Abstract
Context
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.
Objectives
To calculate the spatial configurational entropy of a landscape mosaic based on a statistical metric.
Methods
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.
Results
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.
Conclusions
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.
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Acknowledgements
We thank anonymous reviewers for their constructive comments. This research was supported by the National Natural Science Foundation of China (Grant No. 41431178), the Natural Science Foundation of Guangdong Province in China (Grant No. 2016A030311016), the National Administration of Surveying, Mapping and Geoinformation of China (Grant No. GZIT2016-A5-147) and the Research Institute of Henan Spatio-Temporal Big Data Industrial Technology (Grant No. 2017DJA001).
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Zhao, Y., Zhang, X. Calculating spatial configurational entropy of a landscape mosaic based on the Wasserstein metric. Landscape Ecol 34, 1849–1858 (2019). https://doi.org/10.1007/s10980-019-00876-x
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DOI: https://doi.org/10.1007/s10980-019-00876-x