delineate the extents of metro areas. Cores are pre-defined from a global settlement point layer<sup>9</sup> based on a population threshold. Rather than rely on sub-national administrative units, the AI instead relies on a globally gridded population data set. In such a data set, the underlying units that undergo aggregation are grid cells that are of a uniform geographic size – in practice, 30-arc seconds, which is approximately 1 km<sup>2</sup> at the equator.

Constructing the AI first requires the specification of three thresholds – a minimum population threshold to identify settlement points that qualify as metro cores, a travel time threshold, and a population density threshold. While Uchida and Nelson (2009) experimented with a range of thresholds, the AI has become synonymous with thresholds of 50,000 for the population of the core, 60 minutes for travel time, and 150 people per km<sup>2</sup> for population density. Hence, the AI defines a group of population grid cells as constituting a metro area if each of those grid cells have a population density of at least 150 people per km<sup>2</sup> and fall within a 60-minute travel time radius of a settlement point that has an associated population of at least 50,000. An important feature of the AI is that it, in contrast to the other two “satellite data based” approaches, _does not include a contiguity requirement_ . This means that, in principle, a metro area may not consist of a single contiguous block of grid cells. Another important feature of the AI is that if there are two or more cores that fall within 60 minutes travel time of each other then they, effectively, merge into a single extended metro area.

# **_Approach #3: The cluster algorithm_**

Rather than attempting to delineate a metro area based on its functional area, using either commuting flow data or estimated travel times, Dijkstra and Poelman’s (2014) cluster algorithm simply identifies a metro area as a dense population cluster. The algorithm was originally developed with the European Union in mind, but has since been applied globally and, given the simplicity of its data requirements, is emerging as the preferred algorithm of not only the European Commission, but also of a coalition of international agencies that further includes the Organisation for Economic Co-operation and Development (OECD) and the World Bank. As with the AI, the cluster algorithm relies on a gridded population data set of resolution 30 arc-seconds – i.e. approximately 1 km<sup>2</sup> at the equator – as input. Given these data, it identifies a _spatially contiguous_ set of population grid cells as a metro if each of those grid cells satisfies a population density threshold, T<sup>�</sup> �, and, collectively, the population of the grid cells exceeds a population threshold, T<sup>�</sup> �.

In practice, the cluster algorithm has become associated with two different sets of thresholds. The first set of thresholds is T<sup>�</sup> � = 300 people per km<sup>2</sup> and T<sup>�</sup> � = 5,000 with the resultant areas that are delineated being referred to as _“Urban Clusters”_ (UC). Meanwhile, the second set of thresholds is T<sup>�</sup> � = 1,500 people per km<sup>2</sup> and T<sup>�</sup> � = 50,000 with the areas that result being labelled _“High Density Clusters”_ (HDC) (Dijkstra and Poelman, 2014).

# **_Approach #4: Thresholding of nighttime lights (NTL) data_**

The use of nighttime lights (NTL) data to identify metro areas, and, more generally, urban settlements, originated in the remote sensing literature with early applications including Imhoff _et_

> 9 Namely, CIESIN’s Global Rural – Urban Mapping Project (GRUMP) Settlement Point layer (http://sedac.ciesin.columbia.edu/data/set/grump-v1-settlement-points-rev01).

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