Abstract
As well as in other natural processes, it has been frequently observed that the phenomenon arising from the rainfall generation process presents fractal self-similarity of statistical type, and thus, rainfall series generally show scaling properties. Based on this fact, there is a methodology, simple scaling, which is used quite broadly to find or reproduce the intensity–duration–frequency curves of a place. In the present work, the relationship of the simple scaling parameter with the characteristic rainfall pattern of the area of study has been investigated. The calculation of this scaling parameter has been performed from 147 daily rainfall selected series covering the temporal period between 1883 and 2016 over the Catalonian territory (Spain) and its nearby surroundings, and a discussion about the relationship between the scaling parameter spatial distribution and rainfall pattern, as well as about trends of this scaling parameter over the past decades possibly due to climate change, has been presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aronica GT, Freni G (2005) Estimation of sub-hourly DDF curves using scaling properties of hourly and sub-hourly data at partially gauged site. Atmos Res 77(1–4):114–123. https://doi.org/10.1016/j.atmosres.2004.10.025
Bara M, Kohnová S, Gaál L, Szolgay J, Hlavčová K (2009) Estimation of IDF curves of extreme rainfall by simple scaling in Slovakia. Contrib Geophys Geod 39(3):187–206
Bara M, Gaál L, Kohnová S, Szolgay J, Hlavčová K (2010) On the use of the simple scaling of heavy rainfall in a regional estimation of IDF curves in Slovakia. J Hydrol Hydromech 58(1):49–63. https://doi.org/10.2478/v10098-010-0006-0
Bell FC (1969) Generalised rainfall–duration–frequency relationships. J Hydraul Division ASCE 95(1):311–327
Buonomo E, Jones E, Huntingford C, Hammaford J (2007) On the robustness of changes in extreme precipitation over Europe from two high resolution climate change simulations. Quart J R Meteorol Soc 133:65–81. https://doi.org/10.1002/qj.13
Burlando P, Rosso R (1996) Scaling and multiscaling models of depth-duration-frequency curves for storm precipitation. J Hydrol 187:45–64. https://doi.org/10.1016/S0022-1694(96)03086-7
Casas MC, Codina B, Redaño A, Lorente J (2004) A methodology to classify extreme rainfall events in the western Mediterranean area. Theoret Appl Climatol 77:139–150. https://doi.org/10.1007/s00704-003-0003-x
Casas-Castillo MC, Rodríguez-Solà R, Navarro X, Russo B, Lastra A, González P, Redaño A (2018) On the consideration of scaling properties of extreme rainfall in Madrid (Spain) for developing a generalized intensity-duration-frequency equation and assessing probable maximum precipitation estimates. Theor Appl Climatol 131(1):573–580. https://doi.org/10.1007/s00704-016-1998-0
Christensen JH, Christensen OB (2003) Severe summertime flooding in Europe. Nature 421:805–806. https://doi.org/10.1038/421805a
Desramaut N (2008) Estimation of intensity Duration Frequency Curves for Current and Future Climates [Thesis of Master], Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec (Canada). http://digitool.library.mcgill.ca/R/-?func=dbin-jump-full&object_id=40816¤t_base=GEN01
Esteban P, Prohom M, Aguilar E (2013) Tendencias recientes e índices de cambio climático de la temperatura y la precipitación en Andorra, Pirineos (1935-2008). Pirineos. Revista de ecología de montaña 167:89–108. https://doi.org/10.3989/Pirineos.2012.167005
Ferreri G, Ferro V (1990) Short-duration rainfalls in Sicily. J Hydraulic Eng ASCE 116(3):430–435. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:3(430)
Gupta VK, Waymire E (1990) Multiscaling properties of spatial rainfall and river flow distributions. J Geophys Res 95(D3):1999–2009. https://doi.org/10.1029/JD095iD03p01999
Huntington TG (2006) Evidence for intensification of the global water cycle: review and synthesis. J Hydrol 319(1–4):83–95. https://doi.org/10.1016/j.jhydrol.2005.07.003
Kendall MG (1975) Rank correlation methods. Charles Griffin, London, p 6
Koutsoyiannis D, Foufoula-Georgiou E (1993) A scaling model of storm hyetograph. Water Resour Res 29(7):2345–2361. https://doi.org/10.1029/93WR00395
Koutsoyiannis D, Kozonis D, Manetas A (1998) A mathematical framework for studying rainfall intensity-duration-frequency relationships. J Hydrol 206(1–2):118–135. https://doi.org/10.1016/S0022-1694(98)00097-3
Mann HB (1945) Nonparametric tests against trend. Econometrika 13:245–259
Menabde M, Seed A, Pegram G (1999) A simple scaling model for extreme rainfall. Water Resour Res 35(1):335–339. https://doi.org/10.1029/1998WR900012
Pérez FF, Boscolo R (2010) Clima en España: Pasado, presente y futuro. Informe de Evaluación del Cambio climático Regional. Red Temática CLIVAR-España. http://clivar.iim.csic.es/files/informe_clivar_final.pdf
Pérez-Zanón N, Casas-Castillo MC, Rodríguez-Solà R, Peña JC, Rius A, Solé JG, Redaño A (2015) Analysis of extreme rainfall in the Ebre Observatory (Spain). Theor Appl Climatol 124(3–4):935–944. https://doi.org/10.1007/s00704-015-1476-0
Rodríguez R, Navarro X, Casas MC, Ribalaygua J, Russo B, Pouget L, Redaño A (2014) Influence of climate change on IDF curves for the metropolitan area of Barcelona (Spain). Int J Climatol 34:643–654. https://doi.org/10.1002/joc.3712
Rodríguez-Solà R, Casas-Castillo MC, Navarro X, Redaño A (2017) A study of the scaling properties of rainfall in Spain and its appropriateness to generate intensity-duration-frequency curves from daily records. Int J Climatol 37(2):770–780. https://doi.org/10.1002/joc.4738
Schertzer D, Lovejoy S (1987) Physical modelling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J Geophys Res 92(D8):9693–9714. https://doi.org/10.1029/JD092iD08p09693
Schertzer D, Lovejoy S (2011) Multifractals, generalized scale invariance and complexity in geophysics. Int J Bifurc Chaos 21(12):3417–3456. https://doi.org/10.1142/S0218127411030647
Servei Meteorològic de Catalunya (2017) Butlletí Anual d’Indicadors Climàtics 2016. Departament de Territori i Sostenibilitat. Generalitat de Catalunya. http://static-m.meteo.cat/wordpressweb/wp-content/uploads/2017/05/29072030/00_BAIC-2016_TOT.pdf
Yu PS, Yang TC, Lin CS (2004) Regional rainfall intensity formulas based on scaling property of rainfall. J Hydrol 295(1–4):108–123. https://doi.org/10.1016/j.jhydrol.2004.03.003
Acknowledgements
We gratefully acknowledge to Servei Meteorològic de Catalunya (Generalitat de Catalunya) and Observatori de l’Ebre for providing the data analyzed in this work. We are also grateful to the anonymous referees for their useful suggestions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Rights and permissions
About this article
Cite this article
Casas-Castillo, M.C., Llabrés-Brustenga, A., Rius, A. et al. A single scaling parameter as a first approximation to describe the rainfall pattern of a place: application on Catalonia. Acta Geophys. 66, 415–424 (2018). https://doi.org/10.1007/s11600-018-0122-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11600-018-0122-5