Análisis Latitudinal de la Intensidad de Lluvias y Precipitación Media Anual en Chile

Abstract

The study and analysis of precipitation has become a crucial tool in understanding the temporal and spatial behavior of water resources, in terms of availability and impact on extreme events. The objective of this study was to evaluate different rainfall parameters (intensities for 1-h duration D = 1 h and return periods of T = 5 and 100 yr, and mean annual precipitation) for different latitudinal and climatic zones in Chile. We analyzed the information recorded on thousands of pluvial bands and rain gauges for 49 stations; this because it is unclear how rainfall intensities change along the country (though total amounts do), in addition to a lack of literature focused on ranges and amounts on the behavior of rainfall variables. The Gumbel probability distribution function (PDF) and mathematical rainfall intensity formulas were used to develop intensity-duration-frequency (IDF) curves for each station. Maximum and minimum rainfall intensity values for T = 100 yr ranged from 8.79 (hyperarid zone) to 40.17 mm h-1 (subhumid-humid zone). Total annual rainfall values ranged between 43.9 (hyperarid zone) and 3891.0 mm yr-1 (humid zone). Additionally, the real maximum intensity registered on each station was analyzed, determining its exceedance probability. Likewise, multiple comparisons were made to detect significant differences between the gauge stations and different climatic zones using the Kruskal Wallis test (alpha = 0.05). Differences between maximum and minimum values registered for all stations were as much as 80 times for total rainfall amounts and 4.5 times for rainfall intensities (T = 100 yr). However, maximum rainfall intensities values were similar at different latitudes, suggesting the absence of correlation between maximum rainfall intensity and annual rainfall amount, as the latter variable increased gradually with latitude.

Full text

253252 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
RESEARCH
LATITUDINAL ANALYSIS OF RAINFALL INTENSITY AND MEAN ANNUAL
PRECIPITATION IN CHILE
Roberto Pizarro1, Rodrigo Valdés1*, Pablo García-Chevesich2, Carlos Vallejos1, Claudia Sangüesa1,
Carolina Morales1, Francisco Balocchi1, Alejandro Abarza1, and Roberto Fuentes1
The study and analysis of precipitation has become a crucial tool in understanding the temporal and spatial behavior
of water resources, in terms of availability and impact on extreme events. The objective of this study was to evaluate
different rainfall parameters (intensities for 1-h duration D = 1 h and return periods of T = 5 and 100 yr, and mean annual
precipitation) for different latitudinal and climatic zones in Chile. We analyzed the information recorded on thousands of
pluvial bands and rain gauges for 49 stations; this because it is unclear how rainfall intensities change along the country
(though total amounts do), in addition to a lack of literature focused on ranges and amounts on the behavior of rainfall
variables. The Gumbel probability distribution function (PDF) and mathematical rainfall intensity formulas were used to
develop intensity-duration-frequency (IDF) curves for each station. Maximum and minimum rainfall intensity values for T
= 100 yr ranged from 8.79 (hyperarid zone) to 40.17 mm h-1 (subhumid-humid zone). Total annual rainfall values ranged
between 43.9 (hyperarid zone) and 3891.0 mm yr-1 (humid zone). Additionally, the real maximum intensity registered on
each station was analyzed, determining its exceedance probability. Likewise, multiple comparisons were made to detect
signicant differences between the gauge stations and different climatic zones using the Kruskal Wallis test (alpha = 0.05).
Differences between maximum and minimum values registered for all stations were as much as 80 times for total rainfall
amounts and 4.5 times for rainfall intensities (T = 100 yr). However, maximum rainfall intensities values were similar at
different latitudes, suggesting the absence of correlation between maximum rainfall intensity and annual rainfall amount,
as the latter variable increased gradually with latitude.
Key words: Precipitation, frequency-duration-intensity curves, IDF curves, rainfall intensity.
1University of Talca, Facultad de Ciencias Forestales, Casilla 747,
Talca, Chile. *Corresponding author (rodrigovaldes@utalca.cl).
2University of Arizona, Department of Agricultural and Biosystems
Engineering, Shantz Bldg #38, Room 403, PO Box 210038, Tucson,
Arizona, USA.
Received: 4 October 2011.
Accepted: 25 May 2012.
recipitation is often the principal hydrological
contribution for a watershed and usually improves
the general conditions of drainage. Nevertheless, extreme
precipitation events often cause serious problems
worldwide, such as ooding and their consequences for
human lives and property (Maidment, 1996).
Hydrologic phenomena, such as precipitation, oods,
and droughts, are inherently random by nature. These
physical processes are not fully understood due to the
complexity of the hydrologic cycle; for instance, reliable
deterministic mathematical models have yet to be
developed. Statistical approaches have been commonly
adopted in order to provide useful analyses for design of
hydraulic pathways and structures (Grimaldi et al., 2011).
In this context, rainfall can be characterized in terms of
its frequency, duration, and intensity, with intensity being
most relevant to the less frequent but more damaging
high-intensity events. Using statistical techniques these
P
three variables (intensity, duration, and frequency) can
be correlated to create intensity-duration-frequency (IDF)
curves, based on maximum precipitation intensities. IDF
curves are crucial in the design of storm water management
structures (Haan, 2002) and are useful tools for watershed
management, such as prediction of water erosion. Such
phenomenon has been evaluated using rainfall simulators
(Sangüesa et al., 2010), that generate rainfall with a known
intensity and duration on an erosion plot in a controlled
manner, thus making it possible to quantify supercial
runoff and soil loss and predict erosion with a high
level of detail (Martínez-Mena et al., 2001). Articially
generated rainfall in these simulators must be calibrated
according to maximum values of rainfall intensity (IDF
curves) corresponding to the location of the study site.
Additionally, IDF curves are used to determine design
parameters for soil and water conservation practices.
