Comparison and analysis of two fractal dimension computing algorithms for upscaling remote sensing Leaf Area Index map

The Leaf Area Index (LAI) values derived from remote sensing images with different resolutions can be different, because of the heterogeneity of land surface. To validate the coarse resolution LAI product, the in situ LAI measurements and the high resolution LAI map need to be upscaled to the coarse resolution(such as 1 km). As the principle of fractal geometry has been applied to describe the irregular distribution of vegetation, the measured LAI can be upscaled using Fractal Dimension (FD) which is the key parameter of fractal geometry. In this paper two FD computing algorithms, Triangular Prism Surface Area method (TPSA) and Differential Box Counting algorithm (DBC), were compared in two aspects. One aspect was the ability of describing heterogeneity of LAI in different landscapes; another was the spatial distribution of FD and upscaled LAI. The log-log curves of computing algorithms showed that TPSA performs better to capture the difference between different landscapes than DBC algorithm does. Also TPSA can detect the scale inflexion of LAI spatial distribution but the DBC can't. The pattern of FD and upscaled LAI map using TPSA is similar with the real pattern of vegetation, while the FD and upscaled LAI map using DBC algorithm cannot capture the real pattern of vegetation.