Fig. 184—To illustrate the canting of the snowline. A-B is the snowline depressed toward the north (right) in response to heavier precipitation. The line a-b represents a depression in the opposite direction due to the different degree of insolation on the northern (sunny) and southern (shady) slopes.
To these diversifying influences must be added the effect of warm up-valley winds that precede the regular afternoon snow squalls and that melt the latest fall of snow to exceptionally high elevations on both the valley floor and the spurs against which they impinge. The influence of the warmer air current is notably confined to the heads of those master valleys that run down the wind, as in the valley heading at the first pass, Cordillera Vilcapampa, and at the heads of the many valleys terminating at the passes of the Maritime Cordillera. Elsewhere the winds are dissipated in complex systems of minor valleys and their effect is too well distributed to be recognized.
It is clear from the conditions of the problem as outlined on preceding pages that the amount of canting may be expressed in feet of difference of the snowline on opposite sides of a range or in degrees. The former method has, heretofore, been employed. It is proposed that this method should be abolished and degrees substituted, on the following grounds: Let A and B, 190 , represent two mountain masses of unequal area and unequal elevation. Let the opposite ends of the snowlines of both figures lie 1,000 feet apart as between the windward and leeward sides of a broad cordillera (A), or as between the relatively sunnier and relatively shadier slopes of individual mountains or narrow ranges in high latitudes or high altitudes (B). With increasing elevation there is increasing contrast between temperatures in sunshine and in shade, hence a greater degree of canting (B). Tending toward a still greater degree of contrast is the effect of the differences in the amounts of snowy precipitation, which are always more marked on an isolated and lofty mountain summit than upon a broad mountain mass (1) because in the former there is a very restricted area where snow may accumulate, and (2) because with increase of elevation there is a rapid and differential decrease in both the rate of adiabatic cooling and the amount of water vapor; hence the snow-producing forces are more quickly dissipated.
Fig. 185—Glacial features in the Peruvian Andes near Arequipa. Sketched from a railway train, July, 1911. The horizontal broken lines represent the lower limit of light snow during late June, 1911. There is a fine succession of moraines in U-shaped valleys in all the mountains of the Arequipa region. A represents a part of Chacchani northwest of Arequipa; B is looking south by east at the northwest end of Chacchani near Pampa de Arrieros; C also shows the northwest end of Chacchani from a more distant point.
Fig. 186—Canted snowline in the Cordillera Vilcapampa between Arma and Choquetira. Looking east from 13,500 feet.
Fig. 187—Glacial topography between Lambrama and Antabamba in the Central Ranges. A recent fall of snow covers the foreground. The glaciers are now almost extinct and their action is confined to the deepening and steepening of the cirques at the valley heads.
Fig. 188—Asymmetrical peaks in the Central Ranges between Antabamba and Lambrama. The snow-filled hollows in the photograph face away from the sun—that is, south—and have retained snow since the glacial epoch; while the northern slopes are snow-free. There is no true glacial ice and the continued cirque recession is due to nivation.
Fig. 189—Glacial topography north of the divide on the seventy-third meridian. Maritime Cordillera. Looking downstream at an elevation of 16,500 feet (5,030 m.).
Furthermore, the leeward side of a lofty mountain not only receives much less snow proportionally than the leeward side of a lower mountain, but also loses it faster on account of the smaller extent of surface upon which it is disposed and the proportionally larger extent of counteractive, snow-free surface about it. Among the volcanoes of Ecuador are many that show differences of 500 feet in snowline elevation on windward and leeward (east) slopes and some, as for example Chimborazo, that exhibit differences of 1,000 feet. The latter figure also expresses the differences in the broad Cordillera Vilcapampa and in the Maritime Cordillera, though the rate of canting as expressed in degrees is much greater in the case of the western mountains.
Fig. 190—To illustrate the difference in the degree of canting of the snowline on large and on small mountain masses.
The advantages of the proposed method of indicating the degree of canting of the snowline lie in the possibility thus afforded of ultimately separating and expressing quantitatively the various factors that affect the position of the line. In the Cordillera Vilcapampa, for example, the dominant canting force is the difference between sun and shade temperatures, while in the volcanoes of Ecuador, where symmetrical volcanoes, almost on the equator, have equal insolation on all aspects and the temperature contrasts are reduced to a minimum—the differences are owing chiefly to varying exposure to the winds. The elusive factors in the comparison are related to the differences in area and in elevation.
