Modeling short duration extreme precipitation patterns using copula and generalized maximum pseudo-likelihood estimation with censoring |
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| Institution: | 1. ENIT, Université de Tunis El Manar, Civil Engineering School, bp 37, 1002 Tunis, Tunisia\n;2. IWS, Stuttgart University, Stuttgart, Germany;1. Center for Applied Geoscience, University of Tübingen, Germany;2. Institute of Fluid Mechanics and Environmental Physics in Civil Engineering, University of Hannover, Germany;1. Department of Physical Geography, Stockholm University, Stockholm, Sweden;2. Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden.;3. Department of Crop Production Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden;4. Department of Civil and Environmental Engineering, University of California, Berkeley, CA, USA;1. INRA, AgroParisTech, UMR 1402 ECOSYS, Thiverval-Grignon F-78850, France;2. Department of Soil Science, University of Kassel, Nordbahnhofstr. 1a, Witzenhausen D-37231, Germany;3. UMMISCO-Cameroun, UMI 209 UMMISCO, University of Yaoundé, IRD, University of Paris 6, Bondy Cedex F-93143, France;4. CEA Saclay, DEN/DANS/DM2S/STMF/LATF, Gif-sur-Yvette F-91191, France;5. Institute of Materials Research, Helmholtz-Zentrum Geesthacht, Max-Planck-Str. 1, D-21502 Geesthacht, Germany;6. Laboratory of Soil and Water Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA;1. Department of Civil Engineering, Monash University, Building 60, Melbourne, 3800 Victoria, Australia;2. Center for the Study of the Biosphere from Space (CESBIO), Toulouse, France;1. Institute Center for Water and Environment (iWATER), Masdar Institute of Science and Technology, P.O. Box 54224 Abu Dhabi, United Arab Emirates\n;2. INRS-ETE, 490 de la Couronne, Quebec, QC GIK 9A9, Canada\n |
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| Abstract: | The paper aims to develop researches on the spatial variability of heavy rainfall events estimation using spatial copula analysis. To demonstrate the methodology, short time resolution rainfall time series from Stuttgart region are analyzed. They are constituted by rainfall observations on continuous 30 min time scale recorded over a network composed by 17 raingages for the period July 1989–July 2004. The analysis is performed aggregating the observations from 30 min up to 24 h. Two parametric bivariate extreme copula models, the Husler–Reiss model and the Gumbel model are investigated. Both involve a single parameter to be estimated. Thus, model fitting is operated for every pair of stations for a giving time resolution. A rainfall threshold value representing a fixed rainfall quantile is adopted for model inference. Generalized maximum pseudo-likelihood estimation is adopted with censoring by analogy with methods of univariate estimation combining historical and paleoflood information with systematic data. Only pairs of observations greater than the threshold are assumed as systematic data. Using the estimated copula parameter, a synthetic copula field is randomly generated and helps evaluating model adequacy which is achieved using Kolmogorov Smirnov distance test. In order to assess dependence or independence in the upper tail, the extremal coefficient which characterises the tail of the joint bivariate distribution is adopted. Hence, the extremal coefficient is reported as a function of the interdistance between stations. If it is less than 1.7, stations are interpreted as dependent in the extremes. The analysis of the fitted extremal coefficients with respect to stations inter distance highlights two regimes with different dependence structures: a short spatial extent regime linked to short duration intervals (from 30 min to 6 h) with an extent of about 8 km and a large spatial extent regime related to longer rainfall intervals (from 12 h to 24 h) with an extent of 34 to 38 km. |
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