Stochastic Formulation of Storm Pattern and Rainfall Intensity-Duration Curve for Design Flood

Abstract

A stochastic single storm pattern, which preserves stochastic properties of actual storm rainfall, is theoretically derived from Freund’s bivariate probability density function. Two typical design storm patterns, namely, the last and the central peaked types are defined by the three parameters: the reduced variate y_p of the peak rainfall intensity, the autocorrelation index k related to the autocorrelation coefficient of the rainfall intensities, and the conditional probability F. Integration of the given stochastic design hyetograph gives a new ‘conditional probability’ intensity-duration formula. Furthermore, a practical estimation method of the three parameters: k, F, and y_p is clearly shown. The conditional probability intensity-duration curve is demonstrated duration curve is demonstrated by using actual hourly rainfall data. Design intensities for shorter duration than 1 hr can be easily estimated from the available hourly data.