The value of arriving finally at close snowline analyses grows out of (1) the possibility of snowline changes in short cycles and (2) uncertainty of arriving by existing methods at the snowline of the glacial period, whose importance is fundamental in refined physiographic studies in glaciated regions with a complex topography. To show the application of the latter point we shall now attempt to determine the snowline of the glacial period in the belt of country along the route of the Expedition.
In the group of peaks shown in 188 between Lambrama and Antabamba, the elevation of the snowline varies from 16,000 to 17,000 feet (4,880-5,180 m.), depending on the topography and the exposure. The determination of the limit of perpetual snow was here, as elsewhere along the seventy-third meridian, based upon evidences of nivation. It will be observed in 191 that just under the snow banks to the left of the center are streams of rock waste which head in the snow. Their size is roughly proportional to the size of the snow banks, and, furthermore, they are not found on snow-free slopes. From these facts it is concluded that they represent the waste products of snow erosion or nivation, just as the hollows in which the snow lies represent the topographic products of nivation. On account of the seasonal and annual variation in precipitation and temperature—hence in the elevation of the snowline—it is often difficult to make a correct snowline observation based upon depth and apparent permanence. Different observers report great changes in the snowline in short intervals, changes not explained by instrumental variations, since they are referred to topographic features. It appears to be impossible to rely upon present records for small changes possibly related to minor climatic cycles because of a lack of standardization of observations.
Nothing in the world seems simpler at first sight than an observation on the elevation of the snowline. Yet it can be demonstrated that large numbers of observers have merely noted the position of temporary snow. It is strongly urged that evidences of nivation serve henceforth as proof of permanent snow and that photographic records be kept for comparison. In this way measurements of changes in the level of the snowline may be accurately made and the snow cover used as a climatic gauge.
Farther west in the Maritime Cordillera, the snowline rises to 18,000 feet on the northern slopes of the mountains and to 17,000 feet on the southern slopes. The top of the pass above Cotahuasi, 17,600 feet (5,360 m.), was snow-free in October, 1911, but the snow extended 500 feet lower on the southern slope. The degree of canting is extraordinary at this point, single volcanoes only 1,500 to 2,000 feet above the general level and with bases but a few miles in circumference exhibit a thousand feet of difference in the snowline upon northern and southern aspects. This is to be attributed no less to the extreme elevation of the snow (and, therefore, stronger contrasts of shade and sun temperatures) than to the extreme aridity of the region and the high daytime temperatures. The aridity is a factor, since heavy snowfall means a lengthening of the period of precipitation in which a cloud cover shuts out the sun and a shortening of the period of insolation and melting.
Contrasts between shade and sun temperatures increase with altitude but their effects also increase in time. Of two volcanoes of equal size and both 20,000 feet above sea level, that one will show the greater degree of canting that is longer exposed to the sun. The high daytime temperature is a factor, since it tends to remove the thinnest snow, which also falls in this case on the side receiving the greatest amount of heat from the sun. The high daytime temperature is phenomenal in this region, and is owing to the great extent of snow-free land at high elevations and yet below the snowline, and to the general absence of clouds and the thinness of vegetation.
On approach to the western coast the snowline descends again to 17,500 feet on Coropuna. There are three chief reasons for this condition. First, the well-watered Majes Valley is deeply incised almost to the foot of Coropuna, above Chuquibamba, and gives the daily strong sea breeze easy access to the mountain. Second, the Coast Range is not only low at the mouth of the Majes Valley, but also is cut squarely across by the valley itself, so that heavy fogs and cloud sweep inland nightly and at times completely cover both valley and desert for an hour after sunrise. Although these yield no moisture to the desert or the valley floor except such as is mechanically collected, yet they do increase the precipitation upon the higher elevations at the valley head.
