Quantifying the urbanization level is an essential yet challenging task in urban studies because of the high complexity of this phenomenon. The urbanization degree has been estimated using a variety of social, economic, and spatial measures. Among the spatial characteristics, the Shannon entropy of the landscape pattern has recently been intensively explored as one of the most effective urbanization indexes. Here, we introduce a new measure of the spatial entropy of land that characterizes its parcel mosaic, the structure resulting from the division of land into cadastral parcels. We calculate the entropies of the parcel areas’ distribution function in different portions of the urban systems. We have established that the Shannon and Renyi entropies $R_0$ and $R_{1/2}$ are most effective at differentiating the degree of a spatial organization of the land. Our studies are based on 30 urban systems located in the USA, Australia, and Poland, and three desert areas from Australia. In all the cities, the entropies behave the same as functions of the distance from the center. They attain the lowest values in the city core and reach substantially higher values in suburban areas. Thus, the parcel mosaic entropies provide a spatial characterization of land to measure its urbanization level effectively.

中文翻译：

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地块马赛克的熵作为城市化程度的度量

由于城市现象的高度复杂性，量化城市化水平是城市研究中必不可少但具有挑战性的任务。已经使用各种社会，经济和空间措施来估算城市化程度。在空间特征中，景观模式的香农熵最近被作为最有效的城市化指标之一进行了深入研究。在这里，我们介绍了一种表征土地包裹马赛克的土地空间熵的新方法，该结构是将土地划分为地籍地块的结果。我们计算了城市系统不同部分的地块面积分布函数的熵。我们已经确定了香农和仁义熵${\mathrm{[R}}_0$ 和 ${\mathrm{[R}}_{\mathrm{1个}/\mathrm{2个}}$在区分土地的空间组织程度方面最有效。我们的研究基于位于美国，澳大利亚和波兰的30个城市系统以及来自澳大利亚的三个沙漠地区。在所有城市中，熵的行为与距中心的距离的函数相同。它们在城市核心地区的价值最低，而在郊区地区则达到较高的价值。因此，地块镶嵌熵提供了土地的空间特征，以有效地测量其城市化水平。