In general a permanent stream at one point in a valley means a continuous stream from that point to the sea or lake which the valley joins; but to this rule there are many exceptions. They are likely to arise where a stream heads in a region of abundant precipitation, and flows thence through an arid tract where the ground-water level is low, and evaporation great. In such cases, evaporation and absorption may dissipate the water gathered above, and the stream disappears (Fig. 2, Pl. III, near Paradise, Nev.).
Other modes of valley development.—If as a new area of land emerges from the sea its surface has a depression without an outlet, and such an assumption is by no means improbable, the depression would be filled with sea-water. The inflowing water from the surrounding land might fill the basin to overflowing, and the outflow, finding exit at the lowest point in the rim of the basin, would flow thence toward the sea. Such a stream would develop a valley, the history of which would be somewhat different from that which has been sketched. Instead of developing headward from the sea, the valley would be in process of excavation all the way from the initial basin to the sea at the same time (Fig. 54). The upper end of the valley might ultimately be cut to the level of the bottom of the basin, when the lake would disappear. The head of the valley might then work back across the former site of the lake into the territory beyond. Valleys might have developed above the lake before it was drained, and after this event, such valleys would make connections with the valley below (Fig. 55). A valley developed in this manner is not simply a gully grown big by head erosion, and the valley would not precede the stream.
If a surface of land were notably irregular before valleys were developed in it, there might be many lakes, and the flow from a higher lake might pass to a lower. If the lakes were ultimately drained, the several sections of the valley would be joined to one another without intervening basins. In certain regions, especially those which have been affected by continental ice-sheets, this has been a common method of valley development in post-glacial time. In this case also the stream precedes its valley, and not the valley its stream. Many post-glacial valleys, on the other hand, antedated their permanent streams, as in the cases first described.
If the gradient of a slope on which valleys are to develop is notably unequal, though without basins, the development of valleys may follow somewhat different lines. If on emergence the seaward part of a new land area assumes the form of a plain, bordered landward by a steeper slope (Fig. 56), the most notable early growth of the valleys would be on the latter. The run-off would develop gullies on the steep slope, but on reaching the plain below the velocity of the water would be checked, and it would drop much of the detritus washed down from above. This deposition would build up (aggrade) the surface, and much or even all the water might sink into and seep through the débris thus deposited, and disappear altogether from the surface, as at b, Fig. 56. This would be most likely to occur where the débris is abundant and coarse, and the precipitation slight. If the water disappears at the base of the mountain (see Fig. 2, Pl. III), the early growth of the valley may be confined to the steep slope remote from the sea (ab, Fig. 56); but on the slope where the valley is growing there will be headward lengthening, as in the general case already considered. If the surface drainage does not disappear at the base of the steep slope, the run-off will find its way over the plain along the lowest accessible route to the sea (de, Fig. 56). In this case the valley may be growing throughout its length at the same time.
The conditions represented by ab, Fig. 56, may be no more than temporary. Sooner or later a valley developing headward across the plain (hi, Fig. 56) may provide a channel for the water descending from the higher land beyond. In this case the valley develops in sections, the one on the slope above, the other on the plain below, and their union (compare fghi, Fig. 56, with Fig. 57) results from their growth.
The principles here sketched have been in operation wherever land areas were so elevated as to give rise to unequal slopes, and this has perhaps been the rule rather than the exception. The results effected by the operation of these principles would of course be dependent on the varieties of slope, on the abruptness with which a slope of one gradient gave place to another, on the texture of the rock, the amount and distribution of precipitation, etc., etc.
In the preceding paragraphs the lengthening of a valley at its upper end by head erosion has been repeatedly referred to. If all valleys began their development at the sea and lengthened headward, it might seem that their seaward ends should be their oldest parts; but since the development of valleys is begun somewhat promptly after the land appears above the sea, and since the emergence is generally gradual, that part of a valley which is at the seashore at one time may be far inland a little later, because the land has been extended seaward. On an emerging land area therefore the normal growth of a valley involves its lengthening at its lower end as well as at its upper. The lengthening of a valley, or at least the lengthening of a stream, also takes place at its lower end if the land in which it lies is being extended seaward by deposition.
