Thermodynamics in landscape ecology: the importance of integrating measurement and modeling of landscape entropy

Cushman, Samuel A.

doi:10.1007/s10980-014-0108-x

Cited by 41 publications

(49 citation statements)

References 6 publications

(10 reference statements)

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“…The second law of thermodynamics has been considered to be fundamental in the field of landscape ecology, and researchers have paid great attention to the application of configurational entropy to landscape pattern analysis (Cushman 2015(Cushman , 2016Vranken et al 2015). However, success is very limited due to the two facts described in the previous paragraph.…”

Section: Resultsmentioning

confidence: 99%

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A hierarchy-based solution to calculate the configurational entropy of landscape gradients

2017

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Context The second law of thermodynamics is fundamental in landscape ecology, and Shannon entropy has been employed as an important means of analyzing landscape patterns. However, the thermodynamic basis of Shannon entropy has been recently questioned because such entropy considers only probability and not configurational information. As a result, Boltzmann entropy (also called configurational entropy), which is the basic measure in thermodynamics, has been revisited, and some thoughts on its calculation have been put forward. Nevertheless, a comprehensive calculation method is still lacking.Objectives The objective of this study is to propose a feasible solution for the calculation of configurational entropy for landscape gradients. Methods To calculate the configurational entropy, the first step is to define a good macrostate and then to determine the number of microstates. The macrostate of a landscape gradient is defined as its abstract (i.e., upscaled) representation. The number of microstates is calculated by determining all the possible ways of downscaling from the macrostate to the original. Results Both simulated and real-life landscape patterns were used for experimental validation. The results show that the entropy calculated using the proposed method successfully captures the disorder of landscape gradients in terms of both composition and configuration. Conclusions Configurational entropy, calculated using the proposed method, can serve as a thermodynamics-based metric to describe gradient-based landscapes and their changes across space and through time. With this metric, it becomes possible to interpret landscape ecological processes based on thermodynamic insights.

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Section: Resultsmentioning

confidence: 99%

“…As a result, scholars (Cushman 2015(Cushman , 2016Vranken et al 2015) have recently revisited the Boltzmann entropy (also called configurational entropy; Callens et al 2004), which is the classical measure of disorder in thermodynamics. Such entropy remains, however, at a conceptual level in landscape ecology.…”

Section: Introductionmentioning

confidence: 99%

A hierarchy-based solution to calculate the configurational entropy of landscape gradients

2017

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“…However, it has been reported recently by Vranken, Baudry, Aubinet, Visser, and Bogaert () that the thermodynamic interpretations based on Shannon's entropy are always questionable through their comprehensive review. This finding may shake the foundation of thermodynamic insights obtained using Shannon's entropy for geographic/landscape dynamics, and it is described as “astounding for a field that has been so obsessed with measuring and interpreting landscape patterns” (Cushman, , p. 8). In addition, the applicability of Shannon's entropy to characterizing the disorder of spatial data is also questionable (Cushman, ; Goodchild, ; Li, Liu, & Gao, ; Tobler, ), because it captures only the non‐spatial component of disorder (i.e., compositional disorder; the spatial component of disorder can be termed configurational disorder).…”

Section: Introductionmentioning

confidence: 96%

“…However, to the best of our knowledge, there is still no confirmed relevance between Shannon's entropy and thermodynamics, as also observed by Vranken et al (). Another solution to the problems, as suggested by Cushman (), is to revisit thermodynamics where the concept of entropy originates and to use Boltzmann's equation to compute entropy (referred to as Boltzmann's entropy, also called the thermodynamic entropy and sometimes the configurational entropy). Boltzmann's entropy is naturally related to thermodynamic interpretations and characterizes disorder in terms of both composition and configuration.…”

Section: Introductionmentioning

confidence: 99%

An efficient analytical method for computing the Boltzmann entropy of a landscape gradient

Gao

Zhang

2018

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Entropy is a central concept in thermodynamics and plays a fundamental role in understanding nature. It is commonly computed using Shannon's equation, and has been widely used to characterize disorder and to bridge the gap between disorder and thermodynamic interpretations. However, the thermodynamic basis of Shannon entropy is questioned by researchers, and it is suggested to use Boltzmann entropy as an alternative. Very recently, the first and only computation method has been proposed for the Boltzmann entropy of a landscape gradient, but the method is not efficient as it involves a series of numerical processes, which are computation‐intensive and time‐consuming. To improve it, a novel method is proposed in this study by developing an analytical solution to the key mathematical problem of the original method and incorporating a parallelization strategy. Experimental results demonstrate that the proposed method is both effective and efficient. Developed based on the proposed method, a software tool (as well as its source code) is released for free use. The proposed method and the developed tool shall contribute to an easy computation of the Boltzmann entropies of not only landscape gradients, but also remote sensing images and other quantitative raster data.

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“…For this purpose, some advanced computational means, such as parallel [98,99] and cloud computing [100,101], may be of use. Second, a comparison can be made between the improved Shannon entropies and Boltzmann entropy, which is "both configurational and compositional" [102] and has been recommended for use as an alternative to Shannon entropy in characterizing spatial disorder [31,103].…”

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confidence: 99%

Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images

Gao

Zhang

2018

Entropy

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Abstract:The quality of an image affects its utility and image quality assessment has been a hot research topic for many years. One widely used measure for image quality assessment is Shannon entropy, which has a well-established information-theoretic basis. The value of this entropy can be interpreted as the amount of information. However, Shannon entropy is badly adapted to information measurement in images, because it captures only the compositional information of an image and ignores the configurational aspect. To fix this problem, improved Shannon entropies have been actively proposed in the last few decades, but a thorough evaluation of their performance is still lacking. This study presents such an evaluation, involving twenty-three improved Shannon entropies based on various tools such as gray-level co-occurrence matrices and local binary patterns. For the evaluation, we proposed: (a) a strategy to generate testing (gray-level) images by simulating the mixing of ideal gases in thermodynamics; (b) three criteria consisting of validity, reliability, and ability to capture configurational disorder; and (c) three measures to assess the fulfillment of each criterion. The evaluation results show only the improved entropies based on local binary patterns are invalid for use in quantifying the configurational information of images, and the best variant of Shannon entropy in terms of reliability and ability is the one based on the average distance between same/different-value pixels. These conclusions are theoretically important in setting a direction for the future research on improving entropy and are practically useful in selecting an effective entropy for various image processing applications.

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Thermodynamics in landscape ecology: the importance of integrating measurement and modeling of landscape entropy

Cited by 41 publications

References 6 publications

A hierarchy-based solution to calculate the configurational entropy of landscape gradients

A hierarchy-based solution to calculate the configurational entropy of landscape gradients

An efficient analytical method for computing the Boltzmann entropy of a landscape gradient

Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images

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