Estimation of a large quantile of the distribution of multi-day seasonal maximum rainfall: the value of stochastic simulation of long-duration sequences

The usefulness of time-series simulation of daily rainfall for estimating large quantiles of the distribution of 10 d seasonal maximum rainfall is questioned. The emphasis is on rare 10 d events having a mean recurrence time much longer than the length of the historical record. Time-series simulation uses nonparametric resampling. With a theoretical example assuming no temporal dependence, it is shown that simulation of a long-duration sequence by resampling from the original historical record using the standard bootstrap method yields a much better estimate of a large quantile of the 10 d seasonal maximum distribution than fitting a Gumbel or Generalized Extreme Value (GEV) distribution to the 10 d seasonal maxima from the original data. This is because a sample of daily values contains more information on the distribution of the 10 d maxima than the individual 10 d seasonal maxima from the sample. Using observed daily rainfall data from Stuttgart (Germany), it is demonstrated that the tail of the distribution of the daily rainfall amounts and temporal dependence strongly influence the distribution of extreme 10 d rainfalls. The incorporation of temporal dependence into the simulated data using nearest-neighbour resampling is considered. Using a firstand second-order resampling model, it is demonstrated that misspecification of the order of dependence may lead to a substantial bias in the quantiles of the 10 d seasonal maximum distribution. It is shown that the underestimation of large quantiles of the distribution of the 10 d maxima, resulting from the inability to generate larger daily values than those observed, is small. Despite these biases, it is expected that, in the case of temporal dependence of daily rainfall data, nearest-neighbour resampling is able to provide reliable estimates of large quantiles of the distribution of multi-day rainfall amounts, as in the example of no dependence.