Structural valleys.—In mountain regions valleys are sometimes formed by the uplift of parallel mountain folds, leaving a depression between (Fig. 58). Drainage will appropriate such a valley so that it becomes in some sense a river valley. But it is not a river valley in the sense in which the term has been used in the preceding pages. It is rather a structural valley. In its bottom a river valley may be developed (a, Fig. 58).
The foregoing illustrations by no means exhaust the list of conditions under which valleys develop, but they suffice for the present.
The courses of valleys.—River valleys are rarely straight. To understand why they are crooked it is only necessary to understand the methods by which they grow. In so far as a river valley is a gully grown big, that is, in so far as its length is the result of head erosion, its course was determined by the course of the antecedent gully. If in the case shown in Fig. 59 the slope of the surface above the head of the gully is uniform, its material homogeneous, and the rainfall everywhere equal, more water will come into the gully from the direction a than from any other. In this case there would be more wear in the direct line of its extension than elsewhere, and the head would advance in a straight line. But if there be inequalities of slope about the head of a gully at any stage of its development more water may come in from some direction other than that in the direct line of its extension. In Fig. 59, for example, more water may enter from the direction of b than from that of a. Since most wear is likely to be affected along the line of greatest inflow, the head of the gully will be turned in that direction (Fig. 60). Started in this course it will continue in the new direction so long as erosion in this line is greater than that elsewhere; but whenever the configuration of the surface causes more water to enter the head of the gully from some direction other than that in which it is headed, the line of axial growth is again changed, as toward c, Fig. 60. Since new land surfaces are probably more or less undulatory, crookedness should be the rule among valleys developed from gullies by head erosion. Streams and valleys the courses of which are determined by the original slope of the land are said to be consequent.
Inequalities of material, leading to unequal rates of erosion, effect the same result, in the absence of inequalities of slope. If at any stage of a valley’s development erosion were equal in two directions at its head, and at the same time greater than at points between, two gullies would result (Fig. 61) diverging from the point in question.
In the case of a valley developed by overflow from a lake its course is determined by the lowest line of flow to which the water has access. If this line be straight the valley will be straight; if it is crooked, as it generally is, the valley is crooked also.
The development of tributaries.—Thus far valleys leading immediately to the sea have been considered, and no account taken of tributaries. As a matter of fact most considerable valleys have numerous tributaries. It is now in order to inquire into their mode of development.
So soon as a gully is started, the water flowing into it from either side wears back the slopes. The least inequality of slope, or the least variation in the character of the material, is sufficient to make the lateral erosion unequal at different points, and unequal erosion in the slopes results in the development of tributary gullies. The oldest tributaries may be nearly as old as the main which they join, and from which they developed, for the possibilities of unequal side erosion exist as soon as a gully is opened. While the main gully is developing into a ravine, and the ravine into a valley, the tributary gullies are likewise developing into maturer stages. Tributary to a young valley, therefore, there may be gullies near its head, ravines in its middle course, and small valleys along its oldest portion. It is not to be understood, however, that the oldest tributaries are necessarily the largest, for because of more favorable conditions for growth the younger tributaries often outstrip the older.
The position of tributaries with reference to their mains is worthy of note. The water flowing down a slope follows the line of steepest descent. A gully is usually wider at its lower end, and narrower at its upper. Wherever this is true the line of steepest descent down its side is not a line perpendicular to its axis, but a line slightly oblique to it (ef, Fig. 62), and oblique in such a direction that it meets the axis with an obtuse angle below and an acute angle above. It is in the direction corresponding to this line that tributary gullies tend to develop. Thus at the inception of its history a tributary gully is likely to join its main with an angle slightly acute on the up-stream side. If the tributary did not begin until after its main was farther advanced this tendency would be less and less pronounced. Inequalities of material or slope would often counteract this tendency, which, at best, would cause the courses of tributaries to depart but little from perpendicularity to their mains.
