论文标题

地理建模:从特征量表到缩放

Geographical Modeling: from Characteristic Scale to Scaling

论文作者

Chen, Yanguang

论文摘要

通过地理的定量革命成功量化了地理研究。但是,地理的后续理论遇到了无法克服的困难。地理理论的最大障碍在于无处不在的地理现象的无规模分布。科学研究的第一个范式是数学理论。定量测量和数学建模的关键是找到有效的特征量表。不幸的是,对于许多地理系统,没有特征性的规模。在这种情况下,应采用缩放方法进行空间测量并进行数学建模。缩放的基本思想是使用可变尺度和相应测量结果之间的双对数线性关系找到功率指数。指数是遵循比例分布的特征参数,可用于表征无尺度现象。对于科学家来说,扩展分析在地理上的重要性变得越来越明显。

Geographical research was successfully quantified through the quantitative revolution of geography. However, the succeeding theorization of geography encountered insurmountable difficulties. The largest obstacle of geography's theorization lies in scale-free distributions of geographical phenomena which exist everywhere. The first paradigm of scientific research is mathematical theory. The key of a quantitative measurement and mathematical modeling is to find a valid characteristic scale. Unfortunately, for many geographical systems, there is no characteristic scale. In this case, the method of scaling should be employed to make a spatial measurement and carry out mathematical modeling. The basic idea of scaling is to find a power exponent using the double logarithmic linear relation between a variable scale and the corresponding measurement results. The exponent is a characteristic parameter which follows a scaleful distribution and can be used to characterize the scale-free phenomena. The importance of the scaling analysis in geography is becoming more and more evident for scientists.

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