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Observed Changes in Return Values of Annual Temperature Extremes over Argentina
MATILDE RUSTICUCCI
AND
BÁRBARA TENCER
Departamento de Ciencias de la Atmósfera y los Océanos, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,
and Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, Argentina
(Manuscript received 14 August 2007, in final form 14 March 2008)
ABSTRACT
Extreme temperature events are one of the most studied extreme events since their occurrence has a huge
impact on society. In this study, the frequency of occurrence of absolute extreme temperature events in
Argentina is analyzed. Four annual extremes are defined based on minimum and maximum daily data: the
highest maximum (minimum) temperature of the year, and the lowest maximum (minimum) temperature
of the year. Applying the extreme value theory (EVT), a generalized extreme value (GEV) distribution is
fitted to these extreme indices and return values are calculated for the period 1956–2003. Its spatial
distribution indicates that, for warm extremes, maximum temperature (Tx) is expected to be greater than
32°C at least once every 100 yr throughout the country (reaching values even higher than 46°C in the central
region), while minimum temperature (Tn) is expected to exceed 16°C (reaching 30°C in the central and
northern regions). Cold annual extremes show larger gradients across the country, with Tx being lower than
8°C at least once every 100 yr, and Tn lower than 0°C every 2 yr, with values even less than ⫺10°C in the
southwestern part of the country.
However, the frequency of occurrence of climatic extremes has changed throughout the globe during the
twentieth century. Changes in return values of annual temperature extremes due to the 1976–77 climatic
shift at six long-term datasets are then analyzed. The lowest Tx of the year is the variable in which the
1976–77 shift is less noticeable. At all the stations studied there is a decrease in the probability of occurrence
of the highest Tx if the study is based on more recent records, while the frequency of occurrence of the
highest Tn increases at some stations and decreases at others. This implies that in the “present climate”
(after 1977) there is a greater frequency of occurrence of high values of Tn at Observatorio Central Buenos
Aires and Río Gallegos together with a lower frequency of occurrence of high values of Tx, leading to a
decrease in the annual temperature range.
The most noticeable change in return values due to the 1976–77 shift is seen in Patagonia where the 10-yr
return value for the highest Tn increases from 13.7°C before 1976 to 18.6°C after 1977. That is, values of the
highest Tn that occurred at least once every 10 yr in the “past climate” (before 1976) now happened more
than once every 2 yr.
1. Introduction
Extreme events have a huge impact on society and
the ecosystem. Particularly, high and low temperatures
are one of the most studied extreme events, since their
occurrence severely influences agriculture (many crops
are affected by the number of frost days or the amount
of hot days per year), human health (the heat wave that
affected Europe in 2003 caused between 22 000 and
Corresponding author address: Matilde Rusticucci, Departamento de Ciencias de la Atmósfera y los Océanos, FCEN, Universidad de Buenos Aires, Ciudad Universitaria Pab II (1428),
Buenos Aires, Argentina.
E-mail: [email protected]
DOI: 10.1175/2008JCLI2190.1
© 2008 American Meteorological Society
35 000 deaths according to Schär and Jendritzky 2004;
see Schär et al. 2004 for a statistical analysis of the heat
wave), demand for energy, water resources, and the
availability of drinkable water, among others. Under a
climatic change, a small variation in the mean values of
temperature can be associated with large changes in the
frequency of extreme events (Katz and Brown 1992).
Identifying trends in climatic extremes implies an extra demand on data quantity and quality than the study
of changes in mean values. This is because even a relatively small amount of missing data raises the possibility
that an extreme event has not been recorded, especially
when absolute extreme events are being studied. Also,
when investigating trends at the extreme ends of a climatic distribution, the quality of data can also influence
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the results since an outlier can be incorrectly considered
as a true extreme value or vice versa (a genuine extreme may be rejected as an outlier).
