地理建模：从特征尺度到比例尺
Geographical Modeling: from Characteristic Scale to Scaling
摘要：
通过地理学的定量革命，地理学研究成功地被量化。然而，地理学的成功理论化遇到了难以克服的困难。地理学理论化的最大障碍在于无处不在的地理现象的无标度分布。科学研究的第一范式是数学理论。定量测量和数学建模的关键是找到一个有效的特征尺度。不幸的是，对于许多地理系统来说，没有特征尺度。在这种情况下，应采用定标的方法进行空间测量和数学建模。标度的基本思想是利用变量标度与相应测量结果之间的双对数线性关系求幂指数。指数是一个遵循标度分布的特征参数，可以用来表征无标度现象。尺度分析在地理学中的重要性越来越受到科学家的重视。
英文摘要：
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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