## 1 Introduction  
Mountain areas account for approximately 1/5 of the world's land area, and provide diverse goods and services to human society [1]. Meanwhile, mountain ecosystems are the sensitive indicators to the rapid global development. It is essentially important to monitor the mountain ecosystem change and protect the mountain environment [2]. The development of remote sensing technique has unprecedentedly facilitated the detection of change and development in mountainous areas. Nevertheless, many difficulties and challenges are encountered in the remote sensing applications in mountainous areas. Compared to horizontal land surfaces, remotely sensed images of rugged areas possess pronounced topographic effect, which severely impacts the accuracy of the images' quantitative applications [3]. Firstly, rugged terrain re-distributes the solar irradiance received by the terrestrial surfaces. Sun-facing slopes receive apparently more radiation than sun-averted slopes (except for shadowed sun-facing areas), and the recorded signals by satellite sensors from identical land cover type but different slope orientations may differ [4]. Secondly, tilted surfaces modify the angular configuration of sun-target-sensor (STS) geometry [5]. As for the ubiquitous non-Lambertian targets in the real world [6], different STS geometry often means different bi-directional reflectance (effect of bidirectional reflectance distribution function, BRDF) [7]. And this will very likely lead to phenomenon of the \"same targets showing different reflectance and different targets showing same reflectance\", which severely reduces the accuracy of quantitative applications of remote sensing, such as biophysical parameter inversion and land use/cover change detection [8,9]. Therefore, topographic correction, aiming at elimination or at least reduction of terrain effect, is a necessity before the imagery of mountainous areas is used in quantitative analysis. Previous contributions have reported a lot about empirical or semi-empirical topographic correction models, like cosine correction, C correction, SCS correction and SCS+C correction [10, 11, 12, 13]. Cosine correction model treats the land surfaces as Lambertian and only adjusts the direct solar irradiance with simple cosine formula. This model tends to cause severe over-correction when local incidence angle is high [14,15]. C correction model reduces the over-correction to some extent by adding the C correction factor, obtained from the statistical relationship between the cosine of the relative solar incident angle and radiance received by the sensor [16,17]. Considering that trees are geotropic and topography has no control over the sun-crown geometry, [PERSON] and [PERSON] (1998) proposed the SCS correction model to correct topographic effects on forest images. However, over-correction still exists for faintly illuminated slopes in the SCS model [10]. Based on SCS and C correction models, [PERSON] _et al._ (2005) introduced a semi-empirical C factor to account for the diffuse irradiance and developed the SCS+C model [11]. Overall, the aforementioned models all assume that land surfaces are Lambertian, and only correct for the direct solar irradiance or compensate for the diffuse component using statistical method, which lacks sound physical bases. Along with the further research on remote sensing theory and development of quantitative remote sensing, physics-based topographic correction models are developed based on the physical process between sunlight, atmosphere and land surface. The parameters in the physics-based model possess explicit mathematical and physical meanings. For example, [PERSON] and [PERSON] (1997) employed the \"Second Simulation of the Satellite Signal in the Solar Spectrum (6S)\" model to calculate direct and diffuse solar irradiance, and then corrected them for terrain effect, respectively [5]. This model (referred to as Sandmeier model in the following) avoids the empirical regression in traditional methods, and possesses relatively solid physical foundation.