During the last few years new datasets of daily temperature in different parts of the globe have become
available allowing the study of trends in extreme temperature events. The majority of the findings revealed
that the persistence and intensity of extreme temperature values has changed—globally, but not homogeneously—throughout the period of observation (Trenberth et al. 2007). Frich et al. (2002) used extreme temperature indices based on daily minimum and
maximum temperature series to investigate possible
global changes in the frequency and/or severity of climatic extremes during the second half of the twentieth
century. They found an increase in warm summer
nights, a decrease in the number of frost days and a
reduction of intra-annual extreme temperature range.
Alexander et al. (2006) reported that most of the global
land area sampled in their study showed a significant
decrease in the annual occurrence of cold nights and a
significant increase in the annual occurrence of warm
nights, which implies a positive shift in the distribution
of daily maximum temperature throughout the globe.
Over Australia, the study of trends in extreme temperature indices revealed that the frequency of warm
temperature extreme events has generally increased
over the period 1957–96, while the number of extremely cool temperature events has decreased, consistently with increasing trends in mean minimum and
maximum temperatures during that period (Collins et
al. 2000). In Southeast Asia and the South Pacific, Manton et al. (2001) also found significant increases in the
annual number of hot days and warm nights and significant decreases in the annual number of cool days and
cold nights in the period 1961–98. These trends were
stronger for indices based on minimum temperature
than for those based on maximum temperature. In Europe, Klein Tank and Können (2003) observed a symmetric warming of the cold and warm tails of the daily
minimum and maximum temperature distributions during 1946–99. However, this symmetry disappeared
when trends were analyzed in two consecutive periods:
for the 1946–75 subperiod (an episode of slight cooling), the annual number of warm extremes decreased,
but the annual number of cold extremes did not increase; for the 1976–99 subperiod (an episode of pronounced warming), the annual number of warm extremes increased two times faster than the decrease in
the number of cold extremes.
Significant increasing trends in the percentage of
warm nights and decreasing trends in the number of
cold nights were found at many stations in South
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America according to Vincent et al. (2005). The authors
believe that this warming is mostly due to more warm
nights and fewer cold nights during the summer (December–February) and fall (March–May). They also
found that trends in indices based on daily maximum
temperature were not consistent and that the stations
with significant trends were located closer to the west
and east coasts of the continent.
In Argentina, Rusticucci and Barrucand (2004)
showed that the strongest (positive) changes over time
occurred in mean summer minimum temperature,
while its standard deviation decreased. On the other
hand, mean maximum summer temperatures mostly
decreased over time in northern Argentina, but increased in Patagonia (southern Argentina). Overall,
negative trends were obtained for the number of cold
nights and warm days per summer, while the number of
warm nights and cold days has increased at certain locations. They also studied the relationship between seasonal mean temperature and the frequency of occurrence of extremely warm and cold days. Results indicate that an increase in the summer mean temperature
is mostly due to an increase in the frequency of warm
events in the central and northern part of the country,
and to a decrease in the number of cold events in the
southern region (Barrucand and Rusticucci 2001).
All the studies mentioned above use the empirical
distribution function to study extreme events. Nonetheless, very small discrepancies in the estimate of the empirical distribution function can lead to substantial discrepancies in the distribution of extreme events (Coles
2001). Therefore, an alternative approach consists of
applying the extreme value theory (EVT) to study extreme events and extrapolate information to unobserved levels. Based on the annual and daily rainfall
data on the central coast of Venezuela and using different modeling strategies and inference approaches,
Coles et al. (2003) showed that the 1999 rainfall, which
caused the worst environmentally related tragedy in
Venezuelan history, was extreme, but not implausible
given the historical evidence.
Statistical modeling of extreme values has been applied to daily data throughout the globe in order to
extrapolate the probability of occurrence of events that
are more extreme than any other observed. In this context, Zwiers and Kharin (1998) applied the statistical
modeling of extremes to observed daily records of minimum and maximum temperature and they compared it
to the extremes of climate simulated in an equilibrium
doubled CO2 experiment conducted with a general circulation model (GCM). Bonsal et al. (2001) fitted a
generalized extreme value (GEV) distribution to the
annual extremes of daily minimum and maximum tem-
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perature in Canada. They found that 20-yr return values of annual extremes of daily minimum temperature
increase approximately 4°C from the period 1900–49 to
1950–98 over southern Canada, while for maximum
temperature return values decrease by 1°C.
