Calculating spatial configurational entropy of a landscape mosaic based on the Wasserstein metric

Entropy is an important concept traditionally associated with thermodynamics and is widely used to describe the degree of disorder in a substance, system, or process. Configurational entropy has received more attention because it better reflects the thermodynamic properties of physical and biological processes. However, as the number of configuration combinations increases, configurational entropy becomes too complex to calculate, and its value is too large to be accurately represented in practical applications. To calculate the spatial configurational entropy of a landscape mosaic based on a statistical metric. We proposed a relative entropy using histograms to compare two ecosystems with the Wasserstein metric, and used six digital elevation models and five simulated data to calculate the entropy of the complex ecosystems. The calculation and simulation showed that the purposed metric captured disorder in the spatial landscape, and the result was consistent with the general configurational entropy. By calculating several spatial scale landscapes, we found that relative entropy can be a trade-off between the rationality of results and the cost of calculation. Our results show that the Wasserstein metric is suitable to capture the discrepancy using complex landscape mosaic data sets, which provides a numerically efficient approximation for the similarity in the histograms, reducing excessive expansion of the calculated result.