Settlement percolation: global maps of Critical Distances

Abstract

A substantial share of the Earth's land surface is managed by humans, with cities representing the most extreme form of anthropogenic land use. There are zillion ways in which settlements can be arranged across a given area, and their specific spatial configuration has important consequences for both urban systems and the natural environment. Here, we introduce a novel approach to characterizing settlement configuration by systematically quantifying it in terms of a transition resembling percolation -- that is, by identifying the critical distance at which isolated settlements merge into a giant, overarching settlement cluster. We estimate this critical distance across multiple spatial scales and units, including national and subnational levels, non-overlapping tiles, and moving windows, covering the entire globe. The critical distance provides an independent measure of settlement connectivity and thus adds value to spatial analyses of settlement structure and its social, economic, and ecological impacts. Accordingly, our Global Settlement Percolation (GSP) dataset is relevant to a wide range of research communities, including those studying urban morphology, land-use patterns, and landscape ecology.

Figures (11)

• Figure 1: Illustration of how clusters in tiles can be connected across tiles. For performance reasons, spatial clustering via a distance threshold had to be done in separate tiles. Thus, each of the three boxes on the left contains independent clusters. However, clusters can extend beyond the limits of these tiles, so that in a next step they need to be consolidated. Then, on the right, the purple cluster extends across the entire area (which previously consisted of three tiles).
• Figure 2: Example of the percolation-like transition of settlements. The maps show the settlement areas in central Peru (Huancavelica, Huanuco, Junin, and Pasco regions) where the largest four clusters are colored. The four panels exhibit the clusters for the distance thresholds (a) $l=$1,500 m; (b) $l=$2,500 m; (c) $l=$3,000 m; (d) $l=$3,500 m. With increasing thresholds the clusters grow, panels (a)-(c), but beyond $l=$3,500 m the largest cluster dominates, panel (d), while remaining clusters are relatively small. The respective cluster sizes are plotted in Figure \ref{['fig:PERr106']}.
• Figure 3: Example of Critical Distance identification. For central Peru (Huancavelica, Huanuco, Junin, and Pasco regions) the sizes of the largest four clusters, as shown in Figure \ref{['fig:crit_dist_example']}, are plotted against the distance threshold. It can be seen that with increasing distance threshold the clusters grow. This growth happens because (i) more points are assigned to the clusters and (ii) the merging of clusters. At the Critical Distance (blue vertical line) there is a phase transition resembling percolation where the largest cluster dominates and the smaller clusters become negligible. The underlying cluster size was determined based on the calculated geodetic area rather than the number of pixels.
• Figure 4: Illustration of the moving window analysis. The Critical Distance of the settlement areas (red) is determined within a circle of a predefined radius (top). The resulting value is assigned to the raster cell in the center of the circle. The circle is then shifted to the next cell and the procedure is repeated. If the respective circles are non-empty, every cell obtains an estimate (bottom). We use a sampling resolution of 1 km. In contrast to the grid cell analysis, the circles overlap (see Table \ref{['tab:files']}).
• Figure 5: Global map of Critical Distances at 2.5$^\circ$ grid. Every grid cell has been colored according to the Critical Distance that we estimated within it. Grey: no data.