Geographical centre

In geography, the centroid of the two-dimensional shape of a region of the Earth's surface (projected radially to sea level or onto a geoid surface) is known as its geographic centre or geographical centre or (less commonly) gravitational centre. Informally, determining the centroid is often described as finding the point upon which the shape (cut from a uniform plane) would balance.[1] This method is also sometimes described as the "gravitational method".[2]

One example of a refined approach using an azimuthal equidistant projection, also potentially incorporating an iterative process, was described by Peter A. Rogerson in 2015.[3][4] The abstract says "the new method minimizes the sum of squared great circle distances from all points in the region to the center". However, as that property is also true of a centroid (of area), this aspect is effectively just different terminology for determining the centroid.

In 2019, New Zealand's GNS Science also used an iterative approach (and a variety of different projections) when determining a centre position for New Zealand's Extended Continental Shelf.[5]

However, other methods have also been proposed or used to determine the centres of various countries and regions. These include:

• centroid of volume (incorporating elevations into calculations), instead of the more usual centroid of area as described above.[6]
• centre point of a bounding box completely enclosing the area. While relatively easy to determine, a centre point calculated using this method will generally also vary (relative to the shape of the landmass or region) depending on the orientation of the bounding box to the area under consideration. In this sense it is not a robust method.
• finding the longitude that divides the region into two equal area parts to the east and west, and then similarly the latitude that divides the region into two equal area parts to the north and south.[7] Like the bounding box approach described above this method would not generally locate precisely the same point if the same shaped region was oriented differently.

As noted in a United States Geological Survey document, "There is no generally accepted definition of geographic center, and no completely satisfactory method for determining it."[1]

In general, there is room for debate around various details such as whether or not to include islands and similarly, large bodies of water, how best to handle the curvature of the Earth (a more significant factor with larger regions) and closely related to that issue, which map projection to use.