3.1. Identification of the Optimal Horizon of Perception
The horizon of perception is a critical element of the WUP. It corresponds to the maximum distance at which a focus cell (residential cell in our adapted method) is influenced (perceived sprawl) by the presence of other built-up cells (both residential and commercial/industrial). Figure 3
illustrates this concept.
To identify which horizons of perception would be most suitable to characterize sprawl in cities across Europe, we conducted an analysis of the variation in WUP values averaged across 1 km-wide concentric rings (from 1 to 30 km) centered on city-centers. The use of concentric rings rather than city boundaries (which can vary greatly) allowed us to provide a common metric that could be uniformly applied across European urban areas.
To compensate for the fact that a higher horizon of perception leads to higher WUP values and allows averaged WUP values to be compared across horizons of perception within cities, we plotted for each of the 672 European cities’ variations in WUP and normalized them as a function of the maximum value recorded within the concentric rings for each specific horizon of perception. This analysis identified two main city profiles:
Cities where the normalized WUP value profile remained almost identical across horizons of perception (see Figure 4
Cities where the normalized WUP value profile varied strongly across horizons of perception (see Figure 5
The high variations in WUP across concentric rings were likely caused by the spatial heterogeneity in population and the distribution of population within areas surrounding the cities (for example a small city surrounded by multiple smaller, dense villages (Figure 6
)) as well as by the presence of certain landscape features (such as coastline, or mountains).
To identify the “optimal horizon of perception” most suitable to highlight variations in population distribution across rings for the EU28, we looked, for each city, at the sum of absolute differences of normalized average WUP values across the concentric rings for each horizon of perception. We computed for each horizon of perception the absolute difference in normalized WUP value between ring 1 and ring 2, and then added it to the absolute difference between ring 2 and ring 3, etc.
From this analysis, we summed the number of cities, which displayed the highest variability (sum of absolute differences) for each investigated horizon of perception. For most cities, a horizon of perception of 2 km provided the highest sum of absolute difference in average WUP when accumulated across concentric rings from 1 to 30 km distance from the city centers (see Figure 7
). We observed that this value of horizon of perception also provided the highest sum of absolute difference when considering concentric rings from 1 to 5 km, and from 1 to 15 km.
As a result, we concluded that a horizon of perception of 2 km was the best choice to highlight the most variability within European cities.
3.2. Towards a New Indicator of Sprawl
Using a 2 km horizon of perception, we could create a WUP profile for all European cities by averaging the WUP values across 1 km concentric rings. An example of such a profile is presented in Figure 8
. The average concentric WUP profile for European cities shows a relatively compact city center rapidly becoming more sprawled and peaking at 4 to 5 km distance before slowly decreasing and plateauing past 15 km. The relatively high WUP values of this plateau is likely attributable to the fact that most small and medium cities do not extend very far and that past 15 km, a large proportion of habitations are relatively spread out, isolated, and therefore characterized by high WUP values. The profile for the agglomeration of Munich, Germany indicates a compact city center with very low WUP values, gradually becoming less compact and reaching a plateau from a 10 km distance from the center. The profile for the city of Udine, Italy shows an opposite trend, with a sprawled center (high WUP values), becoming less sprawled past 6 km from the center (where more compact small towns and villages are present), and plateauing past 10 km.
We believe this type of city profiling can provide a valuable tool to compare sprawl in cities and their surrounding areas and understand how their profiles differ spatially from each other. However, such profiles are too complex to compare across a large number of cities and a more concise indicator is needed. To identify a simple, more concise indicator relative to sprawl, we investigated three possible candidates derived from the averaged concentric ring WUP profile: (1) the sum of concentric WUP; (2) the average of concentric WUP; and (3) the average WUP aggregated at the level of the Functional Urban Area (FUA) [8
]. These candidate indicators were selected because they are simple to calculate and explain to non-technical audiences.
Each of the three candidate indicators were calculated for all 672 cities in the EU28. The obtained values were then compared with the work published on urban sprawl by the European Environment Agency and European Commission’s Joint Research Centre [8
], who ranked 22 European cities based on their level of sprawl (see Table 1
). This report provided a ranking, split into a 4-category classification, of the most sprawled and compact cities in Europe, by combining six indicators taking into consideration elements such as the growth of built-up areas, the share of residential areas, population density, and growth rates. It identified Udine, Italy as the most sprawled city and Bilbao, Spain as the most compact. Although the European Environment Agency published an updated report on urban sprawl in Europe in 2016, this updated report did not provide any ranking of cities based on their level of urban sprawl, and could not be used as an updated reference in our analysis.
