diff --git a/vignettes/josis.csl b/vignettes/josis.csl new file mode 100644 index 0000000..438208b --- /dev/null +++ b/vignettes/josis.csl @@ -0,0 +1,16 @@ + + diff --git a/vignettes/paper.Rmd b/vignettes/paper.Rmd index cdfb00d..a731de7 100644 --- a/vignettes/paper.Rmd +++ b/vignettes/paper.Rmd @@ -2,19 +2,19 @@ title: "ClockBoard: a zoning system for urban analysis" runningtitle: "The ClockBoard Zoning System" # # For paper: uncomment below for LaTeX version -# output: -# bookdown::pdf_book: -# base_format: rticles::josis_article -# For R package vignette output: - bookdown::html_vignette2: + bookdown::pdf_book: + base_format: rticles::josis_article + keep_tex: true +# For R package vignette +# output: bookdown::word_document2 author: - name: Robin Lovelace affiliation: Institute for Transport Studies and Leeds Institute for Data Analytics, University of Leeds, UK - name: Martijn Tennekes - affiliation: Center for Big Data Statistics, Centraal Bureau voor de Statistiek, The Netherlands + affiliation: Department of Methodology, Statistics Netherlands, The Netherlands - name: Dustin Carlino - affiliation: Independent Software Engineer, Lead Developer of A/B Street, USA + affiliation: Alan Turing Institute, London, UK vignette: > %\VignetteIndexEntry{ClockBoard: a zoning system for urban analysis} %\VignetteEngine{knitr::rmarkdown} @@ -24,7 +24,7 @@ pkgdown: set_null_theme: false keywords: "zoning, areal data, zoning systems, modifiable area unit problem" bibliography: references.bib -# csl: josis.csl +csl: josis.csl abstract: | Zones are the building blocks of urban analysis. Fields ranging from demographics to transport planning routinely use zones --- spatially @@ -39,7 +39,7 @@ abstract: | 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. + We set out to develop a flexible, 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). @@ -79,7 +79,7 @@ RefManageR::WriteBib(refs, "vignettes/references.bib") u = "www.zotero.org/styles/open-geospatial-data-software-and-standards" download.file(u, "vignettes/josis.csl") piggyback::pb_upload("cities_p1.png") -piggyback::pb_upload("cities_p2.png") +piggyback::pb_upload("cities_p2-scale.png") piggyback::pb_download_url("cities_p1.png") # [1] "https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/cities_p1.png" @@ -94,113 +94,129 @@ file.rename("vignettes/zonebuilder-paper.pdf", "zonebuilder-paper.pdf") browseURL("zonebuilder-paper.pdf") piggyback::pb_upload("zonebuilder-paper.pdf") piggyback::pb_upload("vignettes/zonebuilder-paper.tex") +piggyback::pb_download("vignettes/zonebuilder-paper.tex") piggyback::pb_download_url("zonebuilder-paper.pdf") # [1] "https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/zonebuilder-paper.pdf" + remotes::install_github("paleolimbot/rbbt") # library(rbbt) # rbbt::bbt_update_bib(path_rmd = "vignettes/paper.Rmd") + +# Create diff file +wd_old = setwd("vignettes") +piggyback::pb_download("vignettes.zonebuilder-paper.tex") +system("latexdiff -h") +rmarkdown::render("paper.Rmd") +system("latexdiff vignettes.zonebuilder-paper.tex zonebuilder-paper.tex > diff.tex") +tinytex::pdflatex("diff.tex") +browseURL("diff.pdf") +piggyback::pb_upload("diff.pdf") +piggyback::pb_download_url("diff.pdf") +setwd(wd_old) ``` # 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. +Zoning is the process of generating areal units for aggregating, visualizing, and potentially modeling geographic datasets. +The resulting zones --- also commonly referred to as 'areal units' or 'small areas' in the literature --- have long been used to support analysis of human systems. Historical examples highlighting the importance of zone layouts include 'tithe maps' determining land ownership and taxes in 18th Century England [@bryant_worcestershire_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_zoning_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_persistence_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_taming_2006]. +The gerrymandering problem is a manifestation of the modifiable area unit problem (MAUP), 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_taming_2006]. +Our aim in this paper is not to tackle the MAUP directly, but to provide a 'ready made' zoning system that can demonstrate some of its effects by providing another way to aggregate and present data. + 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](http://www.iasi.cnr.it/ewgt/13conference/145_binetti.pdf). -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_modifiable_1996; @chandra_multi-objective_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_optimal_1977]. +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_modifiable_1996; @chandra_multi-objective_2021]. +Although the range of outcomes is a finite combinatorial optimization 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_optimal_1977]. + +Pre-existing zoning systems are often based on administrative regions and reflect the hierarchical organizational structure of statistical agencies. +Well-designed administrative zones are advantageous for many applications, especially in relation to aggregated administrative datasets, but have disadvantages for certain applications. +First, the administrative regions often change over time, hindering spatio-temporal analysis. +Second, since the administrative zones have different sizes and shapes in different cities, they may not be ideal when comparing cities. +In order to address these shortcomings of zoning systems based on administrative regions, our aim in this paper is to build a zoning system from scratch, i.e. to divide a *continuous* geographic space into zones **starting from a blank slate**. -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_optimal_1977], pointing to car crashes, shop locations, species identification data and dozens of other phenomena that can be understood as 'point pattern processes'. +The statement that "existence of individual or non-spatially aggregated data is rare in geography", used by @openshaw_optimal_1977 to justify the BSU grouping approach, may have been true in the 1970s when it was written. +Today dis-aggregated geographic datasets are common. +Open datasets exist on phenomena including 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_evaluating_2019; @hesselbarth_landscapemetrics_2019]. +A number of approaches have tackled the question of how to best divide up geographical space for analysis and visualization purposes, with a variety of applications. +Functional zone classification is common in the field of remote sensing and associated sub-fields involved in analyzing and classifying raster datasets [@ciglic_evaluating_2019; @hesselbarth_landscapemetrics_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. +Approaches to creating zoning systems *starting from* origin-destination have also been developed [@zhang_detecting_2021] and, although these approaches tend also to start from BSUs, they could be extended to generate 'bottom up' datasets starting from individual-level GPS type datasets. 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_modeling_2018], population density (isopleths) [@lin_cartographic_2017] and model parameters which continuous geographical space [@paez_exploring_2006]. +This has been done using lines representing points with equal journey time from locations (isochrones) and the areas bound by them [@long_modeling_2018], population density (isopleths) [@lin_cartographic_2017] and model parameters which continuous geographical space [@paez_exploring_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_ecologically_2017]. The approach has been used to generate spatial entities including roads [@galin_procedural_2010], indoor layouts of buildings [@anderson_augmented_2018] and urban layouts [@mustafa_procedural_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_routes_2015]. +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_ecologically_2017]. The approach has been used to generate spatial entities including roads [@galin_procedural_2010], indoor layouts of buildings [@anderson_augmented_2018] and urban layouts [@mustafa_procedural_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 visualization [@teulade-denantes_routes_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_pictorial_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_spatial_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_which_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_problems_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_gridsample_2017]. +New visualization techniques are needed to represent new (or newly quantifiable) concepts and emerging datasets (such as OpenStreetMap) in urban analysis. +The visualization 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_pictorial_1967]. Circular visualization 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_spatial_2021]. The resulting visualizations are attractive and easy to interpret, but are not geographical, in the sense that they cannot meaningfully be overlaid on mapped data. -Unlike BSU based zoning systems, grid sampling strategies require no prior zones. +The approach we present in this paper is more closely analogous to 'grid sample' approaches used in ecological and population research [@hirzel_which_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_problems_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_gridsample_2017]. + +Unlike BSU based zoning systems, the use of rectangular grids or 'quadrats' was common [@holmes_problems_1967]. +The approach was particularly useful before administrative zones became widespread. 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. +However, 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; specifying the lines that define them ensures that they do not change over time, unlike administrative regions. +Like the zoning system presented in this paper, grid tiles depend on a CRS and may become distorted over large (continental) spatial scales (this is not much of an issue for zoning systems that only aim to provide zones for a single city at a time like that presented here). +Another downside from a statistical perspective is that population density tends to increase towards a central point. +As a consequence, smaller zones are often preferable in denser areas, which often means towards the city center: for this reason administrative regions are often smaller in central areas and larger on the outskirts of cities, as illustrated with reference to London in Figure \@ref(fig:cityscale). -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: +The overall aim of this paper is to highlight the potential for new zoning systems to support urban analysis. +We do this by presenting a zoning system that enables inter-city comparison using zones of the same size and shape regardless of the city's location, which can be generated rapidly and in a reproducible manner with minimal data requirements. +The specific motivations for embarking on the idea, and its implementation in open source software, were as follows: -- 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. +- Locating phenomena in cities. + Automated zoning systems based on a clear center-point can support map interpretation by making it immediately clear where the city center 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. +- Aggregation for descriptive statistics. + It is often useful or necessary to present geographical data in an aggregate form. + A consistently sized and shaped set of zones can support attractive, clear and meaningful visualization. -- Modelling urban cities. - The zoning system can be used to model urban mobility. +- Comparing 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. 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 ClockBoard zoning system {#clockzs} 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. +The requirements of urban analysts, geographers, transport modelers and others working with geographic data across cities are diverse, but all rely on zoning systems as a foundation for modeling and visualization. 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. +Considering urban analysis, modeling and wider research, visualization 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 +- contain intuitively named zones, enabling public communication of research, e.g. with reference common perceptions of space in terms of distance from the city center 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 visualization 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 +- include zones of consistent and useful sizes, for example with zone areas increasing with distance from the urban centers 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 \@ref(fig:options). 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_persistence_2016], as shown in Figure \@ref(fig:options) (A). +- **Concentric rings** --- formally called 'concentric annuli' --- which emphasize central locations and have been used to explore the relationships between the characteristics of 'focal trees' and surrounding trees in ecological research [@wills_persistence_2016], as shown in Figure \@ref(fig:options) (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 \@ref(fig:options) (B). @@ -209,7 +225,7 @@ After a period of informal testing and feedback that lasted approximately six mo 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. +It became apparent that zoning systems based on the two organizing 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. @@ -234,15 +250,14 @@ qtm(zb_zone(london_c(), n_segments = z1_areas_relative, labeling = "clock", dist 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 \@ref(fig:options) (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_multi-objective_2021]. +This sequence of numbers can increase by a fixed amount --- e.g. with the outer border of each annuli being 1 km from the center than the preceding annulus, as shown in Figure \@ref(fig:options) (C) --- or by varying amounts. +In many cases it is useful for zones to be smaller near the center of the study region surrounding cities, whether the zones are used for the publication of statistical data (often referred to as 'census tracts' in the USA and 'output areas' in the UK, for example) or transport models, which often use dedicated zones referred to as traffic analysis zones (TAZ) [@chandra_multi-objective_2021]. -After experimenting with various ways of incrementing the annuli width, +After experimenting with various ways to increment 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](https://en.wikipedia.org/wiki/Triangular_number) [@ross_dicuil_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_spatio-temporal_2007]. +This means that all points in the first annuli (labelled A) are up to 1 km away from the city center; 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_spatio-temporal_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 \@ref(fig:london)). This and other other attributes of the first set of 9 zones in the ClockBoard zoning system in Table \@ref(tab:t1). @@ -252,8 +267,8 @@ t2$`Outer annuli label` = LETTERS[1:9] t2$`N. zones` = t2$`N. annuli` * 12 - 11 t2$`Radius (km)` = zonebuilder::zb_100_triangular_numbers[1:9] t2$`Area (sqkm)` = pi * t2$`Radius (km)`^2 -t2$`Average zone size (km)` = t2$`Area (sqkm)` / t2$`N. zones` -knitr::kable(t2, booktabs = TRUE, caption = "Key attributes of first 9 rings used in the ClockBoard zoning system.", digits = 0) +t2$`Av. zone size (km)` = t2$`Area (sqkm)` / t2$`N. zones` +knitr::kable(t2, booktabs = TRUE, caption = "Key attributes of the ClockBoard zoning system, highlighting its flexibility ranging from a single central zone (zone A is a circle with radius of 1 km) to a zoning system with a radius of 45 km and 97 zones. The number of rings can be varied to match the size of the city under investigation.", digits = 0) ``` ## Number of segments @@ -264,13 +279,13 @@ On the other hand, too many segments would result in small zones and make the zo 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_use_1991]. +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_use_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 \@ref(fig:london). +As outlined in the Introduction, the primary motivation for developing the system was urban analysis and the description, visualization and exploratory analysis of large cities with well-defined central areas such as London, as illustrated in Figure \@ref(fig:london). ```{r london, fig.cap="The clockboard zoning system, applied to Greater London, UK.", out.width="70%"} @@ -281,7 +296,7 @@ zb_plot(london_zones, palette = "hcl") ## 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 tools described below allow people to create ClockBoards in a reproducible way from command line environments and even from a web browser, to minimize barriers to entry. ### The zonebuilder R package @@ -298,7 +313,10 @@ library(zonebuilder) ``` -A simple zoning system for Tokyo can be created as follows, resulting in the map shown in Figure \@ref(fig:tokyo): +A simple zoning system for Tokyo is created and plotted in the R code chunk below, resulting in the map shown in Figure \@ref(fig:tokyo). +In the code chunk below, the character string "Tokyo" is the first argument in the `zb_zone()` function (which can also be a spatial point object). +When the first argument is a text string, as is the case here, the package automatically converts it into a geographic location using the Nominatim online service, which is based on data from OpenStreetMap; the `zb_view()` function creates an interactive map. + ```{r, echo=FALSE, eval=FALSE} tokyo = tmaptools::geocode_OSM("tokyo", as.sf = TRUE) @@ -309,8 +327,9 @@ tokyo_area = osmdata::getbb ('tokyo', format_out = 'sf_polygon') mapview::mapview(tokyo_area$multipolygon) ``` -```{r, echo=TRUE} +```{r, echo=TRUE, eval=FALSE} ClockBoard_tokyo = zb_zone("Tokyo", n_circles = 5) +zb_view(ClockBoard_tokyo, alpha = 0.8) ``` ```{r, eval=FALSE} @@ -322,17 +341,17 @@ zb_view(ClockBoard_tokyo, alpha = 0.8) ```{r tokyo, fig.cap="ClockBoard zoning system applied