A third factor is the size of Coropuna itself. The mountain is not a simple volcano but a composite cone with five main summits reaching well above the snowline, the highest to an elevation of 21,703 feet (6,615 m.). It measures about 20 miles (32 km.) in circumference at the snowline and 45 miles (72 km.) at its base (measuring at the foot of the steeper portion), and stands upon a great tributary lava plateau from 15,000 to 17,000 feet above sea level. Compared with El Misti, at Arequipa, its volume is three times as great, its height two thousand feet more, and its access to ocean winds at least thirty per cent more favorable. El Misti, 19,200 feet (5,855 m.) has snow down as far as 16,000 feet in the wet season and rarely to 14,000 feet, though by sunset a fall of snow may almost disappear whose lower limit at sunrise was 16,000 feet. Snow may accumulate several thousand feet below the summit during the wet season, and in such quantities as to require almost the whole of the ensuing dry season (March to December) for its melting. Northward of El Misti is the massive and extended range, Chachani, 20,000 feet (6,100 m.) high; on the opposite side is the shorter range called Pichu-Pichu. Snow lies throughout the year on both these ranges, but in exceptional seasons it nearly disappears from Chachani and wholly disappears from Pichu-Pichu, so that the snowline then rises to 20,000 feet. It is considered that the mean of a series of years would give a value between 17,000 and 18,000 feet for the snowline on all the great mountains of the Arequipa region.[57] This would, however, include what is known to be temporary snow; the limit of “perpetual” snow, or the true snowline, appears to lie about 19,000 feet on Chachani and above El Misti, say 19,500 feet. It is also above the crest of Pichu-Pichu. The snowline, therefore, appears to rise a thousand feet from Coropuna to El Misti, owing chiefly to the poorer exposure of the latter to the sources of snowy precipitation.
It may also be noted that the effect of the easy access of the ocean winds in the Coropuna region is also seen in the increasing amount of vegetation which appears in the most favorable situations. Thus, along the Salamanca trail only a few miles from the base of Coropuna are a few square kilometers of quenigo woodland generally found in the cloud belt at high altitudes; for example, at 14,000 feet above Lambrama and at 9,000 feet on the slope below Incahuasi, east of Pasaje. The greater part of the growth is disposed over hill slopes and on low ridges and valley walls. It is, therefore, clearly unrelated as a whole to the greater amount of ground-water with which a part is associated, as along the valley floors of the streams that head in the belt of perpetual snow. The appearance of this growth is striking after days of travel over the barren, clinkery lava plateau to eastward that has a less favorable exposure. The quenigo forest, so-called, is of the greatest economic value in a land so desolate as the vast arid and semi-arid mountain of western Peru. Every passing traveler lays in a stock of fire-wood as he rests his beasts at noonday; and long journeys are made to these curious woodlands from both Salamanca and Chuquibamba to gather fuel for the people of the towns.
The process of nivation, or snow erosion, does not always produce visible effects. It may be so feeble as to make no impression upon very resistant rock where the snow-fall is light and the declivity low. Ablation may in such a case account for almost the whole of the snow removed. On strong and topographically varied slopes where the snow is concentrated in headwater alcoves, there is a more pronounced downward movement of the snow masses with more prominent effects both of erosion beneath the snow and of accumulation at the border of the snow. In such cases the limit of perpetual snow may be almost as definitely known as the limit of a glacier. Like glaciers these more powerful snow masses change their limits in response to regional changes in precipitation, temperature, or both. It would at first sight appear impossible to distinguish between these changes through the results of nivation. Yet in at least a few cases it may be as readily determined as the past limits of glaciers are inferred from the terminal moraines, still intact, that cross the valley floors far below the present limits of the ice.
In discussing the process of nivation it is necessary to assume a sliding movement on the part of the snow, though it is a condition in Matthes’ original problem in which the nivation idea was introduced that the snow masses remain stationary. It is believed, however, that Matthes’ valuable observations and conclusions really involve but half the problem of nivation; or at the most but one of two phases of it. He has adequately shown the manner in which that phase of nivation is expressed which we find at the border of the snow. Of the action beneath the snow he says merely: “Owing to the frequent oscillations of the edge and the successive exposure of the different parts of the site to frost action, the area thus affected will have no well-defined boundaries. The more accentuated slopes will pass insensibly into the flatter ones, and the general tendency will be to give the drift site a cross section of smoothly curved outline and ordinarily concave.”[58]
From observations on the effects of nivation in valleys, Matthes further concludes that “on a grade of about 12 per cent ... névé must attain a thickness of at least 125 feet in order that it may have motion,”[59] though as a result of the different line of observations Hobbs concludes[60] that a somewhat greater thickness is required.