In this paper, we use a theoretical distribution function to model extreme temperature events observed
during the second half of the twentieth century in Argentina. A GEV distribution is fitted to annual extremes of daily minimum and maximum temperature at
different stations in the country for the period 1956–
2003. Then, return levels of annual extremes are estimated and their spatial distribution is analyzed.
However, the frequency of occurrence of climatic
means and extremes has changed throughout the globe
during the twentieth century. Several studies have analyzed the presence of climatic changes in different atmospheric and oceanic variables. Trenberth (1990)
found a different regime after 1976 evident both in the
time series of Pacific mean sea level pressure and in the
temperature anomalies. In the Southern Hemisphere,
Seidel et al. (2004) found a warming of a few tenths of
degree in different upper-air temperature datasets
while Huang et al. (2005) observed a decrease in January–May precipitation over the Amazon region and the
southern tip of South America together with an increase of rainfall in the sub-Amazonian South America.
Therefore, this paper also aims to study the effects of
the 1976–77 climate shift on return levels of annual
temperature extremes. For this reason, the longest annual extreme series available in Argentina are divided
into two consecutive subperiods: before 1976 (pre1976) and thereafter (post-1976), and the GEV distribution is fitted to each subperiod. Annual extreme return levels are then recomputed and possible changes in
the frequency of occurrence of extreme temperatures
due to the regime shift are analyzed.
The outline for the remainder of this paper is as follows. The data and methodology used are described in
section 2. Results obtained for the period 1956–2003
are shown in section 3 and the influence of the 1976–77
shift is analyzed in section 4. A summary and conclusions are presented in section 5.
2. Data and methodology
Daily data of maximum and minimum temperature
(Tx and Tn, respectively) for 43 stations over the period
1956–2003, provided by the Servicio Meteorológico Nacional (National Weather Service), were used to estimate the spatial distribution of fixed annual extreme
return levels and periods in Argentina (Fig. 1). An exhaustive quality control of these data was performed by
Barrucand and Rusticucci (2001).
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FIG. 1. Stations used in this study. Stars indicate stations with
longer-term data records.
Another longer-term dataset was used to assess
changes in annual extreme return levels throughout the
observational period. This dataset consists of six stations from Argentina with record lengths between 67
and 110 yr: San Miguel de Tucumán, Tucumán (TUC,
26.80°S, 65.20°W, 1891–2000); Observatorio Central
Buenos Aires, Buenos Aires (OCBA, 34.58°S,
58.48°W, 1906–2004); Pergamino, Buenos Aires (PGM,
33.93°S, 60.55°W, 1931–2004); Pilar, Córdoba (PIL,
31.66°S, 63.88°W, 1931–2004); Santa Rosa, La Pampa
(SRS, 36.56°S, 64.26°W, 1937–2003); Río Gallegos,
Santa Cruz (RGA, 51.61°S, 69.28°W, 1896–2004). A
supplementary internal consistency analysis was made
prior to return level calculations, by searching the time
series for outliers and indisputable erroneous data
(such as Tn greater than Tx). At these stations, changes
in return levels due to the 1976–77 climate shift were
studied by comparing the distribution of annual temperature extreme return levels based on the observational period pre-1976 (beginning of the time series–
1976) and post-1976 (1977–end of the time series).
Four different annual temperature extremes based
on daily data were calculated for each station and each
period studied: the highest maximum (minimum) tem-
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perature of the year called HTx (HTn), and the lowest
maximum (minimum) temperature of the year, called
LTx (LTn). For warm extremes (HTx, HTn), the year
was considered as the period of time from 1 July to 30
June next year so that austral summer was not broken.
For cold extremes (LTx, LTn), the calendar year was
used.
An extensive analysis of missing data was conducted
at each station record individually. The year was considered missing for the series of warm (cold) annual
extremes when 20 (or more) nonconsecutive days, or 10
(or more) consecutive days were missing in the period
from December to February (June to August).
