4. UA Variables

All UA variables are measured such that lower or negative values are good, whereas higher values are bad. (Exceptions are neutral variables such as population density which are nevertheless straightforward to interpret.) For example, unemployment or transport times are both better when values are lower. Indices of bicycle infrastructure and access to natural spaces are also transformed so that lower values indicate better or more of either. In these cases, the transformations are simply one minus the respective proportions of journeys out to a fixed distance travelled along bicycle infrastructure, or through or alongside natural spaces. Values of 0 then reflect 100% of all journeys spent on bicycle infrastructure or in natural spaces, while values of 1 would represent complete absence of either bicycle infrastructure or natural spaces.

Variables are measured for every way, path, or street intersection within each city. Values for the maps are aggregated within polygons defined by the Socio-demographic variables described in the following sub-section, while values within the statistics page are aggregated across entire cities. Unless explicitly described otherwise, values of all variables are weighted by population density. This means that, for example, distances to nearest schools represent average distances that each person must travel to get to school. Full descriptions of the calculation of all variables are given in the Software and Algorithms chapter.

4.1. Socio-demographic variables

The extent and structure of each city is defined by its “socio-demographic variable,” or “social variable” for short. These are taken from open-source datasets provided by the cities as a series of geographic areas, defined as polygonal shapes, and some corresponding measure of socio-demographic disadvantage. The cities themselves decide the resolution and extent of these polygonal data. These polygons then define the extent and shape of cities analysed in Urban Analyst, and the individual polygons into which the map data are aggregated.

Values of these socio-demographic variables are the only aspect that differs between different cities. One of the simplest versions is unemployment rate, generally measured either as a percentage (0-100), or a proportion (0-1). The UA platform selects the most representative measure of general social disadvantage provided by each city, and defaults to rates of unemployment only where no more comprehensive of integrative measures are openly provided by cities.

4.2. Travel Variables

Urban Analyst provides highly detailed statistics on transport systems. Many of these are derived from estimates of times required to travel fixed distances of 10km. This value is chosen to capture the general efficiency of public transport systems. Shorter distances do not sufficiently capture the influence of transport modes such as express or long-distance train services, while longer distances unfairly penalise smaller cities in which most journeys are only of shorter distances.

Values at this distance of 10km are obtained by following these three steps, taking the example statistic of travel times:

  1. Calculate total travel times from all street intersections to all other street intersections within a city.

  2. Calculate a straight line of “best fit” (a “least squares regression” line) which describes how travel times vary with distance.

  3. Use that line to obtain the “average” value of travel time at the distance of 10km.

Values shown in the maps are aggregated within each polygon of a chosen city, while values shown in the statistics page are aggregated over entire cities.

The remainder of this section describes the five travel variables:

  • Absolute travel times

  • Relative travel times

  • Numbers of transfers

  • Intervals between consecutive services

  • Compound travel statistic

4.2.1. Absolute and Relative Travel Times

Urban Analyst enables comparisons of travel times between two primary modes of transport:

  • Private Automobile. Travel times with private automobile are used as a benchmark for measures of travel time using other modes. UA generates realistic estimates of private automobile travel times through scaling to empirically observed data on actual vehicular travel times. (Calibration procedures are implemented and documented in this GitHub repository.) Importantly, UA includes an additional, unique aspect of automobile travel times not quantified in any other equivalent system, through an algorithm to accurately estimate the likely time required to park a private vehicle, and then to walk to a desired destination. These parking times are crucial, as direct travel times to many inner-city destinations do not provide realistic estimates of actual journey times to locations where it may be impossible to actually park a private automobile.

  • Multi-Modal Transport. UA’s “multi-modal travel times” represent fastest possible times taken for journeys from every single point in a city to travel 10km using any combination of transport modes excluding private automobile. The primary modes considered are walking, bicycling, and all available modes of public transport within each city. Where it is faster to cycle 10km than to take public transport (such as from locations with very poor public transport connections, or on the top of long hills where downhill cycling may actually be faster), these times will represent the single mode of cycling only, but multi-modal times will generally reflect fastest times formed by combining multiple modes of transport.

Travel times measured these two ways are then combined to generate the following two primary travel time statistics:

  • Absolute travel times as the multi-modal travel times; that is, using any mode except private automobile.

  • Relative travel times as the ratios of absolute travel times compared with equivalent travel times with private automobile. Relative travel times of less than one indicate that multi-modal transport is faster than equivalent transport with private automobile, while values greater than one indicate that private automobile transport is faster.

4.2.2. Intervals and Numbers of Transfers

In addition to travel times, UA also includes the following two additional statistics quantifying other aspects of public transport systems. Both are measured for every point of origin with a city, with final values again derived by following the steps described above to obtain average values of each for all trips of 10km distance. Numbers of transfers are thus the average number required for all journeys of 10km, while intervals are the required waiting times for the next equivalent journey out to that distance.

