Travel time to major cities: A global map of Accessibility

What is accessibility?

Africa We define accessibility as the travel time to a location of interest using land (road/off road) or water (navigable river, lake and ocean) based travel. This accessibility is computed using a cost-distance algorithm which computes the "cost" of travelling between two locations on a regular raster grid. Generally this cost is measured in units of time. The cells in this raster grid contain values which represent the cost required to travel across them, hence this raster grid is often termed a friction-surface.

The friction-surface contains information on the transport network and environmental and political factors that affect travel times between locations. Transport networks can include road and rail networks, navigable rivers and shipping lanes. Environmental factors generally contribute to travel speeds off the transport network, such as land cover and slope. Political factors - such as national boundaries and border crossings - can act as barriers or travel delays.

The locations of interest are termed targets and range from cities, markets, health facilities, educational establishments, protected areas, or any type of location where for which you want to estimate the potential accessibility. The range of applications for this type of accessibility map is covered in detail in the reference list.

What is a cost-distance model?

The accessibility maps described here used the cost-distance functions which are available in ESRITM products such as ArcInfo Workstation GRID, ArcView 3 with Spatial Analyst and ArcGIS Desktop with Spatial Analyst. The following description assumes familiarity with one or more of these products. See the software link for more information including options for accessibility modelling in other GIS packages.

A cost-distance model requires two inputs, (i) a target raster map containing the locations for which you want to compute travel time to, and (ii) a friction-surface raster where each pixel contains the estimated time required to cross that pixel. The next section describes how to make such a friction surface.

How to make a friction surface

  1. Choose a suitable projection for the data. Any equal area projection will do. All the input data should be projected to the same equal area projection.
  2. Choose a spatial resolution for the friction surface and resulting accessibility map. i.e. 100m, 1km, 5km.
  3. Identify all the relevant spatial datasets that can be used to define the friction surface. This can include roads, railways, landcover, slope etc. The layers will depend on the assumptions about modes of travel as well as the locations to be accessed. Example assumptions include: road travel is by motorised vehicle and road speed depends on road type, while off road travel is foot based and walking speed is determined by the land cover and slope. The layers used in the global accessibility maps are listed on the data sources page.
  4. Convert these data to raster using the chosen resolution and projection. Also convert the targets or locations of interest to the same resolution and projection. Each target must have a unique value in the raster.
  5. Assign a travel speed to each class in each raster. If the road data contains different classes of road then assign each one a speed. If the land cover data contains different land cover types then assign each one a speed. If there is a slope or elevation layer, then convert them into speed reducing factors. The travel speeds and speed reducing factors used for the global accessibility map are listed on the data sources page.
  6. Based on points 2 and 5, create a friction raster for each input raster layer by computing the time required to cross 1 pixel. Use the same time units for each layer. For example, if the resolution is 500m and the road layer has two road types; motorway at 120km per hr and main roads at 90km per hour, then the time required to cross 500m is 15 seconds for a motorway pixel, and 20 seconds for a main roads pixel. So all motorway pixels in the road friction raster will have a value of 15 and main roads will have a value of 20. This is repeated for each layer that must be travelled across (road, river, rail, landcover, international border etc.). For international borders, the travel time across border pixels can be extremely high between certain countries and almost zero for others (i.e. countries that are in the Schengen Agreement). Where appropriate these layers should be multiplied by any slope or elevation factors to increase the travel time over steep slopes or very high altitudes.
  7. Merge these friction components into a single friction surface. ArcInfo Workstation contains a function called MERGE which will combine a set of rasters into one single raster where the order of the input defines the order of precedence, i.e. borders overlay roads which in turn overlay rivers which in turn overlay land cover.
  8. Run the cost-distance function. Use the friction surface and raster of target locations to compute the travel time from each pixel in the study area to the nearest target location.
  9. Convert to sensible time units. The above example used seconds in point 6. It may make sense to convert to minutes or even hours.
  10. Reproject back to the original or desired projection.