Rainfall generator for the Rhine basin: multi-site generation of weather variables by nearest-neighbour resampling

This report presents the second phase of a project on the development of a rain-fall generator for the Rhine basin. The request for this generator arose from the need to study the likelihood of extreme river discharges in the Netherlands, using a hydrological/hydraulic model. The first phase dealt with the single-site genera-tion of weather variables by nearest-neighbour resampling for seven stations in the German part of the Rhine basin. The second phase is concerned with the multi-site extension of the first phase, using daily precipitation and temperature data for twenty-five stations (1961–1995) in the German part of the Rhine basin. Joint simulation of daily precipitation and daily temperature is necessary to ac-count for the effect of snow and frozen soils on large river discharges.  

The nearest-neighbour resampling technique is a method of simulation that can easily handle multi-site daily precipitation and temperature data without making restrictive assumptions concerning the joint distribution of those data. The es-sence of this technique is that the variables for a new day are sampled with re-placement from a selected set of historical data (the nearest neighbours or ana-logues). In order to generate weather variables for day t, the method needs a fea-ture (or state) vector Dt to find nearest neighbours in the historical data. For un-conditional simulation, Dt contains variables that characterise the state of the weather on day t–1, like summary statistics of the daily precipitation and tem-perature fields and atmospheric circulation indices. Conditional simulation on the atmospheric flow is also possible with the nearest-neighbour resampling tech-nique. Circulation indices for day t are then included in Dt. A (weighted) Euclid-ean distance measure is used to determine the k nearest neighbours of Dt. From the k nearest neighbours, one day is sampled with a predefined probability.