After the head of a tributary has worked back from the immediate slope of its main every condition which determines the course of a gully is likely to affect it, and it is by no means certain that it will continue to lengthen in the direction in which it started. Since the general slope of the surface into which the tributary works is likely to be seaward, more water is likely to enter from the landward than from the seaward side of its head, so that, except where there are notable irregularities of slope, its tendency will be to turn more and more toward the direction of its main (efg, Fig. 62).
In depth the tributary is always limited by its main. The principles which determine the length and width of a main valley determine also the length and width of a tributary (see p. 67 et seq.).
From what has preceded it is clear that the topography of a region undergoing erosion will change greatly from time to time. The first effect of erosion is to roughen the surface by cutting out valleys, leaving ridges and hills. The final effect is to make it smooth again by cutting the ridges and hills down to the level of the valleys.
The base-level of erosion has already been defined; but the mode of its development may now be illustrated in the light of the preceding discussion. Suppose a land surface affected by a series of parallel young valleys without tributaries (Fig. 63). Between them there is a series of upland plateaus. The profile of the surface between two adjacent valleys is represented in section by the uppermost line in Fig. 64. As the valleys are widened from 1–1 and 1,′–1′, to 2–2 and 2′–2′, the intervening plateau is correspondingly narrowed. When the valleys have attained the form represented by 3–3 and 3′–3′, the intervening upland has been narrowed to a ridge, a, and the valley flats have become wide. With continued erosion the ridge will be lowered (to b and below), and in time the surface will approach a plain. In this condition it is known as a peneplain (an “almost-plain”). Finally, when running water has done its utmost, the ridges will be essentially obliterated and a base-leveled plain (e, e′, e″) results. The figure expresses the fact that the base-level develops laterally from the axis of the valley. It also develops headward from the seaward end of the valley. Similarly, taking into account all the valleys which affect it, the seaward margin of a base-leveled plain is developed first, and thence it extends itself inland.
Tributaries are tolerably sure to develop along each main valley. The heads of the tributaries work back across the uplands between the main valleys, dissecting them into secondary ridges (Fig. 65). Tributaries will develop on the tributaries, and these tertiary valleys dissect the secondary ridges into those of a lower order. This process of tributary development goes on until drainage lines of the fourth, fifth, sixth, and higher orders are formed (Fig. 66). Since the process of valley development under such circumstances is also the process of ridge dissection, a stage is presently reached where the ridges are cut into such short sections that they cease to be ridges, and become hills instead. Even then the processes of erosion do not stop, for the rain-water falling on the hills washes the loose material from their surfaces, and starts it on its seaward journey. Thus the “everlasting hills” themselves are lowered, and, given time enough, will be carried to the sea. Under these conditions, as under those already discussed, the final result of stream erosion is the reduction of the land to base-level. The base-leveled surface, as before, would not be absolutely flat. The area reduced by each stream will have a slight gradient down-stream, and from each lateral divide toward the axis of the valley. The crests of the scarcely perceptible elevations which remain will be in the position of the former divides, and these will be highest where most distant from the sea by the course which this part of the drainage took. Even the insensible divides between streams flowing in a common direction may disappear, for when valleys have reached their limits in depth, their streams do not cease to cut laterally. Meandering in their flat-bottomed valleys, they often reach and undercut the divides (Pl. VII), whether they be high or low. By lateral planation, therefore, the divides between streams may be entirely eaten away.
It has now been seen that by whatever method erosion by running water proceeds, whether there be many valleys, or few or none, the final result of subaërial erosion must be the production of a base-level. It has also been seen that the base-level is first developed at the lower ends of the main streams, and that it extends itself systematically up the main valleys and up all tributaries. The time involved in the reduction of a land area to base-level is a cycle of erosion.
