ClockBoard: a zoning system for urban analysis

Robin Lovelace

Institute for Transport Studies and Leeds Institute for Data Analytics, University of Leeds, UK

Martijn Tennekes

Center for Big Data Statistics, Centraal Bureau voor de Statistiek, The Netherlands

Dustin Carlino

Independent Software Engineer, Lead Developer of A/B Street, USA

Abstract

Zones are the building blocks of urban analysis. Fields ranging from demographics to transport planning routinely use zones — spatially contiguous areal units that break-up continuous space into discrete chunks — as the foundation for diverse analysis techniques. Key methods such as origin-destination analysis and choropleth mapping rely on zones with appropriate sizes, shapes and coverage. However, existing zoning systems are sub-optimal in many urban analysis contexts, for three main reasons: 1) administrative zoning systems are often based on somewhat arbitrary factors; 2) zoning systems that are evidence-based (e.g. based on equal population size) are often highly variable in size and shape, reducing their utility for inter-city comparison; and 3) official zoning systems in many places simply do not exist or are unavailable. We set out to develop a fexible, open and scalable solution to these problems. The result is the ClockBoard zoning system, which consists of 12 segments emanating from a central place and divided by concentric rings with radii that increase in line with the triangular number sequence (1, 3, 6 km etc). ‘ClockBoards’ thus create a consistent visual frame of reference for monocentric cities that is reminiscent of clocks and a dartboard. This paper outlines the design and potential uses of the ClockBoard zoning system in the historical context, and discusses future avenues for research into the design and assessment of zoning systems.

Published paper

Note: this is a fully reproducible version of the paper “ClockBoard: a zoning system for urban analysis” by Lovelace, Tennekes, and Carlino (2022) published in the Journal of Open Source Software. The paper is available at doi:10.5311/JOSIS.2022.24.172.

Introduction

Zoning systems have long been used for a variety of administrative and practical purposes. Zones demarcating parcels of land have been integral to land ownership, rents and urban policies for centuries, forming the basis of a range of social and economic practices. Historical examples highlighting the importance of zone layouts include ‘tithe maps’ determining land ownership and taxes in 18th Century England (Bryant and Noke 2007) and the division of cities into discrete areas including legally defined “business, industrial, and residential zones” to tame chaotic urban growth in the exploding US cities in the early 1900s (Baker 1925).

In the 19th Century, zoning systems became known for political reasons, with ‘gerrymandering’ entering public discourse and academic research following Elbridge Gerry’s apparent attempt to gain political advantage by creating an electoral district in an odd shape that was said to resemble a salamander (hence the term’s name combining ‘Gerry’ and ‘salamander’) in 1812 (Orr 1969). Gerrymandering has since been the topic of countless academic papers that is the beyond the scope of the present paper.

Research has made great progress in mathematical analysis of zones and more objective assessment of the impacts that the nature of zoning systems can have on zone-based statistics (such as number of votes for a particular party in each zone) and outcomes. The gerrymandering problem (in itself is a manifestation of the modifiable area unit problem) can be described as a mathematical optimization problem: “\(n\) units are grouped into \(k\) zones such that some cost function is optimized, subject to constraints on the topology of the zones” (Chou and Li 2006). Prior work has demonstrated the sensitivity of urban analysis outcomes to zone system design, from the way cities are visualized to the impact of the nature of ‘traffic analysis zones’ on transport model outputs. In fact, this problem is a concise definition of the broader “zoning problem” that starts from the assumption that zones are to be composed of one or more basic statistical units (BSUs) (Jelinski and Wu 1996; Chandra et al. 2021) . Although the range of outcomes is a finite combinatorial optimisation problem (which combination of BSU-zone aggregations satisfy/optimize some pre-determined criteria) the zoning problem is still hard: “there are a tremendously large number of alternative partitions, a similar number of different results, and only a slightly smaller number of different interpretations” (Openshaw 1977).

The problem that we tackle in this paper is different, however. It is ‘zoning from scratch’: the division of geographic space into zones starting from a blank slate, without reference to pre-existing areal units. The focus of much preceding zoning research on BSU partitioning can be explained by the fact that much geographic data available to academics comes in ‘pre-packaged’ small areas and because creating zones from nothing is a harder problem. We disagree with the statement that “existence of individual or non-spatially aggregated data is rare in geography” (Openshaw 1977), pointing to car crashes, shop locations, species identification data and dozens of other phenomena that can be understood as ‘point pattern processes’. And with advances in computer hardware and software, the ‘starting from scratch’ approach to zoning systems is more feasible.