According to Pizarro et al. (2005), the design must
include at least four basic hydrological parameters: a
return period, an IDF curves, a runoff coefcient, and
soil inltration capacity. IDF curves can be represented
as mathematical functions used to determine rainfall
intensity by inputting frequency values (years) and
duration (minutes or hours). Furthermore, IDF curves
have been widely used by different authors. Willems

253252 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
(2000) separated both convective and frontal storms in
terms of their peak-over-threshold intensity distributions
in Belgium, helping to better understand what factors
affect IDF curves and their scaling properties. Bougadis
and Adamowski (2006) used traditional techniques to
compare the scaling properties of extreme rainfall IDF
curves using data collected in Ontario, Canada. The
authors concluded that the scale approaches were more
efcient and gave more accurate estimates through
comparing observed data. Other authors have focused
IDF research on analyzing and developing mathematical
functions (Veneziano and Furcolo, 2002; Pereyra-Díaz et
al., 2004; Langousis and Veneziano, 2007), the effects of
topography and elevation (Dairaku, 2004), and studying
ungauged areas of watersheds (Watkins et al., 2005).
IDF curves analyses have been conducted in Vietnam
(Minh Nhat et al., 2006), Japan (Minh Nhat et al., 2008),
Mexico (Hallack-Alegria and Watkins Jr., 2007), and many
other places worldwide. Pizarro et al. (2001) developed
IDF curves for the Maule Region in Chile and UNESCO
(2007) updated IDF curves for a great portion of the
Chilean territory (between Coquimbo and La Araucanía
Regions). However, there is no scientic evidence
regarding the values and existing differences among the
curves developed for the country, including geographical
extremes of Chile. Therefore, the objective of this study
was to evaluate maximum rainfall intensities (D = 1 h
and T = 5 and 100 yr) and mean annual precipitation for
different latitudes and climatic zones of Chile, based on
information obtained from pluvial bands and rain gauges
from 49 stations distributed along the country, in order to
determine if a pattern able to explain the behavior of IDF
curves at different latitudes (e.g. under different climates)
exists.
MATERIAL AND METHODS
The study was done using information on rainfall
intensity, obtained from 49 gauge stations distributed
along the country (Figure 1A), property of Chile’s
Water General Direction (Dirección General de Aguas),
and installed under the norms and specications of the
World Meteorological Organization (WMO). Stations
were located under different climates, varying from
hyperarid and semiarid zones to humid and cold semiarid
(UNESCO, 2006; 2010), all within the 12 Chilean
rst-order administrative regions (Figure 1B). Chile’s
geography is unusual, being the country with the world’s
largest length-to-width ratio (4300 km to about 177 km
in average) (IGM, 2008). But most importantly for this
study is to notice the wide heterogeneity of the country’s
climates, a direct consequence of large latitudinal changes
(high and low atmospheric pressure zones), combined
with important topographic features, like the presence of
Los Andes and La Costa mountain ranges, and the cold
Humboldt Current in the Pacic Ocean. Moreover, this
north-to-south general climatic variability begins with
the extreme aridity of desert zones, ends with cold-rainy
climates in the extreme south of the country, passing
through temperate-warm climates in central Chile (INE,
2007).
For 86% of the rain gauges IDF curves were obtained
using maximum annual precipitation intensities. However,
partial time series, as described by Linsley et al. (1977)
were used for the remaining stations (14%) since were
recently established and had less than ve years’ worth
of data. A selection criterion of two or three storm events
per year was established to increase the number of data
available for analysis. It is also not worthless to mention
Figure 1. (A) Spatial distribution of the 49 gauge stations on each administrative Region of Chile. (B) Spatial distribution of the 49 gauge stations on each
climatic zone of Chile.

255254 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
that the historical data documented at the analyzed
stations were between 10 and 40 records (47% with more
than 20 records, 39% between 15 and 19 records, and
14% between 10 and 14 records).
Table 1 lists general information about the gauge
stations (number of years on record, administrative
region, geographical coordinates, and climatic zone).
The Gumbel procedure (Gumbel, 1958) was applied to
each data series listed on Table 1 in order to obtain a
probability distribution for return periods of T = 5 and 100
yr for each station. The Gumbel probability distribution
function (PDF) is expressed as F(x) = e-e-d•(x–u), where x is
the value of the random variable, d and u are parameters
of the function, and e is the Neper constant. Similarly, the
probability of occurrence, or the probability for a random
variable to have a value equal or lower than a certain
number X, is given by the probability distribution function
dened as ∫ _∞f(x)dx = P (x ≤ X) = 1– (1/T), (where T
represents the return period in years). The probability
of exceedence, dened as the probability for the random
variable to exceed a given value, is determined by the
expression P(x > X) = 1 – F(x) = 1/T. On the same way, it
is important to add that the Gumbel function has been used
in studies related to extreme meteorological events, and has
provided a precise t to daily and annual hydrological values
(Mintegui y Robredo, 1993). Similarly, Stol (1971), cited in
Dickinson (1977), states that Gumbel is the best approach
in representing extreme annual rainfall. Additionally, the
Gumbel function has been cited extensively in related
literature due to its ability to t extreme values (e.g. Linsley
et al., 1977; Témez, 1978; Pizarro, 1986; Ponce, 1989;
Chow et al., 1994; Monsalve, 1999).