to Tokyo, the result of running the reproducible code used to demonstrate the zonebuilder R package.", out.width="75%"} # library(tmap) # load mapping package -# tmap_mode("view") # interactive visualisation mode +# tmap_mode("view") # interactive visualization mode # tm_shape(ClockBoard_tokyo) + # tm_borders() + # tm_text("label") + # tm_scale_bar() # from system command line: # pngquant -f --ext .png --quality 60-85 vignettes/tokyo.png -knitr::include_graphics("https://user-images.githubusercontent.com/1825120/128613050-96fd8882-10c5-47d8-af2f-90fceeba8d81.png") +# knitr::include_graphics("https://user-images.githubusercontent.com/1825120/128613050-96fd8882-10c5-47d8-af2f-90fceeba8d81.png") # LaTeX version: -# download.file("https://user-images.githubusercontent.com/1825120/128613050-96fd8882-10c5-47d8-af2f-90fceeba8d81.png", "tokyo.png") -# knitr::include_graphics("tokyo.png") +download.file("https://user-images.githubusercontent.com/1825120/128613050-96fd8882-10c5-47d8-af2f-90fceeba8d81.png", "tokyo.png") +knitr::include_graphics("tokyo.png") ``` Note that the `n_circles` argument was set to 5, resulting in a zoning system 15 km in radius (see Table \@ref(tab:t1)). @@ -373,34 +392,38 @@ To enable creation of ClockBoard zones for non-programmers and to encourage peop u = "https://user-images.githubusercontent.com/1825120/128508694-5b5485ca-6f1b-4c21-bdb6-9269a7981dd5.png" -# for html version: -knitr::include_graphics(u) +# # for html version: +# knitr::include_graphics(u) -# # for pdf version: -# f = basename(u) -# download.file(u, f) -# knitr::include_graphics(f) +# for pdf version: +f = basename(u) +download.file(u, f) +knitr::include_graphics(f) ``` # Applications -The zoning system presented in this paper is a specific implementation concentric segmented annuli, that was designed to support description, exploration and visualisation of monocentric cities. +The zoning system presented in this paper is a specific implementation concentric segmented annuli, that was designed to support description, exploration and visualization of monocentric cities. The zoning system presented, and modifications of the system, could be useful in a range of other areas. The examples below are designed to provide an insight into how the zoning system could be used. -## Navigation and location +## Describing location + +A potential application of the zoning system is to indicate approximate locations with reference to a known central point or area, e.g. to describe a segment of a city. +ClockBoard zones offer a level of intermediate-to-low accuracy in between the simple use of quadrants to identify parts of a city verbally on one hand, and more sophisticated ways of communicating location to the nearest few meters on the other. +Dividing cities into quadrants and referring to them with names such as 'north', 'northeast', etc. is common in everyday speech and academic writing: a paper on the impact of open spaces on house prices stated that traffic noise was expected to have a negative impact on house prices in "south-east, north-east, and north Portland", with reference to an accompanying map, for example [@bolitzer_impact_2000]. +Location services such as 'what3words' and open source implementations such as 'whatfreewords' and '[goehashphrase](https://www.qalocate.com/solutions/geohashphrase/)' take the concept of converting coordinates into memorable words/phrases a step further, offering accuracy measured in meters rather than kilometers in situations where coordinates may not be appropriate or possible [@raposo_virtual_2019]. -The most basic application of the zoning system could be to provide approximate locations and navigation guidance to people in cities. -As demonstrated by location services such as 'what3words' and open source implementations such as 'whatfreewords' and '[goehashphrase](https://www.qalocate.com/solutions/geohashphrase/)', there is demand for easy-to-remember words/phrases to specify locations in situations where there is no address and where providing longitude/latitude coordinates may not be appropriate or possible [@raposo_virtual_2019]. -While not the primary purpose of the ClockBoard zoning system, it can be used to communicate locations in a city. +With 49 zones covering an area just over 700 square km, the ClockBoard system offers an intermediate level of resolution between the simple quadrant method and complex 'geohash' approaches to referring to locations outlined above. +Like the quadrant approach, the ClockBoard system relies on a central point. +The ClockBoard system shares the advantage of the quadrant approach to locating objects that the location can worked out by people without reliance on a computer to translate coordinates into a geohash, although the calculation is substantially harder, requiring memorization or quick calculation of the triangular number sequence (1, 3, 6, 10, 15 etc) and knowledge of the boundaries of a clock face such that "E03" is understood as being between 10 and 15 km East of the center. -We have tested this use case by using the zoning system to agree on meeting points to collaborate on the project. -An illustration of how the zoning system was used is shown in Figure \@ref(fig:location), which shows how the ClockBoard zoning system could be used to communicate key locations in a city, from the train station (zone A) to a park (zone C01) and on to the city of Bradford (zone E09) to orientate people new to the city and to describe geographically where things are located using a small amount of information (3 characters). -Without needing to process much data or look at the map, a person who is new to to the city would know that the park is relatively close to the rail station (between 3 and 6 km from the city centre) while Bradford in zone E09 is between 15 and 21 km from the city centre. -Note that although Bradford is a city on its own and can therefore have its own zoning system, in this example it is placed in the context of the metropolitan area of Leeds. -Of course the locations are not geographically specific; the zones would be used a broad brush descriptions of place locations before more detailed locations are provided, e.g. through a postcode, an address, or coordinates. +An illustration of using the ClockBoard zoning system to locate places is presented in Figure \@ref(fig:location). +This shows how it could be used to communicate key locations, including a train station (zone A) a park (zone C01) and the center of a neighboring city (zone E09), with reference to the city center of Leeds, UK. +In a hypothetical use case, the example could be used to communicate the fact that the park is relatively close to the rail station (between 3 and 6 km from the city center) while Bradford in zone E09 is between 10 and 15 km from central Leeds. +Of course, the locations are not geographically specific; the zones would be used a broad brush descriptions of place locations before more detailed descriptions of locations such as directions from key landmarks or coordinates are used. -```{r location, out.width="85%", fig.cap="Illustration of how the ClockBoard system could be used to describe the approximate location of places. In this hypothetical example, someone is describing key places to visit in and around Leeds to someone who arrives at the train station in zone A, visits the city's famous Roundhay Park in zone C01, before travelling for an evening meal in Bradford, in zone E09."} +```{r location, out.width="85%", fig.cap="Illustration of how the ClockBoard system could be used to describe the approximate location of places. In this hypothetical example, the system is used to locate places in and around Leeds: the train station in the central zone A, Roundhay Park wich is located around 5 km North of the center in zone C01, and central Bradford which is located around 14 km due East of the center in zone E09."} # ClockBoard_leeds = zb_zone(x = "leeds") # ClockBoard_leeds$label_locations = "" # i = grepl(pattern = "A|C01|E09", x = ClockBoard_leeds$label) @@ -415,14 +438,17 @@ Of course the locations are not geographically specific; the zones would be used # "https://user-images.githubusercontent.com/1825120/127722684-e4f0f58a-44b2-48b9-8bdd-cd09bae4e250.png", # "navigation-small.png" # ) -# download.file( -# "https://user-images.githubusercontent.com/1825120/127722701-36ca3674-0522-40d6-9a69-e745ca628bca.png", -# "navigation.png" -# ) -# knitr::include_graphics("navigation.png") -knitr::include_graphics("https://user-images.githubusercontent.com/1825120/127722701-36ca3674-0522-40d6-9a69-e745ca628bca.png") +download.file( + "https://user-images.githubusercontent.com/1825120/127722701-36ca3674-0522-40d6-9a69-e745ca628bca.png", + "navigation.png" +) +knitr::include_graphics("navigation.png") +# knitr::include_graphics("https://user-images.githubusercontent.com/1825120/127722701-36ca3674-0522-40d6-9a69-e745ca628bca.png") ``` +The ClockBoard zoning system was not designed for locating objects in space in this way; the real world utility of such low resolution indications of spatial location has yet to be tested; and understanding of the zoning system would need to be widespread for it to catch on. +However, the example demonstrates how the system communicates potentially useful location data with a small amount of verbal information. +More plausible use cases include exploring city scale data (covered in the next section) and inter-city comparisons of geographically variable phenomena (covered in the section after). ## Exploring city scale data @@ -432,13 +458,13 @@ The presentation of the same data at four different levels of geographic resolut The most geographically detailed zoning system in which the data is available is the rectangular grid shown in the far left facet (A). This presentation of the data is ideal for many purposes, demonstrating the variability in air quality over relatively small areas (1 km grid cells) across London. -In cases when geographic aggregation is required, e.g. to present the data in small graphics that will be printed at low resolution (e.g. newspaper visualisations and infographics), two common approaches are to use an existing administrative zoning system (with well known London Borough boundaries used to aggregate the data presented in facet B in Figure \@ref(fig:cityscale)) and to use a simplified geographical representation or geographically arranged facets [@dorling_area_2011]. +In cases when geographic aggregation is required, e.g. to present the data in small graphics that will be printed at low resolution (e.g. newspaper visualizations and infographics), two common approaches are to use an existing administrative zoning system (with well known London Borough boundaries used to aggregate the data presented in facet B in Figure \@ref(fig:cityscale)) and to use a simplified geographical representation or geographically arranged facets [@dorling_area_2011]. Both approaches have advantages, with existing and well-known zoning systems enabling map readers familiar with the city to orient themselves and interpret the map. In this context and with reference to Figure \@ref(fig:cityscale), the ClockBoard zoning system has the following advantages as a basis for choropleth maps: - Simple and consistent zone shapes for easy map reading - The circular shape of zone boundaries make the results easy to place, requiring a 1:1 aspect ratio (except when the zones are clipped, as in map D) -- The shape of the zones draws attention to citywide spatial patterns, with map C highlighting the clear tendency for air quality to improve with distance from the city centre and the comparatively poor air quality in segments 3 and 9 +- The shape of the zones draws attention to citywide spatial patterns, with map C highlighting the clear tendency for air quality to improve with distance from the city center and the comparatively poor air quality in segments 3 and 9 The final advantage is particularly notable when comparing the ClockBoard zoning system with large official zone (borough) boundaries in London. Because of the large and irregular zone shapes in map B, the strength of the relationship between distance from central London and air quality is not as clear as when using ClockBoard zones as the frame of reference in maps C and D in Figure \@ref(fig:cityscale). @@ -454,13 +480,13 @@ This benefit is especially noticeable towards the outskirts of London, where lar # tm1 u = "https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/cityscale.png" -# f = basename(u) -# if(!file.exists(f)) download.file(url = u, destfile = f) -# knitr::include_graphics(f) # for local high-res version, not working -knitr::include_graphics(u) +f = basename(u) +if(!file.exists(f)) download.file(url = u, destfile = f) +knitr::include_graphics(f) # for local high-res version, not working +# knitr::include_graphics(u) ``` -The example of air quality presented in Figure \@ref(fig:cityscale) highlights that the ClockBoard zoning system is well suited for the analysis and visualisation of phenomena in which a central place (London city centre in this case) plays a major role, directly or indirectly. +The example of air quality presented in Figure \@ref(fig:cityscale) highlights that the ClockBoard zoning system is well suited for the analysis and visualization of phenomena in which a central place (London city center in this case) plays a major role, directly or indirectly. (Not all cities have a 'monocentric' structure, something we discuss in Section \@ref(discussion).) The prevalence of particulate matter in the air relates to the level of industrial, transport and other activities in the surrounding area, which clearly increases with proximity to central London. The same can be said of many other phenomena which become more, less, or more and then less, common with distance from central places. @@ -471,82 +497,97 @@ The tragic phenomena of road traffic casualties --- which relate to travel volum ## Inter-city comparison of geographically variable phenomena The ClockBoard zoning system can enable effective comparison between cities by providing a consistent frame of reference. -While official boundaries can vary greatly in size and shape, based on sometimes arbitrary factors such as historic boundaries, ClockBoard zones are always the same size, shape and orientation. -Using the system can provide a basis of evidence-based discussion of a wide range of phenomena. -The example shown in Figure \@ref(fig:intercity) demonstrates this with reference to a policy-relevant example: the number of people killed and seriously injured while cycling in major UK cities. -Addressing issues associated with reporting only number of casualties per unit area, a practice that can miss dangerous places which have a high casualty rate per unit time or distance cycled [@mindell_exposure-based_2012], we show data on the number of people killed and seriously injured while cycling per billion kilometres based on estimates from the Propensity to Cycle Tool [@lovelace_propensity_2017]. +While official boundaries can vary greatly in size and shape, based on sometimes arbitrary factors such as historic boundaries (as shown in Figure \@ref(fig:intercity), top), ClockBoard zones are always the same size, shape and orientation (as shown in Figure \@ref(fig:intercity), bottom). +Using the system can provide a basis of evidence-based discussion of geographically aggregated results representing urban phenomena. +The example demonstrates this with reference to a policy-relevant example: the number of people killed and seriously injured while cycling in major UK cities. +Addressing issues associated with reporting only number of casualties per unit area, a practice that can miss dangerous places which have a high casualty rate per unit time or distance cycled [@mindell_exposure-based_2012], we show data on the number of people killed and seriously injured while cycling per billion kilometers based on estimates from the Propensity to Cycle Tool [@lovelace_propensity_2017]. - -```{r intercity, fig.width=7, message=FALSE, warning=FALSE, fig.cap="Use of the ClockBoard zoning system to support inter-city comparison of policy-relevant data, on road traffic casualties. The maps show the spatial distribution of cycling casualties per billion km cycled, a measure that requires spatial data aggregation for meaningful results.", out.width="85%"} +```{r intercity, fig.width=7, message=FALSE, warning=FALSE, fig.cap="Comparison of administrative zones (top) and zones in the ClockBoard zoning system (bottom) to support inter-city comparison of policy-relevant data, on road traffic casualties. The maps show the spatial distribution of cycling casualties per billion km cycled, a measure that requires spatial data aggregation for meaningful results.", out.width="85%", fig.show='hold'} # download preprocessed data (processing script /data-raw/crashes.R) -df = readRDS(gzcon(url("https://github.com/zonebuilders/zonebuilder/releases/download/0.0.1/ksi_bkm_zone.rds"))) -uk = readRDS(gzcon(url("https://github.com/zonebuilders/zonebuilder/releases/download/0.0.1/uk.rds"))) -thames = readRDS(gzcon(url("https://github.com/zonebuilders/zonebuilder/releases/download/0.0.1/thames.rds"))) +uk = readRDS(url("https://github.com/zonebuilders/zonebuilder/releases/download/0.0.1/uk.rds")) +thames = readRDS(url("https://github.com/zonebuilders/zonebuilder/releases/download/0.0.1/thames.rds")) # df = readRDS("ksi_bkm_zone.rds") # uk = readRDS("uk.rds") # thames = readRDS("thames.rds") # filter: set zones with less than 10,000 km of cycling per yer to NA + +# admin zone version +# download preprocessed data (processing script /data-raw/crashes.R) +df = readRDS(url("https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/ksi_cycl_per_admin_zone.Rds")) +df_filtered = df %>% + mutate(ksi_bkm = ifelse((bkm_yr * 1e09) < 2e04, NA, ksi_bkm)) +tmap_mode("plot") +tm_shape(uk) + + tm_fill(col = "white") + +tm_shape(df_filtered, is.master = TRUE) + + tm_polygons("ksi_bkm", breaks = c(0, 1000, 2500, 5000, 7500, 12500), textNA = "Too little