Conversion of Unit Hydrographs by Complementary Hydrograph Method

A method to convert a known unit hydrograph to unit hydrographs of different durations, as an alternative to the S-Hydrograph method, is introduced. The method—called the Complementary Hydrograph method—involves a process of decomposing a known unit hydrograph of duration $t_o$ into a pair of “complementary” hydrographs associated with two sequential rainfalls with the sum of their durations equal to $t_o\text{.}$ In converting the $t_o$-hour unit hydrograph into a $t_a$-hour unit hydrograph, the method produces a unit hydrograph of duration $t_b=(t_o-t_a)$ concurrently. In hydrograph conversion, the Complementary Hydrograph method produces an identical result to the well-established S-Hydrograph method and involves a comparable number of computational steps. In certain special cases, such as converting a unit hydrograph into one with half its duration, the new method requires fewer computational steps. While the two methods employ different approaches in their solutions of hydrograph conversion problems, the agreement in their results stems from the fact that both methods are founded on the same principles of superposition and linearity of the unit hydrograph method. The S-Hydrograph method can also be viewed as a special case of the Complementary Hydrograph method in which the known hydrograph is associated with a storm of infinite duration and uniform intensity. The Complementary Hydrograph method offers a more unified and versatile approach in dealing with various types of unit-hydrograph conversion problems. For example, the method can be extended to derive unit hydrographs from a hydrograph associated with a multiperiod, varied intensity rainfall. The use of S-Hydrograph method for hydrograph derivation can only be applied to hydrographs resulting from a single-period rainfall of uniform intensity.