Monday, June 7, 2010

Intersection Density and Convergence Factor


In the urbanism blogosphere, there has been a good amount of buzz generated recently from a study by professors Reid Ewing and Robert Cervero of Utah and Cal-Berkeley, respectively where they determined that intersection density is the number one predictor of walkability.

Intuitively this makes sense in that the smaller the blocks, the greater number of intersections, the more storefronts, the more choice of route, etc. We have also known that intersection density is an indicator of traffic safety, based on a study that I cited here in Livability Indicator - Grid vs. Cul-de-sac.

Each of these compares suburbia to grid-like patterns and the results are predictable. But, what if we compared apples to apples, ie downtowns to downtowns? That would be great wouldn't. Well, fear not dear reader for I have begun to do exactly that. I've begun with a comparison of downtown Portland and downtown Dallas, but will be expanding to many other cities when I have the chance.

If intersection density is indicative of walkability, would walkability then be indicative of a more successful downtown? Let's back up to the original notion of what walkability is in the first place.

WalkScore is commonly used to measure the walkability of a place. What walkscore does is formulate the distance to the common destinations based on the input of a certain address. You get to 100 if you have everything you need within walking distance. We've pointed out WalkScore's primary flaw in that it only measures the quantitative, the distance, rather than the qualitative: Do I feel safe on this walk? Will cars run me over? Is it a comfortable walk? Is there plenty of visual interest along the way?

Plugging the center of downtown Portland and downtown Dallas into Walkscore and see who wins:

Downtown Dallas:

Downtown Portland:

Huh. Well that's no fun. They both achieve a perfect 100, "Pedestrian Paradise." Right. So what is the problem now with walkscore? Well, for one it doesn't calculate variety. Since I might be .2 miles from a McDonald's, I'm within walking distance of food. But, what if I want to eat something else? Shouldn't they also factor in distance to a variety of cuisines or a variety of clothing stores, etc?

For example, if you are at a strip center that has a fitness center, a super target, a drive-thru bank, a cinema, a bus stop, and pad sites including a starbucks and a McDonald's, you have pretty much everything you need within a 10-minute walk. You'd also be stuck in the middle of a sea of pavement. Good luck if it happens to be Summer in Texas, which it is. Once again, no measure of variety nor quality of place or experience.

Therefore, the metric of intersection density is still better at determining not only walkability, but overall population density and diversity as well.

I don't want to dwell on WalkScore's inherent simplicity, but rather analyze the idea of intersection density. Intersection density suggests a place that is more interconnected, a necessity of urban places. What bothers me is that it also suggests that all intersections are perceived equally. Here is something I recently wrote in regards to the original study:
Furthermore, Density is merely the response to desirability and walkable urban form is what accommodates a range of densities based on demand. Diversity, well that is simply a by-product of livability, which has at its root mobility where walkability is still the best mode with the most positive and least negative externalities.

Like all 'alpha' studies, I find the simple measure of intersections per square area, while helpful, overly abstract. In one instance, they seem to be saying that two-way intersections are better for walkability than four-way because they lead to denser intersections. What about dense network of four-way intersections?

This goes beyond walkability and more toward the "neural network" and interconnectivity of the grid in general, but as we all know a four-way intersection generates traffic from 4-directions rather than 2 creating a higher degree of traffic (by foot or car) which retailers need, which in turn can (dependent upon design) generate more foot traffic.

This study could get "smarter," in my opinion if instead of merely counting intersections it assigned a rating system to each of those intersections. In a way measuring node density (or quality thereof) rather than just intersection density and the node rankings would be based on two factors off the top of my head:

1) amount of directions intersecting the intersection, ie a four-way is better than a two-way (distance of which is mitigated by the density calc) and then;

2) a professional subjective factor of quality of pedestrian experience.
This post will examine #1 within the simple metric of intersection density if for no other reason, but to see what happens. The hypothesis is that there exists a need for another overlay, to add a measure of hierarchy to the intersections. At the root of this exercise is my theory of convergence. If you need a primer on convergence, click here for a detailed description. As mentioned in that post, places like Champs Elysees, DuPont Circle, Times Square, and pick a trivium in Rome are of extreme convergence. The high value of these places is a direct correlation to it convergence. Since we are dealing with intersections for the purposes of this study, this post will only discuss 2-dimensional convergence or that of the street grid.

I like the idea of convergence because it assesses the hierarchy of a given site or street. Where is it in relation to its context. How much traffic would be moving by the site. This is predictive of ultimate real estate value. In a conventional urban setting, the place with the highest degree of convergence was the "high street" or "main street". All roads led to those. Because they experienced the greatest degree of convergence, the most amount of traffic, the most density agglomerated around those areas.