cycling", title = "Killed and seriously injured cyclists\nper billion cycled kilometers\nAdministrative zones") + + tm_facets(by = "city", ncol=4) + + tm_shape(uk) + + tm_borders(lwd = 1, col = "black", lty = 3) + + tm_shape(thames) + + tm_lines(lwd = 1, col = "black", lty = 3) + + tm_layout(bg.color = "lightblue") + +df = readRDS(gzcon(url("https://github.com/zonebuilders/zonebuilder/releases/download/0.0.1/ksi_bkm_zone.rds"))) df_filtered = df %>% mutate(ksi_bkm = ifelse((bkm_yr * 1e09) < 2e04, NA, ksi_bkm)) tmap_mode("plot") tm_shape(uk) + tm_fill(col = "white") + tm_shape(df_filtered, is.master = TRUE) + - tm_polygons("ksi_bkm", breaks = c(0, 1000, 2500, 5000, 7500, 12500), textNA = "Too little cycling", title = "Killed and seriously injured cyclists\nper billion cycled kilometers") + + tm_polygons("ksi_bkm", breaks = c(0, 1000, 2500, 5000, 7500, 12500), textNA = "Too little cycling", title = "Killed and seriously injured cyclists\nper billion cycled kilometers\nClockBoard zones") + tm_facets(by = "city", ncol=4) + tm_shape(uk) + tm_borders(lwd = 1, col = "black", lty = 3) + tm_shape(thames) + tm_lines(lwd = 1, col = "black", lty = 3) + tm_layout(bg.color = "lightblue") + ``` -The results illustrated in Figure \@ref(fig:intercity) show that while London has a high absolute crash rate, it is relatively safe per km cycled. +The results presented in Figure \@ref(fig:intercity) (top) using administrative zones demonstrate the issues with using commonly available zones provided by statistical authorities: areal units vary dramatically in terms of size and shape; and the definition of each city's boundary distorts the results, with Manchester represented by a long and thin region that does not fit well within facetted maps. +The results aggregated at the level of ClockBoard zones, illustrated in Figure \@ref(fig:intercity) (bottom), show overcome these issues. +Because of its high population density and size, London has many small administrative zones that made it hard to understand the levels and spatial distributions of cycling safety in the city. +The results for London presented at the level of ClockBoard zones show a clearer picture that can be compared with other cities: while London has a high absolute crash rate, it is relatively safe per km cycled. The ClockBoard zoning system also allows for aggregation at a consistent spatial resolution, enabling the identification of potential crash hotspots in specific parts of Birmingham (zones D12 and E06) and Sheffield (zone D11). Another example of using ClockBoards to compare cities (and phenomena that take place in them) is shown in Figure \@ref(fig:popdens), which shows population density in 36 major cities using the ClockBoard zoning system not as unit for aggregation but as a reference grid. -The 7 rings A to G cover a radius up to 28 km from the city centre. +The 7 rings A to G cover a radius up to 28 km from the city center. The colors of the panel labels in Figure \@ref(fig:popdens) indicate the continent of the city. The value of comparing cities in a single geographic frame of reference is shown by inspecting Singapore and Sydney with reference to ClockBoard zones. -While these cities have similar total official populations (of 5.8 and 5.3 million people, respectively), based on the number of people with their respective administrative boundaries, the size and shape of each city is very different, highlighted by the fact that in Singapore there are few people beyond ring F (located 15 to 20 km from the centre), while in Sydney (and many other cities) there are substantial numbers of people living in ring I (located 36 to 45 km from the centre). +While these cities have similar total official populations (of 5.8 and 5.3 million people, respectively), based on the number of people with their respective administrative boundaries, the size and shape of each city is very different, highlighted by the fact that in Singapore there are few people beyond ring F (located 15 to 20 km from the center), while in Sydney (and many other cities) there are substantial numbers of people living in ring I (located 36 to 45 km from the center). - + -```{r popdens, fig.cap="ClockBoard for 36 cities. The blue raster grid cells represent open access population estimates from the WorldPop project.", out.width="100%"} -u = "https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/cities_p2.png" +```{r popdens, fig.cap="ClockBoard zoning systems with 7 rings (A to G) supplied used to communicate the spatial distribution of populations for for 36 cities. The blue raster grid cells represent open access population estimates from the WorldPop project.", out.width="100%"} +u = "https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/cities_p2-scale.png" -# For HTML version: -knitr::include_graphics(u) +# # For HTML version: +# knitr::include_graphics(u) -# # For LaTeX version -# f = basename(u) -# if(!file.exists(f)) download.file(u, f) -# knitr::include_graphics(f) +# For LaTeX version +f = basename(u) +if(!file.exists(f)) download.file(u, f) +knitr::include_graphics(f) ``` The administrative borders of six cities shown in Figure \@ref(fig:popdens) are depicted as red lines in Figure \@ref(fig:popdens2), highlighting the importance of sometimes arbitrary city boundaries. The ClockBoard zones applied to Amsterdam not only cover Amsterdam but also a few other small Dutch cities and towns. Most of them are economically attached to Amsterdam, but a few of them also to other major Dutch cites. -The benefits of using a single zoning systems across multiple cities is highlighted by comparing London and Paris. -Official figures suggest that the two cities have very different sizes: the population within their official boundaries depicted in Figure \@ref(fig:popdens2) are 9 million (Greater London) and 2 million (Paris). -However, the metropolitan population, which we define as the population living in the ClockBoard zones (within 28 km from the city centre) of those two cities are similar (about 10 million each). -The example highlights the utility of ClockBoard for communicating not only inter-city differences in the magnitude and spatial distribution of phenomena, but also geographical extent. - - ```{r popdens2, fig.cap="ClockBoard for 6 cities with boundaries shown in red. The blue raster grid cells represent open access population estimates from the WorldPop project; the red lines are administrative borders.", out.width="70%"} u = "https://github.com/zonebuilders/zonebuilder/releases/download/v0.0.2.9000/cities_p1.png" -# For HTML version: -knitr::include_graphics(u) +# # For HTML version: +# knitr::include_graphics(u) -# # For LaTeX version -# f = basename(u) -# if(!file.exists(f)) download.file(u, f) -# knitr::include_graphics(f) +# For LaTeX version +f = basename(u) +if(!file.exists(f)) download.file(u, f) +knitr::include_graphics(f) ``` @@ -554,46 +595,76 @@ knitr::include_graphics(u) -# Discussion and conclusion +# Discussion and conclusion {#discussion} -The ClockBoard zoning system presented in this paper was designed to overcome some well known and long standing issues associated with commonly available administrative zoning systems [@openshaw_optimal_1977; @jelinski_modifiable_1996]. -Despite over 100 years of use in some places, and their design not responding to growth in changes in cities in many others, administrative zoning systems are still often used as the default unit of analysis for urban analysis in many parts of the world. -Instead of tackling the problem by developing new ways to aggregate basic statistical units (BSUs, the basic building blocks of hierarchical administrative zoning systems) the approach taken in this paper is to start from a blank slate and design zoning systems from scratch, with the aim of creating zones that would be intuitively labelled, of consistent size and shape for creating readable and easy-to-interpret maps, and focussed on the central point on monocentric cities. +The ClockBoard zoning system presented in this paper was designed to provide a new tool for visualizing and communicated about geographic data in relation to cities and, more broadly, to provoke discussion of the pros and cons of different zoning systems including possible future systems that have yet to be developed. +Issues associated with administrative zoning systems are well known [@openshaw_optimal_1977; @jelinski_modifiable_1996] yet accessible zoning systems that highlight the importance of areal units are comparatively rare. +Great strides have been made in the design of administrative zoning systems systems and they are understandably the default unit of analysis for urban analysis in many parts of the world [@martin_application_2001; @mokhele_development_2016]. +The dominance of administrative zones in urban analysis has advantages, but also has unintended consequences, including making it hard for people to refer to specific administrative units, irregular sizes and shapes, and lack of comparability between geographically aggregated results from city to city. -Based on these criteria the ClockBoard zoning systems was developed, which consists of regularly spaced rings forming 'dohnuts' (technically annuli) emanating from the city centre and labelled A, B, C etc. At the centre of the ClockBoard zoning system lies zone A, a circle measuring 1 km in radius. -Beyond zone A, each circular annuli is devided 12 evenly spaced segments labelled 1 to 12, with segment 12 representing land due North of the zone A. -The ClockBoard zoning system is a specific implementation of an approach to zone creation that we label concentric segmented annuli; adjusting the sequence of outer ring diameters and number of segments could result in a wide range of alternative zoning systems, each of which would have advantages and disadvantages, just as the ClockBoard zoning system does. +Instead of tackling these problems by developing additional approaches for the "re-aggregation of the raw data into a more +appropriate output geography" [@martin_optimizing_1998], we started from scratch focusing on the key spatial attributes of distance and and bearing from the center. +Our criteria, based on our work in the broadly defined field or Urban Analytics, were: intuitively labelled and easy-to-communicate zones, consistently sized and shaped zones for creating readable and easy-to-interpret maps, and a system that would be accessible for use and modification. -Any such circular zoning system can provide a consistent geographic frame of reference for monocentric cities, or indeed any geographic system with a clear central point. The zones in the ClockBoard zoning system were designed to be sufficiently large so that each could be seen when printed in a low resolution map representing a large city. -The relatively large zones (which get bigger further from the city centre as density of urban phenomena tends to decrease) also enables labels that are easy to communicate. -Zone labels contain only three characters (with the exception of zone A) and and clearly demarcate the location of phenomena in terms of angle and distance from the centre, with zone C09 located between 3 and 6 km to the West of the city centre. -The even growth of rings also enable understanding of the scale of cities and urban phenomena within them, regardless of the size of often arbitrary and historic official boundaries; the first nine rings in the zoning systems (labelled A, B, ... I) grow at constant rate, with radii of 1, 3, 6, 10, 15, 21, 28, 36 and 45 km. - -The consistency of zone sizes and shapes, and the uniform sizes of all ClockBoards that share the same number of rings, could enable more objective and easier to interpret inter-city comparison projects. - -The ClockBoard zoning system is not without limitations, however: it represents a series of compromises in which the tendency was towards simplicity and ease of understanding. -Perhaps the biggest limitation of the system is its implicit assumption that cities are monocentric entities in which urban activity (and hence the need for spatial resolution) declines gradually with distance from the city centre. -While this assumption broadly holds for phenomena such as air pollution in London, as illustrated in Figure \@ref(fig:cityscale), it needs to be relaxed in many other cases [@alidadi_beyond_2018]. -The ClockBoard zoning system can thus be seen as a zoning system best suited for the analysis of monocentric cities, rather than polycentric conurbations. - -A question for further research is how to fit one or several ClockBoards to a dense urban area consisting of several cities, of which none is clearly dominant. +The relatively large zones (which get bigger further from the city center as density of urban phenomena tends to decrease) also enable zone labels with only three characters (with the exception of zone A). +Zone label give insight into their location, with the ClockBoard zone 'E09 Leeds' illustrated in Figure \@ref(fig:location) indicating the fact that it is located between 10 and 15 km West of the city center. +The equivalent official 'MSOA' zone code is 'E02002221': longer, harder to remember, and devoid of geographic meaning. + + + +It is important to emphasize that ClockBoard zoning system is a specific implementation of an approach to zone creation that we label 'concentric segmented annuli' and that a wide family of zoning systems could be created based on the approach: variations can be obtained by adjusting the sequence of outer ring radii (so they have values other than 1, 3, 6, 10, 15 and 21 km, resulting from the triangular number sequence used in the ClockBoard system) and number of segments (with values other than 1 for the central annuli and 12 for all others). +To encourage use of and adaptation of the system, we have implemented methods for creating 'ClockBoards' and other zoning systems based on concentric segmented annuli in R and Python packages, and Rust crate `zonebuilder`. +These can be installed from the '[CRAN](https://cran.r-project.org/package=zonebuilder)', '[crates.io](https://crates.io/crates/zonebuilder)', and '[PyPI](https://pypi.org/project/zonebuilder/)' repositories, respectively. +To further reduce barriers to entry in the creation of ClockBoards to meet specific needs and for fun/education, we have created a simple web application available at [zonebuilders.github.io/zonebuilder-rust](https://zonebuilders.github.io/zonebuilder-rust/) that allows the user to create and download as .geojson files zoning systems based on concentric segmented annuli anywhere in the world. + +The approach is not without limitations, and these include limitations with the specific ClockBoard system, limitations with concentric segmented annuli and 'from scratch' zoning systems that do not follow local features such as rivers and historic boundaries. +In terms of the limitations of the *ClockBoard implementation of the concentric segmented annuli approach*, it is associated with a fairly wide range of zone sizes and shapes, with zone areas ranging from 2 km^2^ in for zones in doughnut B to 33 km^2^ on the outermost doughnut E in a ClockBoard system with 5 rings (and a radius of 18 km). +This variability makes the system unsuitable for analyses requiring uniform areas or uniform populations. +Raster grid cells or administrative zones that keep the population within each zone relatively fixed may be more appropriate in these cases. + +A broader set of limitations apply to *the general approach of using zones of the same size and shape in many to many cities*: +zone boundaries do not follow local features, with ClockBoard zones covering both sides of the River Thames in London, as illustrated in Figure \@ref(fig:london). +This results in 'zone islands', with areas separated from the rest of the zone of which they are part by physical barriers such as rivers and large roads. +The approach leads to zones are more internally diverse than official zone systems, which tend to include similar types of places into the same zone, wish disadvantages when analyzing systems that require cohesive zones. + +Another potential disadvantage of zoning systems that are invariant from place to place is that city borders are usually irregular. +Clipping the zones to official city boundaries can address this issue, but creates an additional problem: unhelpfully shaped and sized zones in the periphery of large cities, also shown in Figure \@ref(fig:london). +To benefit from the standardized zones provided by ClockBoard, we recommend using the system without clipping: ignoring the historic boundary and defining the city bounds with reference to distance from the center can enable inter-city comparison, without being constrained by their historic boundaries. +The benefits of using a consistent bounding area when comparing multiple cities is highlighted by comparing London and Paris. +Official figures suggest that the two cities have very different sizes: the population within their official boundaries depicted in Figure \@ref(fig:popdens2) are 9 million (Greater London) and 2 million (Paris). +However, the metropolitan populations of the two cities --- defined as the population living in a ClockBoard system with 7 rings (within 28 km from the city center) --- are similar (about 10 million each). + + + + + + +A another limitation of the approach is the implicit assumption that cities are monocentric entities in which urban activity (and hence the need for spatial resolution) declines gradually with distance from the city center. +While this assumption broadly holds for many cities such as London and other cities illustrated in this paper, many cities are polycentric [@alidadi_beyond_2018]. +The zoning system is unsuited to polycentric conurbations and the countryside, limiting its uses substantially, to urban analytics focused on monocentric cities. + +Consideration of polycentric settlements raises the question of how to fit one or several ClockBoards to a dense urban area consisting of several cities, of which none is clearly dominant. For instance, the four