Methods

This page summarises the analytical workflow and explains why each method was chosen. All analysis is implemented in Python using GeoPandas, Shapely, scikit-learn, and Matplotlib.

Data Overview

Three main categories of spatial data are used:

• City boundaries

  • New York City borough boundaries from NYC Open Data.
    
  • Singapore 2019 Master Plan planning area boundary from data.gov.sg.
    
  • Administrative areas for Amsterdam from the Open GEO-Data Amsterdam portal.
    
  • Shanghai municipal boundary from Simplemaps, used as an approximate representation where official open data are not available.

• Bus stop locations

  • NYC bus shelters from NYC Open Data, treated as a conservative proxy for all bus stops.
    
  • Bus stops from the Land Transport Authority (LTA) via data.gov.sg for Singapore.
    
  • Bus stops tagged as highway=bus_stop in OpenStreetMap, retrieved via the Overpass API for Amsterdam and Shanghai.

In addition, a third dataset is used for the network-based analysis:

• Pedestrian street networks

  • For all four cities, pedestrian-accessible street networks are derived from OpenStreetMap using the OSMnx Python package (network_type="walk").
    
  • The resulting graphs provide the geometry and length of walkable street segments and are used to approximate walking distance along the street network rather than in straight lines.

The mix of official and volunteered geographic information reflects a typical situation in comparative urban research, where fully harmonised datasets seldom exist.

Pre-processing and Coordinate Systems

1. Standardising CRS

All datasets are first converted to WGS84 geographic coordinates (EPSG:4326). For distance and area calculations, each city is then reprojected into a suitable projected coordinate reference system:

• New York City and Shanghai – EPSG:3857 (Web Mercator)
  
• Singapore – EPSG:3414 (SVY21 / Singapore TM)
  
• Amsterdam – EPSG:28992 (Amersfoort / RD New)

Using an appropriate metric CRS ensures that area and distance calculations (e.g., buffer radii, nearest-neighbour distances) are interpretable in metres and square kilometres.

2. Cleaning and Merging Boundaries

City boundaries often contain small topological artefacts (e.g. slivers, self-intersections). Boundaries are therefore:

1. Exploded into individual polygons,
   
2. Buffered by 0 m to repair common geometry issues,
   
3. Merged into a single multipolygon per city.

For Shanghai, the municipal boundary is represented as a multi-polygon (including the main urban area and outlying islands such as Chongming). In this project all polygons belonging to the Shanghai municipality are retained. This means that large water bodies, port areas and peri-urban green space are included in the reference area, which tends to dilute density measures (stops per km²) compared with the intensity of bus service in the built-up core.

3. Clipping Bus Stops to City Boundaries

Bus stop points are then clipped to the cleaned boundary of each city. This ensures that all subsequent indicators refer to the same spatial extent when comparing between cities.

4. Constructing Pedestrian Street Networks

For the network-based accessibility indicator, a pedestrian street network is constructed for each city:

1. Using OSMnx, a walkable street network is downloaded from OpenStreetMap for the extent of each city (network_type="walk").
   
2. The resulting graph is projected into the same metric CRS as the city boundary so that edge lengths are expressed in metres.
   
3. Each bus stop is snapped to its nearest network node; these nodes act as origins for network-based walking distance calculations.

Indicators and Analytical Steps

1. Bus Stop Density

Concept. Density is defined as the number of bus stops per square kilometre of city area. It is a simple but intuitive measure of the overall supply of boarding opportunities.

Implementation.

1. Reproject the city boundary to the local metric CRS.
   
2. Compute total area (A) (km²).
   
3. Count the number of bus stops (N) after clipping.
   
4. Calculate：

Density = N / A (stops per km²)

where N is the number of bus stops inside the city boundary and A is the total city area (km²).

Interpretation. High density indicates either closely spaced stops or a large number of routes, but does not directly reveal where within the city stops are concentrated. It is therefore complemented by the spatially explicit methods below.

2. 500 m Walking Coverage

Concept. A 500 m Euclidean buffer is used as a proxy for the area within a reasonable walking distance (approximately 5–7 minutes) of a bus stop. The indicator measures the share of city land that is potentially “bus-accessible”.

Implementation.

1. In the projected CRS, create a 500 m circular buffer around each bus stop.
   
2. Merge all buffers into a single coverage polygon.
   
3. Intersect the merged buffer with the city boundary.
   
4. Compute the ratio：

Coverage_500m = (Area within 500 m of any stop) / (Total city area)

Interpretation. A city with high 500 m coverage has few large gaps in the bus network, whereas low coverage suggests extensive areas without nearby bus stops. This indicator is sensitive both to density and to how evenly stops are spread across the urban fabric.

