On urban boundaries: three methods, three solutions for Brussels

International audienceDelineating urban boundaries is a challenging and important topic for researchers and planners: empirical analyses highly depend on the delineation of the study area and the limits of the cities are of particular interest as they change over time and space. Urban governance can’t be conducted in an efficient way if urban boundaries are not clearly defined.Many scientific methods exist to delineate urban borders. They are mainly based on functional and/or morphological criteria. We here limit ourselves to morphological analyses using the footprint of the builtup as sole input. The first two methods deal with “complex theory” and use respectively the Morpholim methodology - a geographical application of the fractal theory (Tannier et al., 2011) and, the Natural Cities methodology - a topological application of the complex network theory (Jiang and Miao, 2015). The third method is a more classical one using the Euclidean approach: a Local Density Index.Each method leads to specific results (i.e. a different delineation of the urban space). The goal of thisanalysis is to measure and understand each methodology and where/why are the differences. What do they do exactly and what do they show? Specificities and biases are identified and illustrated using theoretical cities and an empirical analysis is provided on the Brussels Metropolitan Area in Belgium.Morpholim measures a distance threshold showing a break in the organisation of the built-up at different scales and without any a priori delineation of the tructure. The presence of a diffuse periurbanisation and/or the presence of a built corridor between two distinct urban structures deeply influence Morpholim results. The absence of contiguity in the Natural Cities methodology, and the use of the centroid of ground surface area of the buildings instead of the cadastral details, explain why the Natural Cities methodology ends up with urban spaces that correspond to the clustering of minimum three centroids. The Density methodology is subject to the well-known “Modifiable Area Unit Problem” and is unable to measure the geographic organisation of the footprints of the buildings.The application of the methods on the Brussels Metropolitan Area allows to confirm that morphologically Brussel sprawls out of its administrative boundary and that each method leads to a different delineation.We already know that the delineation of functional cities deeply depends on the data/method used and that morphological delineations are different from any functional ones (Thomas et al., 2012). This paper further proofs and reminds that method matter for morphological delineations as well and that one is not better than the other; they are simply measuring other things. Indeed, cities can be seen as (1) “hot spots” of buildings (Natural Cities), (2) fractal patterns that differ from their surrounding (Morpholim) or (3) areas having a high-density occupation of the space (Density Index)