major cities in the Netherlands (Amsterdam, Rotterdam, The Hague and Utrecht) are small and located about 40 kilometers from each other, with even smaller cities and towns in between. -In this example, there is no dominant "gravitational force" to construct one ClockBoard around. -ClockBoards could be constructed for each of these four cities, raising the question: -how to design zoning systems for polycentric regions, or large regions that contain multiple monocentric settlements [@chandra_multi-objective_2021]? -We explored the possibility of 'joining' ClockBoard systems that met, with the 'dominant' ClockBoard associated with the larger city, but the results were not promising and we suspect that a new approach altogether, perhaps building on experience from Computational Fluid Dynamics, where grid generation procedures need to take into account multiltiple factors [@hernandez-perez_grid_2011]. - -An alternative and approach to developing zoning systems for complex and polycentric settlements not implemented in this paper is to build them on exisiting Discrete Global Grid Systems (DGGS) such as the S2 and H3 global zoning systems developed by Google and Uber respectively [@bondaruk_assessing_2020], and the [QTM Generator](https://github.com/paulojraposo/QTM) developed by Paulo Raposo [@raposo_virtual_2019]. -This would have advantages for flexibility, with DGGSs able to generate grids with zone sizes that are more evidence-based, for example by respondingM to geographic data such as population density. -DGGS based zoning systems would also enable greater determinism, with each of S2's ~7 quintillion ($6 * 4^{30}$ or $\approx6.9*10^{18}$) and H3's ~700 trillion ($\approx5.7 * 10^{14}$) base zones having a unique reference code that is machine readable (ClockBoards are arguably deterministic with 'zone B12, Leeds, UK' referring to an unambiguous area, although ClockBoards depend on an unambiguous definition of 'city centre' which may not be available or requires a single unique source of city centre points). +In this example, there is no dominant "gravitational force" to construct one ClockBoard around, making this a much harder challenge than designing a zoning system for a single city [@chandra_multi-objective_2021]. + +We explored the possibility of 'joining' ClockBoard systems that met, with the 'dominant' ClockBoard associated with the larger city, but the results were not promising and we suspect that a new approach altogether, perhaps building on experience from Computational Fluid Dynamics, where grid generation procedures need to take into account multiple factors [@hernandez-perez_grid_2011]. + +A broader limitation is that the zoning system has not been tested or assessed, other than in informal settings and in a prototype web application, publicly available at [actdev.cyipt.bike](https://actdev.cyipt.bike/ebbsfleet/accessibility,buildings/#11.69/51.4359/0.3065), to present data on aggregate statistics on the quality active travel provision in the areas surrounding new housing developments [@talbot_active_2021]. +While informal and anecdotal feedback has been positive, user testing is needed to identify for which of the potential applications outlined in this paper the ClockBoard system is best suited. +Such user testing could be based on established approaches for evaluating digital products, including focus groups, surveys or interviews with potential users [@trigg_focus_2007]. +Such user testing is beyond the scope of the present paper, but represents a promising future direction of research to establish how the approach could be used in the real world and future research priorities around zoning systems for urban analysis. + +An alternative and approach to developing zoning systems for complex and polycentric settlements not implemented in this paper is to build them on existing Discrete Global Grid Systems (DGGS) such as the S2 and H3 global zoning systems developed by Google and Uber respectively [@bondaruk_assessing_2020], and the [QTM Generator](https://github.com/paulojraposo/QTM) developed by Paulo Raposo [@raposo_virtual_2019]. +This would have advantages for flexibility, with DGGSs able to generate grids with zone sizes that are more evidence-based, for example by responding to geographic data such as population density. +DGGS based zoning systems would also enable greater determinism, with each of S2's ~7 quintillion ($6 * 4^{30}$ or $\approx6.9*10^{18}$) and H3's ~700 trillion ($\approx5.7 * 10^{14}$) base zones having a unique reference code that is machine readable (ClockBoards are arguably deterministic with 'zone B12, Leeds, UK' referring to an unambiguous area, although ClockBoards depend on an unambiguous definition of 'city center' which may not be available or requires a single unique source of city center points). Theses beneficial features would be gained at the expense of simplicity: DGGSs are complex and have hard-to-remember cell IDs such as [e66ef376f790adf8a5af7fca9e6e422c03c9143f](https://developers.google.com/maps/documentation/gaming/concepts_playable_locations) (S2) and [8a283082a677fff](https://h3geo.org/docs/quickstart) (H3); they also have high computational requirements [@bondaruk_assessing_2020], compared with the comparatively simple ClockBoard system. While the utility of the zoning system is likely to be limited in many settings by the limitations outlined above, we believe that there are settings in which ClockBoard could provide substantial benefits, as demonstrated in three example applications. -These demonstrated potential use cases for informal communication about and navigation within cities; exploratory data analysis and visualisation of geographic data within a single city; and visual and quantitative comparison of geographic phenomena between cities. +These demonstrated potential use cases for informal communication about and navigation within cities; exploratory data analysis and visualization of geographic data within a single city; and visual and quantitative comparison of geographic phenomena between cities. Of these, we expect that the last application of ClockBoard, and similar zoning systems, will be of most use to urban analysts and others working with city-scaled datasets. A direction of future research could be to explore the use of ClockBoard and other discrete geometric zoning systems for other applications, for example as the basis of spatial interaction models, building on established work exploring different zoning systems based on BSUs [@openshaw_optimal_1977]. -A broader point is that too much academic research focusses only on a single city, without going to the effort of generalising the findings to multiple cities [@alidadi_beyond_2018; @chandra_multi-objective_2021]. +A broader point is that too much academic research focuses only on a single city, without going to the effort of generalizing the findings to multiple cities [@alidadi_beyond_2018; @chandra_multi-objective_2021]. We hope that the concept of the ClockBoard zoning system presented in this paper, and the ease with which open access data representing 'ClockBoards' for different cities can be created, will encourage more quantitative urban analytical research comparing different cities, building on recent work in the field [@boeing_spatial_2021]. Moreover, we hope that the implementation of the concept in open source software encourages other zoning systems with different attributes to be developed, to meet different criteria than those that motivated the design of the ClockBoard system. diff --git a/vignettes/references.bib b/vignettes/references.bib index e90de46..da55308 100644 --- a/vignettes/references.bib +++ b/vignettes/references.bib @@ -1,3 +1,109 @@ +@Article{trigg_focus_2007, + title = {A focus group study of factors that promote and constrain the use of satellite-derived fire products by resource managers in southern {Africa}}, + volume = {82}, + issn = {0301-4797}, + url = {https://www.sciencedirect.com/science/article/pii/S0301479706000144}, + doi = {10.1016/j.jenvman.2005.12.008}, + abstract = {Semi-structured focus group interviews were employed to examine factors that affect the likelihood that resource managers in southern Africa will use information on vegetation fires provided by two satellite-derived products: an active fire product and a burned area product. The two products are updated regularly and aim to deliver the state-of-the-art in the global monitoring of fires from satellite remote-sensing. Both products are derived from data transmitted by the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors carried onboard NASA's Aqua and Terra satellites. The active fire product can be accessed for free via the internet and on media by users working anywhere in the world; the burned area product will be accessible in a similar manner in 2006. The MODIS fire products provide systematic, near-global coverage and are freely available; as such, they give resource managers new opportunities to obtain or supplement information they need to manage vegetation fires effectively. However, the availability of these products does not mean that resource managers will use them, and many other factors are involved. To understand factors that affect whether southern African resource managers will use the two products, two focus groups were held with members of the Southern African Fire Network (SAFNet) in Malawi, Africa, August 2004. Analysis of the group discussions reveals a number of factors that influence whether they will use the products. The qualitative, in depth nature of the group discussions revealed 12 main factors that influence product use; not least the low international internet bandwidths for African countries outside of South Africa. Analysis of the group discussions also suggests how the uptake of MODIS fire products by resource managers in southern Africa might be enhanced by affecting specific changes to how MODIS products are packaged and delivered.}, + language = {en}, + number = {1}, + urldate = {2021-12-16}, + journal = {Journal of Environmental Management}, + author = {S. N. Trigg and D. P. Roy}, + month = {jan}, + year = {2007}, + keywords = {Fire, MODIS, Utility, Validation}, + pages = {95--110}, +} + +@TechReport{talbot_active_2021, + title = {Active {Travel} {Oriented} {Development}: {Assessing} the suitability of sites for new homes}, + copyright = {CC0 1.0 Universal Public Domain Dedication}, + shorttitle = {Active {Travel} {Oriented} {Development}}, + url = {https://osf.io/7fuq5/}, + abstract = {The location of new housing developments, and the provision of safe space for walking and cycling to key destinations around them, have major and long lasting impacts on travel behaviour, health, and environmental outcomes. Transit Oriented Development (TOD) is a well-recognised concept in urban planning, but systemic evidence is often lacking on the likely ‘active travel performance’ of new developments, making it hard for the planning process to support sustainable transport objectives. This paper articulates the concept of +‘Active Travel Oriented Development’ (ATOD) and describes methods for operationalising it. We demonstrate the use of a set of simple metrics to assess the active travel performance of new and proposed development sites. ATOD has the benefits of building on the established concept of TOD and being easy to assess. We conclude that ATOD, and tools for measuring it, are needed to ensure that transport and development policies work in harmony.}, + urldate = {2021-09-28}, + institution = {OSF Preprints}, + author = {Joseph Talbot and Martin Lucas-Smith and Andrew Speakman and Megan Streb and Simon Nuttall and Dustin Carlino and Patrick Johansson and Nathanael Sheehan and Nik{\a'e}e Groot and Robin Lovelace}, + month = {sep}, + year = {2021}, + doi = {10.31219/osf.io/7fuq5}, + note = {type: article}, + keywords = {Geography, Social and Behavioral Sciences, Spatial Science, Urban Studies and Planning, active travel, planning, residential development, transport}, +} + +@Article{mokhele_development_2016, + title = {Development of census output areas with {AZTool} in {South} {Africa}}, + volume = {112}, + number = {7-8}, + journal = {South African Journal of Science}, + author = {Tholang Mokhele and Onisimo Mutanga and Fethi Ahmed}, + year = {2016}, + note = {Publisher: Academy of Science of South Africa}, + keywords = {⛔ No DOI found}, + pages = {1--7}, +} + +@Article{martin_optimizing_1998, + title = {Optimizing census geography: the separation of collection and output geographies}, + volume = {12}, + shorttitle = {Optimizing census geography}, + doi = {10/bqqm35}, + number = {7}, + journal = {International Journal of Geographical Information Science}, + author = {David Martin}, + year = {1998}, + note = {Publisher: Taylor \& Francis}, + pages = {673--685}, +} + +@Article{martin_application_2001, + title = {The application of zone-design methodology in the 2001 {UK} {Census}}, + volume = {33}, + doi = {10/fr8qtc}, + number = {11}, + journal = {Environment and Planning A}, + author = {David Martin and Abigail Nolan and Mark Tranmer}, + year = {2001}, + note = {Publisher: SAGE Publications Sage UK: London, England}, + pages = {1949--1962}, +} + +@Article{zhang_detecting_2021, + title = {Detecting {Colocation} {Flow} {Patterns} in the {Geographical} {Interaction} {Data}}, + volume = {n/a}, + issn = {1538-4632}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/gean.12274}, + doi = {10/gnrs75}, + abstract = {The detection of colocation pattern is an important and widely used method to analyze the spatial associations of geographical objects and events. Existing studies primarily focus on discovering colocation patterns and association rules based on point data. A broad range of flow data types, such as population flow, logistics, and information flow, have emerged in recent years. However, colocation patterns and association rules based on flow data are difficult to detect because of their complex structure. This work proposes a colocation pattern detection and spatial association rule discovery approach that treats origin-destination (OD) flow as Boolean spatial features, while considering the spatial proximity of the origins and destinations of OD flows and its direction similarity. The effectiveness of this approach is verified by an artificial data set. Finally, this work analyzes the data of tourists who are traveling from different countries or regions to diverse cities in China. It also proves the application value of the proposed approach, which has general applicability to the mining of colocation patterns and association rules from any type of OD flow data.}, + language = {en}, + number = {n/a}, + urldate = {2021-12-13}, + journal = {Geographical Analysis}, + author = {Haiping Zhang and Xingxing Zhou and Guoan Tang and Xueying Zhang and Jing Qin and Liyang Xiong}, + year = {2021}, + note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/gean.12274}, +} + +@Article{bolitzer_impact_2000, + title = {The impact of open spaces on property values in {Portland}, {Oregon}}, + volume = {59}, + issn = {0301-4797}, + url = {https://www.sciencedirect.com/science/article/pii/S0301479700903517}, + doi = {10/fqhp6p}, + abstract = {Open spaces such as public parks, natural areas and golf courses may have an influence on the sale price of homes in close proximity to those resources. The net effect of open-space proximity is theoretically uncertain because the positive externalities associated with proximity such as a view or nearby recreation facility might be outweighed by negative externalities, for example, traffic congestion and noise. The impact of open-space proximity and type is examined empirically using a data set that includes the sales price for homes in Portland, Oregon, a major metropolitan area in the United States, geographic information system derived data on each home’s proximity to an open-space and open-space type, and neighborhood and home characteristics. Results show that proximity to an open-space and open-space type can have a statistically significant effect on a home’s sale price. These estimates provide an important step in quantifying the overall benefit from preserving open spaces in an urban environment.