A number of approaches have tackled the question of how to best divide up geographical space for analysis and visualisation purposes, with a variety of applications. Functional zone classification is common in the field of remote sensing and associated sub-fields involved in analysing and classifying raster datasets (Ciglic et al. 2019; Hesselbarth et al. 2019). While such pixel-based approaches can yield complex and flexible results (depending on the geographic resolution of the input data), they are still constrained by the building blocks of the pixels, which can be seen as a particular type of areal unit, a uniformly sized and shaped BSU.

In this paper we are interested in the division of continuous space into completely new areal systems. This has been done using contour lines to represent lines of equal height, and the concept’s generalisation to lines of equal journey time from locations (isochrones) (Long 2018), population density (isopleths) (Lin, Hanink, and Cromley 2017) and model parameters which continuous geographical space (P’aez 2006). The boundaries created by these various ‘iso’ maps are ‘procedurally generated’ areal units of the type that this paper focuses, but their variability and often irregular shapes make them impractical for many types of urban analysis.

Procedural generation, which involves the generation of data through a repeated and sometimes randomized computational process has long been used to represent physical phenomena (Onrust et al. 2017). The approach has been used to generate spatial entities including roads (Galin et al. 2010), indoor layouts of buildings (Anderson et al. 2018) and urban layouts (Mustafa et al. 2020). Algorithms have also been developed to place linear features on a map, as illustrated by an algorithm that optimizes the placement of overlapping linear features for cartographic visualisation (Teulade-Denantes, Maudet, and Duchêne 2015). However, no previous research has demonstrated the creation of zoning systems specifically for the purposes of urban analysis.

New visualisation techniques are needed to represent new (or newly quantifiable) concepts and emerging datasets (such as OpenStreetMap) in urban analysis. The visualisation of direction has been driven by new navigational requirements and datasets, with circular compasses and displays common in land and sea navigational systems since the mid 1900s (Honick 1967). Circular visualisation techniques, in the form of rose diagrams, were used in a more recent study to indicate the most common road directions relative to North (Boeing 2021). The resulting visualisations are attractive and easy to interpret, but are not geographical, in the sense that they cannot meaningfully be overlaid on mapped data. The approach we present in this paper is more closely analogous to ‘grid sample’ approaches used in ecological and population research (Hirzel and Guisan 2002) . Historically, environmental researchers have used rectangular (and usually square) grids to divide up space and decide sampling strategies. Limitations associated with this simplistic strategy have been documented since at least the 1960s, with a prominent paper on geographic sampling strategies outlining advantages and disadvantages of simple random, systematic and stratified sampling techniques in 1967 (Holmes 1967). Starting with data at the level of raster grid cells and BSUs, a related approach is to sample from within available ‘pixels’ to generate a representative sample (Thomson et al. 2017).

Unlike BSU based zoning systems, grid sampling strategies require no prior zones. Unlike ‘procedurally generated’ areas, grid-based strategies generate areal units of consistent sizes and shapes. However, grid-based strategies are limited in their applicability to urban research because they seldom generate geographically contiguous results and do not account for the strong tendency of human settlements to have a (more-or-less clearly demarcated) central location with higher levels of activity.

Pre-existing zoning systems are often based on administrative regions. Although those zoning systems are usually in line with the hierarchical organization structure of governmental organizations, and therefore may work well for policy making, there are a couple of downsides to using such zoning systems. First of all, since a city and its politics change over time, the administrative regions often change accordingly. This makes it harder to do time series analysis. Since the administrative regions have heterogeneous characteristics, for instance population size, area size, proximity to the city centre, comparing different administrative regions within a city is not straightforward. Moreover, comparing administrative regions across cities is even more challenging: the average surface area of a administrative zones varies from city to city.

Grid tiles are popular in spatial statistics for a number of reasons. Most importantly the tiles have a constant area size, which makes comparably possible. Moreover, the grid tiles will not change over time like administrative regions. However, one downside is that a grid requires a coordinate reference system (CRS), enforcing (approximately) equal area size. For continents or large countries, a CRS is always a compromise. Therefore, the areas of the tiles may vary, or the shape of the tiles may be sheared or warped.

Another downside from a statistical point of view is that population densities are not uniform within a urban area, but concentrated around a centre. As a consequence, high resolution statistics is preferable in the dense areas, i.e. the centre, and lower resolution statistics in other parts of the city. That is the reason why administrative regions are often smaller in dense areas.

