Drought in the Netherlands – Regional frequency analysis versus time series simulation

Summary The distribution of the annual maximum precipitation deficit is studied for six districts within the Netherlands. Gumbel probability plots of this precipitation deficit show a common extraordinary curvature in the upper tail. A regional frequency analysis yields a regional growth curve that can be approximated by a spline consisting of two linear segments on the standard Gumbel scale and a smooth transition between them. Alternatively, the application of a time series model based on nearest-neighbour resampling is explored. To reproduce the persistence structure a 4-month memory term is needed in the resampling model. Using this memory term there is an enhanced positive correlation between past and future precipitation deficits during extremely dry summers, which seems to be responsible for the curvature in the precipitation deficit distributions. This term, however, also leads to a considerable increase of the standard error of large quantile estimates. Much attention is given to the use of the bootstrap and the jackknife to determine the standard errors of quantile estimates based on nearest-neighbour resampling. A simulation experiment with a first-order autoregressive time series model shows that these standard errors can be biased, in particular for the bootstrap. The relative standard errors of quantile estimates are large in the area of large curvature of the Gumbel probability plots. This holds both for nearest-neighbour resampling and regional frequency analysis. When the two methods are used for extrapolation, nearest-neighbour resampling clearly outperforms the regional frequency analysis. The latter then shows a strong increase in the relative standard error of quantile estimates with increasing return period due to the large uncertainty of the parameters in the spline approximation to the regional growth curve. Using nearest-neighbour resampling and the bootstrap, confidence intervals are constructed for the return periods of the largest observed precipitation deficit for each of the six districts. Although these confidence intervals are quite wide, they are on average a factor of two narrower than the interval expected from the size of the sample only.