Fig. 191—The “pocked” surface characteristically developed in the zone of light nivation. Compare with Fig. 194, showing the effects of heavy nivation.
Fig. 192—Steep cirque walls and valleys head in the Central Ranges between Lambrama and Chuquibambilla. The snow is here a vigorous agent in transporting talus material and soil from all the upper slopes down to the foot of the cirque wall.
The snow cover in tropical mountains offers a number of solid advantages in this connection. Its limits, especially on the Cordillera Vilcapampa, on the eastern border of the Andes, are subject to small seasonal oscillations and the edge of the “perpetual” snow is easily determined. Furthermore, it is known from the comparatively “fixed quality of tropical climate,” as Humboldt put it, that the variations of the snowline in a period of years do not exceed rather narrow limits. In mid-latitudes on the contrary there is an extraordinary shifting of the margin of the snow cover, and a correspondingly wide distribution of the feeble effects of nivation.
Fig. 193—Panta Mountain and its glacier system. The talus-covered mass in the center (B) is a terminal moraine topped by the dirt-stained glacier that descends from the crest. The separate glaciers were formerly united to form a huge ice tongue that truncated the lateral spurs and flattened the valley floor. One of its former stages is shown by the terminal moraine in the middle distance, breached by a stream, and impounding a lake not visible from this point of view.
Fig. 194—Recessed southern slopes of volcanoes whose northern slopes are practically without glacial modifications. Summit of the lava plateau, Maritime Cordillera, western Peru, between Antabamba and Cotahuasi.
Test cases are presented in Figs. 191, 192, and 193, Cordillera Vilcapampa, for the determination of the fact of the movement of the snow long before it has reached the thickness Matthes or Hobbs believes necessary for a movement of translation to begin. 191 shows snow masses occupying pockets on the slope of a ridge that was never covered with ice. Past glacial action with its complicating effects is, therefore, excluded and we have to deal with snow action pure and simple. The pre-glacial surface with smoothly contoured slopes is recessed in a noteworthy way from the ridge crest to the snowline of the glacial period at least a thousand feet lower. The recesses of the figure are peculiar in that not even the largest of them involve the entire surface from top to bottom; they are of small size and are scattered over the entire slope. This is believed to be due to the fact that they represent the limits of variations of the snowline in short cycles. Below them as far as the snowline of the glacial period are larger recesses, some of which are terminated by masses of waste as extensive as the neighboring moraines, but disposed in irregular scallops along the borders of the ridges or mountain slopes in which the recesses have been found.
The material accumulated at the lower limit of the snow cover of the glacial period was derived from two sources: (1) from slopes and cliffs overlooking the snow, (2) from beneath the snow by a process akin to ice plucking and abrasion. The first process is well known and resembles the shedding of waste upon a valley glacier or a névé field from the bordering cliffs and slopes. Material derived in this manner in many places rolls down a long incline of snow and comes to rest at the foot of it as a fringe of talus. The snow is in this case but a substitute for a normal mass of talus. The second process produces its most clearly recognizable effects on slopes exceeding a declivity of 20°; and upon 30° and 40° slopes its action is as well-defined as true glacial action which it imitates. It appears to operate in its simplest form as if independent of the mass of the snow, small and large snow patches showing essentially the same results. This is the reverse of Matthes’ conclusion, since he says that though the minimum thickness “must vary inversely with the percentage of the grade,” “the influence of the grade is inconsiderable,” and that the law of variation must depend upon additional observation.[61]
Let us examine a number of details and the argument based upon them and see if it is not possible to frame a satisfactory law of variation.
In 193 the chief conditions of the problem are set forth. Forward from the right-hand peak are snow masses descending to the head of a talus (A) whose outlines are clearly defined by freshly fallen snow. At (B) is a glacier whose tributaries descend the middle and left slopes of the picture after making a descent from slopes several thousand feet higher and not visible in this view. The line beneath the glacier marks the top of the moraine it has built up. Moraines farther down valley show a former greater extent of the glacier. Clearly the talus material at (A) was accumulated after the ice had retreated to its present position. It will be readily seen from an inspection of the photograph that the total amount of material at (A) is an appreciable fraction of that in the moraine. The ratio appears to be about 1:8 or 1:10. I have estimated that the total area of snow-free surface about the snowfields of the one is to that of the other as 2:3. The gradients are roughly equivalent, but the volume of snow in the one case is but a small fraction of that in the other. It will be seen that the snow masses have recessed the mountain slopes at A and formed deep hollows and that the hollowing action appears to be most effective where the snow is thickest.
