Abstract

The objective of this chapter is to propose methods for estimating the ,,distribution of hourly rainfall based on at-site daily rainfall measurements, and from available regional information. The methods consist of deriving time resolution independent mathematical models to describe the distribution of rainfalls for different time scales at a single site, and for the whole study region. The proposed models are based on the theory of multifractal multiplicative cascades which describes the transfer mechanism of rain flux from large time scales (e.g. days or longer) to smaller time intervals (e.g. hours or shorter). In the present study, using rainfall data from a network of nine recording rain gages in the Montreal region (Quebec, Canada) an empirical investigation is carried out to demonstrate how well rainfall measurements at different time resolutions can be described by such multiplicative cascade processes.

Results of the data analysis in this study have provided some credence to this hypothesis since it was found that the probability distributions of rainfalls over a wide range of time scales can be described by one particular theoretically-derived functional form. Further, the good agreement between computed and observed hourly rainfall distributions have indicated the adequacy of the proposed methods. It is expected that a straightforward extension of the method suggested in this study could be used to obtain rainfall distributions appropriate to other time intervals.

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