Hyperarid Arica y Parinacota Putre (*) 1 18°12’ 69°35’ 2004-2008 15
Parinacota (*) 2 18°12’ 69°16’ 2004-2007 12
Central Chapiquiña (*) 3 18°23’ 69°33’ 2005-2008 12
Atacama Iglesia Colorada 4 28°10’ 69°52’ 1988-2008 20
Santa Juana 5 28°40’ 70°39’ 1988-2005 17
Albaricoque (*) 6 28°56’ 70°09’ 1988-2008 30
Arid-semiarid Coquimbo Rivadavia 7 29°58´ 70°34´ 1976-2001 25
Embalse La Paloma 8 30°41´ 71°02´ 1962-2002 40
Embalse Cogotí 9 31°00´ 71°06´ 1966-2002 33
Illapel 10 31°38´ 71°10´ 1976-2002 27
La Tranquilla 11 31°54´ 70°39´ 1966-2002 34
Los Cóndores 12 32°07´ 71°19´ 1978-2002 22
Quelón 13 32°09´ 71°10´ 1973-2002 27
Semiarid Valparaíso Hacienda Pedernal 14 32°06´ 70°48´ 1978-2001 10
Quillota 15 32°53´ 71°15´ 1979-2002 12
Embalse Lliu-Lliu 16 33°08´ 71°13´ 1979-2002 14
Lago Peñuelas 17 33°09´ 71°33´ 1974-2001 21
Metropolitana Embalse Rungue 18 33°01´ 70°55´ 1984-2000 16
Cerro Calán 19 33°23´ 70°32´ 1983-2000 17
Los Panguiles 20 33°26´ 71°00´ 1985-2000 15
Pirque 21 33°40´ 70°36´ 1984-2000 17
Semiarid-Mediterranean Libertador General Bernardo O’Higgins Rengo 22 34°25´ 70°53´ 1970-2002 26
Central Las Nieves 23 34°29´ 70°42´ 1971-2002 27
Convento Viejo 24 34°46´ 71°07´ 1972-2002 21
Mediterranean Maule Los Queñes 25 35°00´ 70°49´ 1988-2002 15
Potrero Grande 26 35°12´ 71°07´ 1988-2002 15
Pencahue 27 35°23´ 71°48´ 1982-1998 17
Talca 28 35°26´ 71°35´ 1982-1998 17
San Javier 29 35°36´ 71°44´ 1988-2002 15
Colorado 30 35°38´ 71°16´ 1982-1998 14
Melozal 31 35°45´ 71°47´ 1982-1998 17
Embalse Ancoa 32 35°54´ 71°17´ 1988-2002 15
Parral 33 36°09´ 71°50´ 1982-1998 17
Embalse Digua 34 36°15´ 71°32´ 1988-2002 15
Embalse Bullileo 35 36°17´ 71°26´ 1982-1998 16
San Manuel (*) 36 36°21´ 71°39´ 1996-2002 14
Subhumid humid Biobío Embalse Coihueco 37 36°35´ 71°47´ 1984-2003 20
Chillán Viejo 38 36°38´ 72°08´ 1974-2003 29
Embalse Diguillín 39 36°50´ 71°44´ 1965-2003 38
Quilaco 40 37°41´ 72°00´ 1965-2003 39
Cerro El Padre 41 37°46´ 71°53´ 1976-2003 28
Humid La Araucanía Traiguén 42 38°15´ 72°40´ 1988-2003 16
Curacautín 43 38°26´ 71°53´ 1991-2003 13
Pueblo Nuevo 44 38°44´ 72°45´ 1989-2003 15
Pucón 45 39°16´ 71°58´ 1984-2003 20
Los Ríos Lago Calafquén (*) 46 39°34´ 72°15´ 1997-2008 24
Llancahue 47 39°50´ 73°10´ 1977-2007 31
Los Lagos Puelo (*) 48 41°38´ 72°16´ 1997-2008 24
Cold-semiarid Magallanes y la Antártica Chilena Punta Arenas 49 53°10´ 70°54´ 1983-2008 26
Table 1. Climatic zone, administrative Region, location, and years of record for each gauge station.
(*) Stations in which two or three annual data were considered.
S lat W long
Station/LocationRegionClimatic zone Map
number Registration
period Range
(n)

255254 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
In Chile, the Gumbel function was used by Pizarro et
al. (2008) to characterize annual precipitation in central
Chile. It is also important to add that national experience
on recent studies in process of publication demonstrate
that the Gumbel function more accurately ts to extreme
precipitation and runoff values than other functions,
such as Log-Normal or Goodrich and Pearson Type
III. However, these latter functions t more accurately
for data in arid and semiarid climates (mostly between
south 29° and 32° latitude), where data is more variable.
However, Linsley et al. (1977) mentioned that although
effort has been focused on better dening hydrological
data, research suggests that there isn’t a unanimously
superior distribution. Thus we continued the use of the
Gumbel function and validated the results with the
Kolomogorov-Smirnov (K-S) Goodness of Fit Test
(Massey, 1951), a non-parametric test used on continuous
distribution functions F(x), which is based on comparing
the absolute value of the maximum difference between the
cumulative distribution functions (observed) in the sorted
sample Fo(x) and the distribution proposed under the
null hypothesis F(x). If the comparison has a sufciently
signicant difference between the sample and the
proposed distribution function, then the null hypothesis
(i.e. the distribution is F(x)) is rejected. One hundred
percent of the results applied to intensity data were
accepted with this test. The coefcient of determination
(R2) was used to explain the percentage of variation for
the dependent variable of the model (Dougherty et al.,
2000). In this context, most of the obtained R2 values
were over 0.8. In other words, 100% of the results were
considered acceptable by this test, with an average value
of 0.9, supporting the superiority of the Gumbel function
for modeling extreme climatic data.
Once the t was made, the relationships between
intensity (mm h-1), duration (1, 2, 4, 6, 12, and 24 h), and
frequency (5, 10, 20, 30, 40, 50, 60, 75, and 100 yr) were
determined. Finally, a family of nine negative exponential
curves (IDF curves) was built for each gauge station,
though only a portion of them was considered for use in
this study, as is explained later.
IDF curves are often expressed as a function, to
minimize errors and avoid graphical reading (Chow et al.,
1994). Hence, a mathematical equation was developed
for each family curve. These equations are based on the
model proposed by Bernard (1932): I = (k ∗ Tm) ∗ D-n,
where I is the maximum rainfall intensity (mm h-1), T is
the return period (yr), and D is the duration of the storm
(h). Also, k, m, and n are the regression’s parameters.
Once the IDF curves and their respective functions were
done for each of the 49 stations, we decided to analyze
rainfall intensities for a duration D = 1 h (because is the
minimum time that human eye can obtain from weekly
pluvial bands, being these, the most commonly bands
used in Chile), considering return periods of T = 5 and 100
yr. In this context is important to mention that extreme
events that generate larger impact are generally associated
with short durations, even less than 1 h. Similarly, T =
5 and 100 yr were selected to analyze the two extreme
frequencies associated to all the frequencies dened from
IDF curves. Additionally, the real maximum intensity
registered on each station was analyzed, determining its
exceedance probability. Likewise, multiple comparisons
were made to detect signicant differences between the
gauge stations and different climatic zones using the
Kruskal Wallis test (alpha = 0.05), a non-parametric
statistical test that determines whether samples derive
from the same population. This test evaluates the null
hypothesis that the means are statistically similar, and
is an extension of the Mann-Whitney U test for three or
more groups (in this case 49) (Kruskal and Wallis, 1952).
A latitudinal analysis of rainfall intensities (D = 1 h, T
= 5 and 100 yr) was performed, with the results expressed
graphically. The latitudinal distribution of mean annual
precipitation was also considered to nd possible
correlation and trends.
