空间玻尔兹曼熵的研究进展与应用

doi:10.11821/dlxb202107001

地理学报 ›› 2021, Vol. 76 ›› Issue (7): 1579-1590.doi: 10.11821/dlxb202107001

• 研究综述 • 下一篇

空间玻尔兹曼熵的研究进展与应用

高培超¹^,²^,³(), 程昌秀³^,⁴(), 叶思菁³, 沈石³, 张红⁵^,⁶

1.北京师范大学地表过程与资源生态国家重点实验室,北京 100875
2.香港理工大学土地测量与地理资讯学系,香港 999077
3.北京师范大学地理科学学部地理数据与应用分析中心,北京 100875
4.国家青藏高原科学数据中心, 北京 100101
5.华东师范大学城市与区域科学学院,上海 210046
6.西南交通大学地球科学与环境工程学院,成都 611756

收稿日期:2020-03-31 修回日期:2021-03-25 出版日期:2021-07-25 发布日期:2021-09-25
通讯作者: 程昌秀(1973-), 女, 新疆人, 教授, 主要从事地理时空数据分析等研究。E-mail: chengcx@bnu.edu.cn
作者简介:高培超(1991-), 男, 河南人, 讲师, 中国地理学会会员(S110014357M), 主要从事信息地理学研究。E-mail: gaopc@bnu.edu.cn
基金资助:
第二次青藏高原综合考察研究(2019QZKK0608);香港研究资助局基金(152219/18E);国家自然科学基金项目(41901316);成都市重点研发支撑计划(2019-YF05-02119-SN);地表过程与资源生态国家重点实验室开放基金(2020-KF-03);中央高校基本科研业务费专项资金(2019NTST02)

The review and applications of spatial Boltzmann entropy

GAO Peichao¹^,²^,³(), CHENG Changxiu³^,⁴(), YE Sijing³, SHEN Shi³, ZHANG Hong⁵^,⁶

1. State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China
2. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong 999077, China
3. Center for Geodata and Analysis, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
4. National Tibetan Plateau Data Center, Beijing 100101, China
5. School of Urban & Regional Science, East China Normal University, Shanghai 210046, China
6. Faculty of Geosciences & Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China

Received:2020-03-31 Revised:2021-03-25 Published:2021-07-25 Online:2021-09-25
Supported by:
Second Tibetan Plateau Scientific Expedition and Research Program(2019QZKK0608);Research Grants Council of Hong Kong(152219/18E);National Natural Science Foundation of China(41901316);Key Research and Development Program of Chengdu(2019-YF05-02119-SN);State Key Laboratory of Earth Surface Processes and Resource Ecology(2020-KF-03);Fundamental Research Funds for the Central Universities(2019NTST02)

摘要/Abstract

摘要：

区域性、综合性、复杂性是新时代地理学的三大特征,其中复杂性研究是地理学飞跃的新路径。熵作为系统复杂性的核心指标,其研究、推广和应用对新时代的地理学有着重要意义。近年来地理学中熵的研究热点为玻尔兹曼熵（玻熵）。玻熵的概念最早提出于1872年,是著名的热力学第二定律的核心,但玻熵在地学的应用长期停滞在探讨层面。其瓶颈在于缺乏针对空间数据计算玻熵的模型和方法,但该瓶颈在近5年得以突破。本文从玻熵的热力学概念与地理学推广难题、空间数据的玻熵计算模型、计算方法、实际应用4个方面进行及时且系统地综述。主要结论有：① 目前的研究热点集中在空间栅格数据的玻熵,已研发出针对定性和定量型栅格数据的计算模型;② 算法百家齐放,已呈现出基于边缘总长度、基于Wasserstein距离、基于多尺度层次的三大类算法;③ 已形成景观生态学和遥感图像处理两类应用;④ 未来研究需重视针对更多类型的空间数据的算法、使用玻熵替代香农熵验证先前研究中的结论、拓展玻熵应用等。

关键词: 空间数据, 玻尔兹曼熵, 香农熵, 空间信息论, 景观生态学, 区域可持续性

Abstract:

The field of geography has three unique characteristics, namely, regionality, integration, and complexity. Among them, complexity has become increasingly crucial to geography in the current era. Entropy is a key concept and an indicator of the complexity of a system; thus, the research and application of entropy play a fundamental role in the development of geography. During recent years, Boltzmann entropy (i.e., thermodynamic entropy) has emerged as a research hotspot in the entropy for geography. Proposed as early as the year 1872, it is the core of the well-known Second Law of Thermodynamics. However, its application in geography had remained at a conceptual level for lack of computational methods with spatial data. Fortunately, much progress has been made globally towards computing and applying spatial Boltzmann entropy (i.e., the Boltzmann entropy of spatial data). This paper aims to perform a comprehensive review of such progress, in terms of the thermodynamic origination of Boltzmann entropy, the difficulties in applying it to geography, computational models and algorithms of spatial Boltzmann entropy, and all the applications up to now. Four major conclusions can be drawn as follows: (1) The current focus of research is placed on the Boltzmann entropy of spatial raster data. Models have been developed for computing Boltzmann entropy with both qualitative and quantitative raster data. (2) Many algorithms have been developed and can be classified into three categories, namely total edge-based, Wasserstein distance-based, and multiscale hierarchy-based. (3) It has witnessed two groups of applications of spatial Boltzmann entropy to geography, namely landscape ecology and remote sensing image processing. (4) Future research is recommended to develop algorithms for more types of spatial data, validating previous conclusions drawn using Shannon entropy, and extending the applications of spatial Boltzmann entropy.

Key words: spatial data, Boltzmann entropy, Shannon entropy, spatial information theory, landscape ecology, reginal sustainability

高培超, 程昌秀, 叶思菁, 沈石, 张红. 空间玻尔兹曼熵的研究进展与应用[J]. 地理学报, 2021, 76(7): 1579-1590.

GAO Peichao, CHENG Changxiu, YE Sijing, SHEN Shi, ZHANG Hong. The review and applications of spatial Boltzmann entropy[J]. Acta Geographica Sinica, 2021, 76(7): 1579-1590.

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空间玻尔兹曼熵的研究进展与应用

The review and applications of spatial Boltzmann entropy

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