}, + language = {en}, + number = {3}, + urldate = {2021-12-12}, + journal = {Journal of Environmental Management}, + author = {B Bolitzer and N. R Netusil}, + month = {jul}, + year = {2000}, + keywords = {economics., hedonics, open spaces}, + pages = {185--193}, +} + @Article{bondaruk_assessing_2020, title = {Assessing the state of the art in {Discrete} {Global} {Grid} {Systems}: {OGC} criteria and present functionality}, volume = {74}, diff --git a/vignettes/responses.Rmd b/vignettes/responses.Rmd new file mode 100644 index 0000000..ff8f42b --- /dev/null +++ b/vignettes/responses.Rmd @@ -0,0 +1,273 @@ +--- +output: pdf_document +--- + +```{r, echo=FALSE, eval=FALSE} +# render the output to github +rmarkdown::render(input = "vignettes/responses.Rmd", output_file = "responses.md") +rmarkdown::render(input = "vignettes/responses.Rmd", output_file = "responses.pdf") +``` + +Dear Editor, + +Many thanks for the invitation to resubmit and to the reviewers for detailed and constructive comments. +We are confident that we have responded to every comment from the reviewers and that the paper is greatly improved as a result, particularly with regard to the discussion of the limitations of the system and how it could realistically be used in practice. + +The comments below are presented in order and numbered to ease any further discussion, with the review comments and then our response below. + +# Reviewer B: + +The authors present a good case for a new zoning system, based on annuli and radii, forming a web-type structure called ClockBoard. This zoning system is said to be a new approach that would add to more popular grid-based and even-more-popular administrative zone system. The authors put forth an R package that allows users to create this system, and give two examples of air quality, and traffic casualties using the ClockBoard system. + +This paper is relevant to JOSIS because it takes on a fundamental GIScience representation issue, and is driven by technology. It is pertinent to the journal and I think readers would enjoy it. + +1. Because this paper is a bit theoretical, there is not much empirical evaluation. Regarding evaluation, there is no user study done, but perhaps there does not need to be at this juncture. The example of the clock board viz in Figure 6 is very helpful and illustrative of what this method could do for geographers. For figure 7, could the authors add what the traffic deaths look like with the more traditional administrative boundaries? This would help as well. + + **Response:** This is an important point: we are not claiming that the ClockBoard system is an ideal solution but that it has certain advantages for comparing the geographic distribution of variables between monocentric settlements. + Visualisation of the data shown in Figure 7 using administrative zones could make this point more clearly and we thank the reviewer for this idea. + We have updated Figure 7 to include 'before' and 'after' representations of road traffic casualty data using administrative zones and ClockBoard zones. + +1. The limitations section left me a bit wanting---there are significant limitations that should be pointed out more clearly. First, curved administrative boundaries do not work well with our ‘straight line’ bounding boxes—the ridge shape is a bit hard and is divorced from natural features we are used to seeing (albeit not with grids). Secondly, and relatedly, many administrative units that we use tend to follow waterways or roads, making them quite handy dividers. This method does not allow for this. Also, we get quite a bit of knowledge about the city form (like poly-centricity and the expanse of the urban downtown) from these administrative units---that is lost with this method. A strange artifact, as well, are cities that are halved by a water body, like Chicago. They only get a half a clock, whereas another inland city gets a whole clock. These limitations need to be stated more clearly. + + **Response:** We agree that these more immediate issues were not addressed sufficiently in the paper. We have updated the limitation section with a more comprehensive and firmer discussion of the limitations of the approach which should help the reader understand the circumnstances when the proposed zoning system is, and is not, likely to be appropriate. The limitations were too focussed on the assumption that the user needed a zoning system to compare two or more cities based on the preceding section but of course this is not the case and previously unspoken assumptions about what the reader may intend to do, and how that may impact the suitability of different zoning systems, are now stated explicitly. + See the 'diff.pdf' file for details. + +1. I am not quite certain that the ‘meeting up’ portion of this paper serves as sufficient data for justifying this system, but perhaps others understood and were more convinced by it. It seems as though if you have city knowledge already it seems much easier to point out a landmark. + + **Response:** We agree that the example was not described convincingly or realistically, but would counter that the purpose of the section was not to justify the system. The purpose of the section is to continue to introduce the system and how it could be used in a variety of ways. The primary and strongest use case is, as reviewers say, to present the geographical distribution of variables in a consistent way between different monocentric settlements. We considered removing this section but think that the section serves will to 'build up' the concept from verbal description of locations -> visualisations of a single city -> inter-city comparisons. To address the issue we have re-written the section focussing on what the zonebuilder system is and how zones are referred to with concrete examples, focussing on the places and distances from the centre rather than the specific (and we agree rather implausible and unhelpful) hypothetical example of guiding someone around the city: we keep the examples of Leeds rail station, Roundhay Park and Bradford as they demonstrate how the system can indicate bearing and distance from the center. + +1. Regarding significance, this paper is mid-level but I do find the paper to be very creative and original. the motivation for this work is well-founded and sufficient literature has been presented. I would suggest that authors include literature on bottom-up regionalization (that is, creating zones based on modularity partitioning of origin-destination networks) and ‘what-3-words’—pardon if I missed this. I would like to hear from more actual administrators who may use these new zones on what their opinion may be. It may help to interview a few. + + + **Response:** We agree that the approach of 'bottom-up regionalisation' based on origin-destination data is interesting and worthy of mention. While the approach does not address the central problem that the ClockBoard system was designed to tackle --- creating a simple and easy-to-use division of space for inter-city comparison of geographically variable phenomena --- because zone sizes and shapes would vary from city to city, it is relevant in the introductory comments on the importance of zoning systems and how to create zoning systems that are appropriate for different purposes. We could not find much literature on the topic, however, and after searching [Google Scholar](https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=zones+origin-destination+data) and Web of Science decided to describe the approach briefly in the introductory sentence, with reference to a recent paper (Zhang et al. 2021) on the related process of detecting colocation flow patterns. + +1. I suspect that the method will be useful, but in fewer cases than originally purported. One of the strongest features seems to be the earmarking system with the B3, F12, etc. which, as stated, is helpful to let the user know automatically how far from the city they are and what direction. This is a nice contribution. In addition, the arbitrary starting point of a grid is solved a bit by this method. Comparing across cities seems like a great use for this method. + + **Response:** We agree that the approach could be useful only in a few specific cases, but we are not sure which areas, if any, it will see use. To deal with this uncertainty, and to deal with comments to the effect that the paper makes broad claims, with have rewritten many sections to be more modest in our claims. In response to this comment (and also responding to other comments) we have shifted the emphasis of the first section on applications away from navigation and towards labelling places. While being less sweeping in our statements about the method, we also focus more on what seems to be it's key strength: inter-city comparison of geographic data. + +1. The presentation is generally good and clear to follow. Again, the limitations section should be more forthright, as this new method does have some significant drawbacks. I have a few recommendations: + + **Response:** We have rewritten much of content on limitations, which is now more clear and direct. + +1. P 2: “
to represent lines of equal height, and
population density.” I found it odd to bring up contour lines when the authors are specifically talking about continuous space. I realize that these lines demarcate continuous space, but they are rarely used to actually do this. Please remove. At the same time, it is very undervalued that you cannot do table joins with the clockboard method, as you could when aggregating to existing units. (More for the limitations.) + + **Response:** We agree, this was not helpful. The sentence is now shorter and clearer: "This has been done using lines representing points with equal journey time from locations (isochrones) and the areas bound by them" + +1. P 3: OSM is also odd to bring up as ‘emerging datasets’---it doesn’t have any thematic data, which I think is a big selling point of your method. At least the case studies on pollution and traffic suggest so. Please substitute it. + + **Response:** We agree, OSM was not the most relevant example. We have rewritten the text to highlight the impact of new datasets and approaches for comparing multiple cities, now supported by a new citation: "There is demand for visualisations techniques to represent new urban datasets within and cities, with the shift away from single-city case studies towards multi-city comparison research" + +1. P 3: Can you elaborate on reference [21], it sounds important. + + **Response:** This is indeed an important (and we believe under-cited) reference. We have updated the text to explain the core findings from this paper. + +1. P 3: Paragraph starting with “Pre-existing zoning systems” does not seem to belong here. It seems to need to come earlier. + + **Response:** We agree and have moved the paragraph to earlier in the introduction. We have also shortened and simplified what was a rather clunky paragraph. + +1. P 4: “Modelling urban cities
” bullet point is quite vague and I’m not sure what it adds. + + **Response:** We agree and have removed the bullet point. We also noticed that the preceding bullet point contained to points and have divided it in two. + +1. P 6: “The trueism is often reflected
.” Census zones are way more popular than TAZes, I found this odd to mention TAZes instead. + + **Response:** we have re-worded this section and indeed the paragraph to make it clearer. TAZs are, like other types of zoning system, designed with a particular use in mind and this is worthy of mention. + +1. Table 1: Please make it clearer that N. zones is cumulative. + + **Response:** Good point that we missed. We tried altering the column heading to say (cumulative) but found that this issue is best resolved by making it clear from the table caption what the datasets are referring to. The meaning of the table is now clearer and mentions concrete examples that should make it clear that ClockBoard systems of different sizes are appropriate for cities of different sizes. + +1. —one part of ‘o clock may need to be lowercased. + + **Response:** Godo point, just realised: o'clock is correct, not O'clock. Fixed! + +1. -P 8: does “Tokyo” call anything when it’s used as a variable in ClockBoard_Tokyo? Please clarify. + + **Response:** Yes, it calls the Nominatim geolation service. This is now explained. + +1. -Fig 8: Could you please provide a scale bar? + + **Response:** A scale bar, highlighting the fact that the radius of a ClockBoard system with 7 zones is 28 km, has been added. + + +# Reviewer C: + +This paper proposes a new process for subdividing metropolitan areas into monocentric, areally consistent regions to enable more easy cognition and orientation. I will provide comments below in the framework JOSIS provides. + +**Scientific and technical quality:** Is the submission technically sound? Are the submission\'s claims and conclusions adequately supported? + +The submission is technically comprehensive in terms of explaining the +logics for deducing the rings and segments within each ring and how this +would be comparable across cities. Fundamentally, this paper seems to be +addressing the modifiable areal unit problem (MAUP) and makes an attempt +to create generalized regions within the city. While I think the +technical considerations of the MAUP is thoughtful, the submission's +main claims are not clear in terms of how this framework's will resolve +a broad range of use case issues in the current framing of this paper. +Because I consider these issues to align more with "Evaluation" and +"Significance" questions, I will address my main comments and concerns +there. + +1. One small point in this section: The authors did not explicitly state +why the areal unit is problematic and it would be helpful for the reader +to be explicit about stating this. The same holds true for authors' +mention of "continuous space" and why it is particularly important. + + **Response:** We agree that the problem statement can be made more explicitly. Therefore, we reorganized the introduction to make the problem statement clearer. + +**Evaluation:** + +Does the paper present an objective (experimental or +theoretical) evaluation of its results? If not, how are the results +evaluated, and is the evaluation convincing? + +1. The authors state that "A number of approaches have tackled the question +how to best divide up geographical space for analysis and visualization +purposes, with a variety of applications." (pg. 2), which seems to be +one iteration of their objectives in this paper. On pg.4 of the paper, +the authors seem to have another more specific set of criteria that +drive the motivations or use cases for this new type of regionalization. +It's still not clear to me what is the primary motive for creating these +zones are, as none of them seem to address the MAUP problem of +regionalizing space. + + **Response:** The overall aim of the paper is now more clearly stated as follows: "The overall aim of this paper is to highlight the potential for new zoning systems to support urban analysis." We think it relevant to metnion the history of approaches to generate zones and have updated the introduction to make it clear that our aim is not to tackly the MAUP directly, but to provide a new way of demonstrating its effects (visible in the figure of air polution data in London aggregated by administrative zones and by ClockBoard zones). We have also rewritten parts of the discussion to emphasise the fact that the zoning system does not solve the MAUP but provides alternative ways of dividing space up that highlight its impact when default administrative zones are used 'blindly'. + +1. While I think this may be beyond the scope of this paper, I think a true +evaluation of the success of this framework would be something along the +lines of a user survey in addition to explaining the technical rationale +behind these spatial configurations. I see the main use case of the +ClockBoard aligned with subjects like UX/UI design or a Lynchian study +of how people make mental maps and navigate the city [^1]. + + **Response:** We agree that this would be a useful next step for the research. + The fact that there are different possible use cases for the proposed system makes evaluation based on user survey or other means of data collection would be worthwhile. + While that study is beyond the scope of this paper, which focusses on the design of the proposed zoning system and discussion of the importance of alternative zoning systems for urban analysis, we would like to take the ideas forward in future work and have outlined new ideas for that motivated by this comment in the discussion. + +1. One aspect of the design of the framework that was unclear to me is the +monocentric orientation of the city, with each region created based on +distance from the city center. This type of spatial orientation seems +mainly to apply to transit related fields or theoretical understandings +where the distance to the "center of the city". While I appreciate the +importance of this type of analysis, it seems somewhat arbitrary and far +from having "a variety of applications". For instance, in most +non-transit planning scenarios, the spatial configurations of certain +types of communities (for ex: public housing) and their relationship to +gentrifying areas is the primary way policy-makers think about the city. +Another way to think about the city, for residents of a city, who might +have a different mental map that is ego-centric, may be composed on +landmarks around the city familiar to them. + + **Response:** + + We agree that we were at times too vague and sweeping in our statements about the utility of the zoning system presented. + We have made the discussion of applications more specific and clear, including with reference to an updated Figure 7, which now demonstrates specifically the advantages of the zoning system presented over UK administrative boundaries. + For example, we have replaced the following wide ranging sentence with a more specific and clear sentence in the discussion of Figure 7: + - Before: *Using the system can provide a basis of evidence-based discussion of a wide range of phenomena.* + - After: *Using the system can provide a basis of evidence-based discussion of geographically aggregated results representing urban phenomena.