RESULTS AND DISCUSSION
Chile has great climatic diversity, which is explained by
its wide latitudinal extension and the presence of four
well-dened geographic areas: the Andes mountain range
to the east, the La Costa mountain range to the west, the
intermountain valley, and littoral oodplains. The location
of the country next to the Pacic Ocean, the effects of the
Humboldt Current, in addition to the Pacic high-pressure
zone, give rise to a wide variety of climates, varying from
extreme aridity in the north (Arica y Parinacota, and
Atacama Regions), to Mediterranean climates (warm
temperate) in the center (Libertador General Bernardo
O´Higgins and Maule Regions), and cold rainy climates
in the extreme south (Aysén del General Carlos Ibáñez del
Campo and Magallanes y la Antártica Chilena Regions)
(Errázuriz et al., 1998; INE, 2007).
In terms of the length of the analyzed data series, results
presented by Ott (1971) show that with the use of 20 yr
of data there is 80% probability of overestimating the
design runoff, and 45% probability that the overestimated
values exceeding real values in more than 30%. Linsley et
al. (1977) for example recommends avoiding the use of
data series shorter than 20 yr. However, the same authors
state that if necessary, peak ows can be estimated using
2 or 3 yr of observed data. On the other hand, maximum
rainfall intensities documented in Chile do not necessarily
correlate to higher rainfall amounts during wet periods.
In fact, many high intensity values were recorded
during dry periods. Besides, the behavior of rainfall
intensities in arid climates responds similarly to those
in Mediterranean and humid environments (UNESCO,
2007). From a regional perspective and considering the
intensity results given by IDF curves, we can assume
that there are differences in the quality of the generated

257256 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
information, as a consequence of the differences in data
series. However, such differences are not as signicant
as the behavior of rainfall intensities within the national
territory. If such differences are represented by minimum
extreme values, values associated with return periods of
50 or 100 yr would overestimate the maximum recorded
intensity in the data series, meaning that there will always
be higher values that securely allowed the development of
hydrological design. Therefore, the selection of a series to
be analyzed and the return periods to be considered will
depend on the project’s objective, as well as the respective
infrastructure costs. Finally, we should mention that when
hydrological data are not abundant and historical data
series are insufcient for analysis, it is appropriate to
develop a Regional Frequency Analysis (RFA), which is
designed to solve this type of problem (Linsley et al. 1977)
and has been used to estimate and map the frequency of
droughts in northern Chile. The use of RFA implies the
availability of information from stations located in areas
with similar rainfall regimes (Paulhus and Miller, 1957),
generally separated by distances no larger than 160 km
(Ott, 1971).
In this vein, IDF curves were successfully developed
for each of the 49 stations, for durations of 1, 2, 4, 6, 12,
and 24 h and return periods of 5, 10, 20, 30, 40, 50, 60,
75, and 100 yr. As previously mentioned only D = 1 h and
T = 5 and 100 yr were considered (Table 2). The lowest
rainfall intensities for 1 h were recorded at Albaricoque
station (arid climate) for the two studied return periods.
The highest extremes occurred at Lago Peñuelas station
(semiarid climate) for T = 5 yr and Embalse Coihueco
(subhumid climate) for T = 100 yr. Higher values were in
mm mm h-1 mm h-1
Hyperarid Putre 1 237.7 7.9 5.75 10.29
Parinacota 2 394.0 8.5 7.05 10.72
Central Chapiquiña 3 195.5 8.5 6.45 11.04
Iglesia Colorada 4 58.4 7.4 5.73 9.98
Santa Juana 5 43.9 15.5 8.90 19.62
Albaricoque 6 84.9 6.6 4.91 8.79
Arid-semiarid Rivadavia 7 100.1 13.3 7.97 15.38
Embalse La Paloma 8 135.4 20.0 19.00 27.49
Embalse Cogotí 9 168.0 20.6 10.82 20.40
Illapel 10 179.6 16.6 9.76 18.36
La Tranquilla 11 251.0 15.0 9.34 17.09
Los Cóndores 12 241.4 15.0 10.07 18.48
Quelón 13 300.1 15.6 9.67 16.79
Semiarid Hacienda Pedernal 14 247.5 17.8 12.62 20.22
Quillota 15 361.7 18.6 13.10 22.57
Embalse Lliu-Lliu 16 571.2 23.4 19.95 31.77
Lago Peñuelas 17 735.6 30.3 22.22 37.41
Embalse Rungue 18 372.5 17.0 11.63 18.83
Cerro Calán 19 441.5 19.2 13.58 21.53
Los Panguiles 20 361.5 14.8 11.04 19.20
Pirque 21 470.1 15.2 11.53 18.42
Semiarid-Mediterranean Rengo 22 563.8 21.5 13.68 21.43
Central Las Nieves 23 828.9 16.2 13.68 19.37
Convento Viejo 24 721.2 19.3 15.04 23.53
Mediterranean Los Queñes 25 1183.8 25.2 18.89 30.13
Potrero Grande 26 1103.1 25.7 19.14 30.66
Pencahue 27 673.0 15.9 12.37 19.56
Talca 28 661.9 14.3 10.78 16.27
San Javier 29 767.5 14.2 12.14 18.04
Colorado 30 1387.4 25.6 17.15 28.23
Melozal 31 743.3 23.0 13.05 22.68
Embalse Ancoa 32 1506.4 23.4 12.23 23.39
Parral 33 968.8 19.3 14.77 23.68
Embalse Digua 34 1519.8 25.8 20.06 30.91
Embalse Bullileo 35 2157.1 22.4 18.54 25.60
San Manuel 36 1391.7 23.0 17.62 28.49
Subhumid humid Embalse Coihueco 37 1512.8 36.5 21.93 40.17
Chillán Viejo 38 1093.4 22.1 18.33 29.02
Embalse Diguillín 39 2143.5 30.2 20.28 32.20
Quilaco 40 1572.1 26.0 17.62 27.62
Cerro El Padre 41 2131.3 28.8 19.83 30.52
Humid Traiguén 42 1016.2 20.4 13.87 22.03
Curacautín 43 1750.8 15.3 13.98 20.44
Pueblo Nuevo 44 1201.5 14.3 13.09 18.62
Pucón 45 2154.5 18.9 14.18 21.39
Lago Calafquén 46 2113.7 17.8 14.13 19.39
Llancahue 47 1983.1 26.4 17.39 27.05
Puelo 48 3891.0 16.1 12.74 20.21
Cold-semiarid Punta Arenas 49 422.8 13.0 7.59 12.85
Table 2. Maximum rainfall intensity (T = 5 and 100 yr) estimated at each gauge station.