It will have been evident from the preceding pages that the terms “grade,” “graded plain,” and “base-level” and “base-leveled plain,” are somewhat variously, and therefore somewhat confusingly, used. “Grade is a condition of essential balance between corrasion and deposition.”[29] A graded valley is one in which deposition and corrasion are, in the vertical sense, balanced. Its angle of slope is most variable, and is dependent on the capacity of the stream for work, and on the work it has to do. A weak river must have a higher gradient than a strong one; a stream with much sediment must have a higher gradient than one with little, and a stream with a load of coarse material must have a higher gradient than one with a load of fine. Thus the graded valley of the lower Mississippi has an inappreciable angle of slope, but the graded valleys of many of its tributaries have slopes of hundreds of feet per mile. Since both the size of the stream and the amount and coarseness of its load at a given place vary from time to time, it is clear that the inclination of a graded valley must vary also, and further, that it must be in process of continual readjustment. With the changing conditions of advancing years the slope of a graded valley normally decreases. The same principles apply to graded surfaces outside of valleys.
In the continual readjustment of grades incident to a river’s normal history the land is brought nearer and nearer to sea-level without ceasing to be at grade. When the inclination of a graded surface becomes so low that it is sensibly flat, the surface may be said to be at base-level, although this does not mean that the surface can never be degraded further. If the term be used in this way, it is clear that there is no sharp line of distinction between a graded surface and a base-leveled surface, and as the terms are now commonly applied no such distinction exists.
If the term base-level were made synonymous with sea-level, as has been proposed,[30] the term might as well be discarded, for sea-level could always be used in its stead. Furthermore, streams often erode below sea-level. The bottom of the channel of the Mississippi is below sea-level for some 400 miles above its debouchure, and locally (Fort Jackson) it is nearly 250 feet below. This deep channel is the result of the erosive activity of the stream, not of subsidence. Again, the sea-level is itself inconstant. The extent of its changes cannot now be measured, but they have probably been more considerable in the course of geological history than has been commonly recognized. It is true that they take place slowly, as far as known, but it is also true that the duration of an erosion cycle is sufficiently long for even very slow changes to reach great magnitude. The sea-level, therefore, can hardly be accepted as the absolute base-level, unless (1) the absolute base-level is a variable, and unless (2) the absolute base-level be a surface below which rivers may cut to the extent of at least 250 feet.
The ocean may be looked upon as a barrier which in a general way limits the down-cutting of running water; for only very large streams cut much below its level. Other barriers, such as lakes, and the outcrops of hard rock in a stream’s bed, have a comparable, though more temporary, effect on the development of valley plains above. Plains thus developed have been called temporary base-levels. They differ from other graded plains in being controlled primarily by a barrier below, rather than by conditions which exist above.
Since river valleys have a beginning and pass through various stages of development before the country they drain is base-leveled, it is important to recognize their various stages of advancement. Nor is this difficult. An old valley and a young one have different characteristics, and the one would no more be mistaken for the other by those who have learned to interpret them, than the face of an aged man would be mistaken for that of a child.
The cycle begins with the beginning of valley development, and at that stage drainage is in its infancy. The type of the infant valley is the gully or ravine (Figs. 67 and 68). It has steep slopes and a narrow bottom. Fig. 1 of Plate IV represents similar, or rather older, ravines in contour (shore of Lake Michigan, just north of Chicago). With age, the valley widens, lengthens, and deepens, and passes from infancy to youth. In this stage also the valleys are relatively narrow, and the divides between them broad. They may be deep or shallow, according to the height of the land in which they are cut, and the fall of the water flowing through them; but in any case the streams flowing through them have done but a small part of the work they are to do before the country they drain is base-leveled. Figs. 69 and 70, respectively, represent youthful valleys in regions of moderate and great relief. Fig. 2, Plate IV, shows a youthful valley in a region of slight relief (near Casselton, N. D., Lat. 46° 40′, Long. 97° 25′). The uppermost line in Fig. 64 likewise represents topographic youth, as shown in cross-profile.
Not only are narrow valleys said to be young, but the territory affected by them is said to be in its topographic youth, since but a small part of the time necessary to reduce it to base-level has elapsed. An area is in its topographic youth when considerable portions of it are still unaffected by valleys. Thus the areas (as a whole), as well as the valleys, represented on Plate IV, are in their topographic youth. It is often convenient to recognize various sub-stages, such as early, middle, and late, within the youthful stage of valleys or topographies. The different parts of the areas shown on Plate IV, for example, represent different stages of youth.