* + +1. A minor point regarding comparison across different cities: I don't +think the last paragraph on p.13 was clear in terms of what it is trying +to show. It is not clear to me why the inclusion of the metropolitan +region in this example shows the advantages of ClockBoard. Many urban +administrative boundaries and maps only show certain areas because the +broader metropolitan region is beyond its jurisdiction, which is not +necessarily a limitation of administrative boundaries but the nature of +governance systems. + + **Response:** We agree that this paragraph was not clear. We have removed it and made the comment in the discussion, which is the more appropriate place for it. + + **Significance:** How important is the work reported? Does the +submission address a challenging theoretical or practical issue? Does +the work integrate ideas from, or have interesting implications across +multiple disciplines? + +1. The problem statement and the significance of this work is not quite +clear to me: In the first paragraph, the authors seem to suggest that, +because the process of creating areal units is contingent on the +objective for creating the units, there is no one process that satisfies +all possible objectives, which I don't necessarily see as a technical +problem but a governance or civic administration issue. Moreover, it is +unclear why the authors choose to highlight the "blank slate" quality of +this approach. + + **Response:** We have updated the introduction and discussion sections to clarify the problems that the approach sets out to tackle, the motivation, and the overall aim of the paper (which is NOT to solve the MAUP). + Overall, the paper is now more modest and specific in its scope. + The 'blank slate' nature of the approach is worth highlighting, we believe, because it differs from the 'BSU grouping' approach that seems to predominate in the literature. + +1. Fundamentally, the overall objective, target audience, and use cases are +perhaps not what the authors suggest. The authors suggest a somewhat +broad notion of "analysis" and "visualization", but it seems to me that +the ClockBoard proposal simultaneously proposes one way to address the +MAUP problem that has a use case of navigating cities if one is not +familiar with the city. It is difficult for me to image analysts working +with these zones for inter-city comparison as the sample size is small. +Thus, there is a discordance between the stated objective and what this +framework produces. + + **Response:** We have rewritten relevant parts of the paper to emphasise the fact that there are a range of possible users, alongside the limitation that we have not done formal user-testing. We have now cited a paper that makes use of the zoning system in an urban analysis project to support visualisation of active travel provision in the area directly surrounding new housing developments: see https://actdev.cyipt.bike/ebbsfleet/accessibility,buildings/#11.69/51.4359/0.3065 for an example of how the zoning system can support visualisation. While we believe it has use cases in urban analysis, we are not sure it will catch on or if other use cases will emerge. In face of this uncertainty our approach is to try to be specific and humble about the possibilies of the system, while advocating research into alternative zoning systems that overcome some of the limitations associate with the ClockBoard system. + + **Originality:** Does the submission address a new issue, present a new +approach to an issue, or put forward a novel combination of existing +ideas or techniques? Does the submission correctly situate itself within +the context of existing research literature? + +1. There is sufficient originality in this work to justify publication of +the paper with edits to its framing. The paper mentions similar research +and frameworks that are relevant. I think the authors should take care +to limit the use cases and promises of this framework, for reasons +previously mentioned. + + **Response:** We agree and, in line with other comments, have reframed key parts of the paper, including its aims, target use cases (not navigating around a city!) and potential uses. We have also beefed up the limitations and future research that could help overcome these limitations. + + **Style and presentation:** Is the submission clearly written and +logically structured? Does the submission provide adequate motivation +and interesting conclusions? Are the results clearly described and +critically evaluated? + +1. A major issue with this paper is its structure in the introduction which +I found very difficult to navigate given the diverse range of geographic +aggregation issues (for ex: the section about lack consideration for +point data in administrative boundaries), the "blank slate" nature of +the framework, the "continuous space" issue, all of which seem somewhat +tangentially related to the core questions at hand. Also, as I mentioned +above, the objective of this paper is unclear. + + **Response:** We have have updated the introduction to make the objectives more clear and narrowly focused. + I think the 'blank slate' vs 'continuous space' issue could be a bit confusing and we have focussed more on the 'blank slate' zoning system vs 'BSU grouping' approaches to generating zones for urban analysis. + +1. Another major source of confusion is the use of the term 'zones' or +'zoning'., In the urban context, it generally refers to a system of +municipal land use regulation, which is then borne out in the +specification of regions, and not necessarily the concept of +discretizing space that addresses the MAUP problem suggested here, as I +understand this paper. + + **Response:** We have now defined 'zone' and 'zoning' upfront. We agree the terminology was at times confusing and we have tightened it up in this updated submission. + +1. Other minor stylistic notes: + + \- Should be 'flexible' (not 'fexible') in the abstract. + + \- pg.4 'miniminput' should be 'minimum input' ? + + \- p.2 Not sure what 'heigh' is in reference to? + + **Response:** Thanks for these issues. We fixed all of them. + + **Scope and relevance to JOSIS:** Is the paper closely related to the +themes of the journal? Is the content interesting to the journal +readership? Is the submission written in a form readable for a +multi-disciplinary audience? + +1. With some reframing and reworking of the structure, I think this paper +is appropriate for JOSIS and the content would be interesting to the +journal's readership. It presents applications that may be of interest +to a general audience. + + **Response:** We agree that this paper will be of interest to JOSIS readers and thank the reviewer for the suggestions that we think have improved the structure and framing. + +[^1]: Kevin Lynch, *The Image of the City*, vol. 11 (Cambridge, MA: MIT + press, 1960). + +# References \ No newline at end of file diff --git a/vignettes/zonebuilder-paper.tex b/vignettes/zonebuilder-paper.tex new file mode 100644 index 0000000..8cb343b --- /dev/null +++ b/vignettes/zonebuilder-paper.tex @@ -0,0 +1,831 @@ +%% josis.tex 1.4 2016-09-15 JoSIS latex template +%------------------------------------------------------------------ +% Filename: josis_template.tex +% +% This file is intended as a template for typesetting articles for the +% +% Journal of Spatial Information Science. +% +% Please edit this template to generate your own formatted manuscripts +% for submission to JOSIS. See http://josis.org for further details. +% + + +%%% JOSIS checks in typesetting +%%% * All titles and sections lower case *EXCEPT short title [ ] +%%% * Remove author postal addresses, only have geographic places and institutions [ ] +%%% * Consistent use of Section, Figure, Table (capitalized and in full) [ ] +%%% * 10 keywords (and all lower case) [ ] +%%% * Remove all avoidable footnotes [ ] +%%% * Use double quotation marks (``'' not "" or `') [ ] +%%% * Punctuation inside quotations [ ] +%%% * E.g. and i.e. followed by comma [ ] +%%% * cf. followed by tilde [ ] +%%% * Itemize and enumerate correctly punctuated [e.g., "1. x, 2. y, and 3. x." ] +%%% * And/or lists using American English punctuation (e.g., "x, y, and z") [ ] +%%% * Bibliography (e.g., en-dashes for number ranges, consistent "Proc.~" for Proceedings of..., etc.) [] +%%% * Acknowledgment style use section* [ ] +%%% * et al. no italics, but with dot [ ] +%%% * All captions end with full stop [ ] +%%% * Table captions under, not over table [ ] +%%% * Adjust urls with burlalt [ ] +%%% * Check correct use of hyphens, emdashes, endashes [ ] +%%% * Perform spell check [ ] + +%%% JOSIS checks directly before publication +%%% Check DOI, page numbers on article and web site. [ ] +%%% Update web site with final title, abstract, keywords. [ ] +%%% Build with distiller for DOI links. 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\csllabelwidth}{#1}\break} +\newcommand{\CSLIndent}[1]{\hspace{\cslhangindent}#1} + +% Article details for accepted manuscripts will be added by editorial staff +% Omit year if article in press +% Omit number if article under review +\josisdetails{% + number=N, year=YYYY, firstpage=xx, lastpage=yy, + doi={10.5311/JOSIS.YYYY.II.NNN}, + received={August 12, 2021}, + returned={November 11, 2021}, + revised={December 18, 2021}, + accepted={}, } + +\newcommand{\mydoi}[1]{\href{http://dx.doi.org/#1}{doi:\protect\detokenize{#1}}} + +%\renewcommand{\UrlLeft}{http:\sslash} +%\DeclareUrlCommand\myurl{\def\UrlLeft{}\def\UrlRight{}% +%\urlstyle{tt}} + +\urlstyle{rm} +\makeatletter +% Inspired by http://anti.teamidiot.de/nei/2009/09/latex_url_slash_spacingkerning/ +% but slightly less kern and shorter underscore +\let\UrlSpecialsOld\UrlSpecials +\def\UrlSpecials{\UrlSpecialsOld\do\/{\Url@slash}\do\_{\Url@underscore}}% +\def\Url@slash{\@ifnextchar/{\kern-.11em\mathchar47\kern-.2em}% + {\kern-.0em\mathchar47\kern-.08em\penalty\UrlBigBreakPenalty}} +\def\Url@underscore{\nfss@text{\leavevmode \kern.06em\vbox{\hrule\@width.3em}}} +\makeatother + +\hypersetup{ +colorlinks=true, +linkcolor=black, +citecolor=black, +urlcolor=black +} + +% Add the running author and running title information +\runningauthor{\begin{minipage}{.9\textwidth}\centering , \end{minipage}} +\runningtitle{The ClockBoard Zoning System} + +% Document begins +\begin{document} +%\setcounter{page}{33} + + +% Insert your own title +\title{ClockBoard: a zoning system for urban analysis} + +% Insert your manuscipts authors, affiliations, and addresses + \author{Robin Lovelace}\affil{Institute for Transport Studies and Leeds Institute for Data Analytics, University of Leeds, UK} + \author{Martijn Tennekes}\affil{Department of Methodology, Statistics Netherlands, The Netherlands} + \author{Dustin Carlino}\affil{Independent Software Engineer, Lead Developer of A/B Street, USA} + +\maketitle + +% Add 5-10 keywords for every submission +\keywords{zoning, areal data, zoning systems, modifiable area unit problem} + +% Add a short abstract of 150-250 words +\begin{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 flexible, 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. +\end{abstract} + +\hypertarget{introduction}{% +\section{Introduction}\label{introduction}} + +Zoning is the process of generating areal units for aggregating, visualizing, and potentially modeling geographic datasets. +The resulting zones --- also commonly referred to as `areal units' or `small areas' in the literature --- have long been used to support analysis of human systems. +Historical examples highlighting the importance of zone layouts include `tithe maps' determining land ownership and taxes in 18th Century England {[}1{]} 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 {[}2{]}. + +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 {[}3{]}. +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 is a manifestation of the modifiable area unit problem (MAUP), 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'' {[}4{]}. +Our aim in this paper is not to tackle the MAUP directly, but to provide a `ready made' zoning system that can demonstrate some of its effects by providing another way to aggregate and present data. + +Prior work has demonstrated the sensitivity of urban analysis outcomes to zone system design, from the way cities are visualized to the \href{http://www.iasi.cnr.it/ewgt/13conference/145_binetti.pdf}{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) {[}5,6{]}. +Although the range of outcomes is a finite combinatorial optimization 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'' {[}7{]}. + +Pre-existing zoning systems are often based on administrative regions and reflect the hierarchical organizational structure of statistical agencies. +Well-designed administrative zones are advantageous for many applications, especially in relation to aggregated administrative datasets, but have disadvantages for certain applications. +First, the administrative regions often change over time, hindering spatio-temporal analysis. +Second, since the administrative zones have different sizes and shapes in different cities, they may not be ideal when comparing cities. +In order to address these shortcomings of zoning systems based on administrative regions, our aim in this paper is to build a zoning system from scratch, i.e.~to divide a \emph{continuous} geographic space into zones \textbf{starting from a blank slate}. + +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. +The statement that ``existence of individual or non-spatially aggregated data is rare in geography'', used by {[}7{]} to justify the BSU grouping approach, may have been true in the 1970s when it was written. +Today dis-aggregated geographic datasets are common. +Open datasets exist on phenomena including 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 visualization purposes, with a variety of applications. +Functional zone classification is common in the field of remote sensing and associated sub-fields involved in analyzing and classifying raster datasets {[}8,9{]}. +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. +Approaches to creating zoning systems \emph{starting from} origin-destination have also been developed {[}10{]} and, although these approaches tend also to start from BSUs, they could be extended to generate `bottom up' datasets starting from individual-level GPS type datasets. + +In this paper we are interested in the division of \emph{continuous space} into completely new areal systems. +This has been done using lines representing points with equal journey time from locations (isochrones) and the areas bound by them {[}11{]}, population density (isopleths) {[}12{]} and model parameters which continuous geographical space {[}13{]}. +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 {[}14{]}. The approach has been used to generate spatial entities including roads {[}15{]}, indoor layouts of buildings {[}16{]} and urban layouts {[}17{]}. 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 visualization {[}18{]}. +However, no previous research has demonstrated the creation of zoning systems specifically for the purposes of urban analysis. + +New visualization techniques are needed to represent new (or newly quantifiable) concepts and emerging datasets (such as OpenStreetMap) in urban analysis. +The visualization 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 {[}19{]}. Circular visualization techniques, in the form of rose diagrams, were used in a more recent study to indicate the most common road directions relative to North {[}20{]}. The resulting visualizations 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 {[}21{]} . 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 {[}22{]}. 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 {[}23{]}. + +Unlike BSU based zoning systems, the use of rectangular grids or `quadrats' was common {[}22{]}. +The approach was particularly useful before administrative zones became widespread. +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. + +However, 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; specifying the lines that define them ensures that they do not change over time, unlike administrative regions. +Like the zoning system presented in this paper, grid tiles depend on a CRS and may become distorted over large (continental) spatial scales (this is not much of an issue for zoning systems that only aim to provide zones for a single city at a time like that presented here). +Another downside from a statistical perspective is that population density tends to increase towards a central point. +As a consequence, smaller zones are often preferable in denser areas, which often means towards the city center: for this reason administrative regions are often smaller in central areas and larger on the outskirts of cities, as illustrated with reference to London in Figure \ref{fig:cityscale}. + +The overall aim of this paper is to highlight the potential for new zoning systems to support urban analysis. +We do this by presenting a zoning system that enables inter-city comparison using zones of the same size and shape regardless of the city's location, which can be generated rapidly and in a reproducible manner with minimal data requirements. +The specific motivations for embarking on the idea, and its implementation in open source software, were as follows: + +\begin{itemize} +\item + Locating phenomena in cities. + Automated zoning systems based on a clear center-point can support map interpretation by making it immediately clear where the city center is, and what the scale of the city is. +\item + 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. +\item + Aggregation for descriptive statistics. + It is often useful or necessary to present geographical data in an aggregate form. + A consistently sized and shaped set of zones can support attractive, clear and meaningful visualization. +\item + Comparing 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. +\end{itemize} + +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. + +\hypertarget{clockzs}{% +\section{The ClockBoard zoning system}\label{clockzs}} + +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 modelers and others working with geographic data across cities are diverse, but all rely on zoning systems as a foundation for modeling and visualization. +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, modeling and wider research, visualization and communication requirements of zoning systems, we developed the following criteria for successful zoning systems. +Zoning systems for urban analysis should: + +\begin{itemize} +\tightlist +\item + contain intuitively named zones, enabling public communication of research, e.g.