T = 5 T = 100
Station/LocationClimatic zone Map
number Annual rainfall
amount Maximum rainfall
intensity
Intensity of rainfall 1 h

257256 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
general found in Mediterranean and subhumid climates.
The highest values on mean annual precipitation were
obtained in south-central Chile (humid and mediterranean
climates), whereas the lowest amount of rainfall fell, not
surprisingly, over stations located in hyperarid climates.
On the other hand, when verifying the relationship
between rainfall intensity and elevation, there was no
clear trend because similar rainfall intensity values at
different elevations (between 0 and 1200 m a.s.l.) were
found. Similarly, for some stations, such as Putre, Central
Chapiquiña, or Iglesia Colorada, (among others), located
in the northern portion of the country (hyperarid climate)
have altitudes that surpass 1200 m a.s.l., and have
maximum intensities similar to Punta Arenas and other
stations located a few meters above sea level, in south
extreme of Chile.
A relationship between real maximum rainfall
intensities, their corresponding return periods, and
their probability of exceeding the maximum-recorded
value was made for each station, using the obtained
mathematical equations. This analysis allowed the
estimation of the probability of surpassing the registered
real maximum intensity for each data series, as well as its
corresponding return period (Table 3). There was a 15%
probability to surpass 23.4 mm h-1, the recorded maximum
rainfall intensity at Embalse Lliu-Lliu station (semiarid
climate), corresponding to a return period of 7 yr, the
lowest registered return period. This large exceedance
probability suggests that high rainfall intensities at
that location are common. In contrast, a maximum of
23.4 mm h-1 was recorded at Embalse Ancoa station
(Mediterranean climate). Nevertheless, the probability of
Hyperarid Putre 1 7.9 2007 21 4.9
Parinacota 2 8.5 2005 11 9.0
Central Chapiquiña 3 8.5 2007 36 2.8
Iglesia Colorada 4 7.4 1989 9 10.8
Santa Juana 5 15.5 1997 24 4.1
Albaricoque 6 6.6 1992 15 6.5
Arid-semiarid Rivadavia 7 13.3 2000 28 3.6
Embalse La Paloma 8 20.0 1997 33 3.0
Embalse Cogotí 9 20.6 1992 53 1.9
Illapel 10 16.6 1994 30 3.4
La Tranquilla 11 15.0 1997 47 2.1
Los Cóndores 12 15.0 1984 29 3.5
Quelón 13 15.6 1974 34 2.9
Semiarid Hacienda Pedernal 14 17.8 1983 32 3.1
Quillota 15 18.6 2000 19 5.2
Embalse Lliu-Lliu 16 23.4 1984 7 15.0
Lago Peñuelas 17 30.3 1981 11 8.8
Embalse Rungue 18 17.0 1990 48 2.1
Cerro Calán 19 19.2 1986 19 5.3
Los Panguiles 20 14.8 2000 15 6.6
Pirque 21 15.2 1996 40 2.5
Semiarid-Mediterranean Rengo 22 21.5 2001 99 1.0
Central Las Nieves 23 16.2 1981 16 6.2
Convento Viejo 24 19.3 2000 33 3.1
Mediterranean Los Queñes 25 25.2 2000 46 2.2
Potrero Grande 26 25.7 2000 23 4.3
Pencahue 27 15.9 1986 26 3.8
Talca 28 14.3 1987 29 3.4
San Javier 29 14.2 1999 N/A N/A
Colorado 30 25.6 1993 84 1.2
Melozal 31 23.0 1992 48 2.1
Embalse Ancoa 32 23.4 2002 36 2.8
Parral 33 19.3 1993 26 3.9
Embalse Digua 34 25.8 1992 27 3.7
Embalse Bullileo 35 22.4 1995 31 3.2
San Manuel 36 23.0 1998 46 2.2
Subhumid humid Embalse Coihueco 37 36.5 2000 57 1.7
Chillán Viejo 38 22.1 2002 19 5.2
Embalse Diguillín 39 30.2 1974 46 2.2
Quilaco 40 26.0 1970 54 1.9
Cerro El Padre 41 28.8 1980 71 1.4
Humid Traiguén 42 20.4 2003 54 1.9
Curacautín 43 15.3 1994 10 10.4
Pueblo Nuevo 44 14.3 1992 9 11.2
Pucón 45 18.9 1990 45 2.2
Lago Calafquén 46 17.8 2003 75 1.3
Llancahue 47 26.4 1984 65 1.5
Puelo 48 16.1 2004 18 5.6
Cold-semiarid Punta Arenas 49 13.0 1993 47 2.1
Table 3. Return periods and exceedence probabilities for maximum rainfall intensities recorded on 1 h an each gauge station.
Station/LocationClimatic zone Map
number Year of
occurrence Return
period Exceedance
probability
Maximum intensity
of rainfall
mm h-1 yr %
N/A: information not available.

259258 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
exceeding this value is only 2.8%, associated with a return
period of 36 yr. Furthermore, the relationship between the
recorded maximum intensity of each data series and its
corresponding exceedance probability is illustrated in
Figure 2, indicating that the lowest values occurred in the
northern regions (hyperarid and arid climates), compared
to the other analyzed climate types.
In general, the probability of exceeding a recorded
real maximum intensity was less than 10%. However, for
the Embalse Lliu-Lliu, Curacautín, and Pueblo Nuevo
stations, representing semiarid and humid climates,
the recorded maximum intensity was surpassed, which
indicates a higher chance of an extreme event exceed the
maximum recorded in those areas.
Signicant differences between stations and between
climatic zones for rainfall intensities were found by
the Kruskal Wallis test (Table 4). The largest statistical
differences were obtained in the extreme climatic zones,
such as hyperarid and cold semiarid climates (Figure 3).
However, it is important to point out the fact that stations
can reach similar values of maximum rainfall intensity,
despite geographic and climatic differences. For example,
even though there were signicant differences between
northern climates (i.e. hyperarid, arid, and semiarid)
and central climates (Mediterranean and humid), the
largest variability of rainfall intensities happened in arid
environments, where higher intensities were common and
similar to those recorded in central Chile.
