Potential distribution of extreme rainfall in the Basque Country

DOI: 10.3369/tethys.2011.8.01

Tethys no. 8 pp.: 3 - 12

Abstract

The Potential Distribution model can describe at once the probability distribution and temporal distribution of rainfall. It also allows the incorporation of the dependence of the probability with the number of independent stations. This paper analyzes the probability distribution and temporal distribution of extreme rainfall in the Autonomous Community of the Basque Country using daily data from 43 stations, with an average of 31 active stations between 1961 and 2000. It was found that this model provided a good adjustment (NMAE = 1.4%) for rainfall over 115 mm in 24 h, and is consistent with other analyses of extremes. Finally, the article proposes a mathematical relationship to estimate the maximum expected rainfall for a return period equal to or more than 10 years, with a duration longer than 1 minute, and for a given set of independent stations. This relationship depends on two exponents, one for the return period (m = 0.23 ± 0.02) and another for the duration (n = 0.63 ± 0.06). In addition, it also depends on a scale factor, which takes values between Po = 42 ± 2 mm to the south of the region and Po = 71 ± 5 mm to the north, with an average value for the Basque Country equal to 58 ± 2 mm.

References

  • - AEMET, 2010: Valores climáticos extremos, Agencia Estatal de Meteorología (WEB), 11/VI/2010.
  • - Anderson, T. W. and Darling, D. A., 1952: Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes, Annals of Mathematical Statistics, 23, 193–212, doi: 10.1214/aoms/1177729437.
  • - Begueria, S., 2005: Uncertainties in partial duration series modelling of extremes related to the choice of the threshold value, J Hydrol, 303, 215–230, doi: 10.1016/j.jhydrol.2004.07.015.
  • - Ben-Zvi, A., 2009: Rainfall intensity-duration-frequency relationships derived from large partial duration series, J Hydrol, 367, 104–114, ISSN: 0022–1694, doi: 10.1016/j.jhydrol.2009.01.007.
  • - Chow, V. T., 1962: Hydrological determination of waterway areas for the design of drainage structures in small drainage basins, Engineering Experimental Station, Bulletin 462, University of Illinois, Urbana, USA.
  • - Corder, G. W. and Foreman, D. I., 2009: Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach, Wiley, ISBN: 978047045461.
  • - de Salas, L. and Fernández, J. A., 2006: Nueva metodología para el análisis de la variable intensidad máxima anual de precipitación, Ecología, 20, 35–44.
  • - Etoh, T., Murota, A., and Nakanishi, M., 1986: SQRT-Exponential Type Distribution of Maximum, Hydrologic Frequency Modelling, V. P. Shing (Ed.), Reidel Pub. Com, Lousiana State University, USA, Proceedings of the International Symposium on Flood Frequency and Risk Analyses, 14-17 May 1986, 253-264.
  • - Ferrer, F. J., 1996: El modelo de función de distribución SQRT-ETmax en el análisis regional de máximos hidrológicos: aplicación a lluvias diarias, Tesis Doctoral, Universidad Politécnica de Madrid.
  • - Font-Tullot, I., 2000: Climatología de España y Portugal, Universidad de Salamanca, 2a Edición, 422 pp.
  • - Kundzewicz, Z. W. and Robson, A., 2000: World Climate Programe - Water detecting trend and other changes in hydrological data, United Nations Educational Scientific and Cultural Org., Geneva, May, WCDMP, 45 WMO/TD - No. 1013 (PDF).
  • - Lana, X., Burgueño, A. B., Martínez, M. D., and Serra, C., 2009: A review of statistical analyses on monthly and daily rainfall in Catalonia, Tethys, 6, 15–29, doi: 10.3369/tethys.2009.6.02.
  • - Llasat, M. C., Ramis, C., and Barrantes, J., 1996: The meteorology of high-intensity rainfall events over the West Mediterranean region, Remote Sensing Reviews, 14, 51–90.
  • - Marco, J., 1999: Análisis Hidrológico y sus implicaciones en la planificación de una defensa integral frente a las inundaciones de la Ribera del Júcar, CONFEDERACIÓN HIDROGRÁFICA DEL JÚCAR: Estrategias de actuación en la zona inundable de la Ribera del Júcar, Ponencias Técnicas, Volumen I, Alzira, 29-30/III/1999.
  • - Martín-Vide, J., 2004: Spatial distribution of a daily precipitation concentration index in peninsular Spain, Int J Climatol, 24, 959–971, doi: 10.1002/joc.1030.
  • - Ministerio de Fomento, 1999: Máximas lluvias diarias en la España Peninsular, Ministerio de Fomento, Madrid, ISBN: 978-84-498-0419-9 (PDF).
  • - Moncho, R., 2008: Análisis de la intensidad de precipitación. Método de la intensidad contigua, RAM3, Enero.
  • - Moncho, R., Belda, F., and Caselles, V., 2009: Climatic study of the exponent n of the IDF curves of the Iberian Peninsula, Tethys, 6, 3–14, doi: 10.3369/tethys.2009.6.01.
  • - Pereyra-Diaz, D., Pérez-Sesma, J. A. A., and Gómez-Romero, L., 2004: Ecuaciones que estiman las curvas Intensidad-Duración-Período de retorno de la lluvia, GEOS, 24, 46–56 (PDF).
  • - Pérez-Cueva, A., 1983: Precipitaciones extraordinarias en la España Peninsular, Agricultura y sociedad, 28, 189–203, ISSN: 0211–8394 (PDF).
  • - Ruíz-Urrestarazu, E., 1983: Estado actual de las fuentes de los datos climáticos en Álava, Guipúzcoa y Vizcaya y su posible planificación, Eusko Ikaskuntza (Ed.), Encuentro de Geografía Euskal Herria-Catalunya, Donostia-San Sebastián, 395-419, ISSN: 0212-3223 (PDF).
  • - Siegel, S., 1986: Estadística no paramétrica aplicada a las Ciencias de la Conducta, Editorial Trillas, México D.F.
  • - Soro, G. E., Goula Bi, T. A., Kouassi, F.W., and Srohourou, B., 2010: Update of intensity-duration-frequency curves for precipitation of short durations in tropical area of West Africa (Cote D’ivoire), J Appl Sci, 10, 704–715, doi: 10.3923/jas.2010.704.715.
  • - Témez, J. R., 1978: Cálculo Hidrometeorológico de caudales máximos en pequeñas cuencas naturales, Dirección General de Carreteras, Madrid, p. 111.
  • - Ugarte, F. M. and González, J. A., 1984: Precipitaciones de agosto de 1983 en la cuenca del río Oka (ría de Mundaka-Vizcaya): repercusiones geomorfológicos, Cuadernos de investigación geográfica, 10, 201–214, 7 Ref., ISSN: 0211–6820 (PDF).


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Partially funded through grants CGL2007-29820-E/CLI, CGL2008-02804-E/, CGL2009-07417-E and CGL2011-14046-E of the Spanish Ministry of Science and Innovation