~with reference common perceptions of space in terms of distance from the city center and direction relative to North +\item + have a well-balanced number of zones since too many or too few zones may cause issues with analysis and visualization + be easy to visualize without too many or too few zones +\item + include zones of consistent and useful sizes, for example with zone areas increasing with distance from the urban centers to reflect relatively high densities in central locations +\item + 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 +\item + be extensible and based on open source software, enabling others to create alternative zoning systems suited to diverse needs +\end{itemize} + +Considering the above criteria, we explored many zoning options, some of which are illustrated in Figure \ref{fig:options}. +Two key concepts that make up the zoning system described in this paper are concentric annuli and segments defined by radii. + +\begin{itemize} +\item + \textbf{Concentric rings} --- formally called `concentric annuli' --- which emphasize central locations and have been used to explore the relationships between the characteristics of `focal trees' and surrounding trees in ecological research {[}24{]}, as shown in Figure \ref{fig:options} (A). +\item + \textbf{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 \ref{fig:options} (B). +\end{itemize} + +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 \ref{fig:options} (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 organizing 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. + +\begin{figure} + +{\centering \includegraphics[width=0.32\linewidth]{zonebuilder-paper_files/figure-latex/options-1} \includegraphics[width=0.32\linewidth]{zonebuilder-paper_files/figure-latex/options-2} \includegraphics[width=0.32\linewidth]{zonebuilder-paper_files/figure-latex/options-3} + +} + +\caption{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.}\label{fig:options} +\end{figure} + +\hypertarget{annuli-radii}{% +\subsection{Annuli radii}\label{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 center than the preceding annulus, as shown in Figure \ref{fig:options} (C) --- or by varying amounts. +In many cases it is useful for zones to be smaller near the center of the study region surrounding cities, whether the zones are used for the publication of statistical data (often referred to as `census tracts' in the USA and `output areas' in the UK, for example) or transport models, which often use dedicated zones referred to as traffic analysis zones (TAZ) {[}6{]}. + +After experimenting with various ways to increment 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 \href{https://en.wikipedia.org/wiki/Triangular_number}{triangular number sequence} {[}25{]}. +This means that all points in the first annuli (labelled A) are up to 1 km away from the city center; 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 {[}26{]}. +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 \ref{fig:london}). +This and other other attributes of the first set of 9 zones in the ClockBoard zoning system in Table \ref{tab:t1}. + +\begin{table} + +\caption{\label{tab:t1}Key attributes of the ClockBoard zoning system, highlighting its flexibility ranging from a single central zone (zone A is a circle with radius of 1 km) to a zoning system with a radius of 45 km and 97 zones. The number of rings can be varied to match the size of the city under investigation.} +\centering +\begin{tabular}[t]{rlrrrr} +\toprule +N. annuli & Outer annuli label & N. zones & Radius (km) & Area (sqkm) & Av. zone size (km)\\ +\midrule +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\\ +\addlinespace +6 & F & 61 & 21 & 1385 & 23\\ +7 & G & 73 & 28 & 2463 & 34\\ +8 & H & 85 & 36 & 4072 & 48\\ +9 & I & 97 & 45 & 6362 & 66\\ +\bottomrule +\end{tabular} +\end{table} + +\hypertarget{number-of-segments}{% +\subsection{Number of segments}\label{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 {[}26{]} 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 {[}27{]}. +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 . + +\hypertarget{clockboard-zones-for-segmenting-urban-areas}{% +\subsection{ClockBoard zones for segmenting urban areas}\label{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, visualization and exploratory analysis of large cities with well-defined central areas such as London, as illustrated in Figure \ref{fig:london}. + +\begin{figure} + +{\centering \includegraphics[width=0.7\linewidth]{zonebuilder-paper_files/figure-latex/london-1} + +} + +\caption{The clockboard zoning system, applied to Greater London, UK.}\label{fig:london} +\end{figure} + +\hypertarget{using-the-clockboard-zoning-system}{% +\subsection{Using the ClockBoard zoning system}\label{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 minimize barriers to entry. + +\hypertarget{the-zonebuilder-r-package}{% +\subsubsection{The zonebuilder R package}\label{the-zonebuilder-r-package}} + +The concepts were initially implemented in the statistical programming language R, which is available from the Comprehensive R Archive Network (\href{https://cran.r-project.org/package=zonebuilder}{CRAN}) and can be installed from the R command line as follows: + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{install.packages}\NormalTok{(}\StringTok{"zonebuilder"}\NormalTok{)} +\end{Highlighting} +\end{Shaded} + +After the package has been installed, its functions can be attached (made available) to the user's workspace as follows: + +\begin{Shaded} +\begin{Highlighting}[] +\FunctionTok{library}\NormalTok{(zonebuilder)} +\end{Highlighting} +\end{Shaded} + +A simple zoning system for Tokyo is created and plotted in the R code chunk below, resulting in the map shown in Figure \ref{fig:tokyo}. +In the code chunk below, the character string ``Tokyo'' is the first argument in the \texttt{zb\_zone()} function (which can also be a spatial point object). +When the first argument is a text string, as is the case here, the package automatically converts it into a geographic location using the Nominatim online service, which is based on data from OpenStreetMap; the \texttt{zb\_view()} function creates an interactive map. + +\begin{Shaded} +\begin{Highlighting}[] +\NormalTok{ClockBoard\_tokyo }\OtherTok{=} \FunctionTok{zb\_zone}\NormalTok{(}\StringTok{"Tokyo"}\NormalTok{, }\AttributeTok{n\_circles =} \DecValTok{5}\NormalTok{)} +\FunctionTok{zb\_view}\NormalTok{(ClockBoard\_tokyo, }\AttributeTok{alpha =} \FloatTok{0.8}\NormalTok{)} +\end{Highlighting} +\end{Shaded} + +\begin{figure} + +{\centering \includegraphics[width=0.75\linewidth]{tokyo} + +} + +\caption{ClockBoard zoning system applied to Tokyo, the result of running the reproducible code used to demonstrate the zonebuilder R package.}\label{fig:tokyo} +\end{figure} + +Note that the \texttt{n\_circles} argument was set to 5, resulting in a zoning system 15 km in radius (see Table \ref{tab:t1}). +This can be changed; replacing \texttt{5} with \texttt{9}, for example, would results in a zoning system with an outer circle radius of 45 km. +Furthermore, passing an object representing the geographic extent of Tokyo as a polygon to the \texttt{area} argument of the \texttt{zb\_zone()} function would result in a zoning system that is intersected by Tokyo's boundary. + +\hypertarget{the-zonebuilder-rust-crate}{% +\subsubsection{The zonebuilder Rust crate}\label{the-zonebuilder-rust-crate}} + +To make the project and resulting zones available to more people, we subsequently developed a Rust crate, that enables the creation of ClockBoard zones on all major platforms using a command line interface. +See \href{https://github.com/zonebuilders/zonebuilder-rust}{github.com/zonebuilders/zonebuilder-rust} for details. +The crate is available on the main Rust package repository crates.io and can be installed on any computer that already has the Rust toolchain installed from the system command line as follows: + +\begin{Shaded} +\begin{Highlighting}[] +\ExtensionTok{cargo}\NormalTok{ install zonebuilder} +\end{Highlighting} +\end{Shaded} + +After installing the \texttt{zonebuilder} crate and assuming that \texttt{cargo} is executable the following commands will print instructions on how to use the command line interface and generate zones for Leeds, UK, respectively: + +\begin{Shaded} +\begin{Highlighting}[] +\ExtensionTok{zonebuilder} \AttributeTok{{-}h} \CommentTok{\# see usage instructions} +\ExtensionTok{zonebuilder} \OperatorTok{\textgreater{}}\NormalTok{ zones.geojson }\CommentTok{\# create zones.geojson zone object} +\end{Highlighting} +\end{Shaded} + +\hypertarget{interactive-zonebuilder-web-application}{% +\subsubsection{Interactive zonebuilder web application}\label{interactive-zonebuilder-web-application}} + +To enable creation of ClockBoard zones for non-programmers and to encourage people to explore alternative zoning systems, we created a simple web application hosted at \href{https://zonebuilders.github.io/zonebuilder-rust/}{zonebuilders.github.io/zonebuilder-rust/} (see Figure \ref{fig:interactive}). This app leverages the Rust implementation for generating ClockBoards, compiling it to WebAssembly and using the standard open-source \href{https://leafletjs.com}{leafletjs.com} mapping library as an interface. + +\begin{figure} + +{\centering \includegraphics[width=0.85\linewidth]{128508694-5b5485ca-6f1b-4c21-bdb6-9269a7981dd5} + +} + +\caption{Screenshot of the zonebuilder web application for creating and downloading ClockBoard zones interactively. The example shows Erbil, Northern Iraq, which was found to have a road layout resembling the ClockBoard zoning system, highlighting the importance of interactive alignment and selection of number of rints. See the interactive version at zonebuilders.github.io/zonebuilder-rust/.}\label{fig:interactive} +\end{figure} + +\hypertarget{applications}{% +\section{Applications}\label{applications}} + +The zoning system presented in this paper is a specific implementation concentric segmented annuli, that was designed to support description, exploration and visualization of monocentric cities. +The zoning system presented, and modifications of the system, could be useful in a range of other areas. +The examples below are designed to provide an insight into how the zoning system could be used. + +\hypertarget{describing-location}{% +\subsection{Describing location}\label{describing-location}} + +A potential application of the zoning system is to indicate approximate locations with reference to a known central point or area, e.g.~to describe a segment of a city. +ClockBoard zones offer a level of intermediate-to-low accuracy in between the simple use of quadrants to identify parts of a city verbally on one hand, and more sophisticated ways of communicating location to the nearest few meters on the other. +Dividing cities into quadrants and referring to them with names such as `north', `northeast', etc. is common in everyday speech and academic writing: a paper on the impact of open spaces on house prices stated that traffic noise was expected to have a negative impact on house prices in ``south-east, north-east, and north Portland'', with reference to an accompanying map, for example {[}28{]}. +Location services such as `what3words' and open source implementations such as `whatfreewords' and `\href{https://www.qalocate.com/solutions/geohashphrase/}{goehashphrase}' take the concept of converting coordinates into memorable words/phrases a step further, offering accuracy measured in meters rather than kilometers in situations where coordinates may not be appropriate or possible {[}29{]}. + +With 49 zones covering an area just over 700 square km, the ClockBoard system offers an intermediate level of resolution between the simple quadrant method and complex `geohash' approaches to referring to locations outlined above. +Like the quadrant approach, the ClockBoard system relies on a central point. +The ClockBoard system shares the advantage of the quadrant approach to locating objects that the location can worked out by people without reliance on a computer to translate coordinates into a geohash, although the calculation is substantially harder, requiring memorization or quick calculation of the triangular number sequence (1, 3, 6, 10, 15 etc) and knowledge of the boundaries of a clock face such that ``E03'' is understood as being between 10 and 15 km East of the center. + +An illustration of using the ClockBoard zoning system to locate places is presented in Figure \ref{fig:location}. +This shows how it could be used to communicate key locations, including a train station (zone A) a park (zone C01) and the center of a neighboring city (zone E09), with reference to the city center of Leeds, UK. +In a hypothetical use case, the example could be used to communicate the fact that the park is relatively close to the rail station (between 3 and 6 km from the city center) while Bradford in zone E09 is between 10 and 15 km from central Leeds. +Of course, the locations are not geographically specific; the zones would be used a broad brush descriptions of place locations before more detailed descriptions of locations such as directions from key landmarks or coordinates are used. + +\begin{figure} + +{\centering \includegraphics[width=0.85\linewidth]{navigation} + +} + +\caption{Illustration of how the ClockBoard system could be used to describe the approximate location of places. In this hypothetical example, the system is used to locate places in and around Leeds: the train station in the central zone A, Roundhay Park wich is located around 5 km North of the center in zone C01, and central Bradford which is located around 14 km due East of the center in zone E09.}\label{fig:location} +\end{figure} + +The ClockBoard zoning system was not designed for locating objects in space in this way; the real world utility of such low resolution indications of spatial location has yet to be tested; and understanding of the zoning system would need to be widespread for it to catch on. +However, the example demonstrates how the system communicates potentially useful location data with a small amount of verbal information. +More plausible use cases include exploring city scale data (covered in the next section) and inter-city comparisons of geographically variable phenomena (covered in the section after). + +\hypertarget{exploring-city-scale-data}{% +\subsection{Exploring city scale data}\label{exploring-city-scale-data}} + +The ClockBoard zoning system is well suited to exploratory analysis of city-scale spatial data. +An example that demonstrates how the system can simplify the presentation of spatially variable data is shown in Figure \ref{fig:cityscale}, which presents open access data on air quality from the London Atmospheric Emissions Inventory. +The presentation of the same data at four different levels of geographic resolution highlights the impacts that zoning system choice can have on data analysis, with each having advantages and disadvantages. +The most geographically detailed zoning system in which the data is available is the rectangular grid shown in the far left facet (A). +This presentation of the data is ideal for many purposes, demonstrating the variability in air quality over relatively small areas (1 km grid cells) across London. + +In cases when geographic aggregation is required, e.g.~to present the data in small graphics that will be printed at low resolution (e.g.~newspaper visualizations and infographics), two common approaches are to use an existing administrative zoning system (with well known London Borough boundaries used to aggregate the data presented in facet B in Figure \ref{fig:cityscale}) and to use a simplified geographical representation or geographically arranged facets {[}30{]}. +Both approaches have advantages, with existing and well-known zoning systems enabling map readers familiar with the city to orient themselves and interpret the map. +In this context and with reference to Figure \ref{fig:cityscale}, the ClockBoard zoning system has the following advantages as a basis for choropleth maps: + +\begin{itemize} +\tightlist +\item + Simple and consistent zone shapes for easy map reading +\item + The circular shape of zone boundaries make the results easy to place, requiring a 1:1 aspect ratio (except when the zones are clipped, as in map D) +\item + The shape of the zones draws attention to citywide spatial patterns, with map C highlighting the clear tendency for air quality to improve with distance from the city center and the comparatively poor air quality in segments 3 and 9 +\end{itemize} + +The final advantage is particularly notable when comparing the ClockBoard zoning system with large official zone (borough) boundaries in London. +Because of the large and irregular zone shapes in map B, the strength of the relationship between distance from central London and air quality is not as clear as when using ClockBoard zones as the frame of reference in maps C and D in Figure \ref{fig:cityscale}. +This benefit is especially noticeable towards the outskirts of London, where large outer boroughs such as Bromley (far southeast London) fail to communicate the fact that PM10 levels drop below 1 ug/m\^{}3 in outer London. + +\begin{figure} + +{\centering \includegraphics[width=1\linewidth]{cityscale} + +} + +\caption{Illustration of the ClockBoard zoning system used to visualize a geographically dependendent phenomena: air quality, measured in mass of PM10 particles, measured in micrograms per cubic meter, from the London Atmospheric Emissions Inventory (LAEI). The facets show the data in spatial grid available from the LAEI, facet Am and aggregated to London boroughs B, to ClockBoard zones covering all the input data shown in C, and ClockBoard zones clipped by the administrative boundary of Greater London in D.