We performed a comparison between the city ranking proposed by [8
] and the ranking provided by each of the three proposed indicators. The ranking provided by the average of concentric WUP (Figure 9
) and by the sum of concentric WUP (Figure 10
) followed a similar pattern. However, the ACWUP presented an advantage over the sum of concentric WUP in that ACWUP values could be compared across different aggregation levels.
To account for the fact that most cities have a radius inferior to 30 km, we identified for each city an edge within which concentric WUP values could be averaged. The edges of these cities were identified by converting population raster to vectors, selecting population polygons within 5 km distance from the city center, and then selecting the intersection of polygons with city rings. For cases where the rings of nearby cities overlapped, checking and individual adjustment were applied. To compensate for potential uncertainty, the edge distance was rounded up to the closest even number of rings. For example, 5 km would become 6, 1 become 2, etc.
The incorporation of a city’s edge to identify the level of aggregation at which to average concentric WUP values (Figure 11
) improved the matching of the sprawling status of cities with the European Environment Agency and European Commission’s Joint Research Centre’s classification compared to averaging done from 1 to 5 km, 1 to 15 km, and 1 to 30 km (see Figure 9
). This ACWUP ranking, using city’s edge, also provided a better match to that obtained using the FUA WUP average (Figure 10
) and was therefore selected as the preferred sprawl indicator.
] does not provide quantitative values characterizing sprawl in cities, but rather a classification, we could not provide a rigorous comparison of the performance of our indicator with their estimation. However, by averaging concentric WUP values from 1 km to the city’s edge (see Table 1
and Figure 12
: Classification of European cities based on their ACWUP score. Cities are placed in order of their level of sprawl based on the European Environment Agency and European Commission’s Joint Research Centre’s classification.) split into 4 classes (compact below 3200, dense below 3600, sparse below 4100 and sprawled above 4100), we could fit our distribution to match 18 cities out of 22 (81% match) with the EEA sprawl ranking [8
]. The main discrepancies found were for Helsinki, Finland, classified as very highly sprawled while listed as high by the European Environment Agency and European Commission’s Joint Research Centre report, Pordenone, Italy, classified as high but listed as very high, Milan, Italy, classified as medium but listed as sprawled, and Trieste, Italy, classified as sprawled but listed as medium.
Assuming that the correspondence ratio between our classification and the work [28
] extends to the rest of cities in the EU28, the averaged concentric WUP could provide a cheap, first-pass indicator to classify cities as a function of their sprawl.
We propose the Averaged Concentric Weighted Urban Proliferation (ACWUP) index as a new metric to quantify sprawl for European urban areas. Its application to classify cities, using the above-defined classification, in the EU28 for the year 2010 is presented in Figure 13
. These results indicate that overall, Greece appears to have the most cities with a low ACWUP and therefore potentially the least sprawl while Belgium appears to have the most sparse and sprawled cities. Table 2
provides a list of 15 highly populated cities (population higher than 500,000) with the highest (most sprawled) and lowest (most compact) ACWUP values. It confirms the trend visible in Figure 13
, where the most sprawled cities seem to be found in the northern half of Europe, while the most compact cities tend to be in the southern half, with the exception of Freiburg, and Frankfurt, Germany, Amsterdam, and Rotterdam, the Netherlands, and Rennes, France.
Looking at European extremes, we identified the region centered on the town of Kavala, Greece as having the lowest ACWUP value (Figure 14
), and the area surrounding Brandenburg an der Havel, Germany as having the highest value (Figure 15
We propose the ACWUP be used as a first-pass investigation of sprawl and be complemented by an analysis of the average WUP profile to identify local spatial variability. For example, a closer observation of the average WUP variations between Kavala (Figure 14
) and Brandenburg an der Havel (Figure 15
) provides a clearer picture of their structure.
The WUP profile for the city of Kavala (blue line in Figure 16
) shows very low WUP values in the city center, then slowly increasing up to a distance of 4 km and following a wave pattern while remaining in the lower European WUP distribution. This wave pattern indicates the presence of sparse, dense aggregations of population (villages) around the city center.
The WUP profile for the city of Brandenburg an der Havel (red line in Figure 16
), shows very high WUP values in the city center indicating a relatively open and spatially spread center, decreasing steadily and stabilizing past 6 km distance from the center.