From 2019... Urban spatial order: street network orientation, configuration, and entropy

From 2019... Urban spatial order: street network orientation, configuration, and entropy. Geoff Boeing. Applied Network Science volume 4, Article number: 67. Aug 23 2019. https://appliednetsci.springeropen.com/articles/10.1007/s41109-019-0189-1

Abstract: Street networks may be planned according to clear organizing principles or they may evolve organically through accretion, but their configurations and orientations help define a city’s spatial logic and order. Measures of entropy reveal a city’s streets’ order and disorder. Past studies have explored individual cases of orientation and entropy, but little is known about broader patterns and trends worldwide. This study examines street network orientation, configuration, and entropy in 100 cities around the world using OpenStreetMap data and OSMnx. It measures the entropy of street bearings in weighted and unweighted network models, along with each city’s typical street segment length, average circuity, average node degree, and the network’s proportions of four-way intersections and dead-ends. It also develops a new indicator of orientation-order that quantifies how a city’s street network follows the geometric ordering logic of a single grid. A cluster analysis is performed to explore similarities and differences among these study sites in multiple dimensions. Significant statistical relationships exist between city orientation-order and other indicators of spatial order, including street circuity and measures of connectedness. On average, US/Canadian study sites are far more grid-like than those elsewhere, exhibiting less entropy and circuity. These indicators, taken in concert, help reveal the extent and nuance of the grid. These methods demonstrate automatic, scalable, reproducible tools to empirically measure and visualize city spatial order, illustrating complex urban transportation system patterns and configurations around the world.

Discussion

The urban design historian Spiro Kostof once said: “We ‘read’ form correctly only to the extent that we are familiar with the precise cultural conditions that generated it… The more we know about cultures, about the structure of society in various periods of history in different parts of the world, the better we are able to read their built environment” (Kostof 1991, p. 10). This study does not identify whether or how a city is planned or not. Specific spatial logics cannot be conflated with planning itself, which takes diverse forms and embodies innumerable patterns and complex structures, as do informal settlements and organic urban fabrics. In many cities, centrally planned and self-organized spatial patterns coexist, as the urban form evolves over time or as a city expands to accrete new heterogeneous urban forms through synoecism.

Yet these findings do, in concert, illustrate different urban spatial ordering principles and help explain some nuances of griddedness. For example, gridded Buenos Aires has a φ value suggesting it only follows a single grid to a 15% extent. However, its low circuity and high average node degree values demonstrate how it actually comprises multiple competing grids—which can indeed be seen in Figs. 4 and 5—and it clusters accordingly in Figs. 6 and 7 with gridded American cities. Jointly considered, the φ indicator, average circuity, average node degree, and median street segment length tell us about the extent of griddedness and its character (curvilinear, straight-line, monolithic, heterogeneous, coarse-grained, etc.). Charlotte further illustrates the importance of taking these indicators together. Although its φ and orientation entropy are more similar to European cities’ than American cities’, it is of course an oversimplification to claim that Charlotte is therefore the US city with the most “European” street network—in fact, its median street segment length is about 50% longer than that of the average European city, and among European cities, Charlotte clusters primarily with those of the Communist Bloc. Pittsburgh, on the other hand, sits alone in a small sub-cluster with Munich and Vienna.

We find that cities with higher φ values also tend to have higher node degrees, more four-way intersections, fewer dead-ends, and less-winding street patterns. That is, cities that are more consistently organized according to a grid tend to exhibit greater connectedness and less circuity. Interestingly, the Ηo and Ηw orientation entropies are extremely similar and strongly correlated: the weighted curvatures (versus straight-line orientation) of individual street segments have little impact on citywide orientation entropy, but the average circuity of the city network as a whole positively correlates with orientation entropy. This finding deserves further exploration.

These results also demonstrate substantial regional differences around the world. Across these study sites, US/Canadian cities have an average φ value nearly thirteen-times greater than that of European cities, alongside nearly double the average proportion of four-way intersections. Meanwhile, these European cities’ streets on average are 42% more circuitous than those of the US/Canadian cities. These findings illustrate the differences between North American and European urban patterns. However, likely due to such regional heterogeneity, this study finds statistical relationships somewhat weaker (though still significant) than prior findings examining cities in the UK exclusively.

Accordingly, given the heterogeneity of these world regions, future research can estimate separate statistical models for individual regions or countries—or even the neighborhoods of a single city to draw these findings closer to the scale of planning/design practice. The methods and indicators developed here offer planners and designers a toolbox to quantify urban form patterns and compare their own cities to those elsewhere in the world. Our preliminary results suggest trends and patterns, but future work should introduce additional controls to clarify relationships and make these findings more actionable for researchers and practitioners. For instance, topography likely constrains griddedness and influences circuity and orientation entropy: a study of urban elevation change and hilliness in conjunction with entropy and circuity would help clarify these relationships. Additionally, further research can unpack the relationship between development era, design paradigm, city size, transportation planning objectives, and street network entropy to explore how network growth and evolution affect spatial order. Finally, given the importance of taking multiple indicators in concert, future work can develop a grid-index to unify them and eventually include streetscape and width attributes as further enrichment to explore walkability and travel behavior.