2019 Volume 32 Issue 2 Pages 82-93
The Talbot formula R = at /(t + b) and the Sherman formula R = ctn were fitted to the relation between probable rainfall depth and duration, where R and t respectively represent the probable rainfall depth and the duration, and a, b, c, and n are constants.
On the whole, value n in the Sherman equation and value b in the Talbot equation, both of which represent the continuity of heavy rainfall, respectively decreases and increases as the durations in a duration range increase. However, the variations of the values with the duration range are markedly different among stations.
When the magnitude of the variation of a constant in a rainfall depth-duration formula with the duration range is expressed by the coefficient of variation, a strong negative correlation can be found between the coefficients of variation of the constants in the Talbot and the Sherman formulas.
For durations in a duration range that are short (e.g., 1-24 h) or long (e.g., 10-72 h), the number of stations at which the Sherman formula provides the better fit is greater. For durations in a duration range that are medium (e.g., 3-40 h), the number of stations at which the Talbot formula provides the better fit is greater. The constants in a rainfall depth-duration formula that provides the better fit vary little with the duration range. In southern and northern Japan, respectively, the Sherman and the Talbot formulas provide the better fit.