What this also helps to measure is the urban vs. the anti-urban. The urban experiences a great deal of traffic, but maintains walkability and density. In the anti-urban development density withdraws from traffic. This is the difference between good traffic and bad traffic. In the urban setting buildings/streets/places interact with each other. In the anti-urban, each component exists disconnected from each other or only loosely connected at best, generating a place that is generally worth less than the sum of its parts. This characteristic is felt through the experience of each place.

Another hypothesis is that this also allows us to determine whether the vitality of a place matches its convergence. I would theorize that if the empirical vitality, the livelihood we see out on the street every day of pedestrians, successful storefront businesses, and occupied real estate density matches the degree of convergence or exceeds it, you have a truly walkable urban place. If not, there are barriers to overcome in order to achieve highest value and best use of a site.

  • I will be using 1-square mile areas of downtowns, with what I determine to be the heart of the downtown as the center point of the 1-mile square as a control.
  • I have established a weighting system for various intersections which is as follows:

  • As you can see, rather than each intersection being counted as one, various types of intersections get "bonuses" if you will for greater degree of convergence (people arriving from more directions).
1 - A common T-intersection
2 - One-way street crosses another one-way street
3 - One-way street crosses a two-way street
4 - Four-way intersection
(If greater than four, the points will be determined by points or directions of arrival, ie six-way intersection gets 6 points.)
  • The purpose of adding directional analysis to the intersections is because of its predictability for retail success and visitors ability to navigate streets.
  • It is understood that this alone doesn't establish a greater degree of walkability, but various intersections will have more traffic moving past, meaning increased hierarchy of presence of place.
  • This will not count mergers or off-ramps as intersections because they are designed to keep traffic flowing at a rate of speed hostile to pedestrian activity. Furthermore, they typically come from the same direction.
  • With that said, Texas U-turns will also not count as additional points beyond whatever intersections are also occurring on site.
  • This also will not count parking lot or site access ingresses or egresses. These are not streets.
  • For now, this also doesn't count pedestrian ways. The only reasoning is that Dallas doesn't currently have the density to support them, but in time it is expected that I will add a pedestrian component, particularly to begin comparisons with say, Venice.
  • For the time being, transit-only "malls" also will not count.
  • I haven't done this yet, but in later versions of the study I reserve the right to "ding" or administer (-1) demerits to certain intersections that are particularly anti-pedestrian despite their point rating, i.e. if there are rolling right turns or a road is overly wide with no pedestrian refuge or crosswalk. My guess is that once I start applying professional opinion, this will increase the overall intelligence and value of each study. For the time being however, we will remain within the realm of objectivity.
  • Two-way boulevards with median will count as a typical two-way street unless the open space between the two lanes is wide enough to support development within it. This is important with regard to Portland's many one-way couplets with open space esplanades within. Those will count as two one-way streets.
  • Also, for the time-being this does not account for where a particular road comes from, an influence from Space Syntax, ie a road that runs a long-way with numerous intersections will have a greater degree of convergence than a similar one. Eventually, I want to get into multiplier effects for this, but just haven't had time to administer that kind of complexity.
  • Eventually, I also want to add another level to this and that is the measure of "bondedness" between blocks. Rather than intersections this will be measuring the street between the intersections (as well as the intersection) to determine the permissibility of a street to facilitate crossing. My guess is there are three kinds of "bonded" streets: 0 street - virtually nobody crosses, 1 street - where people will cross at crosswalks at intersections, and 2 street - where jaywalking is common and pedestrians cross at will. For the time being this has also been left out of this study.
  • Lastly, like all studies and statistics this is a rhetorical abstraction. It is by no means meant to explain every attribute of the City.

First, you will see a 1-square mile of downtown Dallas with red dots placed at every intersection. If it reveals anything yet, it illustrates the negative effect certain buildings and in some cases roads have on walkability or the interconnection of urban places.

Next is Portland:

You can see how small Portland's typical block size is of 200' x 200' square and the incredibly intricate gridded web of their downtown. It is also important to note that the majority of Portland streets are one-way, possibly necessary given the scale of the streets and blocks, although they seem to be slowly but surely implementing two-way streets into their downtown. On several streets, I had to double check whether they were one-way or two-way using google earth aerial imagery, streetview, and mapquest.

Downtown Dallas: 186 intersections per square mile
Downtown Portland: 356 intersections per square mile

Next, I added a numeral figure to each intersections detailing what degree of convergence each intersection had:



You can click to enlarge each image, but I decided that this isn't graphically revealing. So I decided to add "weight" to each of the dots. The size I chose was rather arbitrary, and chosen specifically for the graphic:

1 - 20 px
2 - 40 px
3 - 80 px
4 - 160 px

My hope is that increasing the size of the dots exponentially in relation to their convergence rating might help to reveal a multiplier factor but that is to be determined.


