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[1] An abundance of methods have been developed over the years to perform the frequency analysis (FA) of extreme environmental variables. Although numerous comparisons between these methods have been implemented, no general comparison framework has been agreed upon so far. The objective of this paper is to build the foundation of a data-based comparison framework, which aims at complementing more standard comparison schemes based on Monte Carlo simulations or statistical testing. This framework is based on the following general principles: (i) emphasis is put on the predictive ability of competing FA implementations, rather than their sole descriptive ability measured by some goodness-of-fit criterion; (ii) predictive ability is quantified by means of reliability indices, describing the consistency between validation data (not used for calibration) and FA predictions; (iii) stability is also quantified, i.e., the ability of a FA implementation to yield similar estimates when calibration data change; and (iv) the necessity to subject uncertainty estimates to the same scrutiny as point estimates is recognized, and a practical approach based on the use of the predictive distribution is proposed for this purpose. This framework is then applied to a case study involving 364 gauging stations in France, where 10 FA implementations are compared. These implementations correspond to the local, regional, and local-regional estimation of Gumbel and generalized extreme value distributions. Results show that reliability and stability indices are able to reveal marked differences between FA implementations. Moreover, the case study also confirms that using the predictive distribution to indirectly scrutinize uncertainty estimates is a viable approach, with distinct FA implementations showing marked differences in the reliability of their uncertainty estimates. The proposed comparison framework therefore constitutes a valuable tool to compare the predictive reliability of competing FA implementations, along with the reliability of their uncertainty estimates.

Abstract. This paper presents a coupled observation and modelling strategy aiming at improving the understanding of processes triggering flash floods. This strategy is illustrated for the Mediterranean area using two French catchments (Gard and Ardèche) larger than 2000 km 2 . The approach is based on the monitoring of nested spatial scales: (1) the hillslope scale, where processes influencing the runoff generation and its concentration can be tackled; (2) the small to medium catchment scale (1-100 km 2 ), where the impact of the network structure and of the spatial variability of rainfall, landscape and initial soil moisture can be quantified; (3) the larger scale (100-1000 km 2 ), where the river routing and flooding processes become important. These observations are part of the HyMeX (HYdrological cycle in the Mediterranean EXperiment) enhanced observation period (EOP), which will last 4 years (2012)(2013)(2014)(2015). In terms of hydrological modelling, the objective is to set up regional-scale models, while addressing small and generally ungauged catchments, which represent the scale of interest for flood risk assessment. Topdown and bottom-up approaches are combined and the models are used as "hypothesis testing" tools by coupling model development with data analyses in order to incrementally evaluate the validity of model hypotheses. The paper first presents the rationale behind the experimental set-up and the instrumentation itself. Second, we discuss the associated modelling strategy. Results illustrate the potential of the approach in advancing our understanding of flash flood processes on various scales.

International audienceGiven the coarse spatial resolution of General Circulation Models, finer scale projections of variables affected by local-scale processes such as precipitation are often needed to drive impacts models, for example in hydrology or ecology among other fields. This need for high-resolution data leads to apply projection techniques called downscaling. Downscaling can be performed according to two approaches: dynamical and statistical models. The latter approach is constituted by various statistical families conceptually different. If several studies have made some intercomparisons of existing downscaling models, none of them included all those families and approaches in a manner that all the models are equally considered. To this end, the present study conducts an intercomparison exercise under the EURO- and MED-CORDEX initiative hindcast framework. Six Statistical Downscaling Models (SDMs) and five Regional Climate Models (RCMs) are compared in terms of precipitation outputs. The downscaled simulations are driven by the ERAinterim reanalyses over the 1989–2008 period over a common area at 0.44° of resolution. The 11 models are evaluated according to four aspects of the precipitation: occurrence, intensity, as well as spatial and temporal properties. For each aspect, one or several indicators are computed to discriminate the models. The results indicate that marginal properties of rain occurrence and intensity are better modelled by stochastic and resampling-based SDMs, while spatial and temporal variability are better modelled by RCMs and resampling-based SDM. These general conclusions have to be considered with caution because they rely on the chosen indicators and could change when considering other specific criteria. The indicators suit specific purpose and therefore the model evaluation results depend on the end-users point of view and how they intend to use with model outputs. Nevertheless, building on previous intercomparison exercises, this study provides a consistent intercomparison framework, including both SDMs and RCMs, which is designed to be flexible, i.e., other models and indicators can easily be added. More generally, this framework provides a tool to select the downscaling model to be used according to the statistical properties of the local-scale climate data to drive properly specific impact models

Density estimators that can adapt to asymmetric heavy tails are required in many applications such as finance and insurance. Extreme value theory (EVT) has developed principled methods based on asymptotic results to estimate the tails of most distributions. However, the finite sample approximation might introduce a severe bias in many cases. Moreover, the full range of the distribution is often needed, not only the tail area. On the other hand, non-parametric methods, while being powerful where data are abundant, fail to extrapolate properly in the tail area. We put forward a non-parametric density estimator that brings together the strengths of non-parametric density estimation and of EVT. A hybrid Pareto distribution that can be used in a mixture model is proposed to extend the generalized Pareto (GP) to the whole real axis. Experiments on simulated data show the following. On one hand, the mixture of hybrid Paretos converges faster in terms of log-likelihood and provides good estimates of the tail of the distributions when compared with other density estimators including the GP distribution. On the other hand, the mixture of hybrid Paretos offers an alternate way to estimate the tail index which is comparable to the one estimated with the standard GP methodology. The mixture of hybrids is also evaluated on the Danish fire insurance data set.

[1] We present a new class of stochastic downscaling models, the conditional mixture models (CMMs), which builds on neural network models. CMMs are mixture models whose parameters are functions of predictor variables. These functions are implemented with a one-layer feed-forward neural network. By combining the approximation capabilities of mixtures and neural networks, CMMs can, in principle, represent arbitrary conditional distributions. We evaluate the CMMs at downscaling precipitation data at three stations in the French Mediterranean region. A discrete (Dirac) component is included in the mixture to handle the ''no-rain'' events. Positive rainfall is modeled with a mixture of continuous densities, which can be either Gaussian, log-normal, or hybrid Pareto (an extension of the generalized Pareto). CMMs are stochastic weather generators in the sense that they provide a model for the conditional density of local variables given large-scale information. In this study, we did not look for the most appropriate set of predictors, and we settled for a decent set as the basis to compare the downscaling models. The set of predictors includes the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalyses sea level pressure fields on a 6 Â 6 grid cell region surrounding the stations plus three date variables. We compare the three distribution families of CMMs with a simpler benchmark model, which is more common in the downscaling community. The difference between the benchmark model and CMMs is that positive rainfall is modeled with a single Gamma distribution. The results show that CMM with hybrid Pareto components outperforms both the CMM with Gaussian components and the benchmark model in terms of log-likelihood. However, there is no significant difference with the lognormal CMM. In general, the additional flexibility of mixture models, as opposed to using a single distribution, allows us to better represent the distribution of rainfall, both in the central part and in the upper tail.Citation: Carreau, J., and M. Vrac (2011), Stochastic downscaling of precipitation with neural network conditional mixture models,

[1] 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.Citation: Carreau, J., P. Naveau, and E. Sauquet (2009), A statistical rainfall-runoff mixture model with heavy-tailed components, Water Resour. Res., 45, W10437,

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