Probability distribution of velocity in natural channel cross sections

The probability distribution of velocities in idealized parabolic channels and in regular and highly irregular natural stream cross sections follows a power law: F(v)=(v/V)c, where F(v) is the cumulative frequency distribution of velocity v, Vis the maximum velocity in the cross section, and c is a shape parameter. Values of Vand c can be estimated from current meter measurements via moments, maximum likelihood, or regression analysis; maximum likelihood is most precise. The distribution is useful in stream habitat studies because it provides immediate information about the fraction of a cross section containing velocities in any range. For stream gaging, one can use this distribution to estimate the mean cross-sectional velocity E(v), where E(v)=[c/(c + 1)]V without invoking assumptions about the location of the mean velocity in each profile. One can also immediately determine the energy coefficient α as α=(c + 1)3/[c2(c + 3)] and use this information to improve the accuracy of field measurements of reach resistance.