Extreme value analysis was performed in this study
by fitting the GEV distribution to the sample of annual
extremes defined above at each station using the
method of maximum likelihood estimation (MLE). Following Coles (2001), the GEV distribution for warm
annual extremes is described by
再 冋 冉 冊册 冎
G共z兲 ⫽ exp ⫺ 1 ⫹ ␰
z⫺␮
␴
⫺1
Ⲑ␰
共1兲
,
defined for {z:1 ⫹ ␰(z ⫺ ␮)/␴ ⬎ 0}, ⫺⬁ ⬍ ␮ ⬍ ⬁, ␴ ⬎
0, and ⫺⬁ ⬍ ␰ ⬍ ⬁, where ␮, ␴, and ␰ are the adjustable
parameters of the distribution that determine the location, scale, and shape of the distribution, respectively.
The GEV distribution function for cold annual extremes is
再 冋 冉 冊册 冎
G共z兲 ⫽ 1 ⫺ exp ⫺ 1 ⫹ ␰
z ⫺ ␮˜
␴
⫺1
Ⲑ␰
,
共2兲
defined for {z:1 ⫺ ␰(z ⫺ ␮˜ )/␴ ⬎ 0}, ⫺⬁ ⬍ ␮˜ ⬍ ⬁, ␴ ⬎
0, and ⫺⬁ ⬍ ␰ ⬍ ⬁, where again ␮˜ , ␴, and ␰ are the
location, scale, and shape parameters of the distribution. The P-yr return level is defined as the value that is
exceeded by an annual extreme at least once every P
years, and is obtained by inverting the fitted GEV distribution. In this study, 2-, 10-, and 100-yr return levels
are calculated at each station both for warm and cold
annual extremes.
Different goodness-of-fit (GOF) tests were used to
examine whether the GEV distributions fit the empirical distributions of annual extremes. As suggested by
Coles (2001), we firstly analyzed the probability plot
(PP plot) and the quantile plot (QQ plot), which allow
visual comparison between the theoretical and the empirical distributions for the annual extremes. Since linearity represents a perfect fit, the level of agreement
between both distributions can also be measured with
the linear correlation coefficient.
Furthermore, we applied a standard Kolmogorov–
Smirnov (KS) GOF test that measures the overall dif-
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ference between two cumulative distribution functions.
The KS statistic D is defined as the maximum absolute
difference between two distribution functions:
D ⫽ max |SN 共x兲 ⫺ F 共x兲|,
⫺⬁⬍x⬍⬁
where F(x) is the fitted distribution function (GEV)
and SN(x) is the empirical distribution function estimated from a sample of N observations as the proportion of data values less than or equal to x. The null
hypothesis that the annual extremes are drawn from a
GEV distribution is rejected when the value of D is
greater than a critical value. This critical value is determined by the parametric bootstrapping technique
(Kharin and Zwiers 2000). In this procedure, 1000
samples of annual extremes are generated from the
original sample by random resampling with replacement. These “new” samples are the same size as the
original and are used to reestimate the GEV distribution parameters and the corresponding D value. The
limit of the 90% confidence interval of the sample of D
is then used as the critical value for the rejection of the
null hypothesis at the 10% significance level.
3. Spatial distribution of annual extremes in the
period 1956–2003
In this section, results based on the period in which
most of the stations have available information, 1956–
2003, are shown. First, the presence of linear trends in
the four annual temperature extremes defined in the
previous section is analyzed. Then, the spatial distributions of return levels and return periods are shown.
Since we needed detrended series to fit the stationary
GEV distribution, we used the method of least squares
in order to detect the presence of linear trends in the
series of annual extremes. Figure 2 shows the sign and
magnitude of the linear trends found in HTx, HTn,
LTx, and LTn for 43 stations in the period 1956–2003.
Significant values at the 5% level are marked with filled
symbols. It can be seen that HTx has negative significant trends in the central-eastern part of the country.
