# The Method of Derived Distributions Applied to Peak Flows

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*by*Ivan Muzik, Univ of Calgary, Calgary, Canada,

**Document Type:**Proceeding Paper

**Part of:**Engineering Hydrology:

**Abstract:**Random variables which are functionally related have their probability distributions also related in a prescribed manner. Thus, in theory, the probability distribution of peak discharge could be derived from a known probability distribution of rainfall. The rainfall-runoff relationship, however, is a complex one, involving stochastic parameters, precluding analytical solution. Monte Carlo simulation has to be employed instead. The theory of derived distributions is briefly reviewed. Application of Monte Carlo simulation in deriving synthetic flood frequency curves, using modified Soil Conservation Service runoff curve method and dimensionless unit hydrograph, is illustrated by examples.

**Subject Headings:**Probability distribution | Probability | Flow distribution | Flood frequency | Peak flow | Rainfall-runoff relationships | Frequency distribution | Water discharge | Flow simulation | Monte Carlo method | Europe | Monaco | Monte Carlo

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