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Heatmap - Gravity

A color-coded map to visualize the accessibility of points (such as POI) from surrounding areas.

1. Explanation​

Visualized as a color-coded hexagonal grid, the heatmap takes into account real-world transport and street networks to compute accessibility. After specifying a routing type (Walk, Bicycle, etc.), opportunity layer and travel time limit, the result will display a color-coded hexagonal grid for all areas accessible under these conditions. The color scale refers to local accessibility.

INFO

An Opportunity layer contains geographic point data. Select one or more such layers containing your destination points (opportunities) as input to the heatmap.

Unique to the gravity-based heatmap, customizable properties such as sensitivity, the impedance function and destination potential give you minute control over the method used and metadata taken into account while computing the accessibility value for an area. Influenced by these properties, the accessibility of a point can model complex real-world human behavior and is a powerful measure for transport and accessibility planning.

Pro tip

Described shortly, accessibility heatmaps are a visualization representing access from various unspecified origins, to one or more specified destinations. This is in contrast to catchment areas which represent egress from one or more specified origins to various unspecified destinations.

Gravity-based Heatmap in GOAT

info

Heatmaps are available in certain regions. Upon selecting a Routing type, a geofence will be displayed on the map to highlight supported regions.

Coverage for Gravity-based Heatmaps

If you would like to perform analyses beyond this geofence, feel free to contact us. We would be happy to discuss further options.

2. Example use cases​

  • Which neighborhoods or areas have limited access to public amenities, such as parks, recreational facilities, or cultural institutions, and may require targeted interventions to improve accessibility?

  • Are there areas with high potential for transit-oriented development or opportunities for improving non-motorized transportation infrastructure, such as bike lanes or pedestrian-friendly streets?

  • What is the impact of a new amenity on local accessibility?

  • Is there potential to expand the availability of services such as bike sharing or car sharing stations?

  • How does the accessibility in various neighborhoods compare when taking into account the qualitative aspects of amenities (such as frequency of service at bus stops, size of supermarkets, capacity of schools, etc)?

  • What is the real-world accessibility of public transport stations when travel times to these stations impact their accessibility in a non-linear way?

3. How to use the indicator?​

1
Click on Toolbox toolbox.
2
Under the Accessibility Indicators menu, click on Heatmap Gravity.

Routing​

3
Pick the Routing Type you would like to use for the heatmap.

Walk​

Considers all paths accessible by foot. For heatmaps, a walking speed of 5 km/h is assumed.

Hint

For further insights into the Routing algorithm, visit Routing/Walk.

Configuration​

4
Pick the Impedance Function you would like to use for the heatmap.

Gaussian​

This function calculates accessibilities based on a Gaussian curve, which is influenced by the sensitivity and destination_potential you define. For a more in-depth understanding, refer to the Technical details section.

Pro tip

As studies have shown, the relationship between travel time and accessibility is often non-linear. This means that people may be willing to travel a short distance to reach an amenity, but as the distance increases, their willingness to travel rapidly decreases (often disproportionately).

Leveraging the sensitivity you define, the Gaussian function allows you to model this aspect of real-world behaviour more accurately.

Hint

How to choose the sensitivity value?

Selecting the best fitting sensitivity always depends on the context of the analysis, and there are no strict rules.

  • Low β: A good strating point could be to use lower sensitivity on urban scale analyses, beacause it results in sharper accesssibility value drop with increasing travel time. In urban areas there are more opportunities available, and people are more likely to choose the closest one.
  • High β: In contrast, higher sensitivity could be used in regional scale analyses, where opportunities are more sparse and people are more likely to travel further to reach them.

See the Calculation section for a detailed visual explanations on the formula.

Opportunities​

Opportunities are essentially point-based data (such as POI) for which you would like to compute a heatmap. These are the "destinations" (such as transit stations, schools, other amenities, or your own custom point-based data) while surrounding areas are "origins" for which an accessibility value will be computed and visualized.

Additionally, you may create more opportunities via the + Add Opportunity button at the bottom of the drawer. All opportunity layers will be combined to produce a unified heatmap.

5
Select your Opportunity Layer from the drop-down menu. This can be any previously created layer containing point-based data.
6
Choose a Travel Time Limit for your heatmap. This will be used in the context of your previously selected Routing Type.
Hint

Need help choosing a suitable travel time limit for various common amenities? The "Standort-Werkzeug" of the City of Chemnitz can provide helpful guidance.

7
If required, choose a Destination Potential Field. This must be a numeric field from your Opportunity Layer which will be used as a coefficient by the accessibility function.
Pro tip

Destination potential is a useful way to prioritize certain opportunities over others. For example, if there are two supermarkets and one is nearer than the other, it would typically receive a higher accessibility score due to its proximity. However, if the supermarket farther away is larger, you may want to give it a higher level of importance. Destination potential allows you to use an additional property (such as the size of supermarkets) to assign opportunities a "potential" and employ qualitative information while computing accessibility.

