Modeling of Lunar Digital Terrain Entropy and Terrain Entropy Distribution Model

The lunar surface has complex geomorphic characteristics. Since the lunar terrain entropy can reflect the amount of geomorphic information contained in the lunar terrain, this article uses the ratio of the elevation value of a local point on the lunar surface to the total elevation value of the neighborhood to calculate the local terrain entropy value of the Moon. Then, the hierarchical polishing splines algorithm is proposed to construct the digital terrain entropy model (DTEM) of the Moon, wherein the new algorithm produces a sequence of functions based on a hierarchy of coarse-to-fine control lattices to generate the modeling function, which has good modeling performance. Using the proposed algorithm, multiscale DTEMs of the Moon are constructed based on square moving windows with different sizes. From the lunar DTEMs, it can be found that the lunar terrain entropy is sensitive to the size of the square moving window and the resolution of lunar DEM, and the high-resolution lunar DTEM with suitable moving window can well show topographical variations. In addition, the lunar terrain entropy distribution models are created based on the lunar DTEMs, which is significantly important to the study of the lunar terrain entropy distribution law. Besides, two terrain parameters, i.e., surface roughness and surface slope, are selected to show that the geomorphic characteristics of the Moon can be well reflected by the lunar terrain entropy.