Summarizing, we note first, that the roughly equivalent factors are gradient and amount of snow-free surface; second, that the unequal factors are (a) accumulated waste, (b) degree of recessing, and (c) the degree of compacting of snow into ice and a corresponding difference in the character of the glacial agent, and (d) the extent of the snow cover. The direct and important relation of the first two unequal factors to the third scarcely need be pointed out.
We have then an inequality in amount of accumulated material to be explained by either an inequality in the extent of the snow and therefore an inequality of snow action, or an inequality due to the presence of ice in one valley and not in the other, or by both. It is at once clear that if ice is absent above (A) and the mountain slopes are recessed that snow action is responsible for it. It is also recognized that whatever rate of denudation be assigned to the snow-free surfaces this rate must be exceeded by the rate of snow action, else the inequalities of slope would be decreased rather than increased. The accumulated material at (A) is, therefore, partly but not chiefly due to denudation of snow-free surfaces. It is due chiefly to erosion beneath the snow. Nor can it be argued that the hollows now occupied by snow were formed at some past time when ice not snow lay in them. They are not ice-made hollows for they are on a steep spur above the limits of ice action even in the glacial period. Any past action is, therefore, represented here in kind by present action, though there would be differences in degree because the heavier snows of the past were displaced by the lighter snows of today.
While it appears that the case presents clear proof of degradation by snow it is not so clear how these results were accomplished. Real abrasion on a large scale as in bowlder-shod glaciers is ruled out, since glacial striæ are wholly absent from nivated surfaces according to both Matthes’ observations and my own. Yet all nivated surfaces have very distinctive qualities, delicately organized slopes which show a marked change from any original condition related to water-carving. In the absence of striæ, the general absence of all but a thin coating of waste even in rock hollows, and the accumulation of waste up to bowlders in size at the lower edge of the nivated zone, I conclude that compacted snow or névé of sufficient thickness and gradient may actually pluck rock outcrops in the same manner though not at the rate which ice exhibits. That the products of nivation may be bowlders as well as fine mud would seem clearly to follow increase in effectiveness, due to increase in amount of the accumulated snow; that bowlders are actually transported by snow is also shown by their presence on the lower margins of nivated tracts.
Our argument may be made clearer by reference to the observed action of snow in a particular valley. Snow is shed from the higher, steeper slopes to the lower slopes and eventually accumulates to a marked degree on the bottoms of the depressions, whence it is avalanched down valley over a series of irregular steps on the valley floor. An avalanche takes place through the breaking of a section of snow just as an iceberg breaks off the end of a tide-water glacier. Evidently there must be pressure from behind which crowds the snow forward and precipitates it to a lower level.
As a snow mass falls it not only becomes more consolidated, beginning at the plane of impact, but also gives a shock to the mass upon which it falls that either starts it in motion or accelerates its rate of motion. The action must therefore be accompanied by a drag upon the floor and if the rock be close-jointed and the blocks, defined by the joint planes, small enough, they will be transported. Since snow is not so compact as ice and permits included blocks easily to adjust themselves to new resistances, we should expect the detached blocks included in the snow to change their position constantly and to form irregular scratches, but not parallel striæ of the sort confidently attributed to stone-shod ice.
It is to the plasticity of snow that we may look for an explanation of the smooth-contoured appearance of the landscape in the foreground of Fig. 135. The smoothly curved lines are best developed where the entire surface was covered with snow, as in mid-elevations in the larger snowfields. At higher elevations, where the relief is sharper, the snow is shed from the steeper declivities and collected in the minor basins and valley heads, where its action tends to smooth a floor of limited area, while snow-free surfaces retain all their original irregularities of form or are actually sharpened.
The degree of effectiveness of snow and névé action may be estimated from the reversed slopes now marked by ponds or small marshy tracts scattered throughout the former névé fields, and the many niched hollows. They are developed above Pampaconas in an admirable manner, though their most perfect and general development is in the summit belt of the Cordillera Vilcapampa between Arma and Choquetira, 135 . It is notable in all cases where nivation was associated with the work of valley glaciers that the rounded nivated slopes break rather sharply with the steep slopes that define an inner valley, whose form takes on the flat floor and under-cut marginal walls normal to valley glaciation.