Youthful streams, as well as youthful topographies, have their distinctive characteristics. They are usually swift; their cutting is mainly at the bottom rather than at the sides, and their courses are often marked by rapids and falls.
As valleys approach base-level they develop flats. As the valleys and their flats widen, and as their tributaries increase in numbers and size, a stage of erosion is presently reached where but little of the original upland surface remains. The country is largely reduced to slopes. In this condition the drainage and the topography which it has determined are said to be mature. Mature topography is shown in contours in the figures of Plate V, and in the northern part of Plate VI, where slopes, rather than upland or valley flats, predominate. Fig. 1 of Plate V represents an area in southeastern Kentucky (Lat. 37° 12′, Long. 83° 10′); Fig. 2, an area in western Virginia. Plate VI represents an area in southern California, somewhat west of San Bernardino. The three areas are alike in representing mature drainage, though not of equal stages of advancement. The striking differences of topography of the three areas are the result of differences in rock structure and altitude, and will be considered later. Mature topography is also shown in Fig. 71, where the relief is moderate, and in Figs. 72 and 73, where it is great. Figs. 72 and 73 illustrate clearly the universal tendency of rivers in regions of notable relief to develop new flats well below the old surface of the region. At the same time that these low-lying flats are developing, tributary drainage is dissecting and roughening the upper surfaces. This process is well shown in Fig. 73. In both Figs. 72 and 73 the summits of the mountains on either side of the valleys appear to have had about the same elevation. The new flat is therefore developed at the expense of the old flat. As will be seen in the sequel, the first flat which a stream develops along its course is usually somewhat above base-level. It is a graded flat.
The same processes which have made young valleys mature will in time work further changes. When the gradients of the valleys have become low and their bottoms wide, and when the intervening ridges and hills have become narrow and small, the drainage and the drainage topography have reached old age, and the streams are in a condition of senility. This is illustrated by Fig. 1, Plate VII (central Kansas), and in section by the third and lower lines in Fig. 64. Topographic old age sometimes has a different expression; this is shown in Fig. 74, where most of the surface has been brought low. The elevations which rise above the general plain are small in area, but have abrupt slopes. This phase of old-age topography is usually the result of the unequal resistance of the rock degraded. The effects of unequal rock-resistance will be considered later.
The marks of old streams are as characteristic as those of young ones. They have low gradients and are sluggish. Instead of lowering their channels steadily they cut them down in flood, and fill them up when their currents are not swollen. They meander widely in their flat-bottomed valleys (Fig. 1, Pl. VII, Central Kansas) and their erosion, except in time of flood, is largely lateral.
If the processes of degradation were to continue until the land surface was brought to sea-level, and this might be done by solution though not by mechanical erosion of running water, the rivers would no longer flow, and the drainage system would have reached the end of its history—death.
Not only do valleys normally pass from birth to youth, from youth to maturity, and from maturity to old age, but a single river system may show these various stages of development in its various parts. Thus in the area shown in Fig. 2, Plate VII (north central Kansas), there is a tract (extreme southwest) where the erosion history is scarcely begun. The zone of land a little farther northeast, and just reached by the heads of the valleys (same figure), is in its youth. The well-drained and uneven tract southwest of the flat of the Solomon River is in maturity, while the flat of the main valley has the general characteristics of old age.
The age of valleys in terms of erosion is also expressed more or less perfectly by their cross-sections. The line 1–1 (and 1′–1′) of Fig. 64 represents in cross-section a narrow V-shaped valley. Such a section is always indicative of youth. The stream which developed it cut chiefly at its bottom, not at its sides. It was therefore rapid, and rapid streams are young. The line 2–2, (2′–2′) (Fig. 64) shows the same valley at a later and maturer stage when downward cutting has nearly ceased. The widening of the valley by slope wash has become relatively more important than before, and the stream has so far lost velocity as the result of diminished gradient as to be unable to carry away all the detritus washed down from the sides. As a result of deposition at the bases of the side slopes, a concave curve has been developed. Up the valley from the point where such a section as is represented by 2–2 occurs, the valley may still have a section similar to that represented by 1–1.