With these results it is possible to discuss the spatial
variability of precipitation in Chile, in terms of the
proportion between maximum and minimum values for
both intensity and total amounts. Maximum values for
rainfall intensity (subhumid zone) were as much as 4.5
times the minimum documented values (hyperarid zone),
for T = 5 and 100 yr. However, maximum values for total
rainfall (humid zone) surpass by more than 80 times the
minimum recorded values (hyperarid zone). This allowed
us to verify the differences in amplitude for rainfall
Figure 3. Signicant difference on maximum precipitation intensities
among climatic zones, after applying the Kruskal-Wallis test (alpha =
0.05).
Figure 2. Probability of exceeding the maximum-recorded rainfall intensity at each station.
Among climatic zones Hyperarid 106 < 0.05 Rejected
Arid-semiarid 208
Semiarid 122
Semiarid-Mediterranean 74
Mediterranean 187
Subhumid-humid 154
Humid 143
Cold semiarid 26
Table 4. Statistical comparison of rainfall intensities among different
climatic zones, using the Kruskal-Wallis test.
Sample P-value
Type of
comparison Sample
size (n) Null
hypothesis

259258 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
intensity and total annual precipitation, showing a much
larger contrast in the range of the latter variable.
Although some studies have been done in Chile, they
were all focused on the behavior of precipitation. Falvey
and Garreaud (2007), Verbist et al. (2010), and Barrett et
al. (2011), for example, did not consider variables used
in this research. Besides, most of the studies in Chile are
based on demonstrating the interannual variability of
precipitation in the central portion of the country, which
is associated with the El Niño and La Niña phenomena
(Rutllant and Fuenzalida, 1991). Furthermore, Garreaud
and Aceituno (2001) concluded that the number of rainy
days increases during El Niño, particularly moderate (10-
20 mm d-1) and extreme (50 mm d-1) intensities. However,
no signicant differences were found during La Niña,
which means that the number of rainy days during this
phenomenon does not necessarily decrease during that
particular year.
The analysis of these authors, as well as most of the
parametric climate studies developed in Chile, focused
on the behavior of total rainfall amounts as they relate
to atmospheric phenomena at different spatial scales.
However, rainfall intensity is not well understood in
Chile. It is more relevant to move forward using IDF
curves and expand on the few available studies, mostly
because recent statistical analyses show changes in
rainfall intensity, in the form of higher rainfall intensity
values for shorter lapses; thus, design guidelines on
hydraulic structures as well as soil and water conservation
works should be modied.
Finally, the relationship between rainfall intensity
(D = 1h, T = 5 and 100 yr), mean annual precipitation,
and latitude (Figure 4) shows no correlation between
maximum rainfall intensity and mean annual precipitation
in Chile (Table 5), since similar rainfall intensity values
were found throughout the country. However, mean
annual precipitation gradually increases with latitude,
showing a decrease in the extreme south.
Figure 4. Maximum rainfall intensities (T = 5 and 100 yr) and mean annual precipitation at different latitudes in Chile.
mm mm h-1
Hyperarid Arica y Parinacota Santa Juana 5 28°40’ 43.9 19.62
Arid-semiarid Coquimbo Embalse Cogotí 9 31°00´ 168.0 20.40
Semiarid Valparaíso Hacienda Pedernal 14 32°06´ 247.5 20.22
Metropolitana Los Panguiles 20 33°26´ 361.5 19.20
Semiarid-Mediterranean Libertador General Bernardo O’Higgins Central Las Nieves 23 34°29´ 828.9 19.37
Mediterranean Maule Pencahue 27 35°23´ 673.0 19.56
Humid La Araucanía Curacautín 43 38°26´ 1750.8 20.44
Los Ríos Lago Calafquén 46 39°34´ 2113.7 19.39
Los Lagos Puelo 48 41°38´ 3891.0 20.21
Table 5. Annual precipitation and maximum one-hour rainfall intensity (T = 100 yr) for different climatic zones in Chile.
Region Station/LocationClimatic zone Map
number South
latitude
Annual
rainfall
amount
Maximum rainfall
intensity
T = 100 yr

261260 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
CONCLUSIONS
The highest values of rainfall intensity (D = 1 h, T = 5
and 100 yr) in Chile are present in subhumid zones (36°
S lat), and total annual precipitation values are higher in
humid zones (39° S lat). Precipitations in Chile have a
high amount of spatial variability, a consequence of the
wide latitudinal extension of the country. Differences
in annual precipitation are noticeable; maximum values
that can reach more than 80 times minimum values were
observed. However, rainfall intensity does not change
with latitude along the country in general, reaching a
difference of only 4.5 times between maximum and
minimum values.
Finally, we suggest that maximum rainfall intensities
distributed in Chile behave similarly throughout the
country. However, minimum D = 1 h values were
documented at the latitudinal extremes of the country
(north and south). Similarly, there was no correlation
between elevation and rainfall intensity. As indicated
previously, Chile has a large variety of climates, in
which annual precipitation gradually increases from
north to south. However, such pattern has nothing to do
with the way rainfall intensities behave, that is, mean
annual precipitation does not predict rainfall intensity in
Chile.
ACKNOWLEDGEMENTS
The authors of this study sincerely wish to thank the
Dirección General de Aguas of Chile for providing the
necessary information to carry out the statistical analyses,
and the FONDEF project D08I1054, for providing the
necessary funds to obtain the results of this study.
