A study to determine an equation of enveloping curve for regional flood peaks by maximum rainfall data

In this paper, Creagers equation and Groups equation are algebraically examined to determine an equation of an enveloping curve for regional flood peaks from the viewpoint of the curve profile. The applicability of a small drainage area with little observed data on flood peak discharge was examined in comparison to specific flood peak discharge calculated by a rational formula using data of maximum rainfall. In the algebraical consideration, the Creagers equation had an extreme value at a drainage area A=1.0 km², and the specific flood peak discharge became a maximum. Flood peak discharge calculated by Groups equation had an extreme value at a drainage area A=6,568 km², and it became a maximum. Except for Hokkaido, in catchment areas not exceeding 1,178 km², Groups curve q_K was closer to the curve q_DAD of specific flood discharge than Creagers curve qc. From the above research results, the Groups equation is applicability better than the Creagers equation, as the drainage area A is 1,178 km² or less.