Abstract
Investigations on extreme hydrological events are often at the basis of environmental studies related to hydrological cycle changes and more in general with climate change. Design storm represents an important variable for its implications on flood risk assessment and territory protection measures definition. A regional frequency analysis for studying and understanding the annual maxima of daily rainfall, based on the index variable method, is implemented here on the Tuscany Region (Central Italy). According to the hierarchical approach on three levels, the studied area is divided into homogeneous regions and subregions; the statistical homogeneity within the regions is verified through several homogeneity tests. Furthermore, the two-component extreme value probability distribution of the extreme rainfall is considered identical within each homogeneous region unless a scale factor, called index rainfall, is given by a multivariate model based on climatic and geomorphological characteristics. A geoadditive model for extremes assuming that the observations follow generalized extreme value distribution whose locations are spatially dependent is also carried out on the catchment area of Arno River, the main river of Tuscany Region that extends for a large part of the region area. The application of the two methods is discussed considering the comparison of the maps of the design storm for daily duration and 50-year return period.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alila Y (1999) A hierarchical approach for the regionalization of precipitation annual maxima in Canada. J Geophys Res 104:31645–31655. https://doi.org/10.1029/1999JD900764
Alila Y (2000) Regional rainfall depth–duration–frequency equations for Canada. Water Resour Res 36:1767–1778. https://doi.org/10.1029/2000WR900046
Anselin L (1995) Local Indicators of Spatial Association–LISA. Geogr Anal 27:93–115. https://doi.org/10.1111/j.1538-4632.1995.tb00338.x
Beran M, Hosking JRM, Arnell N (1986) Comment on Two-Component Extreme Value distribution for flood frequency analysis by Fabio Rossi, Mauro Florentino, and Pasquale Versace. Water Resour Res 22:263–266. https://doi.org/10.1029/WR022i002p00263
Blöschl G (2011) Scaling and regionalization in hydrology. Treatise on water science, in P. Wild. Academic Press, Oxford, pp 519–535
Blöschl G, Sivapalan M, Wagener T et al (2013) Runoff prediction in ungauged basins? Synthesis across processes, places and scales. Cambridge University Press, Cambridge, p 465
Bocci C, Caporali E, Petrucci A (2013) Geoadditive modeling for extreme rainfall data. AStA Adv Stat Anal 97:181–193. https://doi.org/10.1007/s10182-012-0192-7
Brath A, Castellarin A, Franchini M, Galeati G (2001) Estimating the index flood using indirect methods. Hydrol Sci J 46:399–418. https://doi.org/10.1080/02626660109492835
Brath A, Castellarin A, Montanari A (2003) Assessing the reliability of regional depth-duration-frequency equations for gaged and ungaged sites. Water Resour Res. https://doi.org/10.1029/2003WR002399
Burn DH (1990) Evaluation of regional flood frequency analysis with a region of influence approach. Water Resour Res 26:2257–2265
Caporali E, Cavigli E, Petrucci A (2008) The index rainfall in the regional frequency analysis of extreme events in Tuscany (Italy). Environmetrics 19:714–724. https://doi.org/10.1002/env.949
Caporali E, Manetti S, Chiarello V, Fatichi S (2014) Changes in precipitation regime in Tuscany Region (Italy). Geophys Res Abstr 16:15247
Castellarin A, Burn DH, Brath A (2001) Assessing the effectiveness of hydrological similarity measures for flood frequency analysis. J Hydrol 241:270–285. https://doi.org/10.1016/S0022-1694(00)00383-8
Castellarin A, Burn DH, Brath A (2008) Homogeneity testing: How homogeneous do heterogeneous cross-correlated regions seem? J Hydrol 360:67–76. https://doi.org/10.1016/j.jhydrol.2008.07.014
Chokmani K, Ouarda TBMJ (2004) Physiographical space-based kriging for regional flood frequency estimation at ungauged sites. Water Resour Res 40:W12514. https://doi.org/10.1029/2003WR002983
Coles S (2001) An introduction to statistical modeling of extreme values. Springer, London
Cunderlik JM, Burn DH (2006) Switching the pooling similarity distances: Mahalanobis for Euclidean. Water Resour Res 42:W03409. https://doi.org/10.1029/2005WR004245
Cunnane C (1988) Methods and merits of regional flood frequency analysis. J Hydrol 100:269–290. https://doi.org/10.1016/0022-1694(88)90188-6
Dalrymple T (1960) Flood-frequency analyses, manual of hydrology: Part 3, Flood-flow techniques, Geological Survey Water-Supply Paper 1543-A, United States Government Printing Office, Washington, p 80
de Grehys G (1996) Recherche en hydrologie statistique, presentation and review of some methods for regional flood frequency analysis. J Hydrol 186:63–84. https://doi.org/10.1016/S0022-1694(96)03042-9
Di Baldassarre G, Castellarin A, Brath A (2005) Evidences of relationships between statistics of rainfall extremes and mean annual precipitation: an application for design-storm estimation in northern central Italy. Hydrol Earth Syst Sci Discuss 2:2393–2425. https://doi.org/10.5194/hessd-2-2393-2005
Fatichi S, Caporali E (2009) A comprehensive analysis of changes in precipitation regime in Tuscany. Int J Climatol 29:1883–1893. https://doi.org/10.1002/joc.1921 Review
Fiorentino M, Gabriele S, Rossi F, Versace P (1987) Hierarchical approach for regional flood frequency analysis. In: Singh VP (ed) Regional flood frequency analysis. D. Reidel Publishing Company, pp 35–49
