Entropy of the Land Parcel Mosaic as a Measure of the Degree of Urbanization

Abstract

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 R0 and R1/2 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.

Spatial Diversity Changes in Land Use and Land Cover Mix in Central European Capitals and Their Commuting Zones from 2006 to 2018

“…Similarly, the spatial entropy and Simpson diversity models for LULC classes on the first and third Urban Atlas nomenclature levels proposed here can be a starting point for investigating urbanisation in FUAs and urban sprawl outside UCs. Research suggests that entropy should increase up to 15-20 km from the city centre depending on its history and development [63]. Still, capitals exhibit an increase of up to about 20 km for LULC analysis on the first level of Urban Atlas nomenclature, as shown here.…”

“…Regarding the LULCC on the first level of UA nomenclature, the diversity in UCs increases with the distance to the centre, while in CoZs, it declines as the distance to the UC grows. Bitner and Fialkowski [63] analysed a mosaic of cadastral plots in 30 cities in Poland, the USA and Australia, and they defined a model for growth in the Shannon entropy and Rényi entropy with a growing distance to the city centre. They proposed that the entropy of cadastral parcel mosaic can be a measure of urbanisation.…”

“…Therefore, the LULC change trends identified here in the FUAs would stem to some extent from the implementation of the European spatial policy, particularly a policy based on sustainable development. Future studies could focus on changes in the boundaries of cadastral plots, as land division and fragmentation can be driven by urbanisation [63]. Another future focus could be to compare past cadastral boundaries with current ones using archived base maps [13] to extend the study period.…”

Spatial Multi-Criteria Decision Modeling for Pinus palustris Mill. (Longleaf Pine) Restoration in the South Carolina Sandhills Wiregrass Gap

“…Fialkowski and Bitner (2008) identified 3 parcel types based on size and shape: (1) urbanized core, (2) suburban area, and (3) rural area. Parcel sizes often decrease as urbanization increases, meaning that high- and low-value clustering is likely in a study area that captures both urban and rural environments (Bitner and Fialkowski 2021, Fialkowski and Bitner 2008, Weng 2007). Weng (2007) noted that the degree of habitat fragmentation was positively correlated to the degree of urbanization and that there was an overall decrease in high-intensity land use along an urban–rural gradient.…”