## 4 Results and Evaluation
### Statistical Analysis
#### 4.2.3 Coefficients of Variance  
Coefficient of variance (CV), the ratio of standard deviation to the mean, is a statistical measure of the dispersion of data points. Theoretically, the CV of reflectance of the same land cover type will decrease due to much more consistency expected for the same land cover type from sun-facing and sun-averted slopes after successful topographic correction. Nevertheless, shadow areas, peculiarly prone to be over-corrected during topographic correction, may interfere and even conceal this trend when appraised together with the illuminated areas. Thus, we choose to evaluate the CVs of reflectance of the same land cover type for shadow areas and non-shadow areas separately. Also, by doing this, the improved model's ability to topographically correct illuminated areas and shadow areas can be demonstrated more clearly. Forest pixels in shadow areas and non-shadow areas were extracted separately by referring to the land cover map and DEM-derived shadow mask of the study area. CVs of forest pixels (shadow and non-shadow areas separately) were calculated for each band of the reflectance before and after terrain correction by different models. For spring and autumn scenes, results are illustrated in Figure 6.  
Figure 5: Scatter plots between NIR band reflectance and illumination condition (IC). **(a)** is spring TM scene before correction; and **(b–d)** are correction results by Sandmeier model, Li model and model proposed, respectively. **(e)** is autumn TM scene before correction; and **(f–h)** are correction results by Sandmeier model, Li model and model proposed, respectively.  
It can be seen from Figure 6a,b that degrees of CV alteration for illuminated forests after topographic correction vary obviously among different correction models. For Sandmeier model, the CVs increased for all bands (with visible bands exceptionally conspicuous) for both spring and autumn scenes. Serious overcorrection for steep areas with large incident/exiting angles, leading to extremely large reflectance values, may be responsible for this phenomenon. For spring scene (Figure 6a), Li model and model proposed all succeeded in decreasing CVs to some extent expect for band 7, and model proposed tended to slightly outperform Li model. For autumn scene (Figure 6b), Li model did not reduce the CVs except for band 4, while model improved could still decrease the CVs slightly for each band. Thus, model proposed seems to perform more stably in reducing the CVs for illuminated land covers, at least for forests.  
Figure 6c,d shows the CVs of reflectance for shadowed forests before and after topographic correction. All models tended to increase the CVs, and only band 4 for spring and autumn scenes corrected by model proposed showed some minor reduction. Compared with the other two models, model proposed leaded to less increases of CVs for each band when 3 models all increased CVs. But, overall, topographic modeling for correction of shadow areas may be not enough for all three physics-based models, and modifications for the models are still needed.  
Figure 6: Coefficients of variance of forest pixels for each band before and after topographic correction by different models; (**a**) is for non-shadow forest of spring TM scene; (**b**) for non-shadow forest of autumn TM scene; (**c**) for shadow forest of spring TM scene; and (**d**) for shadow forest of autumn TM scene.