Prominence Theory

It's time for a subjective quiz. Which of the following three lists of peaks in the western 48 contiguous states contains the "best picks" according to overall notoriety, stature, and climb-worthiness? In other words, if you were allowed to climb only 10 peaks in your entire life, which of these lists would you rather complete? Think hard now.

List #1List #2List #3
Gannett Peak Mount Massive Mount Shasta
Kings Peak Mount Harvard Mount Baker
Wheeler Peak NM Mount Williamson San Jacinto Peak
Boundary Peak Blanca Peak San Gorgonio
Granite Peak La Plata Peak Charleston Peak
Borah Peak Uncompahgre Peak Mount Adams
Humphreys Peak Crestone Peak Mount Olympus
Mount Hood Mount Lincoln Mount Hood
Guadelupe Peak Grays Peak Wheeler Peak NV
Harney Peak Mount Antero Glacier Peak

Because Mount Whitney, Mount Rainier, and Mount Elbert actually belong to all three lists, they contribute nothing to the comparison and were therefore omitted.

If you picked List #3, keep reading. Here's how the lists were generated:

List #1: The highest 10 state high points.
List #2: The highest 10 peaks by elevation.
List #3: The 10 peaks with the greatest prominence.

Definition

So what the heck is this thing called prominence in list #3? Several definitions are in use. Of the two shown below (which are mathematically equivalent except for esoteric differences when applied to the highest peak on a planet), the first is the way I prefer to describe it to others, while the second is the standard among my county high points colleagues.
  1. The height of a peak above the highest saddle connecting it to a higher peak. Here "saddle" means the lowest point on a ridge connecting two peaks.
  2. The height of a peak above the highest contour encircling it and no higher summit.
Got all that? If not, think of it as follows. Suppose that sea level were to rise high enough to submerge Peak X (the "Second Great Flood"). Now suppose that the water slowly drops; when the summit of Peak X is exposed, it becomes a tiny island. As the water continues to drop, the island grows larger and merges with other islands. For a while, Peak X will be the highest point on its island. Eventually, however, the Peak X island will merge with another island containing a higher point. The saddle of Peak X is the isthmus, or land bridge, that becomes exposed at the moment the islands touch, and the height of Peak X above the water at this point is its prominence.

If you're a climber, you might think of prominence this way. If you're standing on the summit of Peak X, and you wish to climb a higher peak, the prominence of Peak X is how far you must descend before doing so, no matter the higher peak or route chosen.

Uses

Despite its rather esoteric definition, prominence has a number of practical uses. These stem mostly from the fact that prominence is a measure of how well a peak stands out from its higher neighbors (which in a few cases may be quite some distance away). Prominence is very well-named; if one would describe a peak as "prominent" in plain English, it is probably quite prominent by the mathematical definition also. Similarly, a peak with great mathematical prominence is probably also prominent in plain English. This may seem like reinventing the wheel, but an objective definition turns out to have great practical value.

Although prominence has been used inadvertently for many years for some purposes, it was used only to support some other concept and not as a primary concept in its own right, and it did not even have a name for most of that time. In more recent times, however, prominence has been found to be an interesting and useful concept in its own right.

List Generation

Because prominence is a prophetic indicator of a peak's stature, a list of peaks based on a prominence criterion will often yield the best known and most easily recognized mountains. For example, a list of 5,000+ foot prominence summits in the 48 contiguous states contains many of the most revered, coveted, and sought-after peaks. The peaks with the greatest prominence are among those that give the hiker and climber the greatest sense of accomplishment. Those who seek technical climbing challenges will justifiably argue this point. However their goals are different from the prominence-oriented climber. Hence their respective "ideal lists" necessarily will differ.

One supreme advantage of a prominence-based list is that it is completely objective. In contrast, lists based on subjective considerations of "technical difficulty" necessarily will be different for every person. Unanimous agreement to a list ranking peaks by technical difficulty is impossible.

Comparing altitude above sea level is often like comparing apples and oranges. How can you compare a Colorado 14,000' list with a Washington 14,000' "list"? How can you compare a 6000' southern Appalachian sentinel with a 6000' Rocky Mountain foothill? You can't. But you can still compare prominences across these areas. Prominence comparison is always meaningful, even when altitudes are disparate and altitude comparison is meaningless. A 2000' prominence list for the Appalachians, Rockies, or Cascades would all lead the hiker and climber to the most interesting and climb-worthy peaks in each of these areas. Prominence is much better than elevation above sea level as a means of generating lists. We will see in the next section that prominence, unlike elevation, is capable of being the sole criterion for generating a list.

