A statistical rainfall-runoff mixture model with heavy-tailed components
Carreau, J. | Naveau, P. | Sauquet, E.
We present a conditional density model of river runoff given covariate information which includes precipitation at four surrounding stations. The proposed model is nonparametric in the central part of the distribution and relies on extreme value theory parametric assumptions for the upper tail of the distribution. From the trained conditional density model, we can compute quantiles of various levels. The median can serve to simulate river runoff, quantiles of level 5% and 95% can be used to form a 90% confidence interval, and, finally, extreme quantiles can estimate the probability of large runoff. The conditional density model is based on a mixture of hybrid Paretos. The hybrid Pareto is built by stitching a truncated Gaussian with a generalized Pareto distribution. The mixture is made conditional by considering its parameters as functions of covariates. A neural network is used to implement those functions. A penalty term on the tail indexes is added to the conditional log likelihood to guide the maximum likelihood estimator toward solutions that are preferred. This alleviates the difficulties encountered with the maximum likelihood estimator of the tail index on small training sets. We evaluate the proposed model on rainfall-runoff data from the Orgeval basin in France. The effect of the tail penalty is further illustrated on synthetic data.
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