}\label{fig:cityscale} +\end{figure} + +The example of air quality presented in Figure \ref{fig:cityscale} highlights that the ClockBoard zoning system is well suited for the analysis and visualization of phenomena in which a central place (London city center in this case) plays a major role, directly or indirectly. +(Not all cities have a `monocentric' structure, something we discuss in Section \ref{discussion}.) +The prevalence of particulate matter in the air relates to the level of industrial, transport and other activities in the surrounding area, which clearly increases with proximity to central London. +The same can be said of many other phenomena which become more, less, or more and then less, common with distance from central places. +The tragic phenomena of road traffic casualties --- which relate to travel volumes, speeds and transport infrastructure design --- also relates (albeit in different ways in different cities) to proximity to central places, something we explore in the next subsection to highlight another use of the ClockBoard zoning system: comparison between cities. + +\hypertarget{inter-city-comparison-of-geographically-variable-phenomena}{% +\subsection{Inter-city comparison of geographically variable phenomena}\label{inter-city-comparison-of-geographically-variable-phenomena}} + +The ClockBoard zoning system can enable effective comparison between cities by providing a consistent frame of reference. +While official boundaries can vary greatly in size and shape, based on sometimes arbitrary factors such as historic boundaries (as shown in Figure \ref{fig:intercity}, top), ClockBoard zones are always the same size, shape and orientation (as shown in Figure \ref{fig:intercity}, bottom). +Using the system can provide a basis of evidence-based discussion of geographically aggregated results representing urban phenomena. +The example demonstrates this with reference to a policy-relevant example: the number of people killed and seriously injured while cycling in major UK cities. +Addressing issues associated with reporting only number of casualties per unit area, a practice that can miss dangerous places which have a high casualty rate per unit time or distance cycled {[}31{]}, we show data on the number of people killed and seriously injured while cycling per billion kilometers based on estimates from the Propensity to Cycle Tool {[}32{]}. + +\begin{figure} + +{\centering \includegraphics[width=0.85\linewidth]{zonebuilder-paper_files/figure-latex/intercity-1} \includegraphics[width=0.85\linewidth]{zonebuilder-paper_files/figure-latex/intercity-2} + +} + +\caption{Comparison of administrative zones (top) and zones in the ClockBoard zoning system (bottom) to support inter-city comparison of policy-relevant data, on road traffic casualties. The maps show the spatial distribution of cycling casualties per billion km cycled, a measure that requires spatial data aggregation for meaningful results.}\label{fig:intercity} +\end{figure} + +The results presented in Figure \ref{fig:intercity} (top) using administrative zones demonstrate the issues with using commonly available zones provided by statistical authorities: areal units vary dramatically in terms of size and shape; and the definition of each city's boundary distorts the results, with Manchester represented by a long and thin region that does not fit well within facetted maps. +The results aggregated at the level of ClockBoard zones, illustrated in Figure \ref{fig:intercity} (bottom), show overcome these issues. +Because of its high population density and size, London has many small administrative zones that made it hard to understand the levels and spatial distributions of cycling safety in the city. +The results for London presented at the level of ClockBoard zones show a clearer picture that can be compared with other cities: while London has a high absolute crash rate, it is relatively safe per km cycled. +The ClockBoard zoning system also allows for aggregation at a consistent spatial resolution, enabling the identification of potential crash hotspots in specific parts of Birmingham (zones D12 and E06) and Sheffield (zone D11). + +Another example of using ClockBoards to compare cities (and phenomena that take place in them) is shown in Figure \ref{fig:popdens}, which shows population density in 36 major cities using the ClockBoard zoning system not as unit for aggregation but as a reference grid. +The 7 rings A to G cover a radius up to 28 km from the city center. +The colors of the panel labels in Figure \ref{fig:popdens} indicate the continent of the city. +The value of comparing cities in a single geographic frame of reference is shown by inspecting Singapore and Sydney with reference to ClockBoard zones. +While these cities have similar total official populations (of 5.8 and 5.3 million people, respectively), based on the number of people with their respective administrative boundaries, the size and shape of each city is very different, highlighted by the fact that in Singapore there are few people beyond ring F (located 15 to 20 km from the center), while in Sydney (and many other cities) there are substantial numbers of people living in ring I (located 36 to 45 km from the center). + +\begin{figure} + +{\centering \includegraphics[width=1\linewidth]{cities_p2-scale} + +} + +\caption{ClockBoard zoning systems with 7 rings (A to G) supplied used to communicate the spatial distribution of populations for for 36 cities. The blue raster grid cells represent open access population estimates from the WorldPop project.}\label{fig:popdens} +\end{figure} + +The administrative borders of six cities shown in Figure \ref{fig:popdens} are depicted as red lines in Figure \ref{fig:popdens2}, highlighting the importance of sometimes arbitrary city boundaries. +The ClockBoard zones applied to Amsterdam not only cover Amsterdam but also a few other small Dutch cities and towns. Most of them are economically attached to Amsterdam, but a few of them also to other major Dutch cites. + +\begin{figure} + +{\centering \includegraphics[width=0.7\linewidth]{cities_p1} + +} + +\caption{ClockBoard for 6 cities with boundaries shown in red. The blue raster grid cells represent open access population estimates from the WorldPop project; the red lines are administrative borders.}\label{fig:popdens2} +\end{figure} + +\hypertarget{discussion}{% +\section{Discussion and conclusion}\label{discussion}} + +The ClockBoard zoning system presented in this paper was designed to provide a new tool for visualizing and communicated about geographic data in relation to cities and, more broadly, to provoke discussion of the pros and cons of different zoning systems including possible future systems that have yet to be developed. +Issues associated with administrative zoning systems are well known {[}5,7{]} yet accessible zoning systems that highlight the importance of areal units are comparatively rare. +Great strides have been made in the design of administrative zoning systems systems and they are understandably the default unit of analysis for urban analysis in many parts of the world {[}33,34{]}. +The dominance of administrative zones in urban analysis has advantages, but also has unintended consequences, including making it hard for people to refer to specific administrative units, irregular sizes and shapes, and lack of comparability between geographically aggregated results from city to city. + +Instead of tackling these problems by developing additional approaches for the ``re-aggregation of the raw data into a more +appropriate output geography'' {[}35{]}, we started from scratch focusing on the key spatial attributes of distance and and bearing from the center. +Our criteria, based on our work in the broadly defined field or Urban Analytics, were: intuitively labelled and easy-to-communicate zones, consistently sized and shaped zones for creating readable and easy-to-interpret maps, and a system that would be accessible for use and modification. + +The zones in the ClockBoard zoning system were designed to be sufficiently large so that each could be seen when printed in a low resolution map representing a large city. +The relatively large zones (which get bigger further from the city center as density of urban phenomena tends to decrease) also enable zone labels with only three characters (with the exception of zone A). +Zone label give insight into their location, with the ClockBoard zone `E09 Leeds' illustrated in Figure \ref{fig:location} indicating the fact that it is located between 10 and 15 km West of the city center. +The equivalent official `MSOA' zone code is `E02002221': longer, harder to remember, and devoid of geographic meaning. + +It is important to emphasize that ClockBoard zoning system is a specific implementation of an approach to zone creation that we label `concentric segmented annuli' and that a wide family of zoning systems could be created based on the approach: variations can be obtained by adjusting the sequence of outer ring radii (so they have values other than 1, 3, 6, 10, 15 and 21 km, resulting from the triangular number sequence used in the ClockBoard system) and number of segments (with values other than 1 for the central annuli and 12 for all others). +To encourage use of and adaptation of the system, we have implemented methods for creating `ClockBoards' and other zoning systems based on concentric segmented annuli in R and Python packages, and Rust crate \texttt{zonebuilder}. +These can be installed from the `\href{https://cran.r-project.org/package=zonebuilder}{CRAN}', `\href{https://crates.io/crates/zonebuilder}{crates.io}', and `\href{https://pypi.org/project/zonebuilder/}{PyPI}' repositories, respectively. +To further reduce barriers to entry in the creation of ClockBoards to meet specific needs and for fun/education, we have created a simple web application available at \href{https://zonebuilders.github.io/zonebuilder-rust/}{zonebuilders.github.io/zonebuilder-rust} that allows the user to create and download as .geojson files zoning systems based on concentric segmented annuli anywhere in the world. + +The approach is not without limitations, and these include limitations with the specific ClockBoard system, limitations with concentric segmented annuli and `from scratch' zoning systems that do not follow local features such as rivers and historic boundaries. +In terms of the limitations of the \emph{ClockBoard implementation of the concentric segmented annuli approach}, it is associated with a fairly wide range of zone sizes and shapes, with zone areas ranging from 2 km\textsuperscript{2} in for zones in doughnut B to 33 km\textsuperscript{2} on the outermost doughnut E in a ClockBoard system with 5 rings (and a radius of 18 km). +This variability makes the system unsuitable for analyses requiring uniform areas or uniform populations. +Raster grid cells or administrative zones that keep the population within each zone relatively fixed may be more appropriate in these cases. + +A broader set of limitations apply to \emph{the general approach of using zones of the same size and shape in many to many cities}: +zone boundaries do not follow local features, with ClockBoard zones covering both sides of the River Thames in London, as illustrated in Figure \ref{fig:london}. +This results in `zone islands', with areas separated from the rest of the zone of which they are part by physical barriers such as rivers and large roads. +The approach leads to zones are more internally diverse than official zone systems, which tend to include similar types of places into the same zone, wish disadvantages when analyzing systems that require cohesive zones. + +Another potential disadvantage of zoning systems that are invariant from place to place is that city borders are usually irregular. +Clipping the zones to official city boundaries can address this issue, but creates an additional problem: unhelpfully shaped and sized zones in the periphery of large cities, also shown in Figure \ref{fig:london}. +To benefit from the standardized zones provided by ClockBoard, we recommend using the system without clipping: ignoring the historic boundary and defining the city bounds with reference to distance from the center can enable inter-city comparison, without being constrained by their historic boundaries. +The benefits of using a consistent bounding area when comparing multiple cities is highlighted by comparing London and Paris. +Official figures suggest that the two cities have very different sizes: the population within their official boundaries depicted in Figure \ref{fig:popdens2} are 9 million (Greater London) and 2 million (Paris). +However, the metropolitan populations of the two cities --- defined as the population living in a ClockBoard system with 7 rings (within 28 km from the city center) --- are similar (about 10 million each). + +A another limitation of the approach is the implicit assumption that cities are monocentric entities in which urban activity (and hence the need for spatial resolution) declines gradually with distance from the city center. +While this assumption broadly holds for many cities such as London and other cities illustrated in this paper, many cities are polycentric {[}36{]}. +The zoning system is unsuited to polycentric conurbations and the countryside, limiting its uses substantially, to urban analytics focused on monocentric cities. + +Consideration of polycentric settlements raises the question of how to fit one or several ClockBoards to a dense urban area consisting of several cities, of which none is clearly dominant. +For instance, the four major cities in the Netherlands (Amsterdam, Rotterdam, The Hague and Utrecht) are small and located about 40 kilometers from each other, with even smaller cities and towns in between. +In this example, there is no dominant ``gravitational force'' to construct one ClockBoard around, making this a much harder challenge than designing a zoning system for a single city {[}6{]}. +We explored the possibility of `joining' ClockBoard systems that met, with the `dominant' ClockBoard associated with the larger city, but the results were not promising and we suspect that a new approach altogether, perhaps building on experience from Computational Fluid Dynamics, where grid generation procedures need to take into account multiple factors {[}37{]}. + +A broader limitation is that the zoning system has not been tested or assessed, other than in informal settings and in a prototype web application, publicly available at \href{https://actdev.cyipt.bike/ebbsfleet/accessibility,buildings/\#11.69/51.4359/0.3065}{actdev.cyipt.bike}, to present data on aggregate statistics on the quality active travel provision in the areas surrounding new housing developments {[}38{]}. +While informal and anecdotal feedback has been positive, user testing is needed to identify for which of the potential applications outlined in this paper the ClockBoard system is best suited. +Such user testing could be based on established approaches for evaluating digital products, including focus groups, surveys or interviews with potential users {[}39{]}. +Such user testing is beyond the scope of the present paper, but represents a promising future direction of research to establish how the approach could be used in the real world and future research priorities around zoning systems for urban analysis. + +An alternative and approach to developing zoning systems for complex and polycentric settlements not implemented in this paper is to build them on existing Discrete Global Grid Systems (DGGS) such as the S2 and H3 global zoning systems developed by Google and Uber respectively {[}40{]}, and the \href{https://github.com/paulojraposo/QTM}{QTM Generator} developed by Paulo Raposo {[}29{]}. +This would have advantages for flexibility, with DGGSs able to generate grids with zone sizes that are more evidence-based, for example by responding to geographic data such as population density. +DGGS based zoning systems would also enable greater determinism, with each of S2's \textasciitilde7 quintillion (\(6 * 4^{30}\) or \(\approx6.9*10^{18}\)) and H3's \textasciitilde700 trillion (\(\approx5.7 * 10^{14}\)) base zones having a unique reference code that is machine readable (ClockBoards are arguably deterministic with `zone B12, Leeds, UK' referring to an unambiguous area, although ClockBoards depend on an unambiguous definition of `city center' which may not be available or requires a single unique source of city center points). +Theses beneficial features would be gained at the expense of simplicity: DGGSs are complex and have hard-to-remember cell IDs such as \href{https://developers.google.com/maps/documentation/gaming/concepts_playable_locations}{e66ef376f790adf8a5af7fca9e6e422c03c9143f} (S2) and \href{https://h3geo.org/docs/quickstart}{8a283082a677fff} (H3); they also have high computational requirements {[}40{]}, compared with the comparatively simple ClockBoard system. + +While the utility of the zoning system is likely to be limited in many settings by the limitations outlined above, we believe that there are settings in which ClockBoard could provide substantial benefits, as demonstrated in three example applications. +These demonstrated potential use cases for informal communication about and navigation within cities; exploratory data analysis and visualization of geographic data within a single city; and visual and quantitative comparison of geographic phenomena between cities. +Of these, we expect that the last application of ClockBoard, and similar zoning systems, will be of most use to urban analysts and others working with city-scaled datasets. +A direction of future research could be to explore the use of ClockBoard and other discrete geometric zoning systems for other applications, for example as the basis of spatial interaction models, building on established work exploring different zoning systems based on BSUs {[}7{]}. +A broader point is that too much academic research focuses only on a single city, without going to the effort of generalizing the findings to multiple cities {[}6,36{]}. + +We hope that the concept of the ClockBoard zoning system presented in this paper, and the ease with which open access data representing `ClockBoards' for different cities can be created, will encourage more quantitative urban analytical research comparing different cities, building on recent work in the field {[}20{]}. +Moreover, we hope that the implementation of the concept in open source software encourages other zoning systems with different attributes to be developed, to meet different criteria than those that motivated the design of the ClockBoard system. +The ongoing experience of developing and testing the system suggests that there is a need for such `artificial' and consistent systems and we believe that a range of approaches, ranging from procedural generation to custom zoning systems co-created by citizens to meet specific need, will help develop the diversity of zoning systems that will be needed to meet 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