Análisis latitudinal de la intensidad de lluvias y
precipitación media anual en Chile. El estudio y análisis
de las precipitaciones se ha convertido en una herramienta
vital para conocer el comportamiento temporal y espacial
del recurso hídrico, tanto en términos de disponibilidad,
así como de los posibles impactos asociados a los eventos
extremos. El objetivo de esta investigación fue evaluar
las intensidades máximas (duración D = 1 h y períodos
de retorno T = 5 y 100 años) y los montos anuales de
precipitación para diferentes latitudes y zonas climáticas
de Chile, analizando la información de miles de bandas
pluviográcas y la pluviometría anual de 49 estaciones
de medición. Ello, porque aún no es claro que las
intensidades de precipitación dieren latitudinalmente
en el país, así como lo hacen los montos anuales de
las lluvias. Asimismo, no hay evidencia cientíca de
los rangos y montos de ambas variables. Así, se utilizó
la función de Gumbel y fórmulas matemáticas para
desarrollar las curvas intensidad-duración-frecuencia
(IDF) de cada estación. Los valores mínimos y máximos
de intensidad de precipitación registrados para T = 100
años, fueron 8,79 (zona hiperárida) y 40,17 mm h-1
(zona subhúmeda-húmeda). Respecto al monto anual de
precipitaciones, los valores mínimos y máximos fueron
43,9 (zona hiperárida) y 3891,0 mm año-1 (zona húmeda)
respectivamente. Adicionalmente, la intensidad máxima
real registrada en cada estación fue analizada para
determinar su probabilidad de excedencia. Asimismo,
se realizaron comparaciones múltiples para detectar
diferencias signicativas entre las estaciones de medición
y las diferentes zonas climáticas, mediante el test no
paramétrico Kruskal Wallis (alfa = 0,05). Las diferencias
entre los valores máximos y mínimos registrados en la
totalidad de las estaciones analizadas pueden superar
las 80 veces, para el caso de los montos anuales de las
lluvias, y pueden llegar hasta 4,5 veces para el caso de las
intensidades de precipitación (T = 100 años). Sin embargo,
se encontraron valores máximos similares de intensidad
de precipitación en diferentes latitudes y altitudes del
territorio nacional. Por tanto, se concluye que un mayor
monto anual de lluvia no necesariamente involucra una
mayor intensidad de precipitación.
Palabras clave: Precipitaciones, curvas intensidad-
duración-frecuencia, curvas IDF, intensidad de
precipitaciones.
LITERATURE CITED
Barrett, B.S., D.B. Krieger, and C.P. Barlow. 2011. Multi-day
circulation and precipitation climatology during winter rain
events of differing intensities in central Chile. Journal of
Hydrometeorology 12:1071-1085.
Bernard, M. 1932. Formulas for rainfall intensities of long durations.
Transactions of ASCE 96:592-624.
Bougadis, J., and K. Adamowski. 2006. Scaling model of a rainfall
intensity-duration-frequency relationship. Hydrological Processes
20:3747-3757.
Chow, V., D. Maidment, and L. Mays. 1994. Applied hydrology (en
español). 572 p. McGraw-Hill Interamericana, Bogotá, Colombia.
Dairaku, K. 2004. Rainfall amount, intensity, duration, and frequency
relationships in the Mae Chaem Watershed in Southeast Asia.
Journal of Hydrometeorology 5:458-470.
Dickinson, T. 1977. Rainfall intensity-frequency relationships from
monthly extremes. Journal of Hydrology 35:137-145.
Dougherty, E.R., S. Kim, and Y. Chen. 2000. Coefcient of
determination in nonlinear signal processing. Signal Processing
80(10):2219-2235.
Errázuriz, A.M., P. Cereceda, J. González, M. González, and R.
Rioseco. 1998. Manual de geografía de Chile. 3rd ed. 435 p.
Editorial Andrés Bello, Santiago, Chile.
Falvey, M., and R. Garreaud. 2007. Wintertime precipitation
episodes in Central Chile: Associated meteorological conditions
and orographic inuences. Journal of Hydrometeorology 8:171-
193.
Garreaud, R., and P. Aceituno. 2001. Interannual rainfall variability
over the South American Altiplano. Journal of Climate 14:2779-
2789.
Grimaldi, S., S.C. Kao, A. Castellarin, S.M. Papalexiou, A. Viglione,
F. Laio, et al. 2011. Statistical hydrology. p. 479-517. Treatise on
Water Science, Elsevier, Oxford, UK.
Gumbel, E. 1958. Statistics of extremes. 400 p. Dover Publications,
Mineola, New York, USA.
Haan, C. 2002. Statistical methods in hydrology. 496 p. Iowa State
Press, Ames, Iowa, USA.

261260 CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012CHILEAN JOURNAL OF AGRICULTURAL RESEARCH 72(2) APRIL-JUNE 2012
Hallack-Alegria, H., and D. Watkins Jr. 2007. Annual and warm
season drought intensity-duration-frequency analysis for Sonora,
Mexico. Journal of Climate 20:1897-1909.
IGM. 2008. Atlas geográco de Chile. 280 p. Instituto Geográco
Militar (IGM), Santiago, Chile.
INE. 2007. División político-administrativa y censal 2007. Instituto
Nacional de Estadísticas (INE), Santiago, Chile. Available at
http://www.ine.cl/ (accessed June 2010).
Kruskal, W., and W. Wallis. 1952. Use of ranks in one-criterion
variance analysis. Journal of the American Statistical Association
47(260):583-621.
Langousis, A., and D. Veneziano. 2007. Intensity-duration-frequency
curves from scaling representations of rainfall. Water Resources
Research 43(2). 12 p.
Linsley, R., M. Kohler, and J. Paulus. 1977. Hidrología para
Ingenieros. 2ª ed. 386 p. McGraw-Hill Latinoamericana, D.F.
México.
Maidment, D. 1996. Handbook of hydrology. 784 p. American
Society of Civil Engineers, New York, USA.
Martínez-Mena, M., R. Abadía, V. Castillo, y J. Albaladejo. 2001.
Diseño experimental mediante lluvia simulada para el estudio
de los cambios en la erosión del suelo durante la tormenta.
Cuaternario y Geomorfología 15(1-2):31-43.
Massey, F.J., Jr. 1951. The Kolmogorov-Smirnov test for goodness
of t. Journal of the American Statistical Association 46(253):68-
78.
Minh Nhat, L., Y. Tachikawa, T. Sayama, and K. Takara. 2008.
Estimation of sub-hourly and hourly IDF curves using scaling
properties of rainfall at gauged site in Asian Pacic Region.
Annuals of Disaster Prevention Research Institute, Kyoto
University. Nº 51B.
Minh Nhat, L., Y. Tachikawa, and K. Takara. 2006. Establishment
of Intensity-Duration-Frequency curves for precipitation in
the monsoon area of Vietnam. Annuals of Disaster Prevention
Research Institute, Kyoto University. Nº 49B.
Mintegui, J., and J. Robredo. 1993. Métodos para la estimación
de los efectos torrenciales en una cuenca hidrográca. 88 p.
