As discussed in the introduction, these exercises will teach you about GPU compute through the lens of a tough geophysical problem. It's important to have a good understanding of the problem space before we can design a solution.
2021 was a deadly year for backcountry snow-sports enthusiasts in the United States, with 36 fatalities in the 2020-2021 season, with 15 deaths between January 30th, 2021 and February 6th, 2021. In two notable examples, on February 1, 2021, three men were killed by an avalanche near Ophir Pass, Colorado. On February 7, 2021, two men and two women were killed by an avalanche near Wilson Glades, Utah.
While 2021 was a bad year for avalanches, sadly, accidents with multiple fatalities are not uncommon. In 2003 7 people died in an avalanche at La Traviata Couloir in the Selkirk Mountains of British Columbia, including famed professional snowboarder Craig Kelly. Just weeks later, 7 Canadian students were tragically killed by an avalanche in Glacier National Park, British Columbia, Canada. As a result of these accidents, ParksCanada developed the Avalanche Terrain Evaluation Scale (ATES) so that recreational backcountry skiers could learn about avalanche exposure for popular winter backcountry terrain in Canada. In the US, terrain ratings are available in some guidebooks, but, in general, terrain ratings are not as popular in the US (although that is slowly changing).
Terrain ratings help by presenting analysis created by subject-matter experts in a format suitable for people with less expertise. This means that, after a recent storm, someone might propose "We should travel to the Misty Mountains for some skiing", but upon finding the terrain rated as Complex, they might decide to choose a different area, or to not go out at all. In the backcountry skiing and mountain guiding communities, this is known as "choosing terrain appropriate for conditions". Terrain ratings are important because not everyone is an avalanche expert. It's just a simple fact: you can't get killed by an avalanche if you don't travel in avalanche terrain, and you should only travel in avalanche terrain when it's reasonably safe to do so.
Typically, terrain ratings are created by avalanche professionals. For those not familiar, the term avalanche professional is probably a little vague, but it includes a wide range of people, from researchers with graduate degrees in snow science, and mountain guides, to people who work supervising avalanche control along mountain roads in the winter. Since the professional organizations in the US and Canada that certify snow safety and mountain guiding industries require experience with the specific terrain being rated as a prequisite to developing a rating in the first place, it's likely not possible to construct a terrain rating entirely by computer. However, it would be great if the computer could assist the expert by providing statistical analysis and visualizations with as little human bias as possible.
Let's see what that looks like.
The following terms are used extensively in geophysics, snow safety, and avalanche education in order to describe various geographic features and natural phenomena. These terms are used throughout this document and at other times in this series of exercises.
Table 1.1. Definitions
| Term | Definition |
|---|---|
| Avalanche Path | The downhill path taken by an avalanche. Avalanche paths are composed of a starting zone, a track where the avalanche descends, and runout zone where the avalanche comes to rest. Lots of backcountry skiing takes place in active avalanche paths. |
| Start Zone | The location where the avalanche starts. Technically a starting zone can be anywhere an avalanche starts, but the term starting zone typically refers to a location at the top of a known avalanche path where avalanches start. The return period could be once every twenty years, or one or more times per year. |
| Track | The path followed by the avalanche as it descends from the starting zone to the runout zone. Technically, a track is any path followed by any avalanche, but track typically refers to a location historically descended by avalanches on a regular basis. |
| Runout Zone | The location where the avalanche comes to rest. Technically, a runout zone can be anywhere an avalanche comes to rest, but runout zone typically refers to a location where avalanches are expected to come to rest. The distance from the start zone to the runout zone is variable, depending on how much snow is involved when the avalanche starts, but most avalanche paths have a theoretical maximum (which can include running uphill across the opposite size of a valley). |
| Terrain Trap | Any terrain feature that makes the consequences of an avalanche worse. If an avalanche takes a skier over a cliff, the consequences of the avalanche will be worse. Similarly, if a skier is buried in a gully, they will almost certainly be buried more deeply than if they were buried on generally flat ground. In these examples, the cliff and the gully are examples of terrain traps. |
| Convexity | A convexity is a terrain feature that has a spherical or bulging element to it, so that the snow is not held in place by compression forces at the base like it would be if the slope were flat or convex. Instead, on a convex slope, the snow is subject to tension forces, and it is easier to trigger avalanches on slopes with convex geometry rather than concave geometry. |
| Elevation Band | Typically, mountain terrain is separated into three elevation bands, with transition zones. The primary elevation bands are as follows: below tree line, at tree line, above tree line (alpine). |
| Multiple, Overlapping Runout Zones | An area where multiple avalanche paths deposit snow. |
| Convoluted | Terrain with many ups and downs or a 'rolling' character. Compare this with smooth terrain with a uniform slope angle. |
Stated simply, the Avalanche Terrain Evaluation Scale (ATES) breaks terrain into three groups, where avalanche exposure and risk determinations are rated as Simple, Challenging, and Complex.
