Terrain Analysis of the 50 Largest Cities in the USA

The United States is land of great geographic diversity. It's home to a collection of cities that are very diverse as well, both geographically and culturally. I was curious about which American City is the hilliest. I also wanted to know which was the flattest. Plenty of people were arguing for cities such as San Francisco and Seattle on reddit and other forums, but I knew there had to be a better way to quantify this problem than just basing it on opinion. As an avid GIS student and user, I figured GIS would be a great way to solve this problem.

Besides just being curious, the topography of a city influences a wide variety of things. From transportation to recreation to real estate to city planning, the hilliness of a city plays a large role in shaping where we live. Good luck finding a job at a ski resort if you live in a flat city. However, that flat city might be better for agricultural jobs. The way a city's street system is set up to the where buildings and neighborhoods are located are all influenced by topography.

I had to figure out what it even meant for a city to be hilly and then devise a methodology that allowed me to use spatial data and GIS to rank the cities. Is a city more hilly if it has large mountains surrounding all sides of the city? Or is it more hilly if it has rolling hills throughout? Should a city be considered more hilly if it has an extreme range of elevations throughout the city, or if the downtown has some steep slopes (see Lombard Street in San Francisco above). I don't think there is a definition set in stone for what exactly makes a city more hilly than another, but I tried to devise a scheme that made sense and was well-rounded. In the end, I would use multiple metrics that measure certain components of hilliness to create a composite score that ranks all the cities from hilliest to flattest.

First, let me introduce you to the cities that will be involved in this research. I selected the 50 largest cities (city proper, not metro area) by population based on 2014 estimates. Feel free to zoom around on the terrain basemap and make your predictions. Here are the cities:

The only data needed was information about the city locations and elevation data. For the cities, I created a layer containing the boundaries (city limits) for each city as well as a point layer that represented the downtown area for each city. I downloaded elevation data off the National Map website in the from of 1 arc-second (30m) resolution digital elevation model's. I created a 1-mile buffer polygon around each downtown point that was used for a metric described below, and I also create slope rasters (percent rise) for each DEM. I mosaiced the DEM's together in ArcMap to create a DEM representing all the cities needed.

I wanted to combine several metrics that indicate the hilliness of a city to create a composite score that would be used to rank the cities from hilliest to flattest overall. This composite score would range from 0 to 100. A score of 100 would mean the city had the highest or hilliest value for each of the metrics. A score of 0 would indicate that the city had the lowest value for each metric. After much consideration, I ended up using 4 metrics that would go into my composite score. These metrics were elevation range, elevation standard deviation, mean slope throughout the city boundaries, and mean slope within a mile 1 buffer zone of each cities downtown. Each metric had a scaled value from 0 to 100 that was assigned to each city and then used to create the composite score. The Zonal Statistics to Table tool within ArcGIS Pro was used for calculating the metrics.

The elevation range is the difference between the highest and lowest point within each city boundary. I felt this metric is important because a high range indicates a very prominent hill or even mountain within a city that can be visually striking.

Results:

This metric heavily favored western cities, as the highest city that I wouldn't consider western was San Antonio at 13. Los Angeles was far out in front with a range of over 1,500 meters within city limits. There was a huge gap between the top and the rest of the cities in this metric, as the 6th ranked city (San Jose) had less that half the range of the highest ranked city. Over half of the cities had scaled values under 10 as many cities simply couldn't compete with those in mountainous areas.

The standard deviation metric was also based off values from the DEM, and the entire city area was used in computation. The standard deviation indicates how varied or how spread out the elevation values are for a city. For example, the elevation values of a city that is very flat would not have very spread out values for elevation. If a city had an area that was near sea level and also had areas that rose up thousands of feet in hilly and mountainous terrain, than the values for elevation would be very spread out. The first flat city described would have a standard deviation close to 0, and the city with widespread elevation values would have a higher standard deviation. This metric gives a good overall indication of elevation change throughout the city and will favor cities with large elevation changes across the city boundaries. A high standard deviation, similarly to the range, doesn’t necessarily mean that there are dramatic hills or rolling hills throughout the city, but a high value indicates that the elevation of the city is not static and this would mean that you are often moving uphill or downhill as you transverse the city.  

