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, V is the maximum velocity in the cross section, and c is a shape parameter. Values of V and 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 /[ c 2 ( c + 3)] and use this information to improve the accuracy of field measurements of reach resistance.