Comparison of Three Methods of Estimating Rainfall Frequency Parameters According to the Duration of Accumulation

The ‘Gradex’ method estimates high return period discharges by assuming that the two marginal increases in rainfall and flood volumes are equal for return periods greater than a hundred years. This requires an asymptotically exponential decay of the rainfall distribution, the gradex being the gradient of this exponential. Among several statistical relationships satisfying this requirement, the Gumbel distributin is widely acknowledged to properly fit the extreme value distribution of observed daily rainfalls. However, difficulties may arise for small time steps(from less than one hour up to twelve hours).Among the many reasons for these difficulties, seasonal variation of the distribution parameters and the mixing of rainstorms issuing from different weather conditions are the most frequent. Rainfall distributions should therefore be analyzed using data from a homogeneous season. However, the mixing of weather patterns remains whatever the season considered, and it is important to find a way to estimate the gradex parameter even when the experimental distribution of extreme values does not allow a good Gumbel model fit. One solutions is to fit a two component negative exponential distribution to the complete data set. Such a theoretical distribution is asymptotically parallel to a Gumbel distribution, thus providing an estimate of the gradex.In this communication, three gradex estimators are compared from bias and efficiency standpoints: the moment and maximum likelihood methods used to fit a Gumbel distribution to an extreme value data set, and the moment method used to fit a two component exponential distribution to the complete data set of observed rainfalls. This comparsion can be used to determine the most suitable estimator for subsequent regional regression and mapping of rainfall frequency parameters(see: liner relations between rainfall and morphometric parameters by Slimani and Obled, this symposium).