This is consistent with Rusticucci and Barrucand
(2004), who found negative trends in the maximum
mean summer temperature and in the frequency of occurrence of warm days (based on the 95th percentile) in
Argentina in the period 1959–98. Collins et al. (2000)
found negative significant trends in hot days (frequency
of daily Tx greater or equal than 35°C) in southeast and
southwest Australia. The number of hot days has been
less than normal in eastern China since the 1970s (Zhai
et al. 1999). And a small downward trend was observed
in the frequency of occurrence of warm days in the
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FIG. 2. Spatial distribution of linear trends (in °C 10 yr⫺1) for the four annual
temperature extremes (HTx, HTn, LTx, LTn) in the period 1956–2003. Significant
values at the 5% level in filled symbols.
United States in the period 1910–98 (Easterling et al.
2000). The central-western region shows positive significant trends in HTx. HTn trends are negative in the
central part of the country and positive at the rest of the
stations. However, the significance level is only reached
at a few stations and the pattern is not as clearer as for
HTx. It is noticeable that extremes have less significant
trends than mean values as it can be seen in Rusticucci
and Barrucand (2004). Alexander et al. (2006) found
positive trends in the warm nights in southern South
America, based on gridded data, with the regions of
significant change restricted to northern Argentina and
southern Brazil. The LTx trend is positive at the majority of stations, but only significant in the centraleastern region. LTn has positive trends almost all over
the country, only significant in the western and the central-eastern regions. In Buenos Aires, the largest city in
the country, maximum temperature has a negative nonsignificant trend of 0.179°C/10 yr in its highest value of
the year and a positive significant trend of 0.301°C/10 yr
in the lowest. The highest and lowest minimum temperatures increase significantly at a rate of 0.342° and
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FIG. 3. “Quantile plots” for the GEV distribution fitted to the four annual temperature extremes (HTx,
HTn, LTx, LTn) at station OCBA (1906–2004).
0.542°C every 10 yr, respectively. In the central-western
region, trends are positive both for warm and cold extremes. However, in the central part of the country,
HTx decreases while LTx increases leading to a drop in
the maximum temperature annual range.
After filtering the corresponding linear trends, we
proceeded to fit the GEV distribution to the four annual temperature extremes at each station. Figures 3
and 4 show the QQ plots and the PP plots for the GEV
distribution fitted to the series of annual extremes at
OCBA. From the QQ plots, HTx seems to be the extreme that is worst represented by the GEV distribution since empirical values are lower than theoretical
values when HTx is greater than 40°C. From the PP
plots, LTn is the one that shows less agreement with the
theoretical distribution, since dispersion is greater.
However, linear correlation coefficients are greater
than 0.98 for all cases.
We performed this goodness-of-fit analysis for every
station and we also applied the Kolmogorov–Smirnov
test in order to measure the level of agreement between
the empirical and the GEV distributions. Since both the
graphical and the nonparametric tests were consistent
and brought a 10% level of confidence in that annual
temperature extremes are drawn from a GEV distribution at all the stations studied, we proceeded to analyze
the spatial distribution of return levels in Argentina in
the period 1956–2003. The gridding method used for
interpolation of return values was the kriging method
(Wackernagel 2003).
Figure 5 shows 2-, 10-, and 100-yr return level spatial
distributions for warm annual extremes. Both HTx and
HTn have similar patterns to those of mean daily values
(not shown). According to the GEV distribution fitted
to the highest maximum temperature in the year
(HTx), maximum temperature is expected to be greater
than 32°C at least once every 100 yr throughout all the
country, reaching even 46°C in the central region,
where mean maximum temperature reaches the highest
values of the country. The 2-yr return level distribution
shows that maximum temperature will be greater than
30°C in almost any part of the country with probability
0.5. The theoretical distribution for HTn shows that
minimum temperature is expected to exceed a value of
14°C in any one single year with probability 0.5, and a
value of 16°C with probability 0.01, reaching values
even higher than 30°C in the central and northern part
of the country. As it can be seen, the region of greatest
return levels of HTn is located further north than HTx.