A classification of numerous observations in the Cordillera Vilcapampa and in the Maritime Cordillera between Lambrama and Antabamba may now be presented as the basis for a tentative expression of the law of variation respecting snow motion. The statement of the law should be prefaced by the remark that thorough checking is required under a wider range of conditions before we accept the law as final. Near the lower border of the snow where rain and hail and alternate freezing and thawing take place, the snow is compacted even though but fifteen to twenty feet thick, and appears to have a down-grade movement and to exercise a slight drag upon its floor when the gradient does not fall below 20°. Distinct evidences of nivation were observed on slopes with a declivity of 5° near summit areas of past glacial action, where the snow did not have an opportunity to be alternately frozen and thawed.
The thickness of the former snow cover could, however, not be accurately determined, but was estimated from the topographic surroundings to have been at least several hundred feet. Upon a 40° slope a snow mass 50 feet thick was observed to be breaking off at a cliff-face along the entire cross-section as if impelled forward by thrust, and to be carrying a small amount of waste—enough distinctly to discolor the lowermost layers—which was shed upon the snowy masses below. With increase in the degree of compactness of the snow at successively lower elevations along a line of snow discharge, gradients down to 25° were still observed to carry strongly crevassed, waste-laden snow down to the melting border. It appeared from the clear evidences of vigorous action—the accumulation of waste, the strong crevassing, the stream-like character of the discharging snow, and the pronounced topographic depression in which it lay—that much flatter gradients would serve, possibly not more than 15°, for a snow mass 150 feet wide, 30 to 40 feet thick, and serving as the outlet for a set of tributary slopes about a square mile in area and with declivities ranging from small precipices to slopes of 30°.
We may say, therefore, that the factors affecting the rate of motion are (1) thickness, (2) degree of compactness, (3) diurnal temperature changes, and (4) gradient. Among these, diurnal temperature changes operate indirectly by making the snow more compact and also by inducing motion directly. At higher elevations above the snowline, temperature changes play a decreasingly important part. The thickness required varies inversely as the gradient, and upon a 20° slope is 20 feet for wet and compact snow subjected to alternate freezing and thawing. For dry snow masses above the zone of effective diurnal temperature changes, an increasing gradient is required. With a gradient of 40°, less than 50 feet of snow will move en masse if moderately compacted under its own weight; if further compacted by impact of falling masses from above, the required thickness may diminish to 40 feet and the required declivity to 15°. The gradient may decrease to 0° or actually be reversed and motion still continue provided the compacting snow approach true névé or even glacier ice as a limit.
From the sharp topographic break between the truly glaciated portions of the valley in regions subjected to temporary glaciation, it is concluded that the eroding power of the moving mass is suddenly increased at the point where névé is finally transformed into true ice. This transformation must be assumed to take place suddenly to account for so sudden a change of function as the topographic break requires. Below the point at which the transformation occurs the motion takes place under a new set of conditions whose laws have already been formulated by students of glaciology.
Fig. 195—Curve of snow motion. Based on many observations of snow motion to show minimum thickness of snow required to move on a given gradient. Figures on the left represent thickness of snow in feet. The degrees represent the gradient of the surface. The gradients have been run in sequence down to 0° for the sake of completing the accompanying discussion. Obviously no glacially unmodified valley in a region of mountainous relief would start with so low a gradient, though glacial action would soon bring it into existence. Between +5° and -5° the curve is based on the gradients of nivated surfaces.
