Weighted urban proliferation
This method, first introduced by Jaeger et al. (2010),[1] calculates and presents the degree of urban sprawl as a numeric value.
[2] The WUP method, thus, measures urban sprawl by integrating these three dimensions into a single metric.
{\displaystyle {\begin{aligned}{\text{WUP}}&={\text{UP}}\cdot w_{1}({\text{Dis}})\cdot w_{2}({\text{UD}})\\\\{\text{where}}~&{\begin{cases}{\text{UP}}={\text{Urban Permeation}}\\w_{1}({\text{Dis}})={\text{Weighting}}_{1}({\text{Dispersion}})\\w_{2}({\text{UD}})={\text{Weighting}}_{2}({\text{Utilization Density}})\end{cases}}\end{aligned}}}
Since roads, railway lines, and parking lots are not buildings, they are disregarded in the WUP method of measuring urban sprawl.
The dispersion metric analyses the pattern of built-up area on the landscape from a geometric perspective.
The analysis is performed by taking distance measurements between random points within the built-up area.
This component is based on the premise that as more people and jobs are located in the built-up area, the more efficient the utilization of the land becomes.
The number of jobs is included in the calculation to emphasize that many downtown areas are dominated by office buildings that have very few residents, yet each building, and thus the land they are on, is densely utilized and should not be considered sprawl.
This weighting function allows sections of the built-up area to receive a value between 0 and 1 depending on their utilization density.
This lower weight reflects the understanding that dense subsections of the reporting unit, like inner cities, are not considered as urban sprawl.
Hayek et al. (2010) used settlement development scenarios for Switzerland, to find the causes of urban sprawl in order to reduce undesired future settlement developments.
The results show that overall urban permeation and dispersion of settlement areas is likely to increase, in varying degrees, in all scenarios by 2030.
[5] Jaeger & Schwick (2014) analysed historical changes as well as future scenarios for urban sprawl in Switzerland.
They concluded that the degree of urban sprawl had increased by 155% between 1935 and 2002 and that, within the framework of modelling future scenarios, urban sprawl is likely to further increase by more than 50% by 2050 without abrupt mitigation measures.
[6] Jaeger et al. (2015) analysed the degree of urban sprawl for 32 countries in Europe.
The results show that large parts of Europe are affected by urban sprawl, and that significant increases took place between 2006 and 2009, however, the values of the individual countries differ greatly.
[7] Nazarnia, Schwick & Jaeger (2016) compared patterns of accelerated urban sprawl, between 1951 and 2011, in the metropolitan areas of Montreal and Quebec City Canada, and Zurich in Switzerland.
[8] Torres, Jaeger & Alonso (2016) quantified spatial patterns of urban sprawl for mainland Spain at multiple scales.
They tested the stability, non-stationarity, and scale-dependency of the relationship between landscape fragmentation patterns and urban sprawl.
[9] Weilenmann, Seidl & Schulz (2017) analysed the major socio-economic determinants of change in urban patterns in Switzerland.