2.1 Network-based 500 m Walking Coverage

Concept. The Euclidean 500 m buffer assumes that people can walk in straight lines. In reality, walking paths are constrained by the street network and barriers such as rivers or railways. A complementary indicator therefore measures 500 m walking coverage along the pedestrian street network.

Instead of circles, the network-based coverage approximates the area that can be reached by walking up to 500 m along streets from any bus stop.

Implementation.

1. Start from the projected pedestrian street network for each city.
   
2. Snap each bus stop to its nearest network node.
   
3. For each stop node, run a shortest-path search along the network (Dijkstra) with a maximum path length of 500 m, using edge length as the cost.
   
4. Collect all nodes and edges that lie within 500 m walking distance of at least one stop.
   
5. Buffer the selected street segments by a small distance (e.g. 20–40 m) to turn them into a continuous coverage polygon.
   
6. Intersect this polygon with the city boundary and compute the ratio of covered area to total city area, analogous to the Euclidean measure.

Interpretation. The network-based 500 m coverage is generally more conservative than its Euclidean counterpart, especially in cities with major barriers or coarse street grids. It is more closely aligned with actual walking conditions, but depends on the completeness of pedestrian links in OpenStreetMap. Comparing Euclidean and network-based coverage highlights where straight-line assumptions substantially over-estimate accessibility.

3. Kernel Density Estimation (KDE)

Concept. Kernel density estimation treats bus stops as a spatial point process and estimates a continuous intensity surface: the expected number of stops per unit area at each location, smoothed over a specified bandwidth. KDE is useful for identifying clusters and corridors of high bus service.

Implementation.

1. Extract the projected (x, y) coordinates of all bus stops.
   
2. Fit a Gaussian kernel density estimator from scikit-learn with a city-specific bandwidth (chosen to reflect typical stop spacing).
   
3. Create a regular grid covering the city extent and evaluate the KDE at each grid cell.
   
4. Visualise the resulting intensity surface as a heatmap and overlay the city boundary.

Interpretation. KDE highlights hotspots (dense corridors, terminals, downtown areas) and cold spots (sparsely served edge zones). Comparing heatmaps across the four cities helps to understand whether high densities are concentrated in a small core or more evenly spread.

4. Nearest-Neighbour Distances

Concept. While density summarises the average number of stops per area, the nearest-neighbour distance between stops captures the regularity of spacing along streets and across neighbourhoods. It is derived from point pattern analysis and relates to notions of clustering versus dispersion.

Implementation.

1. Construct a KDTree from stop coordinates in the projected CRS.
   
2. For each stop, query the distance to its second-nearest neighbour (the first neighbour is the stop itself).
   
3. Store this distance as nn_dist in the GeoDataFrame.
   
4. Summarise the distribution (mean, median, 90th percentile, min, max) and map the nn_dist values.

Interpretation.

• Short distances indicate tightly spaced stops or overlapping routes.
  
• Long distances indicate gaps in the network or peripheral areas.
  
• Mapping nn_dist reveals whether gaps are localised (e.g. industrial zones, water bodies) or widely distributed.

5. Joint Interpretation of Indicators

The indicators are designed to be read together:

• A city may have high density but still exhibit low 500 m coverage if stops are clustered in a small core.
  
• KDE highlights where in the city density is concentrated, complementing the scalar density metric.
  
• Nearest-neighbour statistics reveal whether accessibility is relatively uniform or if there are pockets of poor coverage.
  
• Comparing Euclidean and network-based 500 m coverage indicates how strongly physical barriers, street layout, and network structure constrain walking access relative to straight-line assumptions.

By juxtaposing these measures, the analysis moves beyond single-number comparisons and offers a richer picture of bus accessibility in each city.

Limitations

Several limitations should be kept in mind:

• Data completeness and definitions. NYC bus shelters undercount all bus stops; OpenStreetMap coverage for Amsterdam and Shanghai may be incomplete or heterogeneous.
  
• Euclidean distance approximation. The 500 m buffers do not follow the street network, so they may overestimate effective walking access in areas with barriers (motorways, rivers).
  
• Street network data. The network-based 500 m coverage relies on OpenStreetMap representations of walkable streets. Missing paths, misclassified links (e.g. paths mapped as private), or incomplete pedestrian networks can lead to underestimation of walking access in some neighbourhoods.
  
• Temporal dynamics. Service frequency, operating hours, and route patterns are not modelled; the analysis focuses on the spatial geometry of bus stops at a single point in time.

Despite these caveats, the methods provide a transparent and replicable framework for comparing bus accessibility across very different urban contexts.