2018 Volume 31 Issue 3 Pages 166-177
The Talbot formula R=at/(t+b) and the Sherman formula R=ctn were fitted as a rainfall depth-duration formula to the relation between probable rainfall depth and duration (DD relation), where R and t respectively represent the probable rainfall depth and the duration: a, b, c and n are constants.
Both value a/b in the Talbot formula and value c in the Sherman formula represent characteristics of short-duration heavy rainfall. The geographical distributions of the two values show large latitudinal differences. Both value b in the Talbot formula and value n in the Sherman formula represent the continuity of heavy rainfall. The geographical distributions of the two values are closely related to topography.
The DD relation is convex upward on a log-log plot. Therefore, the relation has a characteristic duration. This duration is definable as the duration for which the curvature of the logarithmically transformed Talbot equation is at its maximum [(1+√5)b/2] and can thereby be regarded as a continuous duration of heavy rainfall.
One-to-one correspondence between values b and n and between values b and a/c is provable analytically. Value a/c, as well as values b and n, represents the continuity of heavy rainfall.