The approach presented in this paper aims to miniminput data requirements, generate consistent zones comparable between widely varying urban systems, and provide geographically contiguous areal units. The motivations for generating a new zoning system and use cases envisioned include:

  • Locating cities. Automated zoning systems based on a clear centrepoint can support map interpretation by making it immediately clear where the city centre is, and what the scale of the city is.

  • Reference system for everyday life. The zone name contains information about the distance to the center as well as the cardinal direction. E.g “I live in C12 and work in B3.” or “The train station is in the center and our hotel is in B7”. Moreover, the zones indicate whether walking and cycling is a feasible option regarding the distance.

  • Aggregation for descriptive statistics / comparability over cities. By using the zoning system to aggregate statistics (e.g. on population density, air quality, bicycle use, number of dwellings), cities can easily be compared to each other.

  • Modelling urban cities. The zoning system can be used to model urban mobility.

The paper is structured as follows. The next section outlines the approach, which requires only 2 inputs: the coordinates of the central place in the urban system under investigation, and the minimum radius from that central point that the zoning system should extend. Section 3 describes a number of potential applications, ranging from rudimentary navigation and location identification to mobility analysis. Finally, in Section 4, we discuss limitations of the approach and possible directions of research and development to generate additional zoning systems for urban analysis.

The ClockBoard zoning system

The aim of the ClockBoard zoning system is to tackle the issues associated with available zoning systems and to provide a standard template for research and communication purposes. The requirements of urban analysts, geographers, transport modellers and others working with geographic data across cities are diverse, but all rely on zoning systems as a foundation for modelling and visualisation. To enable flexibility, and to encourage other zoning systems building on it, the ClockBoard zoning system described in this paper is presented as a specific implementation of a more general concept (segmented concentric annuli) and implemented in open source software which can be extended in a range of ways (see Discussion). Considering urban analysis, modelling and wider research, visualisation and communication requirements of zoning systems, we developed the following criteria for successful zoning systems. Zoning systems for urban analysis should:

  • contain intuitively named zones, enabling public communication of research, e.g. with reference common perceptions of space in terms of distance from the city centre and direction relative to North
  • have a well-balanced number of zones since too many or too few zones may cause issues with analysis and visualisation be easy to visualize without too many or too few zones
  • include zones of consistent and useful sizes, for example with zone areas increasing with distance from the urban centres to reflect relatively high densities in central locations
  • be ‘scale agnostic’, capable of representing a range of urban forms ranging from extensive cities such as Mexico City to compact cities such as Hong Kong
  • be extensible and based on open source software, enabling others to create alternative zoning systems suited to diverse needs

Considering the above criteria, we explored many zoning options, some of which are illustrated in Figure 1. Two key concepts that make up the zoning system described in this paper are concentric annuli and segments defined by radii.

  • Concentric rings — formally called ‘concentric annuli’ — which emphasise central locations and have been used to explore the relationships between the characteristics of ‘focal trees’ and surrounding trees in ecological research (Wills et al. 2016), as shown in Figure 1 (A).

  • Segments, defined by radial lines emanating from the central point of the settlement (or other geographic entity) to be divided into zones, as shown in Figure 1 (B).

Combining these two concepts creates a general approach to zone creation that can be described as ‘segmented concentric annuli’, an implementation of which that we considered early in the process of designing the ClockBoard system with roughly equally sized zones (not the ClockBoard system) is shown in Figure 1 (C). After a period of informal testing and feedback that lasted approximately six months, we developed and refined the ‘ClockBoard’ zoning system presented in this paper, which is a specific implementation of the segmented concentric annuli approach to zone creation.

The parameters that define the ClockBoard zoning system were developed in an iterative process. We experimented with a range of ways of dividing the concentric annuli into different zones by modifying the distances between rings (the annuli borders) and the number of segments per annulus. It became apparent that zoning systems based on the two organising principles (and modifiable parameters) of concentric annuli and segments held promise, but selecting appropriate settings for each was key to the development of the ClockBoad zoning system, as outlined below.

Illustration of ideas explored in the lead-up to the development of the ClockBoard zoning system, highlighting the incremental and iterative evolution of the approach.Illustration of ideas explored in the lead-up to the development of the ClockBoard zoning system, highlighting the incremental and iterative evolution of the approach.Illustration of ideas explored in the lead-up to the development of the ClockBoard zoning system, highlighting the incremental and iterative evolution of the approach.

Figure 1: Illustration of ideas explored in the lead-up to the development of the ClockBoard zoning system, highlighting the incremental and iterative evolution of the approach.

