A HeadTail BreaksBased Method for Efficiently Estimating the Absolute Boltzmann Entropy of Numerical Raster Data Shannon entropy is the most popular method for quantifying information in a system. However, Shannon entropy is considered incapable of quantifying spatial data, such as raster data, hence it has not been applied to such datasets. Recently, a method for calculating the Boltzmann entropy of numerical raster data was proposed, but it is not efficient as it involves a series of numerical processes. We aimed to improve the computational efficiency of this method by borrowing the idea of head and tail breaks. This paper relaxed the condition of head and tail breaks and classified data with a heavytailed distribution. The average of the data values in a given class was regarded as its representative value, and this was substituted into a linear function to obtain the full expression of the relationship between classification level and Boltzmann entropy. The function was used to estimate the absolute Boltzmann entropy of the data. Our experimental results show that the proposed method is both practical and efficient; computation time was reduced to about 1% of the original method when dealing with eight 600xc3x97600 pixel digital elevation models.

Landscape Sustainability Evaluation of Ecologically Fragile Areas Based on Boltzmann Entropy From the perspective of landscape, it is important to evaluate the landscape sustainability of ecologically fragile areas and explore temporal and spatial evolution laws to promote their sustainable development. Presently, most studies on the analysis of landscape Boltzmann entropy (also called configurational entropy) are based on a single landscape, and most of these studies are theoretical discussions. However, there are few case studies on landscape ecology. The main objectives of this paper are to explore a quantitative relationship between Boltzmann entropy and landscape sustainability, to propose a method for evaluating landscape sustainability based on Boltzmann entropy, and to evaluate the sustainability of diverse landscapes in Mizhi County, Shaanxi Province, China. This article uses digital elevation model (DEM) data with a spatial resolution of 30 m in Mizhi County. The remote sensing data on Mizhi County from 2000 were obtained by the Landsat Enhanced Thematic Mapper (ETM)  sensor, and the highresolution image of Mizhi County from 2015 was obtained by the Gaofen1 satellite. In this article, the subbasins are taken as the evaluation unit, and the Boltzmann entropy of Mizhi County is calculated based on the expertsu0027 scoring of landscape sustainability in the study area. Through the analysis of landscape sustainability results from 216 subbasins in Mizhi County in 2000 and 2015, the following conclusions are drawn: (1) the evaluation matrix proposed in this paper is effective, and the Boltzmann entropy obtained by this method can directly reflect the level of landscape sustainability; (2) during the research period, the landscape sustainability of Mizhi County showed a good trend overall, especially the three townships of Taozhen, Shadian, and Shigou, which were significantly improved, and these findings were consistent with the field investigation; (3) on the spatial level, the landscape sustainability of mideastern Mizhi County is rela