Figure 1.1. Simple, Challenging, and Complex Terrain
The delineations between simple, challenging, and complex terrain are very obvious in these images, but you might be surprised how difficult it can be for experts and non-experts alike to develop objective ratings.
Now let's consider the ATES technical model, which outlines the parameters to consider when evaluating terrain. Some parameters, such as avalanche frequency or return period, are decidedly not trivial to analyze on a computer, but other parameters can be analyzed by using some surprisingly simple geostatistical methods that help us build very reasonable inferences.
Table 1.2. ATES Technical Model v.1-04
| 1 — Simple | 2 — Challenging | 3 — Complex | |
|---|---|---|---|
| Slope Angle | Angles generally < 30° | Mostly low angle, isolated slopes > 35° | Variable with large % > 35° |
| Slope Shape | Uniform | Some Convexities | Convoluted |
| Forest Density | Primarily treed with some forest openings. | Mixed trees and some open terrain. | Large expanses of open terrain. Isolated tree bands. |
| Terrain Traps | Minimal, some creek slopes or cutbanks. | Some depressions, gullies, and/or overhead avalanche terrain. | Many depressions, gullies, cliffs, hidden slopes above gullies, cornices. |
| Avalanche Frequency (events:years) | Avalanche of size 2 or greater every 30 years | Avalanche smaller than size 2 every year, avalanche greater than or equal to size 2 every 3 years | Avalanche smaller than size 3 every year, avalanche greater than or equal to size 3 every year |
| Start Zone Density | Limited open terrain. | Some open terrain. Isolated avalanche paths leading to valley bottom. | Large expanses of open terrain. Multiple avalanche paths leading to valley bottom. |
| Runout Zone Characteristics | Solitary, well-defined areas, smooth transitions, spread deposits. | Abrupt transitions or depressions with deep deposits. | Multiple converging runout zones, confined deposition area, steep tracks overhead. |
| Interaction With Avalanche Paths | Runout zones only. | Single path or paths with separation. | Numerous and overlapping paths. |
| Route Options | Numerous, terrain allows multiple choices. | A selection of choices of varying exposure, options to avoid avalanche paths. | Limited chances to reduce exposure, avoidance not possible. |
| Exposure Time | None, or limited exposure crossing runouts only. | Isolated exposure to start zones and tracks. | Frequent exposure to start zones and tracks. |
| Glaciation | None. | Generally smooth with isolated bands of crevasses. | Broken or steep sections of crevasses, icefalls or serac exposure. |
Now we find ourselves—as we so often do—at the intersection of things that are very easy for humans to see and reason about, and things that are very difficult for a computer to see or reason about at all. In fact, it's very easy to frame the problem of rating terrain as a problem of machine vision. Using just the elevation data itself, we can't easily measure things like start zone density, route options, or avalanche frequency, since those characteristics have no robust, consistent, easily-identifiable statistical basis. In light of this, we need to reduce the ATES technical model to just the characteristics that we can discern through computer modeling, and by doing so, we hope to rapidly increase the speed at which the analyst can create and verify terrain ratings.