Annuli radii

Each annuli is defined by its inner and outer circle. Given that the radius of the inner circle must the same as the radius of the preceding annuli to ensure geographically contiguity (no gaps) — except in the special case of the first and central annuli which has no inner circle (or an inner circle with a radius of zero) — the annuli sizes can be wholly defined by the sequence of numbers defining their out circle radii.

This sequence of numbers can increase by a fixed amount — e.g. with the outer border of each annuli being 1 km from the centre than the preceding annulus, as shown in Figure 1 (C) — or by varying amounts. In many cases it is useful for zones to be smaller near the centre of the study region surrounding cities. This truism is often reflected in traffic analysis zones (TAZ) used for transport modelling, which tend to be smaller near central areas where more detail is most important for policy-relevant outputs (Chandra et al. 2021).

After experimenting with various ways of incrementing the annuli width, and considering the importance of easy to remember distances from central points from the perspective of readability, interpretation and simplicity of the system, we settled on linear increases in width as a sensible default for the ClockBoard zoning system. This linear growth leads to distances between the outer circles of each annuli and the central point following in the triangular number sequence (Ross and Knott 2019). This means that all points in the first annuli (labelled A) are up to 1 km away from the city centre; a circle with a diameter of 1 km is an easy to remember (albeit not always accurate) way to define the central area of urban areas (Vinoth Kumar, Pathan, and Bhanderi 2007). The furthest points from the central point of the next 8 subsequent annuli in the system (annuli B to I) are 3, 6, 10, 15, 21, 28, 36 and 45 km respectively, meaning that even a large city such as London requires only 8 annuli to cover it entirely (Figure 2). This and other other attributes of the first set of 9 zones in the ClockBoard zoning system in Table 1.

Table 1: Key attributes of first 9 rings used in the ClockBoard zoning system.
N. annuli Outer annuli label N. zones Radius (km) Area (sqkm) Average zone size (km)
1 A 1 1 3 3
2 B 13 3 28 2
3 C 25 6 113 5
4 D 37 10 314 8
5 E 49 15 707 14
6 F 61 21 1385 23
7 G 73 28 2463 34
8 H 85 36 4072 48
9 I 97 45 6362 66

Number of segments

As its name suggests, the ClockBoard zoning system has 12 segments, representing a compromise between specificity of zone identification and ease of comprehension. On one hand, too few segments result in large and/or unusually shaped zones, as illustrated in a segmented concentric annuli zoning system with four segments per annuli developed by Vinoth Kumar, Pathan, and Bhanderi (2007) to model urban expansion. On the other hand, too many segments would result in small zones and make the zone codes harder to understand: imagine a system with 256 segments and saying “I’m in zone E173”!

Another advantage of using 12 segments is that the angular distance between segments are well understood. The ‘clock position’ system describes bearings with reference to the face of a clock, relative to the direction of travel or, as is the case with the ClockBoard zoning system, relative to true North. Under this system, well established in navigation, “12 O’clock” means true North and 3, 6 and 9 O’clock mean East, South and West respectively (Hart and Battiste 1991). Following this convention, the ClockBoard zoning system aligns segment 12 with true North, enabling users to approximate their location in a city with reference to clock position .

ClockBoard zones for segmenting urban areas

The result of applying 12 segments and n concentric rings with external diameter increasing as triangular numbers, with n being sufficient to cover the city extent with, is the Clockboard zoning system. As outlined in the Introduction, the primary motivation for developing the system was urban analysis and the description, visualisation and exploratory analysis of large cities with well-defined central areas such as London, as illustrated in Figure 2.

The clockboard zoning system, applied to Greater London, UK.

Figure 2: The clockboard zoning system, applied to Greater London, UK.

Using the ClockBoard zoning system

To enable easy access to the ClockBoard zoning system, we implemented techniques needed to create them in free and open source software. The tools described below allow people to create ClockBoards in a reproducible way from command line environments and even from a web browser, to minimise barriers to entry.

The zonebuilder R package

The concepts were initially implemented in the statistical programming language R, which is available from the Comprehensive R Archive Network (CRAN) and can be installed from the R command line as follows:

install.packages("zonebuilder")

After the package has been installed, its functions can be attached (made available) to the user’s workspace as follows:

library(zonebuilder)

A simple zoning system for Tokyo can be created as follows, resulting in the map shown in Figure 3:

ClockBoard_tokyo = zb_zone("Tokyo", n_circles = 5)