Why is it Mount Baker and Mount Rainier, and not Baker Mountain or Rainier Peak? Are Peaks really peakier and Mounts more massive, or do summit titles follow too much whim and misnaming for any significant relationships to exist? I first pondered this question a few years ago,
during a cold overnight bivy or an endless snow slog. So, when the final project in my
statistics class involved conducting a regression analysis on a dataset
of our choice, I knew exactly what my topic would be: "Are Summits
Titled by Topography or Whim?
A Multinomial Logistic Regression Study on Mountains, Mounts, and
In this project, I use multinomial logistic regression techniques to show that there are in fact numerically significant differences in the topography of Peaks, Mounts, and Mountains; and that the general characteristics of the three summit types can be quantified in terms of elevation, prominence, and isolation. Using these results, I look at interesting applications such as using the modeling techniques to compare the topography of different mountainous areas (such as Washington vs. Colorado), quantifying the "strength" of a summit's type (such as Prusik Peak being a stronger Peak than Puny Peak), and evaluating if the post-eruption Mount St. Helens is still a real Mount.
I've tried to present the findings in a way that can be
understood by the curious climber. The following page gives a summary of some—thought not all—of the key findings of my study. You can download my full report (link at the top of the page) if you are interested in more.
Enjoy (and learn)!
The dataset used in this analysis lists the 2,027 Peaks, Mounts, and Mountains in Washington state, along with their respective elevations, prominences, and isolations. Although this dataset excludes summits that do not fall within these categories (such as Spires, Towers, numbered ridgeline highpoints, and names that are too creative to be restrained by titles such as Himmelgeisterhorn, The Wart, and Beheaded Dog), the dataset encompasses a majority (roughly 95%) of the significant summits in Washington. The data is freely available online at listsofjohn.com. (See my report for a more complete explanation of how I came to have 2,027 summits in my analysis.)
An interesting characteristic of the data is that there are several summits in Washington that have the same names. This is especially true for the lower profile Mountains that might be known only locally. Also, Mountain-namers have taken a greater liking to colors than have Peak-namers and Mount-namers – there are 17 Green Mountains, 9 Red Mountains, 6 Blue Mountains, 4 White Mountains, 3 Black Mountains, and 1 Purple Mountain in the state.
The goal of this project is to associate the summit class (i.e. Mountain, Mount, or Peak) with elevation, prominence, and isolation. The dependent variable is the summit class, which in this analysis is either "Peak," "Mount," or "Mountain." Since names are categorical and have no order, this is a nominal variable (i.e. cannot be ordered in any meaningful way). There are three continuous independent variables that are analyzed in terms of their relationship towards the summit title:
Multinomial logistic regression exists to handle the case where the dependent variable is nominal and consists of more than two categories. I won't go into the details here (you can see my attached report if you are interested), but in the end I ended up with equations relating the topographical characteristics of the summit (i.e. elevation, prominence isolation) to the probability of the summit being each summit type (i.e. Mountain, Mount, or Peak). The following marginal plots were generated during the regression analysis, and represent the probabilities of summit type and their relationship to the variables in the model (which were elevation, log(isolation), and log(isolation)*prominence).
The results of this regression analysis suggest that there are in fact significant topographical differences between Mountains, Mounts, and Peaks. The trends evidenced for each summit type seem to fit the general mental images one forms when they picture Mountains, Mounts, and Peaks, a fact which adds intuitive support to my model. Despite the fact that no summit-naming convention exists and summit names are often just a result of what sounded good to the namer, it is clear that there is a tendency – subconscious or otherwise – to call low profile masses Mountains, large isolated massifs Mounts, and clustered peaky summits Peaks. Some inconsistencies might result from how a summit is perceived from different angles – such a summit that appears as a rocky bump on one side and a sheer face on the other. Although whim and inconsistency are inherent to naming, in the end any apparent inconsistencies do not invalidate the generality we can derive from the model, but merely point out that there in fact is a generality that can be used to either predict or classify a summit as is a Mountain, Mount, or Peak.
The following figure shows the general characteristics of Mounts, Mountains, and Peaks evidenced by the data.
So, what can we do with the regression results, other than make general conclusions about how topography is related to summit type? An interesting application of the model is to define a factor (which I will call the "Strength" factor, S) that gives an indication of how strongly as summit fits into a particular summit class, based on the model equations. For example, Prusik Peak and Little Tahoma Peak are certainly more "peaky" than Eldorado Peak or Dome Peak, and Glacier Peak seems more of a Mount than a Peak. The Strength factor, S, quantifies the topographic differences between these peaks.
The multinomial logistic regression created two model equations. A summit's set of elev, prom, and iso can be input into the model equations to generate the probability that the summit is either a Peak, Mount, or Mountain. Mathematically, the Strength factor is based on the differences between the predicted probabilities for the three summit types. For more details, including a formula for the strength factor, see my attached paper.
The Strength factor, S, ranges from -1 to 1, where:
The following table provides some examples of some well-known summits that are classified as "strong," "weak," and "mistitled" according to the model.
At 8:32 am on May 18, 1980, Mount Saint Helens became about 1300 ft shorter. Its catastrophic eruption was the deadliest and most economically destructive volcanic event in the history of the United States. An interesting question, based on my regression results, is whether the post-eruption Mount Saint Helens is still indeed a lofty Mount? Or has the loss of 1300ft of elevation (and prominence) qualified it as a more mellow Saint Helens Mountain?
The dataset for the regression analysis listed Mount Saint Helens with its pre-eruption elevation, prominence, and isolation, as these were its statistics at the time the summit was named. According to the odds prediction equations generated by our regression analysis (which predict the odds that a summit is a Mount, Peak, or Mountain given its elevation, prominence, and isolation), the pre-eruption Saint Helens was indeed a Mount, with 74% odds (with only 6% odds of being a Mountain). Plugging the post-eruption statistics into the same equations shows that Saint Helens is still a Mount, but a more "mountainous" Mount now with 59% odds of being a Mount and 18% odds of being a Mountain.
So what scale of eruption would have been required for Saint Helens to become a Mountain? It turns out that in order for the odds of being a Mountain to outweigh the odds of being a Mount, the eruption would have had to blast 1200 more feet from the summit. This would have required orders of magnitude more energy.
And Rainier? Well, it turns out Rainier would remain a Mount until it blew enough of its top to become shorter than any of the summits nearby. If Little Tahoma remained standing, then Rainier would only have to lose 3300 ft to become Rainier Peak.
Regression can be fun and interesting!
The following alternative view of summit-naming was proposed by JScoles on Summitpost.org. Although I can think of several exceptions to Rules 1-3 (such as Sumas or Goat Mountains, Gilbert or Snowfield Peaks, Mount Deception or Torment), I cannot think of any exceptions when Rule 4 is considered.
If it was ever so easy to math it out like that.
In reality in English it follows four very simple rules: