Uncertainty Characterization of Design Rainfall Rates for Stormwater Infrastructure Design

Yi Wang and Edward McBean


Intensity-Duration-Frequency (IDF) curves from which the design rainfall magnitudes are developed, are constructed using rainfall predictions associated with different return periods and durations. However, the degrees of confidence of estimates of rainfall rates as input to stormwater infrastructure design are influenced by the length and character of historical records. The paper develops relations between the period of historical record of rainfalls and uncertainties of predictions for different confidence levels.

A simulated rainfall record is employed to demonstrate the basis for the quantification of the confidence estimates. Methodologies for deriving variances of predictions include both resampling and asymptotic theories. The paper demonstrates that the covariance between the length of record (log transformed) and the ratio of the standard deviations of predictions are high.

The stationarity of real historical records is tested, to ensure all samples are identically distributed and used in the evaluation. It is demonstrated that the historical record and the record length are linearly related. This linear model is developed for confidence levels of 80% and 90%. It is also demonstrated that the length of record needed to maintain specified levels of uncertainty increases as the return period or the durations of rainfall increase.

This paper further develops the uncertainties of predictions over each duration into a regression of ‘uncertainties’ versus ‘duration’, at a given confidence level and return period. This model will provide uncertainties of design rainfalls for any storm duration.

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