Kai Xu, Yale University
This repo provides the Google Earth Engine scripts (in JavaScript) for computing the datumless measures of topographic relief: dominance, jut, submission, and rut. These concepts are explained in my research paper here. For much friendlier explanations, check out these five-minute explanations of dominance, jut, and dominant points (related to submission).
To compute the datumless measures, the first step is to create a Google Earth Engine account here. For the question "What would you like to accomplish with Earth Engine?", say that you are interested in computing the datumless measures of topographic relief, and include the link of the research paper (https://arxiv.org/abs/2208.01600) to increase your chances of approval. Your account should be approved within a few hours to a few days.
Once your account is approved, you can access and run the code here. Instructions are provided in the code as comments.
If you measured a mountain, it would be great to add it to the database of datumless measures for mountains. Mountains are identified by their Peakbagger.com PID, which is found in the URL of a mountain on the website. For instance, the Peakbagger.com URL for Mt. Whitney is https://www.peakbagger.com/peak.aspx?pid=2829 and its PID is 2829.
On Earth, the relief of a mountain or other surface feature is measured with elevation, or height above sea level. However, for elevation to work on planets without a sea level, scientists have to define a "fake sea level" corresponding to zero elevation, also known as a datum. On such planets, the datum doesn't correspond to real surface features, hence the elevation of a point doesn't describe much by itself. Take Mt. Sharp on Mars, whose summit elevation of 728 meters reveals nothing by itself about the approximately 5 kilometer rise of the mountain above the floor of the Gale Crater that it rests within.
Instead, on other planets, the local relief of a point is assessed by comparing its elevation with that of its surroundings. For instance, the height of mountains on other planets is usually listed as base-to-peak height. However, what exactly counts as the base of a mountain? The current approach is to choose a point that "feels like" the base—a method that is undoubtedly arbitrary.
Introducing the datumless measures: a new way of quantifying relief that is based not on elevation, but purely on gravity and the planetary surface. The datumless measures provide a universally consistent way to quantify relief on any terrestrial planet or asteroid, including Earth. The four datumless measures are as follows:
- Dominance measures how much a point rises above its surroundings. Among its applications, it provides a non-arbitrary base-to-peak measure of the height of any mountain on any planet. For a point within a mountain range, dominance usually describes how much it rises from the bottom of the mountain range. A point with a dominance of 0 is known as a submissive point, and is akin to a local low point. After releasing my paper, it was made known to me that the concept for dominance was actually first invented by the mountaineers Jerry Brekhus and Andy Martin in 2006 in a private online forum.
- Jut measures how sharply/impressively a point rises above its surroundings, accounting for both height and steepness. Jut is inspired by the omnidirectional relief and steepness (ORS) measure, also known as the spire measure, which was invented by Edward Earl and David Metzler to quantify the perceived impressiveness of a protruding landform such as a mountain or cliff. Jut achieves a similar goal using a formula that is easier to understand. For a point within a mountain range, jut typically describes how sharply it rises from the bottom of a neighboring valley or a major mountain face. As such, it is particularly useful for detecting sharply rising mountain faces, and is the measure on this list that is most of interest to mountaineers.
- Submission measures how much a point dips below its surroundings. A point with a submission of 0 is known as a dominant point, and is akin to a local high point. For a point within a mountain range, submission usually describes how much it dips below the highest summits of the mountain range.
- Rut measures how sharply/impressively a point dips below its surroundings, accounting for both height and steepness. For a point within a mountain range, rut usually describes how sharply it dips below a neighboring mountaintop.