INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 0: 000 – 000 (2016)
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/joc.4738
A study of the scaling properties of rainfall in spain and its
appropriateness to generate intensity-duration-frequency
curves from daily records
Raúl Rodríguez-Solà •,
a
M. Carmen Casas-Castillo,
b
*
Xavier Navarro
a
and Ángel Redaño
c
AQ1
a
Departament de Física, EPSEVG, Universitat Politècnica de Catalunya, BarcelonaTech (UPC), Vilanova i la Geltrú, Spain
b
Departament de Física, ESEIAAT, Universitat Politècnica de Catalunya, BarcelonaTech (UPC), Terrassa, Spain
c
Departament d’Astronomia i Meteorologia, Facultat de Física, Universitat de Barcelona, Barcelona, Spain
ABSTRACT: A methodology based on the fractal properties of rainfall has been applied to obtain the
intensity-duration-frequency, IDF, curves for 100 pluviometric Spanish stations over the Iberian Peninsula and the Balearic
Islands from their daily precipitation series. The scaling behaviour of maximum rainfall intensities has been investigated and
simple scaling has resulted suitable. This methodology has been veriied in three emblematic observatories with available
sub-daily registers and current known generalized IDF relationships: the Fabra Observatory of Barcelona, the Ebre Obser-
vatory near Tortosa (Tarragona) and the Retiro Observatory of Madrid. Despite some general concordance with the mean
annual rainfall distribution over Spain, the spatial distribution of the scaling parameter found for the 100 stations shows some
discrepancies in diverse areas probably due to the inluence of other features, as the inter-annual rainfall variability and the
contribution of convective rainfall to total precipitation, on the characteristic rainfall pattern in these areas.
KEY WORDS simple scaling; fractal analysis; rainfall intensity; intensity-duration-frequency curves
Received 23 September 2015; Revised 8 March 2016; Accepted 13 March 2016
1. Introduction
The calculation of the intensity-duration-frequency curves
(IDF curves), which remains as an important tool for the
risk analysis of natural hazards and hydrological design,
usually requires a historical series of the maximum rainfall
intensities at a sub-daily durations. Such in most locations
rainfall data are usually available only from totaliser rain
gauges registering 1-day precipitation, a method to infer
intensity-frequency values for short durations from daily
rainfall data can be very useful. There is a methodology
based on the fractal properties of rainfall, or more specif-
ically on the characteristic scale invariance of the fractal
processes (Bendjoudi et al., 1997; De Michele et al., 2002;
Yu et al., 2004), to obtain the disaggregation or down-
scaling of low resolution precipitation data (daily) to high
resolution (sub-daily) (Menabde et al., 1999; Desramaut,
2008; Bara et al., 2010). Many atmospheric processes pro-
duced by complex dynamic mechanisms acting in a wide
temporal range, as rainfall generation, give rise to phe-
nomena that look the same regardless the scale where they
are contemplated (self-similarity). These processes can
be considered of fractal type and their properties exhibit
power laws of the scale parameter , which is the ratio
* Correspondence to: M. C. Casas-Castillo, Departament de Física,
ESEIAAT, Universitat Politècnica de Catalunya, BarcelonaTech (UPC),
Campus de Terrassa, Ediici TR2, C/Colom, 1, 08222 Terrassa, Spain.
E-mail: m.carmen.casas@upc.edu
t
∕
t
0
between any two durations t and t
0
within the scaling
regime. The fractal self-similarity of natural processes,
such as rainfall generation, has a statistical nature, as
opposed to mathematical fractals in which the parties are
an exact copy of the whole. Therefore the scaling proper-
ties of phenomena like rain can be expressed by statistical
relationships describing their fractal behaviour (Schertzer
and Lovejoy, 1987; Schertzer and Lovejoy, 2011). Several
studies analysed the rainfall process in Spain from a fractal
point of view: Oñate Rubalcaba (1997) obtained a mean
fractal dimension of 1.32 ± 0.01 for annual rainfall series
recorded by 10 stations in the Iberian Peninsula, whereas
Meseguer-Ruiz et al. (2014) compared the fractal dimen-
sion of 10-min rainfall data from 20 Spanish observatories
with a concentration index (CI) expressing the relative
weight of the rainiest days of a series on the total accu-
mulated rainfall of that series. Other studies investigated
the multifractal character of rainfall records in Spanish
stations (Valencia et al., 2010, 2015; García-Marín et al.
2008, 2013, 2015; Rodríguez et al., 2013).
It has been widely observed that the probability
distribution of the annual maximum precipitation inten-
sities satisies scale relationships (Koutsoyiannis and
Foufoula-Georgiu, 1993; Burlando and Rosso, 1996;
Menabde et al. 1999), which means that the probability
distribution of the annual maximum daily intensity I
24
(t
0
= 24 h) and the distribution at other scale I
t
can be related
by a factor that is a power function of the scale parameter
. In terms of the moments of order q, I
q
t
, of the intensity
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© 2016 Royal Meteorological Society