In the following table, we've removed most of the ATES parameters. Why can we do this? There's a pretty simple answer: many of the ATES parameters are ultimately related to the amount of open terrain in an area, and to the transitions and changes in the amount of open terrain that occur between elevation bands. Generally speaking, the amount of open terrain increases with elevation as the number of trees decreases. This means that many popular skiing areas are located in alpine terrain at or above the tree line, or in places where natural avalanches have already removed many of the trees. We can factor out the elements we can't test, and make some reasonable assumptions that Simple terrain is generally below tree line, Challenging terrain is generally below tree line or around the tree line, and that Complex terrain is usually at tree line or above tree line. Now, it's very important to note that we can't absolutely rely on these assumptions, so we must rely on the fact that we are providing statistical analysis to an expert who can make sure that the results aren't misinterpreted.
Table 1.3. ATES Technical Model v.1-04 Reduced To Testable Model Parameters
| 1 — Simple | 2 — Challenging | 3 — Complex | 4 — Testability | |
|---|---|---|---|---|
| Slope Angle | Angles generally < 30° | Mostly low angle, isolated slopes > 35° | Variable with large % >35° | We can test this directly and provide a statistic. |
| Slope Shape | Uniform | Some Convexities | Convoluted | Can we use surface area as a proxy? |
| Terrain Traps | Minimal, some creek slopes or cutbanks. | Some depressions, gullies, and/or overhead avalanche terrain. | Many depressions, gullies, cliffs, hidden slopes above gullies, cornices. | Can we use topographic openness as a proxy? |
Solving the research questions in the table above required a fair amount of thinking and tinkering, but a group of avalanche professionals did conclude that tabulating the amount of avalanche terrain, measuring surface area, computing topographic openness, and respecting elevation bands, were acceptable proxies for other ATES parameters that we cannot test or characterize with empirical, statistical methods. To be clear: these statistics are suitable for use and analysis by subject-matter experts who are trained to understand the meaning of the information. Non-expert users must be extremely careful in forming conclusions, because their conclusions are more likely to contain serious errors. Finally, it's worth noting that expert in this context means someone with the requisite experience and technical knowledge, who has direct knowledge and experience with the terrain in question.
Table 1.4. Statistical Signals of Exposure
| Parameter | Explanation |
|---|---|
| Avalanche Terrain | Measure the amount of terrain in the test area that is greater than 35 degrees. This can be done with a high degree of accuracy. |
| Surface Area | Compute the surface area in square meters for the test area. This can be done with a high degree of accuracy. Surface area scores compare the surface area if the region were flat with the surface area after displacement by elevation values. As the surface area increases, the terrain generally becomes steeper and can hold more snow. In many cases, the overall amount of convolution also increases along with surface area. This can indicate the presence of rollovers, depressions, or choke points that increase the likelihood of a deep burial. |
| Terrain Traps | Compute the topographic openness for the test area. This can be done with fairly high accuracy, but we need to be careful in how we interpret this information because it is very sensitive to the scale of the terrain undergoing analysis. Topographic openness scores reflect the amount of openness to the sky found at each point in the terrain, as well as openness in general for sub-regions of the terrain. Sub-regions with low openness are often terrain traps where avalanches form deep deposits, or areas where line of sight may be limited due to obstruction by local terrain features. Broad reductions in openness generally indicate that there are significant limitations to line of sight at various spatial scales. |
| Alpine Terrain | The tree line varies with latitude and aspect. This means that as you travel toward either of the Earth's poles, the tree line gradually becomes lower. At the poles, the tree line is zero because trees cannot grow there. The tree line also varies with aspect, which means that slopes facing away from the sun may generally be cooler, which affects vegetation growth. For these reasons, we can't use an algorithm to establish a general tree line elevation for our analysis, but we can allow the analyst to provide the tree line elevation for the test areas, and we can generate accurate estimates of how much terrain is below tree line, at tree line, and above tree line. |
Now that we understand the problem space, it's time to start thinking about software.