The example below shows how the destination potential can affect the gravity heatmap. Its destination potential is based on the total number of hourly public transport departures from a stop. It will result in a different accessibility distribution, because the area around point with a higher destination potential will be favored in the computation.

gravity-no-destination-potential

The first map is calculated without destination potential.

gravity-with-destination-potential

The second map used the same settings, but added destination potential based on the total number of departures. This altered the accessibility values of each hexagon and they returned in a wider range, because the highest value increased even more. Higher accessibility values are more concentrated around the stops that have larger trip count (red points).

8
Specify a Sensitivity value. This must be numeric and will be used by the heatmap function to determine how accessibility changes with increasing travel time.
9
Click Run to start the calculation of the heatmap.
Hint

Depending on your configuration, the calculation might take a few minutes. The status bar displays current progress.

Results​

10
Once the calculation is complete, a result layer will be added to the map. This Heatmap Gravity layer will contain your color-coded heatmap.

Clicking on any of the heatmap's hexagonal cells will reveal the computed accessibility value for this cell.

Heatmap Gravity-Based Calculation Result in GOAT

Tip

Want to style your heatmaps and create nice-looking maps? See Styling.

4. Technical details​

Calculation​

The accessibility value of each hexagonal cell within a heatmap is calculated with the help of gravity-based measures and can be operationalized as:

Accessibility Formula:

where the accessibility A of origin i is the sum of all opportunities O available at destinations j weighted by some function of the travel time tij between i and j. The function f(tij) is the impedance function, which can be gaussian, linear, exponential, or power. The sensitivity parameter β and the destination potential are used to adjust the accessibility value.

GOAT uses the following formulas for its impedance functions:​

Modified Gaussian, (Kwan,1998):

Cumulative Opportunities Linear, (Kwan,1998):

Negative Exponential, (Kwan,1998):

Inverse Power, (Kwan,1998) (power in GOAT):

Travel times are measured in minutes. For a maximum travel time of 30 minutes, destinations that are farther than 30 minutes are considered non-accessible and therefore not considered in the calculation of the accessibility. The sensitivity parameter determines how accessibility changes with increasing travel time. As the sensitivity parameter is decisive when measuring accessibility, GOAT allows you to adjust this The graph shows how the willingness to walk decreases with increasing travel time based on the selected impedance function and sensitivity value (β).

300,000

Similarly, the destination potential can be changed. Thus, for example, one POI type (e.g. hypermarkets) can be assigned a higher accessibility effect than other POI types (e.g. discount supermarkets). In the Opportunities section, at step 7, we cover the destination potential in detail.

tip

For a calculation example see our tutorial video.

Classification​

In order to classify the accessibility levels that were computed for each grid cell (for color-coded visualization), a classification based on 8 quantile group is used by default. That means, each color covers 12,5 % of the grid cells. The area outside of the computed layer has no access within the defined travel time.

gravity-default-classification

However, various other classification methods may be used instead. Read more in the Data Classification Methods section of the Attribute-based Styling page.

Visualization​

Heatmaps in GOAT utilize Uber's H3 grid-based solution for efficient computation and eacessibisy-to-understand visualization. Behind the scenes, a pre-computed travel time matrix for each routing type utilizes this solution and is queried and further processed in real-time to compute accessibility and produce a final heatmap.

The resolution and dimensions of the hexagonal grid used depend on the selected routing type:

Walk​

  • Resolution: 10
  • Average hexagon area: 11285.6 m²
  • Average hexagon edge length: 65.9 m

Bicycle​

  • Resolution: 9
  • Average hexagon area: 78999.4 m²
  • Average hexagon edge length: 174.4 m

Pedelec​

  • Resolution: 9
  • Average hexagon area: 78999.4 m²
  • Average hexagon edge length: 174.4 m

Car​

  • Resolution: 8
  • Average hexagon area: 552995.7 m²
  • Average hexagon edge length: 461.4 m

5. References​

Kwan, Mei-Po. 1998. “Space-Time and Integral Measures of Individual Accessibility: A Comparative Analysis Using a Point-Based Framework.” Geographical Analysis 30 (3): 191–216. https://doi.org/10.1111/j.1538-4632.1998.tb00396.x.

Vale, D.S., and M. Pereira. 2017. “The Influence of the Impedance Function on Gravity-Based Pedestrian Accessibility Measures: A Comparative Analysis.” Environment and Planning B: Urban Analytics and City Science 44 (4): 740–63. https://doi.org/10.1177%2F0265813516641685.

Higgins, Christopher D. 2019. “Accessibility Toolbox for R and ArcGIS.” Transport Findings, May. https://doi.org/10.32866/8416.