RELATIONSHIPS IN RIVERS (cont.) - ChannelRehabilitation0052

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records and developed hydraulic geometry relationships for the width, depth, velocity, and other

hydraulic characteristics for some streams in the United States. The hydraulic geometry relationships are

of the same general form as Kennedy (1895):

W = a Qb

D = c Qf

V = k Qm

in which W is channel width, Q is discharge, D is depth, and V is velocity.

All of the relationships presented, including the hydraulic geometry relationships, are strictly

empirical, i.e., the relationships describe observed physical correlations. As conditions change from

watershed to watershed, the relationships must be modified. For example, stream width for sandy banks

would be expected to be different from clay banks. Schumm's relationship between width to depth ratio

(F) and the weighted percent silt-clay in the channel perimeter (M) is an empirical relationship that

describes this observation. If Schumm's relationship is correct, then is the hydraulic geometry relationship

valid that predicts width (W) based only as a function of discharge? Both relationships can be valid for the

data set used in developing the relationship.

An example of the improper use of empirical relationships was provided by Mark Twain in Life

on the Mississippi (Clemens, 1944). In his wonderfully sarcastic manner, he describes Mississippi River

cutoffs of which he had knowledge. Therefore, he developed an empirical relationship to predict the

eventual length of the Mississippi River. He eloquently describes the modeling process:

Now, if I wanted to be one of those ponderous scientific people, and "let on" to

prove what had occurred in the remote past by what had occurred in a given time

in the recent past, or what will occur in the far future by what has occurred in late

years, what an opportunity is here! Geology never had such a chance, nor such

exact data to argue from! Nor "development of species," either! Glacial epochs are

great things, but they are vague - vague. Please observe:

In the space of 176 years, the Lower Mississippi has shortened itself 242 miles. That

is an average of a trifle over one mile and a third per year. Therefore, any calm

person, who is not blind or idiotic, can see that in the Old Olitic Silurian Period, just

a million years ago next November, the Lower Mississippi River was upwards of

1,300,000 miles long, and stuck out over the Gulf of Mexico like a fishing rod. And

by the same token, any person can see that 742 years from now the Lower

Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans

will have joined their streets together, and be plodding comfortably along under a

single mayor and a mutual board of aldermen. There is something fascinating about

science. One gets such wholesale returns of conjecture out of such a trifling

investment of fact.