Rainfall generator for the Rhine basin: nearest-neighbour resampling of daily circulation indices and conditional generation of weather variables

This is the third progress report of a project on the development of a rainfall generator for the Rhine basin. The need for such a rainfall generator arose from the wish to study the likelihood of extreme river discharges in the Netherlands, using a hydrological/hydraulic model. The first progress report dealt with the single-site generation of weather variables by nearest-neighbour resampling for seven stations in the German part of the Rhine basin. In the second progress report a multi-site extension was presented, using daily precipitation and temperature data for 25 stations (1961-1995) in the German part of the basin. The present report deals with a number of relevant issues for long-duration (∼ 1000-years) simulations of precipitation and temperature. Such long-duration simulations are needed as input for the hydrological/hydraulic model.

The nearest-neighbour resampling technique is a simulation method that can easily gen- erate multi-site daily precipitation and temperature data without making restrictive assump- tions about the underlying joint distribution of those data. The essence of this technique is that the variables for a new day are sampled with replacement from a selected set of histor- ical data (the nearest neighbours or analogues). In order to generate weather variables for day t, the method needs a feature vector Dt to find the nearest neighbours in the historical data. In the popular first-order model Dt contains variables that characterise the weather on day t − 1. A finite number k of nearest neighbours in terms of a weighted Euclidean distance is selected from the historical record. One of these k nearest neighbours is finally “resampled” using a discrete probability kernel.