  • Intervals to Next Service are measured in minutes. For each point of origin in a city, this statistic measures the waiting time necessary before departing to each destination within a city on the service after the one corresponding to the fastest journey. This delayed service may not be fast as the original, or it may even be faster in some cases, as the UA algorithms also prioritise connections with the fewest possible transfers. It can happen that subsequent services are actually faster, yet involve additional transfers not required in the originally identified “fastest” service.

  • Numbers of Transfers measure the number of transfers necessary for a minimal-transfer journey out to a distance of 10km. These minimal-transfer journeys are selected to allow for journeys slightly slower than absolute fastest journeys (generally by up to 5 minutes) if they involve fewer transfers.

4.2.3. The Compound Travel Statistic

All three of the statistics described above - travel times, intervals, and numbers of transfers - are measured such that lower values are more desirable. Travel times are then directly multiplied by (a logarithmically-transformed version of) intervals between services to generate a “compound travel statistic”. Low values of this statistic only arise in locations which have fast travel times and short intervals between services. Low values may accordingly always be interpreted as indicating overall good transport services. In contrast, high values may arise through various combinations of variables, from extremely high values of one single variable, to less extreme combinations of the two variables. It is thus generally not possible to directly discern reasons for high values of this compound travel statistic. Urban Analyst nevertheless provides direct insight into all individual values, as well as all pairwise combinations of values, permitting indirect insight.

4.3. Population density

Population density values are taken directly from the European Union *Global Human Settlement Layer* data, aggregated into polygons for maps, or across entire cities for statistics.

4.4. Distance to nearest schools

Distances to nearest schools are measured in kilometres, as shortest walking distances from each point to the nearest school. These are network distances, and not simple straight line distances. A single value is ascribed to each point within a city, and all points aggregated after weighting by local population densities.

4.5. Bicycle infrastructure

The bicycle infrastructure index is derived from a measure of the proportion of all possible journeys from each point out to a fixed distance of five kilometres that travel along dedicated bicycle infrastructure. To conform with all other UA variables, the index is one minus this proportion, so that low values reflect high proportions of bicycle infrastructure. Values of zero would then reflect all journeys taken along dedicated bicycle paths, while values of one would mean a complete absence of dedicated bicycle infrastructure.

Travel is calculated using a bicycle-specific algorithm that only extends along ways unsuitable for bicycle travel where no alternatives exist. The weighting scheme used adds total distances for all portions of travel along designated cycleways that are separated from vehicular traffic. Portions of trips extending along other types of ways are added with “half weightings” so, for example, one kilometre along these types is equivalent to two kilometres on dedicated bicycle ways. These “half-weight” ways include residential or “living” streets, unpaved tracks, and bicycle lanes directly alongside automobile lanes. A third category of ways are weighted at one-quarter, including footpaths and general pedestrian areas which permit bicycle travel. The precise weighting scheme can be viewed in this source code file.

The weighted sums of all distances along these types of ways traversed out to five kilometres from any given point are then divided by the sum of all distances travelled regardless of way type to give a ratio between zero and one. This bicycle infrastructure index is then one minus this value.

4.6. Natural space accessibility

Natural space accessibility is measured in a similar way to the bicycle infrastructure variable, except it quantifies proportions of walking distances out to maximal distances of two kilometres that traverse natural spaces. This provides a more realistic measure of natural space than simple aggregations of areas, because it measures the ability of people to directly walk from every point in a city through or alongside nearby natural spaces.

Moreover, aggregate metrics do not generally capture the ability of people to actually access natural spaces. A park may, for example, have restricted or even private access. This would count as a natural space in a simply aggregate metric, yet not in UA because access restrictions are taken into account in the routing algorithms.

The algorithm also measures lengths of ways walked adjacent to water - so-called “blue space”, providing a comprehensive metric of the actual ability to access natural spaces from every point in a city. A natural space index of zero would represent an entire city of natural space, with no built structures at all, while a value of one would represent a complete absence of natural spaces.

4.7. Parking index

The parking index is the ratio of numbers of nearby parking spaces to total volumes of nearby buildings. The parking statistic is calculated for each point by adding all nearby parking spaces with a weighting scheme that decreases exponentially with distance, so that nearby parking spaces count more than parking spaces that are farther away. Building volumes are also aggregated using an identical weighting scheme. The parking index at each point is then the ratio of the sum of distance-weighted numbers of parking spaces to the sum of distance-weighted total building volumes.

All publicly accessible parking spaces are counted, including on-street parking, open parking lots, and multi-level parking garages. Building volumes are aggregated regardless of type or purpose.

4.8. Housing value and rent

For USA cities only, additional statistics are provided for average housing value per room, and average rental per room, both in US dollars.