Lecture II -- June 4, 1997

STREAMS:

We have finished the hydrologic cycle which supplies the water that allows streams to exist and we have finished weathering which supplies the material most usually attacked by erosion. Thus we are ready to consider stream formation and development because these are the most common eroders. Several thoughts are initially important. 1: Why do we have streams at all? Rainfall is rather evenly distributed but streams are linear concentrations? Why the contrast? The former thought of Aristotle etc would explain this because streams, according to Aristotle's ideas were fed by springs. However, rainfall is a different proposition; it has no similarity to streams.

Thus why the concentration of water in streams if rainfall is the main source of the water. 2: John Playfair "explained" part of James Hutton's "Theory of the Earth" in 1802 with something now called Playfairs Law. This is "Every river appears to consist of a main trunk, fed from a variety of branches, each running in a valley proportioned to its size, and all of them together forming a system of valleys, communicating with one another, and having such a nice adjustment of their declivities, that none of them join the principal valley, either on too high or too low a level: a circumstance which would be infinitely improbable, if each of these valleys were not they the work of the stream which flows in it". 3: We have to explain these two points with one argument.

We will explain these two arguments by using extremely elementary physics on running water . That is all energy of water or anything else is explained by velocity ("speed") and mass.

1. Imagine a perfectly smooth, evenly tilted slope , made of completely homogeneous materials, everywhere receives the same rainfall. Also every where has the same runoff caused by its own inability to absorb all the rainfall. Consequently, runoff increases downslope because every place receives all runoff from above in addition to its own runoff. The result is erosion would be faster lower on any slope receiving rainfall. Ultimately, the base of every slope will enter the ocean, so sea level is the lowest running water (driven, you should recall, only by gravity) can erode. This level is called base level . There are also temporary base levels. These are any times a stream enters another stream or a lake or pond it encounters a level (temporary in these cases) below which it cannot erode. Note, for future reference that even the permanent base level is actually temporary because , over long periods of time, sea level itself rises and falls. Anyway, since runoff increases downslope, the erosive power increases downslope and streams (and we have not yet even formed stream valleys) should get larger downstream and so should their valleys.

2. Another item follows pretty much from this analysis. That is that streams are fixed by the base level and cannot erode lower so the lower reaches of streams are flatter than upstream places. In effect, streams get steeper and steeper upstream.

3. We can also look at the effects of irregularities on erosion on our ideal, homogeneous, smooth, evenly tilted, always and everywhere receiving the same amount of rainfall slope. These irregularities run across the slope or down the slope and we will consider across the slope first. We can imagine a small irregularity but in the real world such things (across a stream) are falls and rapids. In a water fall the water as it approaches the falls accelerates because it senses the presence of the increased slope before it gets there. This is sort of like the water near the drain spout in a bath tub; the water there is moving faster than the water at the foot of the tub because it has anticipated the presence of the spout. The point is the water over the top of a falls or rapids is slowly removing the top surface and this is diminishing its size. Furthermore, the face of the falls is being eroded and this is moving the falls or rapids upstream. Thus we can make a generalization. Streams that made their own valleys have few irregularities and any they do have are concentrated upstream and are getting smaller over time.

4. Consider a small irregularity running down a slope. Imagine a highway department has completely smoothed a slope because it doesn't want gullies running towards its highway. No matter how smooth they make the slope there will soon be irregularities because there will be dead worms and other animals, twigs, footsteps of various animals etc. When it rains, any irregularity will concentrate the water in it or beside it and this greater amount of water means every irregularity running downslope will have more runoff near it. Thus every irregularity running downslope will form a valley no matter how trivial the original irregularity. In effect , we can say stream valleys (and streams) are inevitable. This is not to say they are permanent. After all larger ones could expand into smaller ones and make them disappear.

5. Every stream makes a valley sloping toward it. This slope is partly made by the stream and partly retains the original slope upon which the first stream started. Therefore, tributaries, because of this compromise, enter main streams at an acute angle pointed downstream. When the original slope is steeper the acute angle is sharper.

6. One would expect larger streams to get ahead of smaller streams, but this does not happen. If larger streams were to get ahead of smaller streams they would make a steep slope and this would erode faster giving all tributaries smooth change of gradient into the main stream. Small tributaries might be steeper than larger ones, but always the juncture would be continuous and smooth providing the streams made their valleys by erosion.

In effect we have here shown how streams make valleys such as those described by Hutton and Playfair. Elementary physics leads to inevitable consequences as water flows down hills. Stream valleys are inevitable as are their smooth profiles getting steeper upstream. Similarly valley sizes and the nature of tributaries are inevitable.

From this analysis came another extremely important idea. That is that the Earth is exceedingly old. Let us see how this came about. Examine the Grand Canyon. There is a little Colorado River at the bottom and a huge canyon (6000 or so feet deep and miles across). The rate of erosion by the Colorado River could be estimated by determining its average load over a reasonable time including all the variations in rainfall. In addition one might examine old photos and talk to old residents and thereby observe any changes over the past 100 or 150 years. One could also drill the delta in the Gulf of California and see if past streams were ever seriously more energetic than modern ones. It turns out older materials are coarser than modern ones, but there is no evidence (boulders) of a former river seriously more energetic than the modern one. Thus a reasonable rate of erosion might be an inch in 1000 years. Since 6000 feet has 72000 inches, it would, by that analysis have taken 72 million years to make the canyon. Clearly the analysis is not precise and we might be off by an order of magnitude (divide by 10), but even so it would take millions of years to make the canyon. However, look further. The rocks composing the canyon have to be formed. The Vishnu schist is many thousands of feet of metamorphosed sediment that had to be deposited, deformed, metamorphosed and thousands of feet of them removed by erosion before the deposition of the Grand Canyon series which also contains thousands of feet that have to be deposited, deformed and erode before the thousands of feet of more recent materials were deposited. The more recent materials were not continuously deposited (as were not the ancient ones) -- there were many fits and starts represented in part by the many unconformities (stops in deposition) noticed throughout the column of rocks. In effect, when we get done with the analysis we get an imprecise idea that Earth is exceedingly old. That is the basic statement of Uniformitarianism about the age of the Earth

The Europeans did not see the Grand Canyon, they used European examples. C. Darwin remarks, for example, that a conglomerate containing granite pebbles has the "stamp of time" even though conglomerate is formed faster then other sedimentary rocks. After all, to form a granite requires 1) intrusion of melted rock a mile or more below the surface, 2) cooling, 3) erosion of the materials above so as to expose the granite, and 4) the deposition of the eroded granite. Thus Uniformitarianism says "the present is the key to the past" and THEREFORE , the Earth is very old.

In effect, large geologic objects (e.g., the Alps, Grand Canyon, continents etc.) can be explained by this use of "deep time". These objects seem not to change over time, but now with "deep time" their formation by present processes becomes possible.

Biology was not a science until uniformitarianism made it possible. Species don't change over recorded human history. Our evidence comes from descriptions in old writings (Aristotle). Also, after Lamarck's theory of organic evolution was published early in the 19th century, Cuvier (French Comparative Anatomist) -- who much opposed evolution -- examined the animals (lions and elephants etc.) buried in the ancient Ptolomeic etc. tombs and showed they were the same as modern animals (therefore, in his view, disproving evolution). But, of course, he did not understand "deep time" and that was his error.