Leopold and Maddock (1953) compiled a significant statistical data base using USGS gauging

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*

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:

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