LANDSAT multispectral image analysis of bedrock exposure rate in highly heterogeneous karst areas through mixed pixel decomposition considering spectral variability

Mixed pixels and spectral variations commonly occur in images of karst areas because these areas have rugged topography and high surface heterogeneity. Consequently, the bedrock exposure rate cannot be accurately estimated using the existing rock index method based on remote sensing and the fixed endmember mixed pixel decomposition model. In order to solve this problem, using LANDSAT operational land imager/thematic mapper (OLI/TM) images as the data source, this study estimated the bedrock exposure rate based on a generalized linear mixed model (GLMM) considering spectral variability. In addition, this approach was compared with existing commonly used methods for estimating bedrock exposure rate. The results show that: (1) GLMM showed the highest performance in estimating bedrock exposure rate, with a total accuracy of 88.05% and a kappa coefficient of 0.845, and the accuracy exceeded 70% for different levels of bedrock exposure rate. However, the total accuracy of other commonly used bedrock exposure methods is was below 66%, being higher only in areas with bedrock exposure rates less than 20% and more than 70%. (2) By applying each method to different terrain scenes, GLMM was found to be more stable than other methods, and the estimated bedrock exposure rate is the closest to the ground reference value with a root mean square error less than 0.093. Other methods, including fully constrained least squares unmixing (FCLSU) and karst bare-rock index (KBRI), have a certain gap in different scenes, and their accuracy is not high. (3) Without any ground reference data, the accuracy of the direct unmixing result of GLMM is very close to that calculated by the regression model, and the accuracy difference among different grades of bedrock exposure rate is less than 5%, thus outperforming the other methods. GLMM can effectively estimate the bedrock exposure rate at different times using different data. Therefore, GLMM has great potential in extracting rocky desertification information in karst areas. It can also be a reference method for the rapid, accurate, and long-term evaluation of rocky desertification in karst areas.