Mixture models for statistical flood frequency analysis

Statistical flood frequency analysis is commonly used to estimate design floods based on a series of annual maximum discharge data. The current guidelines for flood estimation in Norway recommend the use of a regional model when only a short series of at-site data is available, for 30-50 years of at-site data the two-parameter Gumbel distribution is the recommended statistical model while the three-parameter generalized extreme value (GEV) distribution should be used for more than 50 years of at-site data. This note investigates a mixture model approach that combines all three models with the mixture weights depending on the amount of available at-site data. The mixture weights are derived by assessing the predictive performance of the three models on outof-sample data using proper scoring rules. In a case study of 60 discharge series from Norway it is found that the resulting weighting scheme depends heavily on the scoring rule that is used to obtain the weights. A trend similar to that of the current guidelines is most apparent when using scoring rules that focus on the upper tail, i.e. the quantile score and the quantile-weighted continuous ranked probability score. When the models are estimated based on 10-50 years of data, the weight corresponding to the regional model increases as the number of observations in the training set decreases and opposite for the local GEV and Gumbel models. The Gumbel model receives larger weights than the GEV model, indicating and overall better performance. The drawing on the front page by John William Edy shows Drammenselva in 1800.