In Fig. 6, 2-, 10-, and 100-yr return level spatial distributions for cold annual extremes show larger gradients across the country, especially in the southern part
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FIG. 4. “Probability plots” for the GEV distribution fitted to the four annual temperature extremes
(HTx, HTn, LTx, LTn) at station OCBA (1906–2004).
of Argentina. Maximum temperature is predicted to be
lower than 12°C in any part of the country once every
2 yr and lower than 8°C every 100 yr. Minimum temperature, on the other hand, will be lower than 0°C
every 2 yr in any part of the country, with values even
less than ⫺10°C in the southwestern part of the country. In the Patagonia region, minimum temperatures
are expected to be less than ⫺18°C at least once every
100 yr.
There are other applications—hydrology, oceanography, wind engineering, insurance industry, and risk assessment on financial markets, among others—where a
threshold value might be important. Therefore, we performed the inverse analysis: fixing the return value of
an annual temperature extreme, we studied the spatial
distribution of its return periods in Argentina. Consistent with Fig. 5, a 32°C return level in HTx (not shown)
results in return periods of 1 yr almost all over the
country, except in Patagonia where return periods between 2 and 10 yr are expected. Increasing the HTx
return value to 40°C (Fig. 7), the central region of the
country shows return periods between 1 and 5 yr and
the eastern region, between 5 and 50 yr. There are three
stations (Salta Aero, Malargüe Aero, Río Gallegos
Aero; gray crosses in Fig. 7) that increase their return
periods to values much greater than 100 yr, showing
that this temperature is not likely to occur. For HTn, a
return value of 20°C (not shown) gives return periods
of less than 2 yr throughout the country, while a return
value of 25°C is associated with return periods of less
than 5 yr in the northern region and between 5 and 50
in the central region and northern Patagonia. There
are five stations (Jujuy Aero, Dolores Aero, Río Gallegos Aero, Colonel Suárez Aero, Malargüe Aero;
gray crosses in Fig. 7) with return periods greater than
100 yr.
Figure 7 also shows the spatial distribution of return
periods for fixed cold extreme return levels. It can be
seen that a return value of 6°C in LTx gives return
periods between 1 and 5 yr in the Patagonia and the
central region, between 5 and 50 yr in the central region
and over 100 yr on the coast of Buenos Aires and the
northeastern region. A return level of 10°C (not shown)
gives return periods of 1 yr at all the stations studied,
except in the northeastern region, meaning that maximum temperatures of less than 10°C are likely to happen at least once a year all over the country, except in
the northeast. Minimum temperatures less than 0°C
(not shown) have return periods between 2 and 10 yr in
the northeast and 1 yr in the rest of the country. How-
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FIG. 5. Spatial distribution of return values (in °C) of warm extremes: (top) HTx and
(bottom) HTn for 2-, 10- and 100-yr return periods, drawn from a GEV distribution fitted to
annual extremes in the period 1956–2003.
ever, the analysis of the ⫺5°C return level for LTn gives
return periods greater than 100 yr in the northeast, and
between 1 and 5 yr in almost all the rest of the country.
4. 1976–77 climate shift
With the purpose of analyzing the influence of the
1976–77 shift in the frequency of occurrence of annual
extremes, we study the presence of changes in the annual temperature extreme return values drawn from a
GEV distribution fitted to two consecutive base periods: before 1976 and after 1977.
Time series (not shown) for the annual temperature
extremes defined above for the six long-term stations
used in this study: TUC, OCBA, PGM, PIL, SRS, and
RGA show that even though these extremes refer to
only one day of the year, they do not represent isolated
extremes. For five out of six stations, year 1995 shows a
relative maximum in HTx, while 1967 displays a relative minimum in LTn. Minimum temperature has less
interannual variability than maximum temperature.
Also, 11-yr running means denote the important interdecadal variability that these variables present. At Río
Gallegos cold extremes show greater variability than
warm extremes. It is also evident that HTx has decreased during the period under study at most of the
stations, while LTn has increased, especially at OCBA
and PIL.
