Calculating the Wasserstein metric-based Boltzmann entropy of a landscape Mosaic

Abstract

Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human-computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient.