A Statistical Rainfall-Runoff Mixture Model with Heavy-Tailed Components

1 We present a conditional density model of river runoff given covariate information 2 which includes precipation at four surrounding stations. The proposed model is non3 parametric in the central part of the distribution and relies on Extreme-Value Theory 4 parametric assumptions for the upper tail of the distribution. From the trained con5 ditional density model, we can compute quantiles of various levels. The median can 6 serve to simulate river runoff, quantiles of level 5% and 95% can be used to form a 7 90% confidence interval, finally, extreme quantiles can estimate the probability of large 8 runoff. The conditional density model is based on a mixture of hybrid Paretos. The 9 hybrid Pareto is built by stitching a truncated Gaussian with a Generalized Pareto dis10 tribution. The mixture is made conditional by considering its parameters as functions 11 of covariates. A neural network is used to implement those functions. A penalty term 12 on the tail indexes is added to the conditional log-likelihood to guide the maximum 13 likelihood estimator towards solutions that are preferred. This alleviates the difficulties 14 encounter with the maximum likelihood estimator of the tail index on small training 15 sets. We evaluate the proposed model on rainfall-runoff data from the Orgeval basin in 16 France. The effect of the tail penalty is further illustrated on synthetic data. 17 2 Water Resour. Res., 45, W10437, doi:10.1029/2009WR007880. ha l-0 04 55 64 4, v er si on 1 10 F eb 2 01 0