IS415 AY2022-23T2 - Lesson 10: Modelling Geographic of Accessibility

Content

Basic Concepts of Geography of Accessibility
Accessibility Models
- Stewart Potential model
- Reilly model
- Huff model

What is Geography of Accessibility?

Accessibility is the measure of the capacity of a location to be reached from, or to be reached by, different locations. Therefore, the capacity and the arrangement of transport infrastructure are key elements in the determination of accessibility.

Why Model Geography of Accessibility?

Questions that can be answered by accessibility models:
- Which part of the geographical areas are deprived from getting access to a social service, facility or job opportunity?
- Which part of the geographical areas will be affected by a public policy or business decision such as merging JCs, secondary and primary schools.

Measuring Distances

Different spatial and distance conceptualizations that are commonly employed when measuring and modelling accessibility.

Distance Consideration

Cartesian distance versus Network distance.

Reference: Philippe Apparicio et. al. (2017) “The approaches to measuring the potential spatial access to urban health services revisited: distance types and aggregation‑error issues. International Journal of Health Geographics, pp. 16:32.

The distance friction

Modeling spatial interactions implies quantifying the distance friction or impedance.
The role of the distance can be interpreted as a disincentive to access desired destinations or opportunities (e.g. jobs, shops).

The perception of how far a destination is may not be a linear function of distance. People are more likely to shop at a place close to home than one far away. Distance is viewed as a nonlinear deterrent to movement. This phenomenon can be modeled by using a distance-decay function. The use of a power distance-decay function is borrowed from Newton’s law of gravitation, from which the term gravity model is derived. A distance-decay parameter, symbolized by the Greek letter beta, can be used to exaggerate the distance to destinations. Some activities, such as grocery shopping, have a large exponent, indicating that people will travel only a short distance for such things. Other activities, such as furniture shopping, have a small exponent, because people are willing to travel farther to shop for furniture.

Distance Decay function.

Inverse distance decay, 𝜶∕𝒅_𝜷

Exponential distance decay, 𝜶𝒆^(−𝜷𝒅)

The Geographical Unit

This issue of irregularly shaped polygons created arbitrarily (such as county boundaries or block groups that have been created from a political process).

The Geographical Unit

Using regular shaped geometry such as square, hexagon or triangle to define geographical unit.

The Geographical Unit

Hexagons reduce sampling bias due to edge effects of the grid shape, this is related to the low perimeter-to-area ratio of the shape of the hexagon.
A circle has the lowest ratio but cannot tessellate to form a continuous grid. Hexagons are the most circular-shaped polygon that can tessellate to form an evenly spaced grid.]

The Geographical Unit

An example of 250m radius hexagons covering Singapore main island.

Distance to Nearest Location

The formula:

Limitation of the method:

Does not consider the size/attractiveness of the closest location, thereby implicitly treating all locations as being equally attractive.
Does not consider the cumulative effect of multiple accessible locations (e.g. is a zone that is within 1.1 km of two MRT stations inferior to one that is within 1.0 km of a single station?

The Potential Model

The classic model

The Modified Potential Formula

Real world application of potential model

Accessibility to urban functions study.

Real world application of potential model

Accessibility to shopping centres.

Accessibility to health services

Real world application of potential model

Overall accessibility

Two-step floating catchment area method (2SFCA)

A special case of a potential model for measuring spatial accessibility to primary social services and public facilities.
It was inspired by the spatial decomposition idea first proposed by Radke and Mu (2000).

Reference: Luo, W.; Wang, F. (2003b). “Measures of spatial accessibility to health care in a GIS environment: synthesis and a case study in the Chicago region”. Environment and Planning B: Planning and Design. 30 (6): 865–884.

An earlier version of 2SFCA

Two-step floating catchment area method (2SFCA)

Step 1: For each physician location j, search all population locations (k) that are within a threshold travel time (d0) from location j (that is, catchment area j ), and compute the physician-to-population ratio, Rj, within the catchment area:

An earlier version of 2SFCA

Two-step floating catchment area method (2SFCA)

Step 2: For each population location i, search all physician locations (j) that are within the threshold travel time (d0) from location i (that is, catchment area i), and sum up the physician-to-population ratios, Rj, at these locations:

An earlier version of 2SFCA.

Enhanced Two-step Floating Catchment Area (E2SFCA)

Step 1: The catchment of physician location j is defined as the area within 30-min driving zone(Lee, 1991). Within each catchment, compute three travel time zones with minute breaks of 0–10,10–20 and 20–30min (zones1–3,respectively). Search all population locations(k) that are within a threshold travel time zone (Dr) from location j (this is catchment area j), and compute the weighted physician-to-population ratio, Rj, within the catchment area as follows:

Step 2: For each population location i, search all physician locations (j) that are within the 30min travel time zone from location i (that is,catchment area i), and sum up the physician-to-population ratios (calculated in step1), Rj, at these locations as follows:

Comparing 2SFCA and E2SFCA

Reference: Luo, Wei., Qi, Yi. (2009) “An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians”, Health & Place, 2009, Vol.15 (4), p.1100-1107.

Spatial Accessibility Measure (SAM)

The formula:

where

Aai is the accessibility in ED i,
nj is the capacity of the target facility j.
pi is the demand of this ED, and
dij is the network distance between the EDi and each facility j.

Reference: Stamatis Kalogirou & Ronan Foley (2006) “Health, place and Hanly: Modelling accessibility to hospitals in Ireland”, Irish Geography, Volume 39(1), 2006, 52-68.