The Andes of Southern Peru / Geographical Reconnaissance along the Seventy-Third Meridian

by Isaiah Bowman

Fig. 197—Mode of cirque formation. Taking the facts of snow depth represented in the curve, Fig. [195] , and transposing them over a profile (the heavy line) which ranges from 0° declivity to 50°, we find that the greatest excess of snow occurs roughly in the center. Here ice will first form at the bottom of the snow in the advancing hemicycle of glaciation, and here it will linger longest in the hemicycle of retreat. Here also there will be the greatest mass of névé. All of these factors are self-stimulating and will increase in time until the floor of the cirque is flattened or depressed sufficiently to offset through uphill ice-flow the augmented forces of erosion. The effects of self-stimulation are shown by “snow increase”; the ice shoe at the bottom of the cirque is expressed by “ice factor.” The form accompanying both these terms is merely suggestive. The top of “excess snow” has a gradient characteristic of the surface of snow fields. A preglacial gradient of 0° is not permissible, but I have introduced it to complete the discussion in the text and to illustrate the flat floor of a cirque. A bergschrund is not required for any stage of this process, though the process is hastened wherever bergschrunds exist.

We shall begin with the familiar fact that many valleys, now without perpetual snow, formerly contained glaciers from 500 to 1,000 feet thick and that their snowfields were of wide extent and great depth. At the head of a given valley where the snow is crowded into a small cross-section it is compacted and suffers a reduction in its volume. At first nine times the volume of ice, the gradually compacting névé approaches the volume of ice as a limit. At the foot of the cirque wall we may fairly assume in the absence of direct observations, a volume reduction of one-half due to compacting. But this is offset in the case of a well-developed cirque by volume increases due to the convergence of the snow from the surrounding slopes, as shown in [196] . Taking a typical cirque from a point above Vilcabamba pueblo I find that the radius of the trough’s end is to the radius of the upper wall of the cirque as 1:4; and since the corresponding surfaces are to one another as the squares of their similar dimensions we have 1:4 or 1:16 as the ratio of their snow areas. If no compacting took place, then to accommodate all the snow in the glacial trough would require an increase in thickness in the ratio of 1:4. If the snow were compacted to half its original volume then the ratio would be 1:2. Now, since the volume ratio of ice to snow is 1:9 and the thickness of the ice down valley is, say 400 feet, the equivalent of loose snow at the foot of the cirque must be more than 1:4 over 1:9 or more than two and one-quarter times thicker, or 400 feet thick; and would give a pressure of (900 ÷ 10) × 62.5 pounds, or 5,625 pounds, or a little less than three tons per square foot. Since a pressure of 2,500 pounds per square foot will convert snow into ice at freezing temperature, it is clear that ice and not snow was the state at the bottom of the mass in glacial times. Further, between the surface of the snow and the surface of the bottom layer of the ice there must have been every gradation between loose snow and firm ice, with the result that a thickness much less than 900 feet must be assumed. Precisely what thickness would be found at the foot of the cirque wall is unknown. But granting a thickness of 400 feet of ice an additional 300 feet for névé and snow would raise the total to 700 feet.

The application of the facts in the above paragraph is clearly seen when we refer to [197] . The curve of snow motion of [195] is applied to an unglaciated mountain valley. Taking a normal snow surface and filling the valley head it is seen that the excess of snow depth over the amount required to give motion is a measure at various points in the valley head and at different gradients of the erosive force of the snow. It is strikingly concentrated on the 15°-20° gradient which is precisely where the so-called process of basal sapping is most marked. If long continued the process will lead to the developing of a typical cirque for it is a process that is self-stimulating. The more the valley is changed in form the more it tends to change still further in form because of deepening snowfields until cliffed pinnacles and matterhorns result.

By further reference to the figure it is clear that a schrund 350 feet deep could not exist on a cirque wall with a declivity of even 20° without being closed by flow, unless we grant more rapid flow below the crevasse. In the case of a glacier flowing over a nearly flat bed away from the cirque it is difficult to conceive of a rate of flow greater than that of snow and névé on the steep lower portion of the cirque wall, when movement on that gradient begins with snow but 20 feet thick.

In contrast to this is the view that the schrund line should lie well up the cirque wall where the snow is comparatively thin and where there is an approach to the lower limits of movement. The schrund would appear to open where the bottom material changes its form, i.e., where it first has its motion accelerated by transformation into névé. In this view the schrund opens not at the foot of the cirque wall but well above it as in [198] , in which C represents snow from top to bottom; B, névé; and A, ice. The required conditions are then (1) that the steepening of the cirque wall from x to y should be effected by sapping originated at y through the agencies outlined by Johnson; (2) that the steepening from x to y should be effected by sapping originated at x through the change of the agent from névé to ice with a sudden change of function; (3) and that the essential unity of the wall x-y-z be maintained through the erosive power of the névé, which would tend to offset the formation of a shelf along a horizontal plane passed through y. The last-named process not only appears entirely reasonable from the conditions of gradient and depth outlined on pp. 296 to 298, but also meets the actual field conditions in all the cases examined in the Peruvian Andes. This brings up the second and third of our main considerations, that the bergschrund does not always or even in many cases reach the foot of the cirque wall, and that cirques exist in many cases where bergschrunds are totally absent.

It is a striking fact that frost action at the bottom of the bergschrund has been assumed to be the only effective sapping force, in spite of the common observation that bergschrunds lie in general well toward the upper limits of snowfields—so far, in fact, that their bottoms in general occur several hundred feet above the cirque floors. Is the cirque under these circumstances a result of the schrund or is the schrund a result of the cirque? In what class of cirques do schrunds develop? If cirque development in its early stages is not marked by the development of bergschrunds, then are bergschrunds an essential feature of cirques in their later stages, however much the sapping process may be hastened by schrund formation?

Our questions are answered at once by the indisputable facts that many schrunds occur well toward the upper limit of snow, and that many cirques exist whose snowfields are not at all broken by schrunds. It was with great surprise that I first noted the bergschrunds of the Central Andes, especially after becoming familiar with Johnson’s apparently complete proof of their genetic relation to the cirques. But it was less surprising to discover the position of the few observed—high up on the cirque walls and always near the upper limit of the snowfields.

A third fact from regions once glaciated but now snow-free also combined with the two preceding facts in weakening the wholesale application of Johnson’s hypothesis. In many headwater basins the cirque whose wall at a distance seemed a unit was really broken into two unequal portions; a lower, much grooved and rounded portion and an upper unglaciated, steep-walled portion. This condition was most puzzling in view of the accepted explanation of cirque formation, and it was not until the two first-named facts and the applications of the curves of snow motion were noted that the meaning of the break on the cirque became clear. Referring to [198] we see at once that the break occurs at y and means that under favorable topographic and geologic conditions sapping at y takes place faster than at x and that the retreat of y-z is faster than x-y. It will be clear that when these conditions are reversed or sapping at x and at y are equal a single wall will result. On reference to the literature I find that Gilbert recently noted this feature and called it the schrundline.[63] He believes that it marks the base of the bergschrund at a late stage in the excavation of the cirque basin. He notes further that the lower less-steep slope is glacially scoured and that it forms “a sort of shoulder or terrace.”