L'approche débit-durée-fréquence : historique et avancées

La prévention du risque d'inondation nécessite une connaissance détaillée du régime hydrologique en crue du bassin étudié. Dans ce but, l'approche débit-durée-fréquence (QdF), développée depuis déjà plusieurs années, a permis de définir un modèle statistique décrivant les crues observées en fonction de leur débit, de leur durée et de leur fréquence. Un récent travail a revisité cette approche. Grâce à son nombre réduit de paramètres, le modèle proposé, appelé modèle local convergent, peut être facilement ajusté pour chaque bassin. Dans l'ancienne approche, que nous appelons approche " bassin de référence ", l'ajustement local avait été effectué sur seulement trois bassins, dits de référence, et réputés être chacun représentatif d'une typologie d'écoulement différente. Ces trois paramétrisations types ont ensuite donné lieu à trois modèles adimensionnels, capables de caractériser la majorité des régimes observés. Le modèle adimensionnel correspondant au régime du bassin étudié devait être dénormé par deux caractéristiques locales du bassin : le débit instantané maximal de crue décennale et une durée caractéristique de crue. Une comparaison du nouveau modèle, appelé modèle local convergent, et de l'approche type " bassin de référence " a été effectuée sur une cinquantaine de bassins jaugés. Elle met en évidence la robustesse du modèle convergent et permet de discuter du choix du modèle relatif à l'approche " bassin de référence ". Le modèle local convergent autorise d'envisager le développement d'un modèle QdF régional, s'inspirant de différentes méthodes de régionalisation. Ceci permettra alors une application à des bassins peu ou non observés.Flood risk mitigation requires a good knowledge of hydrological flood regime, which can be described by a flow-duration-frequency (QdF) approach. New developments of this approach are presented and compared to the former method.Usually, flood frequency analysis deals only with the maximum flood peak distribution or the maximum daily discharge distribution. The QdF approach analyses maximum average flows over different durations d (d =1, 3, …, N days). Similar to intensity-duration-frequency curves, each of the QdF curves represents the flood frequency distribution, for the duration d. QdF modelling aims to express QdF curves by a Q(d,T) function (d : the duration; T : the return period).Before this present work, QdF modelling was associated with the "reference basin" approach. In this approach, QdF curves (plotted as a function of d, for fixed T) of many studied basins are converted into a dimensionless form. The two characteristics used are the 10-year peak flood, Q(d=0, T=10 years), and a characteristic flood duration (D) of the studied catchment, calculated from different flood hydrographs. Then, three different families are determined, grouping basins with similar dimensionless QdF curves. For each of these families, one reference basin is chosen. Their dimensionless curves are parameterised, in order to obtain a continuous formulation, as a function on T and d. By denormalising one of these dimensionless QdF models with the local parameters Q(0,10) and D, it is possible to obtain the continuous Q(d,T) formulation for the studied basin. The choice of the correct dimensionless model is made via a choice criterion. It involves Q(0,10), D and shape parameters of local maximal rainfall distributions (a Gumbel law is assumed), for different durations, d. These distributions are obtained according to the intensity-duration-frequency approach. If the studied basin is ungauged, local parameters Q(0,10) and D are estimated by regional formulas, involving significant variables such as catchment area and rainfall.Recent work has improved this "reference basin" approach. A new QdF model, called convergent local, has been developed. For fixed T, the model assumes that the Q(d,T) is described by a hyperbolic form, as a function of d. This choice of the hyperbolic form is based on the observation of many catchments (about one hundred). It has also been observed that QdF curves, plotted for fixed d as a function of T, converge toward the same point, when T decreases. Using these observations as assumptions, the model is then able to calculate Q(d,T) for any return period T and any duration d.If a two-parameter statistical law (such as the exponential law) is adopted, the model contains only 4 parameters. The first parameter is the limit of Q(d,T), when d tends to infinity. It is estimated by calculating the average value over the entire observed period of the Q(t) discharge time series. The second one gives the hyperbolas curvatures and is ∆. The ∆ parameter has a time dimension and is consequently a characteristic duration of the studied basin. The final two parameters are the location and shape parameters, x0 (0) and aq (0), of the exponential maximal flood distribution for d=0. x0 (0), aq (0) and ∆ parameters are directly adjusted on observed QdF curves of the studied basin.The comparison between the convergent local model and the "reference basin" approach has been carried out on about 50 basins, drawn from different regions of France. For each basin, the two approaches have been tested. First, the two characteristic durations D and∆, defined respectively by the "reference basins" approach and the convergent local model, are compared. As mentioned earlier, ∆ characteristic duration is an adjusted parameter and its calculation does not depend on D. In spite of their different definitions, a strong correlation between these two parameters is observed. This shows a good coherence between the two tested approaches. Second, in order to compare results, a relative mean error between calculated and observed values is determined for each basin and each model. Only the observed domain (T ≤ 20 years) has been considered, because the extrapolations cannot been validated with observed data.Concerning the "reference basin" approach, the three reference basin models are studied, and the choice criterion is applied. Results show that this choice criterion is not relevant. Concerning the convergent local model, the observed mean relative error is lower than in the "reference basin" approach. These good results are confirmed by a very small error dispersion. Consequently, the convergent local model is robust.As a conclusion, this paper presents new developments of the QdF approach: the convergent local continuous model. This model, locally adjusted, yields very satisfactory results. The next step is to apply it on ungauged basins, as is possible in the "reference basins" approach. This could be done by adapting regional methods, such as the index flood method

