to perform a second random reshuffling of all grid cells that belong to urban areas to generate a counterfactual population density distribution within those areas. Contiguous urban area grid cells that have an actual population that is above the 95<sup>th</sup> percentile of this second counterfactual distribution are “urban cores”. Any given urban area may have either zero or one or more cores. Urban areas that possess one or more cores are “cities”, while urban areas that lack a core are “towns”.

In applying the above methodology, the criteria used to designate grid cells as potentially habitable are important. Following de Bellefon et al. (2021), we define cells as potentially habitable if they do not: (i) intersect with a water body; (ii) are not at high altitude, defined here as below the 99<sup>th</sup> percentile of grid cells with at least one inhabitant in terms of altitude; and (iii) are not on a very steep slope, defined here as below the 99<sup>th</sup> percentile of grid cells with at least one inhabitant in terms of steepness. We also define as uninhabitable those grid cells which intersect with a desert. We do this for the 14 SSA countries in our sample which have more than 0.5 percent of their land area covered by desert.<sup>16</sup>

# **_2.2. Data_**

The main data that we use as input into the dartboard algorithm is constrained WorldPop gridded population data from the University of Southampton’s WorldPop group for the year 2015.<sup>17</sup> This data has an underlying resolution of approximately 100 m*100 m, but to avoid excessive compute times, we aggregate the data into 250 m*250 m grid cells. This aggregation also ensures compatibility with other spatial layers that we use to classify cells as potentially habitable. As with other “top down” gridded population data sets, the constrained WorldPop algorithm derives a grid by taking population data from national censuses for larger sub-national administrative units and distributing this across the cells that fall within each unit. In the case of constrained WorldPop, population is spread unevenly across cells within a given admin unit based on weights derived from a Machine Learning (ML) model (Stevens et al. 2015), only allocating population to cells that are built-up. In turn, the classification of cells as builtup is based on the extremely detailed map of all building footprints in SSA that was derived under the Gates Foundation sponsored Digitize Africa project.<sup>18</sup> The quality and resolution of this building footprint data is comparable to, if not better than, the building footprint data that de Bellefon et al. (2021) use for France in their original application of the dartboard algorithm.

The spatial data used to define a country’s potentially habitable areas come from two sources. That used to identify water bodies and deserts come from the European Space Agency’s GlobCover product (Bontemps et al. 2013).<sup>19</sup> Meanwhile, the data used to measure elevation and slope come from SRTM30, which is a near-global digital elevation model (DEM) comprising a combination of data from the Space Shuttle Radar Topography Mission flown in February 2000 and the U.S. Geological Survey's GTOPO30 data set.<sup>20</sup>

# **3. Descriptive Analysis of Overall Urbanization Patterns**

# **3.1.** **_Aggregate differences across countries_**

Table 1 presents summary statistics that describe key urbanization and other characteristics across SSA countries, while table 2 identifies the countries that have the three largest and smallest values for each variable presented in table 1. Before commenting on the urbanization characteristics, it is worth noting that SSA countries vary considerably in population, area, and average (overall) population density. Hence, population at the 90<sup>th</sup> percentile of the distribution across countries is 46.8 times that at the 10<sup>th</sup> percentile, while the corresponding ratios for land area and population density are 273.5 and 22.4 (table 1). The particularly large variation for area reflects the fact that SSA consists of both geographically

> 16 The 14 countries are: Botswana, Cabo Verde, Chad, Eritrea, Ethiopia, Kenya, Mali, Mauritania, Mozambique, Namibia, Niger, Somalia, South Africa, and Eswatini.

> 17 We use the “UN adjusted” version of this data in which the national population counts from summing across grid cells match national population counts as reported by the United Nations.

> 18 See https://ui.adsabs.harvard.edu/abs/2019AGUFMIN11D0688H/abstract.

> 19 http://due.esrin.esa.int/page_globcover.php.

> 20 See https://icesat.gsfc.nasa.gov/icesat/tools/SRTM30_Documentation.html for more information.

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