This doesn't reveal any place that is any more or less walkable, but it does highlight places that aren't, in the voids near no or very little red color. To me, this suggests areas that should have high degrees of vitality. Also important to note, is that many of our streets in downtown are quite hostile to pedestrians. They are anti-urban as noted above and we get streets with great potential but very little real, urban vitality in the highly red areas. This is a remnant of transportation planning policies that suggested pedestrians and cars must always be segregated.

I think this means that I need to apply professional and potentially subjective criteria as mentioned above to "demerit" the anti-urban streets or intersections. I think it would make for an interesting contrast to overlay an empirical "heat map" based on real, measured pedestrian traffic day-to-day.

The interesting thing here is that the most walkable place in downtown Dallas is Main Street, between areas of high convergence: the two-way streets of Griffin and Harwood. These two points are exactly where the recently constructed Main Street Garden Park is and where the eventual Belo Garden Park will be, offering anchors to the walkable district.

This would suggest that I probably also need to factor in the multiplier effect of "meta-convergence" or how far are these roads coming from, how big is their draw?


With Portland, you see the splotches of red north of Burnside Street, one of the major streets of "meta-convergence" because it crosses the Willamette River into downtown. The more red indicates the two-way streets Portland has in this part of town. What is interesting, is that aside from Burnside, Portland has largely kept their primary arterials one-way. The areas in dark red are more likely to be residential streets.

Something else interesting is the very little amount of red at edges, suggesting that edges can be problematic for urban places. In this case, it is mostly due to the waterfront, something I wrote about here. Vital urban places want to be internal, central convergence points of an interconnected meshwork. Connections outward from a downtown are critical to vitality.

This also illustrates what a good job Portland has done addressing the 405 Freeway, maintaining the grid for much of downtown except where it falls apart towards the interchange.

You can also see where bridges elevate to cross the river and the off-ramps Portland has off of them, that negatively affect walkability where the dots disappear. This is also noticeable in the Dallas Diagram.


Portland's grid is highly "democratic" in that many of the streets are the same size, scale, shape, and function. There are also other contributing factors to hierarchy that the "red dots" do not measure (yet). In Portland, these include the many green spaces they have in their downtown as well as transit lines. As stated earlier, these will eventually be factored into the equation.

Downtown Dallas: 391 intersection points per square mile
Downtown Portland: 746 intersection points per square mile

You might be surprised to learn that in both cases the Dallas number was 52% of the Portland number. Does that mean Dallas is 52% as walkable? 52% as successful? 52% as vital of a downtown? Or is this a natural correlation to density? Was the hollowing out of the City a byproduct or at least expedited by the larger street and block system of Dallas? Or will they be a barrier to overcome as Dallas looks to revitalize?

All of that is to be determined as I start adding other cities as well.


Off-ramps, merges, and interchanges - while they may deliver people, the form is often anti-urban, disconnected, and hostile to pedestrian connectivity, the neural network of a City. I might liken it to rain water runoff where a natural system slowly filters, absorbs, and releases rainwater into groundwater or bodies of water. But where there is a lot of impervious surfaces, ie roads and parking lots, water is collected and channeled directly into a body of water, typically far more than the ecosystem can handle. The result is vast amounts of erosion and a damaged ecosystem. This is the same for cities when the delivery mechanisms of people to place are too intense. Off-ramps, without being tempered through design, pollute the cities fabric.

Edges are bad - Highways, bodies of water, geographic features, over-scaled buildings, etc all can create edges. These are barriers to connectivity and must be addressed to improve overall vitality.

T-intersections or no intersections at all - These mapped areas are not coincidentally dead zones.

Good Streets - are those that accommodate pedestrians and cars at the very least. Those with greater hierarchy should have more modes also accommodated, ie bike lanes and transit.

The occasional outlier is created by the intersection of minor-streets that both happen to be two-way. I will have to address this. Perhaps only measuring streets that connect beyond a district or applying a categorical hierarchy between the two?

As far as Dallas is concerned, this suggests that streets like Lamar, Harwood and Griffin have vast amounts of unmet potential. Perhaps even enough for me to suggest they should be the priorities moving forward with the downtown plan. Now if someone could just explain to me why Harwood was dead ended at Woodall Rogers Park...

Lastly, this concludes that I am a giant nerd for enjoying this so much and looking forward to improving the metric as well as adding other cities to it.