Fundación Conde del Valle de Salazar, Escuela Técnica Superior
de Ingenieros de Montes, Universidad Politécnica de Madrid,
Madrid, España.
Monsalve, G. 1999. Hidrología en la ingeniería. 2ª ed. 382 p.
Editorial Alfa Omega S.A., Santa Fé de Bogotá, Colombia.
Ott, R.F. 1971. Stream ow frequency using stochastically generated
rainfall. Technical Report 151. 111 p. Department of Civil
Engineering, Stanford University, Palo Alto, California, USA.
Paulhus, J.L., and J.F. Miller. 1957. Flood frequencies derived from
rainfall data. Journal of Hydraulical Division. American Society
of Civil Engineering Paper 1451, Vol. 83. 18 p.
Pereyra-Díaz, D., J.A. Pérez-Sesma, and L. Gómez-Romero. 2004.
Ecuaciones que estiman las curvas intensidad-duración-período
de retorno de la lluvia. Geos 24:46-56.
Pizarro, R. 1986. Elementos técnicos de hidrología. 78 p. Corporación
Nacional Forestal (CONAF), La Serena, Chile.
Pizarro, R., A. Abarza, y J. Flores. 2001. Análisis Comparativo de las
Curvas Intensidad - Duración - Frecuencia (IDF) en 6 Estaciones
Pluviográcas (VII Región del Maule, Chile). Universidad de
Talca, Facultad de Ciencias Forestales, Talca, Chile. Revista
Virtual de UNESCO. 48 p. Available at http://www.unesco.org.
uy/phi/biblioteca/bitstream/123456789/500/1/curvas+idf+maule.
pdf (accessed 5 September 2011).
Pizarro, R., F. Cornejo, C. González, K. Macaya, y C. Morales. 2008.
Análisis del comportamiento y agresividad de las precipitaciones
en la zona central de Chile. Ingeniería Hidráulica en México
23(2):91-109.
Pizarro, R., C. Sangüesa, J. Flores, and E. Martínez. 2005. Elementos
de Ingeniería Hidrológica para el mejoramiento de la productividad
silvícola. Proyecto marco: 00C7FT-08 “Determinación
de estándares de ingeniería en obras de conservación y
aprovechamiento de aguas y suelos para la mantención e
incremento de la productividad silvícola”. Universidad de Talca,
Talca, Chile. 179 p. Available at http://eias.utalca.cl/Docs/pdf/
Publicaciones/libros/elementos_de_ingenieria_hidrologica_para_
el_mejoramiento_de_la_productividad_silvicola.pdf (accessed
29 August 2011).
Ponce, V. 1989. Engineering hydrology: Principles and practices.
640 p. Prentice Hall, Englewood Cliffs, New Jersey, USA.
Rutllant, J., and H. Fuenzalida. 1991. Synoptic aspects of the central
Chile rainfall variability associated whit the Southern Oscillation.
International Journal of Climatology 11:63-76.
Sangüesa, C., J. Arumí, R. Pizarro, and O. Link. 2010. A rainfall
simulator for the in situ study of supercial runoff and soil erosion.
Chilean Journal of Agricultural Research 70:178-182.
Témez, J. 1978. Cálculo hidrometeorológico de caudales máximos
en pequeñas cuencas naturales. 111 p. Dirección General de
Carreteras, Madrid, España.
UNESCO. 2006. Guía metodológica para la elaboración del mapa de
zonas áridas, semi-áridas y sub-húmedas secas de América Latina
y el Caribe. Centro del Agua para Zonas Áridas y Semiáridas de
América Latina y el Caribe (CAZALAC). Documento Técnico
PHI-LAC N° 3. 66 p. Programa Hidrológico Internacional
de la UNESCO para América Latina y el Caribe (PHI-LAC),
Organización de las Naciones Unidas para la Educación, la
Ciencia y la Cultura (UNESCO), Ocina Regional de Ciencia
para América Latina y el Caribe, Montevideo, Uruguay.
UNESCO. 2007. Curvas Intensidad-Duración-Frecuencia para la
zona centro sur de Chile. Roberto Pizarro Tapia, Dayanna Aravena
Garrido, Karina Macaya Pérez, Alejandro Abarza Martínez,
Mariela Cornejo Espinoza, Mauricio Labra Lorca, Marcelo
Pavez Vidal, Leonardo Román Arellano. Editorial Universidad de
Talca, Talca, Chile. Documento Técnico PHI-LAC Nº 7. 135 p.
Programa Hidrológico Internacional de la UNESCO para América
Latina y el Caribe (PHI-LAC), Organización de las Naciones
Unidas para la Educación, la Ciencia y la Cultura (UNESCO),
Ocina Regional de Ciencia para América Latina y el Caribe,
Montevideo, Uruguay.
UNESCO. 2010. Atlas de zonas áridas de América Latina y el
Caribe. Dentro del marco del proyecto “Elaboración del Mapa
de Zonas Áridas, Semi-Áridas y Sub-húmedas Secas de América
Latina y el Caribe”. Documento Técnico PHI-LAC N° 25. 55 p.
Programa Hidrológico Internacional de la UNESCO para América
Latina y el Caribe (PHI-LAC), Organización de las Naciones
Unidas para la Educación, la Ciencia y la Cultura (UNESCO) y el
Centro del Agua para Zonas Áridas de América Latina y el Caribe
(CAZALAC). Available at http://www.cazalac.org/documentos/
Atlas_de_Zonas_Aridas_de_ALC_Espanol.pdf (accessed 10
September 2011).
Veneziano, D., and P. Furcolo. 2002. Multifractality of rainfall and
scaling of intensity-duration-frequency curves. Water Resources
Research 38(12), 1306. doi:10.1029/2001WR000372.
Verbist, K., A.W. Robertson, W.M. Cornelis, and D. Gabriels. 2010.
Seasonal predictability of daily rainfall characteristics in Central
Northern Chile for dry-land management. Journal of Applied
Meteorology and Climatology 49:1938-1955.
Watkins, D. Jr., G. Link, and D. Johnson. 2005. Mapping regional
precipitation intensity duration frequency estimates. Journal of the
American Water Resources Association 41:157-170.
Willems, P. 2000. Compound intensity-duration-frequency-
relationships of extreme precipitation for two season and two
storm types. Journal of Hydrology 233:189-205.