Results:

I expected to see a lot of similarities between these first two metrics, and my expectations were pretty much met. Western cities grouped at the top for this as they did with range. Honolulu was no surprise to top this list, as the city boundaries go well up into the mountains of Oahu at a couple thousand feet and the low values are at sea level. Miami once again found itself at the bottom of list with a standard deviation value at just 1.52. This means that the majority of the elevation throughout the city is about the same. In the case of Miami, this is just a few feet above sea level. A notable change here was Baltimore, jumping up from a range rank of 29 to a standard deviation rank of 17.  

These final two metrics used were based on the mean slope of the cities. I created a slope raster for each city. The slope was defined using percent rise, which takes the rise and divides it by the run before being multiplied by 100. This means a slope of 45 degrees would equal a percent rise of 100%. Basically, higher percent values indicate steeper hills, so the premise is pretty to understand. I felt the mean slope for an entire city did a good job of encapsulating how hilly the city was because it would show the average steepness of land throughout the city limits.

Results:

This metric was not close at the top as Honolulu was a major outlier here with a mean slope throughout the city limits of 28.10%. This was close to tripling the city that came next, which was San Diego at 11.26%. Miami made it’s way out of the basement, coming in at number 49 with Fresno taking the bottom spot with a mean slope of 0.56%. It wasn’t all western cities at the top this time, although they still fared the best compared to the other geographic regions. Nashville, Atlanta, Kansas City, Raleigh, and Washington D.C. represented the central and eastern areas in the top 15 spots. Las Vegas, which ranked very high for both the range and standard deviation, dropped quite a bit to the 23rd spot. 

The downtown mean slope values are the same as mentioned above for the entire city but for an area closer the main center of each city.  I thought it was important to weight the downtown areas of these cities for the final composite ranking because the areas near downtown often play such a large role in the public image of a city. I discovered that a 1-mile radius covered much of the central business district for many of the cities listed, excluding the largest downtown areas like New York, Chicago, and Los Angeles. 

Results:

Portland had the highest mean slope within 1 mile of their downtown with a value of 9.55. This was quite an outlier compared to the other cities. Downtown Portland is actually quite flat where the majority of the buildings and streets are as it sit next to the Willamette River. However, right to the west of downtown are steep hills running parallel to the river that are dotted with expensive homes that offer a great view of downtown. These hills made up a decent portion of the 1-mile buffer zone around downtown and is the reason Portland scored so high here. The Arizona cities of Phoenix and Mesa had the flattest downtowns. Many of the neighborhoods around the Phoenix Valley are very flat but offer views to mountains surrounding the city. I expected the downtown areas to have lower mean slopes than the cities as a whole, and that pattern showed in the results. Only 5 downtowns had mean slopes over 5%, while 18 cities had mean slopes over 5%. The internet forum crowd that kept mentioning San Francisco and Seattle as being among the hilliest cities must’ve been talking about the city centers as both of these cities were among the top 5 here. A surprise to most people who have never visited has to be Kansas City, as it was had the third highest rank. It’s downtown sits upon a bluff overlooking the confluence of the Kansas and Missouri Rivers. 

The composite score represents each cities relative hilliness based on the above metrics. After much thought, I decided to weight each metric equally for their level of contribution to the composite score because I felt each metric represented an important aspect of the perceptive hilliness of a city. The composite score was created by averaging out each cities scaled value for the 4 metrics. I found the scaled score more important than rank because it accounted for how much hillier the first place city was when compared to the second place city for any given metric rather than just accounting for ordinal rank. A composite score of 100 would indicate that the city had a scaled value of 100 for each metric. This means it would have had the highest value among all the cities for each category. A composite score of 0 would mean that it had the lowest value for each city among all categories. I used this scale because it was interesting to see where the majority of the cities fell and how close a city could be to being the hilliest among all metrics measured. The average ranking value was determined by calculating the average rank finish of each city for the 4 metrics. For example, Honolulu ranked 5th, 1st, 1st, and 6th for the metrics, averaging out to be 3.25.