Prior to the GEV fit, a Student’s t test has been carried out in order to evaluate the presence of significant
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5463
FIG. 6. As in Fig. 5, for cold extremes: (top) LTx and (bottom) LTn.
changes between the two periods in the series of annual
extremes. All the stations analyzed in this section show
significant changes in at least one of the annual extremes, with LTx the variable that showed less significant changes. Since the GEV distribution needs stationary series to be fitted, linear trends have been removed
after separating the annual extreme series into two subperiods (pre- and post-1976). This removal enlarges the
existing shift, and sometimes it even changes its significance, leading to a bigger shift between the two consecutive subperiods of the detrended series of annual
extremes. As can be seen in Table 1, HTx shows negative trends both in the complete and the pre-1976 periods at all stations, except at RGA where positive
trends are found, while the last subperiod presents different signs for different stations. Warm and cold extremes in minimum temperature (HTn and LTn) tend
to increase in all of the subperiods analyzed, except at
SRS where trends are negative, but only significant for
HTn in the pre-1976 period. LTx is the extreme variable with the lowest values of trends.
Figures 8–11 show return levels drawn from the GEV
distribution as a function of return periods for each
variable, station and subperiod studied. As can be seen,
LTx is the variable in which the 1976–77 shift is less
noticeable (Fig. 10). In general, the first subperiod (pre1976) shows return values almost equal to those obtained for the complete period (not shown) of each
station. This implies that the behavior of return values
based on the complete period is dominated by the first
subperiod.
At all the stations, HTx return values diminish from
the first to the second subperiod, that is, return periods
for fixed return values increase (Fig. 8). Therefore,
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FIG. 7. Spatial distribution of return periods (in years) of annual temperature extremes for fixed return values (indicated on top of each map), drawn from a GEV
distribution fitted to annual extremes in the period 1956–2003.
there is a decrease in the probability of occurrence of
maximum temperature warm extremes if we base our
study on more recent records. At Río Gallegos, this
statement is only true for return periods greater than 50
yr. At OCBA and Río Gallegos, HTn return values
increase basing our calculations on the second subperiod; that is, the frequency of occurrence of minimum
temperature warm extremes increases (Fig. 9). However, return values at Tucumán and Pilar have the op-
posite behavior since minimum temperature warm extremes become less frequent. At Santa Rosa, the shape
parameter of the GEV distribution changes its sign
from negative in the first subperiod to positive in the
following one. This change of sign implies a crossing of
the two return value distributions.
Although LTx is the variable that shows least change,
return values are slightly higher for the GEV distribution fitted to the last subperiod (Fig. 10). This means
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TABLE 1. Linear trends (in °C 10 yr⫺1) for the four annual temperature extremes and the different periods studied at six stations in
Argentina: TUC, OCBA, PGM, PIL, SRS, and RGA. Significant values at the 5% level in bold.
HTx
HTn
LTx
LTn
Complete
Pre-1976
Post-1976
Complete
Pre-1976
Post-1976
Complete
Pre-1976
Post-1976
Complete
Pre-1976
Post-1976
TUC
OCBA
PGM
PIL
SRS
RGA
⫺0.279
⫺0.219
0.786
⫺0.003
0.044
0.831
⫺0.026
⫺0.140
⫺0.152
0.164
0.074
⫺0.050
⫺0.050
0.012
⫺0.214
0.293
0.270
⫺0.125
0.185
0.185
0.320
0.390
0.303
0.311
⫺0.133
⫺0.181
0.158
0.270
0.320
0.297
0.122
⫺0.085
0.244
0.181
0.204
0.299
⫺0.464
⫺0.461
0.258
0.038
0.090
0.483
0.076
⫺0.158
⫺0.403
0.320
0.258
0.359
⫺0.548
⫺1.093
⫺0.168
⫺0.197
⫺0.962
⫺0.261
0.166
0.056
⫺0.073
0.281
⫺0.485
⫺0.121
0.169
0.134
⫺0.186
0.263
0.209
⫺0.281
⫺0.026
⫺0.221
0.081
0.195
0.186
0.022
that, though not significantly, maximum temperature
cold extremes tend to occur less frequently during the
last part of the century. It should be noticed here the
case of Río Gallegos where, regardless of the base pe-
FIG. 8. Return values (in °C) vs return periods (in years) for
HTx for (top to bottom) TUC, OCBA, PGM, PIL, SRS, RGA.