Gaál L, Kysel J, Szolgay J (2008) Region-of-influence approach to a frequency analysis of heavy precipitation in Slovakia. Hydrol Earth Syst Sci 12:825–839. https://doi.org/10.5194/hess-12-825-2008
Gabriele S, Arnell NW (1991) A hierarchical approach to regional flood frequency analysis. Water Resour Res 27:1281–1289
Gabriele S, Iiritano G (1994) Analisi regionale delle piogge in Basilicata. Rapporto interno n. 414, CNR-IRPI, Rende (Cs)
Griffis VW, Stedinger JR (2007) The use of GLS regression in regional hydrologic analyses. J Hydrol 344:82–95. https://doi.org/10.1016/j.jhydrol.2007.06.023
Grimaldi S, Kao S-C, Castellarin A et al (2011) Regional frequency analysis. In: Wilderer P (ed) Statistical hydrology. Treatise on Water Science, pp 479–517
Hall MJ, Minns aW (1999) The classification of hydrologically homogeneous regions. Hydrol Sci J 44:693–704. https://doi.org/10.1080/02626669909492268
Hazen A (1930) Flood flows: a study of frequencies and magnitudes. Wiley, New York
Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc 52:105–124
Hosking JRM, Wallis JR (1997) Regional frequency analysis, an approach based on L-moments. Cambridge University Press, Cambridge, p 224
Kammann EE, Wand MP (2003) Geoadditive models. Appl Stat 52:1–18
Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Adv Water Resour 25:1287–1304
Laio F, Di Baldassarre G, Montanari A (2009) Model selection techniques for the frequency analysis of hydrological extremes. Water Resour Res 45:1–11. https://doi.org/10.1029/2007WR006666
Laio F, Ganora D, Claps P, Galeati G (2011) Spatially smooth regional estimation of the flood frequency curve (with uncertainty). J Hydrol 408:67–77. https://doi.org/10.1016/j.jhydrol.2011.07.022
Merz R, Blöschl G (2004) Regionalisation of catchment model parameters. J Hydrol 287:95–123. https://doi.org/10.1016/j.jhydrol.2003.09.028
Merz R, Blöschl G (2005) Flood frequency regionalisation–spatial proximity versus catchment attributes. J Hydrol 302:283–306. https://doi.org/10.1016/j.jhydrol.2004.07.018
Ouarda TBMJ, Girard C, Cavadias GS, Bobée B (2001) Regional flood frequency estimation with canonical correlation analysis. J Hydrol 254:157–173
Padoan SA, Wand MP (2008) Mixed model-based additive models for sample extremes. Stat Probab Lett 78:2850–2858. https://doi.org/10.1016/j.spl.2008.04.009
Pandey GR, Nguyen VTV (1999) A comparative study of regression based methods in regional flood frequency analysis. J Hydrol 225:92–101. https://doi.org/10.1016/S0022-1694(99)00135-3
Parajka J, Merz R, Blöschl G (2005) A comparison of regionalisation methods for catchment model parameters. Hydrol Earth Syst Sci Discuss 2:509–542. https://doi.org/10.5194/hessd-2-509-2005
Reed DW, Jakob D, Robson AJ, et al (1999) Regional frequency analysis? A new vocabulary. In: Hydrological extremes: understanding, predicting, mitigating (Proceedings of IUGG 99 symposium HSI, Birmingham) IAHS Publ. no. 255, pp 237–243
Rossi F, Fiorentino M, Versace P (1984) Two-Component Extreme Value distribution for flood frequency analysis. Water Resour Res 20:847–856. https://doi.org/10.1029/WR020i007p00847
Rossi F, Villani P (1994) A project for regional analysis of floods in Italy. In: Rossi G, Harmancioglu NB, Yevjevich V (eds) Coping with floods. Kluwer Academic Publisher, Dordrecht, pp 193–217
Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric regression. Cambridge University Press, Cambridge
Shu C, Burn DH (2004a) Artificial neural network ensembles and their application in pooled flood frequency analysis. Water Resour Res 40:1–10. https://doi.org/10.1029/2003WR002816
Shu C, Burn DH (2004b) Homogeneous pooling group delineation for flood frequency analysis using a fuzzy expert system with genetic enhancement. J Hydrol 291:132–149. https://doi.org/10.1016/j.jhydrol.2003.12.011
Skøien JO, Merz R, Blöschl G (2006) Top-kriging-geostatistics on stream networks. Hydrol Earth Syst Sci 10(2):277–287
Viglione A, Laio F, Claps P (2007) A comparison of homogeneity tests for regional frequency analysis. Water Resour Res 43:1–10. https://doi.org/10.1029/2006WR005095
World Meteorological Organization (1983) Guide to climatological practices. Tech. Report 100, WMO, Geneva, Switzerland
Yadav M, Wagener T, Gupta H (2007) Regionalization of constraints on expected watershed response behavior for improved predictions in ungauged basins. Adv Water Resour 30:1756–1774. https://doi.org/10.1016/j.advwatres.2007.01.005
Acknowledgements
The authors wish to thank the Tuscany Region for co-financing part of the research activity and the Hydrological Service of Tuscany Region for the availability of the dataset. Specific acknowledgments are for Ph.D. Chiara Bocci for her support on the geoadditive model and Ph.D. Giuseppe Rossi for his activities on the Regional Frequency Analysis. The anonymous reviewers and the editors of the journal are also acknowledged for their valuable comments and suggestions to improve the quality of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Handling Editor Pierre Dutilleul.
Rights and permissions
About this article
Cite this article
Caporali, E., Chiarello, V. & Petrucci, A. Regional frequency analysis and geoadditive modeling for design storm estimates in the Arno river basin (Italy). Environ Ecol Stat 25, 31–52 (2018). https://doi.org/10.1007/s10651-018-0399-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10651-018-0399-1