## 1 Introduction
However, with Lambertian assumption, it neglects the reflectance variance resulted from the BRDF effect [5]. Based on the Sandmeier method, [PERSON] and [PERSON] (2003) not only compensated for the different components of illumination, but also normalized the image reflectance to horizontal surface and discussed the necessity of reflectance correction for images in rugged area [18]. Nevertheless, the reflectance of diffuse light is simplified and considered as isotropic, which does not seem reasonable, since diffuse sky light is directional, especially in sunny and misty days. [PERSON] _et al._ (2009) developed a physics-based topographic correction model according to the fact that rugged terrain creates different configurations of STS geometry for the same land cover type, which can be used to derive BRDF shape function of that land cover type [19]. However, representative areas need to be selected and classification be conducted to obtain the reflective anisotropy information of each land cover type, which risks introducing relatively huge subjectivity. Considering the lack of multi-angular moderate-resolution data and depending on MODIS BRDF products (MCD43A1), [PERSON] _et al._ (2012) proposed a topographic correction model (referred to as Li model in the following) based on radiative transfer theory [20]. Topographic correction of Landsat Thematic Mapper (TM) images of Blue Mountain areas in Australia was conducted and satisfactory results were achieved. The methodology takes into account the BRDF effect and avoids the statistical analysis based on single scene, which helps maintain much more consistency and comparability for images acquired by different sensors or at different times. However, the experiment area selected by [PERSON] is only a small sub-scene, and the terrain ruggedness there is not so severe [20]. Moreover, digital surface model (DSM) used in correction is not readily available globally, and simply averaging MODIS parameters to characterize the BRDF effect of the whole study area may still need further discussion. Landsat series satellites have operationally acquired land surface observation data for almost half a century. Along with the launch and successful in-orbit operation of Landsat 8, Landsat series imagery provides important data support for the research of China's mountainous areas for the past 40 years and foreseeable future [21]. As discussed above, and in much literature [18,20], the BRDF effects and radiometric distortions by topographic effects in TM and TM-like fine spatial resolution images need to be considered in the applications in mountainous regions. Thus, studies on topographic correction accounting for BRDF effects are of great practical significance. In this study, we modified [PERSON]'s physics-based topographic correction model mainly by using NDVI-dependent MODIS BRDF parameters, and the specific objectives were to (1) compare the modified model's performance with that of [PERSON] model (with Lambertian assumption) and [PERSON] model (without Lambertian assumption); and (2) attempt to improve the physics-based model to further facilitate and generalize the topographic correction of TM and TM-like imagery.