The foregoing readings of gradient and depth of snow are typical of a large number which were made in the Peruvian Andes and which have served as the basis of 195 . It will be observed that between 15° and 20° there is a marked change of function and again between +5° and -5° declivity, giving a double reversed curve. The meaning of the change between 15° and 20° is inferred to be that, with gradients over 20°, snow cannot wholly resist gravity in the presence of diurnal temperature changes across the freezing point and occasional snow or hail storms. With increase of thickness compacting appears to progress so rapidly as to permit the transfer of thrust for short distances before absorption of thrust takes place in the displaced snow. At 250 feet thorough compacting appears to take place, enabling the snow to move out under its own weight on even the faintest slopes; while, with a thickness still greater, the resulting névé may actually be forced up slight inclines whose declivity appears to approach 5° as a limit. I have nowhere been able to find in truly nivated areas reversed curves exceeding 5°, though it should be added that depressions whose leeward slopes were reversed to 2° and 3° are fairly common. If the curve were continued we should undoubtedly find it again turning to the left at the point where the thickness of the snow results in the transformation of snow to ice. From the sharp topographic break observed to occur in a narrow belt between the névé and the ice, it is inferred that the erosive power of the névé is to that of the ice as 2:4 or 1:5 for equal areas; and that reversed slopes of a declivity of 10° to 15° may be formed by glaciers is well known. Precisely what thickness of snow or névé is necessary and what physical conditions effect its transformation into ice are problems not included in the main theme of this chapter.
It is important that the proposed curve of snow motion under minimum conditions be tested under a large variety of circumstances. It may possibly be found that each climatic region requires its special modifications. In tropical mountains the sudden alternations of freezing and thawing may effect such a high degree of compactness in the snow that lower minimum gradients are required than in the case of mid-latitude mountains where the perpetual snow of the high and cold situations is compacted through its own weight. Observations of the character introduced here are still unattainable, however. It is hoped that they will rapidly increase as their significance becomes apparent; and that they have high significance the striking nature of the curve of motion seems clearly to establish.
The facts brought out by the curve of snow-motion (Fig. 195) have an immediate bearing on the development of cirques, whose precise mode of origin and development have long been in doubt. Without reviewing the arguments upon which the various hypotheses rest, we shall begin at once with the strongest explanation—W. D. Johnson’s famous bergschrund hypothesis. The critical condition of this hypothesis is the diurnal migration across the freezing point of the air temperature at the bottom of the schrund. Alternate freezing and thawing of the water in the joints of the rock to which the schrund leads, exercise a quarrying effect upon the rock and, since this effect is assumed to take place at the foot of the cirque, the result is a steady retreat of the steep cirque wall through basal sapping.
While Johnson’s hypothesis has gained wide acceptance and is by many regarded as the final solution of the cirque problem it has several weaknesses in its present form. In fact, I believe it is but one of two factors of equal importance. In the first place, as A. C. Andrews[62] has pointed out, it is extremely improbable that the bergschrund of glacial times under the conditions of a greater volume of snow could have penetrated to bedrock at the base of the cirque where the present change of slope takes place. In the second place, the assumption is untenable that the bergschrund in all cases reaches to or anywhere near the foot of the cirque wall. A third condition outside the hypothesis and contradictory to it is the absence of a bergschrund in snowfields at many valleys heads where cirques are well developed!
Johnson himself called attention to the slender basis of observation upon which his conclusions rest. In spite of his own caution with respect to the use of his meager data, his hypothesis has been applied in an entirely too confident manner to all kinds of cirques under all kinds of conditions. Though Johnson descended an open bergschrund to a rock floor upon which ice rested, his observations raise a number of proper questions as to the application of these valuable data: How long are bergschrunds open? How often are they open? Do they everywhere open to the foot of the cirque wall? Are they present for even a part of the year in all well-developed cirques? Let us suppose that it is possible to find many cirques filled with snow, not ice, surrounded by truly precipitous walls and with an absence of bergschrunds, how shall we explain the topographic depressions excavated underneath the snow? If cirque formation can be shown to take place without concentrated frost action at the foot of the bergschrund, then is the bergschrund not a secondary rather than a primary factor? And must we not further conclude that when present it but hastens an action which is common to all snow-covered recesses?
It is a pleasure to say that we may soon have a restatement of the cirque problem from the father of the bergschrund idea. The argument in this chapter was presented orally to him after he had remarked that he was glad to know that some one was finding fault with his hypothesis. “For,” he said, with admirable spirit, “I am about to make a most violent attack upon the so-called Johnson hypothesis.” I wish to say frankly that while he regards the following argument as a valid addition to the problem, he does not think that it solves the problem. There are many of us who will read his new explanation with the deepest interest.
Fig. 196—Relation of cirque wall to trough’s end at the head of a glaciated valley. The ratio of the inner to the outer radius is 1:4.
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.”