if �� ��<sup>�</sup> �� and �∑�∈� �����<sup>�</sup> ��, where �<sup>�</sup> �� denotes a population density threshold and �<sup>�</sup> �� a population threshold. In addition, the cell must be spatially contiguous with at least one other cell within the same cluster. In other words, a spatially contiguous group of grid cells will be classified as constituting an urban cluster if each of these cells satisfies a certain minimum population density threshold and the aggregate population of these cells also exceeds some specified threshold value. Given this, a country’s level of urbanization can then be defined as the share of the overall national population living in urban clusters. Dijkstra and Poelman (2014) set values of �<sup>�</sup> �� �300 people per km<sup>2</sup> and �<sup>�</sup> �� �5000. Within urban clusters, they also define a sub-set of “high density clusters”. These high density clusters are defined similarly to urban clusters, but instead use threshold values of 1,500 people per km<sup>2</sup> for population density and 50,000 people for overall population.<sup>23</sup>

# 2.2.3. Comparison between the two approaches

While it is not the intention of this paper to draw any conclusion as to which of the above two methods is to be preferred, some remarks on their similarities and differences are nevertheless in order. Hence, it will be noted that both crucially rely on a source of gridded population data for their implementation. Furthermore, while the AI may well be considered preferable to the cluster method to the extent that it more closely approximates an attempt to identify FUAs, it suffers the disadvantage of being more data-intensive. Thus, in addition to gridded population data, the AI also requires travel time data and a settlement point layer as inputs.

There is also a slight contradiction in how the AI approaches the definition of urban areas insofar as it implicitly relies on national definitions of urban in identifying the “sizeable” settlements around which it defines agglomerations. This is because the population data for the settlement points are invariably derived from national sources.

Finally, while, according to the cluster method, grid cells belonging to a given urban area must be spatially contiguous, the AI imposes no such restriction. As a corollary, development within a given agglomeration area in the AI approach can be discontinuous in the sense that urban cells can be interspersed with non-urban cells. Such a pattern of development may be consistent with the existence of topographical constraints (e.g. a river) that divide a city into different parts or with patterns of leapfrog development.<sup>24</sup>

# **3. Data**

As noted above, both the AI and cluster methods rely on gridded population data for their implementation. In addition, the AI also requires a settlement point layer and travel time data.

> 23 Deuskar and Stewart (2016) analyze the sensitivity of results from the cluster method using a variety of alternative threshold values.  Their analysis is, however, restricted to the use of _WorldPop_ and GHS-Pop gridded population data, and does not consider _Landscan 2012_ data.

> 24 It is easy to imagine a methodology which combines different aspects of the AI and cluster methods.  This methodology could, for example, follow the cluster approach of identifying high-density clusters and then define agglomerations around these clusters using criteria of travel time and population density _à la_ the AI. Adopting this combined methodology would overcome the AI’s weakness of needing an _a priori_ defined layer of settlement points and associated populations.

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