diff --git a/vignettes/paper.Rmd b/vignettes/paper.Rmd index c2b5a16..65ab7fc 100644 --- a/vignettes/paper.Rmd +++ b/vignettes/paper.Rmd @@ -7,7 +7,7 @@ output: base_format: rticles::josis_article keep_tex: true # For R package vignette -# output: bookdown::html_vignette2 +# output: bookdown::word_document2 author: - name: Robin Lovelace affiliation: Institute for Transport Studies and Leeds Institute for Data Analytics, University of Leeds, UK @@ -117,7 +117,7 @@ setwd(wd_old) # Introduction -Zoning is the process of generating areal units for aggregating, visualising, and potentially modelling geographic datasets. +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]. @@ -128,9 +128,9 @@ Research has made great progress in mathematical analysis of zones and more obje 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 visualised to the [impact of the nature of 'traffic analysis zones' on transport model outputs](http://www.iasi.cnr.it/ewgt/13conference/145_binetti.pdf). +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]. +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. @@ -140,12 +140,12 @@ In order to address these shortcomings of zoning systems based on administrative 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 @openshaw_optimal_1977 to justify the BSU grouping approach, may have been true in the 1970s when it was written. -Today disaggregated geographic datasets are common. +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. @@ -153,11 +153,11 @@ In this paper we are interested in the division of *continuous space* into compl 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. +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. 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]. @@ -173,11 +173,11 @@ Another downside from a statistical perspective is that population density tends 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 reproducibly with minimal data requirements. +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 phenomena in cities. - Automated zoning systems based on a clear centerpoint can support map interpretation by making it immediately clear where the city center is, and what the scale of the city is. + 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. @@ -186,7 +186,7 @@ The specific motivations for embarking on the idea, and its implementation in op - 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 visualisation. + A consistently sized and shaped set of zones can support attractive, clear and meaningful visualization. - 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. @@ -201,14 +201,14 @@ Finally, in Section 4, we discuss limitations of the approach and possible direc 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 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 visualisation -be easy to visualise without too many or too few zones +- 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 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 @@ -216,7 +216,7 @@ be easy to visualise without too many or too few zones 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). @@ -225,7 +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. @@ -253,7 +253,7 @@ Given that the radius of the inner circle must the same as the radius of the pre 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]. @@ -285,7 +285,7 @@ Following this convention, the ClockBoard zoning system aligns segment 12 with t ## 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%"} @@ -296,7 +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 @@ -341,7 +341,7 @@ 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") + @@ -403,7 +403,7 @@ 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. @@ -458,7 +458,7 @@ 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: @@ -471,7 +471,7 @@ Because of the large and irregular zone shapes in map B, the strength of the rel 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. -```{r cityscale, fig.height=2, out.width="100%", fig.cap="Illustration of the ClockBoard zoning system used to visualise 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."} +```{r cityscale, fig.height=2, out.width="100%", fig.cap="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."} # file.edit("data-raw/london-figures.R") # to reproduce the figure # For PDF version with vector graphics: @@ -486,7 +486,7 @@ 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 center 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. @@ -597,36 +597,36 @@ knitr::include_graphics(f) # Discussion and conclusion {#discussion} -The ClockBoard zoning system presented in this paper was designed to provide a new tool for visualising 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. +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. 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 focussing on the key spatial attributes of distance and and bearing from the center. +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. 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 containubg only three characters (with the exception of zone A). +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 emphasise 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). +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 dohnut B to 33 km^2^ on the outermost dohnut E in a ClockBoard system with 5 rings (and a radius of 18 km). +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 analysing systems that require cohesive zones. +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). @@ -648,7 +648,7 @@ Consideration of polycentric settlements raises the question of how to fit one o 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 [@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]. +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. @@ -656,15 +656,15 @@ Such user testing could be based on established approaches for evaluating digita 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 respondingM to geographic data such as population density. +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.