Rainfall depth-duration-frequency curves and their uncertainties

Rainfall depth-duration-frequency (DDF) curves describe rainfall depth as a function of duration for given return periods and are important for the design of hydraulic structures. This paper focusses on the effects of dependence between the maximum rainfalls for different durations on the estimation of DDF curves and the modelling of uncertainty of these curves. For this purpose the hourly rainfall depths from 12 stations in the Netherlands are analysed. The records of these stations are concatenated to one station-year record, since no geographical variation in extreme rainfall statistics could be found and the spatial dependence between the maximum rainfalls appears to be small. A generalized extreme value (GEV) distribution is fitted to the 514 annual rainfall maxima from the station-year record for durations of 1, 2, 4, 8, 12 and 24 h. Subsequently, the estimated GEV parameters are modelled as a function of duration to construct DDF curves, using the method of generalized least squares to account for the correlation between GEV parameters for different durations. A bootstrap estimate of the covariance matrix of the estimated GEV parameters is used in the generalized least squares procedure. It turns out that the shape parameter of the GEV distribution does not vary with duration. The bootstrap is also used to obtain 95%-confidence bands of the DDF curves. The bootstrap distribution of the estimated quantiles can be described by a lognormal distribution. The parameter σ of this distribution (standard deviation of the underlying normal distribution) is modelled as a function of duration and return period.