List Criteria

There are many lists of peaks that purport to show all peaks above a certain altitude or the highest n peaks in a certain area, such as the Colorado 14,000' list or the Colorado 100 highest. Any such list must face the criterion of whether to include a certain peak or exclude it because it was deemed a subsidiary of a higher nearby peak. It makes no sense to include every boulder, pinnacle, and crag, so the line must be drawn somewhere. Objective criteria are very important here because otherwise it can be impossible to reach a consensus in finalizing a list since the personal preferences of those with influence in preparing the list will inevitably come into play.

Prominence is a necessary criterion for deciding when to include a peak on an altitude-based list. For the Colorado 14,000' list, a peak must have at least 500' prominence. (Six others are also included because of their historical importance.) Some lists also have a horizontal separation requirement, but a list whose pruning criteria are based strictly on distance and not on prominence would have several undesireable characteristics. We see, then, that even if prominence is not the primary criterion for a list, it is unavoidable as a secondary criterion.

High Points vs. Prominent Points

There are many lists which show the highest point in each of some set of geographic areas, such as the 50 state high points, the counties of a given state, or the seven continental summits. With some types of areas, particularly those defined by political boundaries, the high point is sometimes on the border where rising terrain continues into a neighboring area. In a few of these cases, the high point is on the shoulder of a nearby peak worth climbing. But sometimes the high point is completely nondescript and would be of absolutely no interest if it were not the highpoint of some area. Even when the high point is not a "liner", it is sometimes a minor peak when compared to its surroundings. For example, Boundary Peak, the Nevada high point, would recede to obscurity and receive no attention if it were not a state high point.

Prominence presents a fresh alternative to these problems. Because prominence recognizes stature, the most prominent peak in a geographic area will necessarily be a mountain or hilltop. If the highest point and most prominent point are not the same, the latter will almost certainly be of greater interest to a hiker or climber.

In many cases the highest point and most prominent are the same. Exceptions are most likely when the highest point is near a border, and rising terrain continues beyond. When that happens, the way is cleared for a more prominent point elsewhere. The following table shows the number of highest-point most-prominent-point differences for various sets of areas for which both are known.

Area Set# of areas# of areas in which
the most prominent point
differs from the highest point
The fifty states 5024
California counties 5827
Nevada counties 179
Utah counties 2914
Arizona counties 154

Research and Development

If prominence is such an enlightening idea, why was it not developed earlier? The primary reason is that promenience is brutally tedious to determine in a comprehensive manner. To compute the prominence of a peak usually requires a considerable amount of time and a keen eye for detail in examining the contours on a topographic map to find a saddle connecting a given peak to a higher peak and verifying that there is no higher saddle. Few individuals have been inclined to pursue this task to date.

In cases where prominence was computed for the purpose of determining whether a given peak should be considered a separate peak for inclusion on an altitude-based list, the peak was usually close to a higher peak, and the area that had to be searched was limited. These cases are not very difficult. However, it has been nigh impossible to date to compile a complete list of all peaks in a large area above a certain prominence. Unless the prominence cutoff is very high, there is usually no way to be sure one has considered all possible candidate peaks above that prominence. Similar difficulties sometimes arise in trying to determine the most prominent point in a certain area. In states which are flat or finely convoluted, for example, it is very time-consuming to determine the prominence of perhaps many hundreds or even thousands of hilltops and verify that the search has included the most prominent point.

Another type of difficult and tedious case in prominence computation is that of peaks which are the highest for many miles around. Consider Mount Whitney, whose "prominence island" goes down to 4420' above sea level and has a very complex shape spannning well over 1000 miles from Canada to its saddle in New Mexico and includes all of the Rocky Mountains. To find such a monstrous bounding contour and verify the point of connectivity to a higher area is a monumental effort.

Thanks to the dedicated efforts of several individuals in the last few years, better prominence information is becoming available. The prominence of nearly all major peaks in the United States has been determined. The greatest prominence in most states has also been found with certainty orto a high degree of confidence. The most prominent peak in every county in Arizona and Nevada, California, and Utah has been determined.

Because of a state-of-the art computer algorithm recently developed and implemented, it is now possible to perform a comprehensive prominence analysis of large areas of the United states using digital elevation datafrom the USGS. Because the data available have some inaccuracies, it is necessary to verify the results by hand on a topographic map before placing confidence in them. Nevertheless, this is a useful tool for ensuring that all peaks in a given area have been accounted for. A manual analysis is likely to miss a few. The computer analysis has been used to prepare "50 finest" lists, which are simply the 50 peaks with the greatest prominence, for a few states. Similar lists are pending for more states and the contiguous United States.

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