Spectral reflectance distortions caused by terrain and solar illumination seriously reduce the accuracy of mapping forest carbon density, especially in mountainous regions. Many models have been developed for mitigating or eliminating the terrain effects on the quality of remote sensing images in hilly and mountainous areas. However, these models usually use global parameters, which may lead to overcorrections for regions with poor illumination and steep slopes. In this study, we present a local parameter estimation (LPE) method based on a pixel-moving window for topographic correction (TC), which can be considered as a general optimization framework for most semiempirical TC models. We set seven kernel sizes for the presented framework, which are 15 pixels, 25 pixels, 50 pixels, 100 pixels, 250 pixels, 500 pixels, and 1000 pixels, respectively. The proposed method was then applied to four traditional TC models, Minnaert (MIN), C Correction (CC), Sun Canopy Sensor + C (SCSC) and Statistical Empirical Correction (SEC), to form four new TC models. These new models were used to estimate forest carbon density of a mountainous area in Southern China using field plot data and a Landsat 8 image. Four evaluation methods, including correlation analysis, the stability of land covers, comparison of reflectance between sunlit and shaded slopes, and accuracy assessment of forest carbon density, were employed to evaluate the contributions of moving window sizes, and assess the performance of the TC models for forest carbon density estimation. The results show that the four TC models with LPE perform much better than the traditional TC models in reducing the topographic effects and improving the estimation accuracy of forest carbon density for the study area. Among the traditional TC models, SEC performs slightly better than SCSC, CC, and MIN. Therefore, the SEC-based model with LPE, that is, LPE-SEC, gets greater R2 and smaller relative RMSE values in estimating forest carbon density than other models. Moreover, all the means of the predicted forest carbon density values fall in the confidence interval of the validation data at a significant level of 0.05. Overall, this study implies that the proposed method with LPE provides great potential to improve the performance of TC and forest carbon density estimation for the study area. It is expected that the improved TC method can be applied to other mountainous areas to improve the quality of remotely sensed images.
Elementary Mathematics Education of Preschool Children in the Ukrainian Highlands
