Effect of the time distribution of rainfall intensities on small watershed floods, The: technical report

CER67-68RND14.September 1967.Includes bibliographical references (pages 113-117).The time-intensity pattern of the storm rainfall is described by taking the moments of area of the hyetograph about the intensity-axis and about the time-axis. The effect of these parameters on the shape of the hydrograph is studied by means of multiple regressions. Three groups of hydrograph parameters are used as dependent variables in the regressions. They are: the moments of area of the hydrograph about the discharge-axis; the traditional hydrograph parameters of volume, peak and rise time; and the parameters of a mathematical function fitted to the hydrograph. The fitted function was an incomplete gamma function of the form q = q0 ty e-y(t-r)/ryr where q is the unit discharge in inches/hour, q0 is the peak unit discharge in inches/hour, t is the time in minutes, Y is shape parameter with the units of reciprocal minutes, r is the rise time in minutes, and e is the base of Naperian logarithms. The fitting process was accomplished by the method of weighted least squares, whereby the squared deviations between the observed discharge and computed discharge were weighted in proportion to the observed discharge. The results indicate that the moments of the hyetograph are objective descriptors of the time distribution of rainfall intensities. All three groups of hydrograph parameters can be predicted with nearly equal accuracy. The similarity of the relationships for the observed peak and the fitted peak, and the observed rise time and the fitted rise time attest to the methodology of fitting the three-parameter gamma function to the observed hydrograph