Spatiotemporal Coherent Control of Light through a Multiple Scattering Medium with the Multispectral Transmission Matrix

We report the broadband characterization of the propagation of light through a multiple scattering medium by means of its multispectral transmission matrix. Using a single spatial light modulator, our approach enables the full control of both the spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of light-matter interaction in disordered media, and has potential applications in sensing, coherent control, and imaging

Investigation of tur bulence in magnetized tor oidal plasma by cor r elative enhanced scatter ing diagnostics

The microwave enhanced scattering (ES) schemes in various modifications were developed and tested for investigation of turbulence and transport in magnetized laboratory plasma and tokamaks. The efficiency of ES methods to study internal small-scale fluctuations or waves in nonuniform magnetized plasma was confirmed experimentally for wide spectra of plasma parameters Exper imental r esults The experiments have been performed in ToriX toroidal plasma device (major radius R 0 = 0.61 m, minor radius a = 0.1 m). A plasma with typical parameters (n e = 5 × 10 10 cm -3 , T e = 1.5 3 eV) and nonuniform distributions of density and electron temperature was created by a hot filament discharge at argon pressure 7.5 × 10 -4 Torr and magnetic field ~ 0.3 T. Radial distribution of electron temperature obtained by Langmuir probe measurements is shown i

Разработка метода количественного определения воды в сотовых панелях самолетов методом ИК термографии

Проведено моделирование и экспериментальные исследования по тепловому контролю воды в авиационных сотовых панелях. Рассмотрены случаи разного расположения воды внутри ячеек и разного количества воды. Показана возможность количественной оценки скрытой воды при двухстороннем и одностороннем доступе к объекту контроля. Разработан и реализован алгоритм количественной оценки массы воды для конкретной сотовой панели.Modelling and experimental activities of TNDT jf aviation honeycomb panels are conducted. The cases of various amount and location of water ingress are considered. The possibility of quantitative evaluation of hidden water with one and two side control is illustrated. The algoritm of quantitative evaluation of hidden water content is realized

Usefulness of the Reversible Jump Markov Chain Monte Carlo Model in Regional Flood Frequency Analysis

Regional flood frequency analysis is a convenient way to reduce estimation uncertainty when few data are available at the gauging site. In this work, a model that allows a non-null probability to a regional fixed shape parameter is presented. This methodology is integrated within a Bayesian framework and uses reversible jump techniques. The performance on stochastic data of this new estimator is compared to two other models: a conventional Bayesian analysis and the index flood approach. Results show that the proposed estimator is absolutely suited to regional estimation when only a few data are available at the target site. Moreover, unlike the index flood estimator, target site index flood error estimation seems to have less impact on Bayesian estimators. Some suggestions about configurations of the pooling groups are also presented to increase the performance of each estimator

On random symmetric matrices with a constraint: the spectral density of random impedance networks

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A: Math. Gen. 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi one-dimensional random impedance networks.Comment: 4 pages, 5 figure

A regional Bayesian POT model for flood frequency analysis

Flood frequency analysis is usually based on the fitting of an extreme value distribution to the local streamflow series. However, when the local data series is short, frequency analysis results become unreliable. Regional frequency analysis is a convenient way to reduce the estimation uncertainty. In this work, we propose a regional Bayesian model for short record length sites. This model is less restrictive than the index flood model while preserving the formalism of "homogeneous regions". The performance of the proposed model is assessed on a set of gauging stations in France. The accuracy of quantile estimates as a function of the degree of homogeneity of the pooling group is also analysed. The results indicate that the regional Bayesian model outperforms the index flood model and local estimators. Furthermore, it seems that working with relatively large and homogeneous regions may lead to more accurate results than working with smaller and highly homogeneous regions