Results:

Here is the list ranking the 50 largest cities in the United States of America. There were a lot of cities here that were closer to being one of the flattest cities possible (composite score of 0) than there were to being one of the hilliest cities possible (composite score of 100). This is probably because a city that would score close to 100 would be very hard to build large enough to be one of the most populated cities in the country, and flat land is a very easy and attractive option to build large cities upon. Honolulu was the hilliest city by quite some margin with a composite score of 78.13. Los Angeles came in with a comfortable padding as the second hilliest city with a composite score of 68.74. Miami sure tried to be the flattest city by every metric considered, but it’s very slight downtown slope kept it’s composite score above 0 at 1.25.

Las Vegas and San Diego were two cities among the hilliest in the country that are interesting cases to look at to examine how the metrics worked together. Las Vegas, with a composite rank of 4, doesn’t have a lot of up and down rolling hills in the city. Hence, its mean city slope ranking was near the middle of the pack. However, it had very high scaled values in elevation range and elevation standard deviation. The high range was due to a few mountains making it into the city limits on the western edge of the city, and the high standard deviation is because the city is basically slowly rising uphill from east to west from 1600 feet to 4000 feet. This means that you are always driving slightly uphill or downhill as you cross the city east-west. Even though it may appear to some that Las Vegas is in a flat valley, the valley floor is sloping the entire way and there are mountains making their way into the city on the west side. Thus, Las Vegas should be considered among the hilliest cities in the country because of the sloping valley floor and high elevation range. 

San Diego is an opposite case from what we see with Las Vegas. It ranked very high for the slope metrics, as it was 2nd in each category. It also did pretty well with both elevation range and standard deviation, as those rank 11th and 10th respectively. So with an average rank value of 6.25, which was third lowest among all 50 cities, why does San Diego come in 7th on the composite ranking? This is because it’s scaled values were between 30 and 42 for all categories except mean downtown slope, which was high at 73.78. While it’s elevation range and standard deviation were good overall, they didn’t stack up with the best performers in that category, like Las Vegas. And while San Diego’s mean city slope was very high (2nd rank), the scaled score for that category was just a 38.84 because Honolulu was such an outlier in that category.

When looking regionally, the west dominated in hilliness (if you consider Honolulu and El Paso the west). Nashville was the first non-western city in the ranking at 11, closely followed by Kansas City and Atlanta.  The map below shows how all the cities fared based on their geography.

My goal was to create a definitive ranking of the 50 largest cities in the United States from hilliest to flattest, and I'm pretty happy with the list I ended up with. The west certainly dominated at the top of the list, and I felt like it should based on cities I have been to in this country.

 A few cities that I would like to see stack up against this list include Pittsburgh, Cincinnati, Salt Lake City and Anchorage. Pittsburg has a very hilly reputation and is home to the steepest street in the entire country, Canton Avenue. Cincinnati is another river city that is nicknamed the "City of Seven Hills". Salt Lake City is bounded closely by the Wasatch Mountain Range to the east. The capitol of Utah sits on a prominent hill overlooking downtown. Anchorage is mostly flat, but it also is bounded by prominent mountains, the Chugach Range.

There were a couple considerations I had about changing the methodology. I considered adding metric that was the percentage of total area in the city with a slope over 5%. I also considered making the weight of the elevation range and standard deviation less. Both of these changes would have make the list less dominated by western cities. However, I do believe western cities feel more hilly because of the dramatic topography so I kept the system as is. I also considered using city ranks instead of scaled values for each metric as weighted values for the final composite score. However, I felt the composite score was better because it accounted for proportional differences instead of just ordinal rank. Most cities would have ranked similarly had I used rank values anyways.

This work could be used as a foundation for further research. The topography of a city affects many things like transportation, recreation, urban planning and more. Research could examine the relationship between hilliness and automobile accidents. You could look at how hilly a city is compared to the number of people who bike to work, or compare urban density with the composite score. So many interesting questions could be asked and researched relating hilliness to another topic. GIS would be a powerful tool for those problems as well, just as it was in solving my question.

Now I hope to be able to explore all of these places in person someday to see how hilly they seem when I'm really there. Honolulu is the first place on my list.