Rural Access Index

Define rural areas

Rural and urban boundaries are distinguished using population density or land cover datasets. Common sources include the Global Human Settlement Layer–Degree of Urbanisation (GHS-SMOD) and the Global Rural–Urban Mapping Project (GRUMP).

Map road networks

Road data are obtained from multiple sources in order to maximize completeness and consistency:

• Global Roads Inventory Project (GRIP), which provides information on road condition and classification.
• OpenStreetMap (OSM) for surface type and road classification.
• Satellite imagery: To capture missing roads.

Classify roads

Roads are categorized into:

• All-season roads: paved roads or higher-class roads that are accessible throughout the year, with only minor interruptions, identified via GRIP or OSM (and of sufficient hierarchy).
• Exposed roads: unpaved or lower-quality roads, or those detected only through satellite imagery, which may not remain passable during adverse weather.

Buffer application

A buffer of 2 kilometres is applied around both all-season and exposed roads. The buffered areas are then rasterized to enable spatial overlay with population data.

Calculate passability for exposed roads

Estimate the probability that an exposed road remains passable year-round by applying a passability index (ranging from 0 to 1), based on:

• Slope and terrain characteristics
• Rainfall intensity and patterns
• Proxies for maintenance, such as GDP per capita

Raster algebra combines these factors to calculate a continuous passability score

Population overlay

Population data are combined with the road buffers:

• Populations within 2 km of an all-season road are assigned full access.
• Populations within 2 km of an exposed road are weighted by the passability index.

Where buffers overlap, the maximum access value is applied.

Derive the index

The Rural Access Index is calculated as the ratio of the rural population with access to all-season roads to the total rural population:

• ${\displaystyle R}$: set of rural population locations (cells or villages).
• ${\displaystyle p_{i}}$: population of location ${\displaystyle i}$.
• ${\displaystyle a_{i}}$: access factor assigned to population ${\displaystyle p_{i}}$.
• ${\displaystyle d_{i}}$: distance from location ${\displaystyle i}$ to the nearest road.
• ${\displaystyle \pi _{i}}$: passability probability for exposed roads, between 0 and 1.
• ${\displaystyle s_{i}}$: slope or terrain factor affecting road usability.
• ${\displaystyle r_{i}}$: rainfall intensity affecting seasonal impassability.
• ${\displaystyle m_{i}}$: maintenance proxy (often GDP per capita or local investment).
• ${\displaystyle f(s_{i},r_{i},m_{i})}$: function estimating the year-round passability of an exposed road, combining terrain, climate, and maintenance factors

${\displaystyle \mathrm {RAI} \;=\;{\frac {\sum _{i\in R}p_{i}\,a_{i}}{\sum _{i\in R}p_{i}}}}$

${\displaystyle a_{i}\;=\;{\begin{cases}1,&{\text{if }}d_{i}\leq 2\;{\text{km and road type = all-season}},\\[6pt]\pi _{i},&{\text{if }}d_{i}\leq 2\;{\text{km and road type = exposed}},\\[6pt]0,&{\text{if }}d_{i}>2\;{\text{km}}.\end{cases}}}$

${\displaystyle \pi _{i}\in [0,1],\quad \pi _{i}=f(s_{i},r_{i},m_{i})}$