves [30; 31; 32; 33]. It fully takes into account different spatial scales and further refines canopy structure characteristics. Results of above-mentioned studies have indicated the importance of an accurate description of canopy structure and its shadow conditions. Former studies and their proposed models have considered the impact resulting from canopy shadows, but mainly at the scale of a single tree. Complex parameters and higher-order functions were usually included in the models to explain physical processes and to analyze photon mechanisms between leaves, such as scattering, reflection and absorption.