For observation of small-basin flood peaks, numerous crest-stage gages now are operated at culverts in roadway embankments. To the extent that they obstruct the natural flood plains of the streams, these embankments serve to create detention reservoirs, and thus to reduce the magnitude of observed peak flows. Hence, it is desirable to obtain a factor, I/O, by which the observed outflow peaks may be adjusted to corresponding inflow peaks. The problem is made more difficult by the fact that, at most of these observation sites, only peak stages and discharges are observed, and complete hydrographs are not available.
It is postulated that the inflow hydrographs may be described in terms of Q, the instantaneous discharge; A, the size of drainage area; Pe, the amount of rainfall excess; H, the time from beginning of rainfall excess; D, the duration of rainfall excess; and T and k, characteristic times for the drainage area, and indicative of the time lag between rainfall and runoff. These factors are combined into the dimensionless ratios (QT/APe), (H/T), (k/T), and (D/T), leading to families of inflow hydrographs in which the first ratio is the ordinate, the second is the abscissa, and the third and fourth are distinguishing parameters.
Sixteen dimensionless inflow hydrographs have been routed through reservoir storage to obtain 139 corresponding outflow hydrographs. In most of the routings it has been assumed that the storage-outflow relation is linear; that is, that storage is some constant, K, times the outflow. The existence of nonlinear storage is recognized, and exploratory nonlinear routings are described, but analyses and conclusions are confined to the problems of linear storage.
Comparisons between inflow hydrographs and outflow hydrographs indicate that, at least for linear storage, I/O=f(k/T, D/T, K/T) in which I and O are, respectively, the magnitudes of the inflow and the outflow peaks, and T, k, D, and K are as defined above. Diagrams are presented to show the functional relation indicated by the foregoing equation.