Return values (solid lines) are drawn from a GEV distribution
fitted at each station to the first subperiod, beginning–1976 (gray
lines), and second subperiod, 1977–end (black lines). 95% confidence intervals indicated in dotted lines.
riod, return values abruptly decrease with the increase
of return periods. LTn return values are higher for the
GEV distribution fitted to the last subperiod at all the
stations (Fig. 11). At OCBA, the 1976–77 shift implies
a significant change in return values since the confidence intervals of the two distributions do not overlap,
while at Santa Rosa and Río Gallegos this change is not
significant because of the complete overlapping of the
FIG. 9. As in Fig. 8, for HTn.
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VOLUME 21
FIG. 10. As in Fig. 8, for LTx.
FIG. 11. As in Fig. 8, for LTn.
confidence intervals. At these two stations, return values are greater for the second subperiod only for small
return periods because of the change of sign in the
shape parameter of the GEV distribution.
The most noticeable change in return values due to
the 1976–77 shift is seen in HTn at Río Gallegos where,
for example, the 10-yr return value increases from
13.7°C in the pre-1976 period to 18.6°C in the post-1976
period. At Tucumán, return values for HTx decrease
almost 4°C from one period to the other, while for LTn
they increase between 2° and 5°C, leading to a decrease
in the annual temperature range. At OCBA, changes in
maximum temperature return values are not significant, but the differences in minimum temperature return values show a reduction in the frequency of occurrence of cold extremes and an increase in the occurrence of warm extremes.
have been defined: the highest maximum (minimum)
temperature of the year called HTx (HTn), and the
lowest maximum (minimum) temperature of the year,
called LTx (LTn). As shown by the different goodnessof-fit tests performed in this study, the GEV distribution fits the four annual extremes studied with a significance level of 10%. This analysis of extreme events
allows the estimation of return values for periods
longer than the available records for its application in
different fields, like hydrology, oceanography, wind engineering, insurance industry, and risk assessment on
financial markets, among others.
Results based on the period in which most of the
stations have available and adequate information,
1956–2003, show that the highest annual maximum
temperature (HTx) decreases while the lowest annual
maximum temperature (LTx) increases in central Argentina leading to a drop in the maximum temperature
annual range. In the central-western region trends are
positive both for warm and cold extremes. It was also
found that maximum temperatures greater than 32°C
are expected at least once a year all over the country,
except in the Patagonia, where this value has a return
period of 10 yr. More extreme events indicate that
maximum temperatures greater than 40°C may occur
5. Conclusions
Return levels of extreme minimum and maximum
temperatures have been estimated by fitting a GEV
distribution to blocks of annual maxima. Four different
extremes based on minimum and maximum daily data
1 NOVEMBER 2008
RUSTICUCCI AND TENCER
once a year or every five years in the central and northern regions, where maximum temperatures reach the
highest values of the country. Minimum temperatures
below 0°C happen every 2–10 yr in the northeast and
once a year in the rest of country.
Another aim of this study was to establish how the
1976–77 shift influenced the frequency of occurrence of
annual temperature extremes. By fitting the GEV distribution to annual extremes in the period pre- and
post-1976, we found that GEV distributions based on
the complete period are generally very similar to the
ones based on the period pre-1976. Nevertheless, the
1976–77 shift led to significant changes in return values.
For example, assuming that the period post-1976 can be
considered as the “present climate,” at Río Gallegos
the highest minimum temperature of the year expected
once every 10 yr increased from 13.7°C in the past to
18.6°C in the present. At OCBA, where the urban heat
island is more intense, an increase of 3.3°C was found
after 1976 in the lowest minimum temperature of the
year that occurs every 10 yr and 4.1°C in the one that
happens every 100 yr.
Acknowledgments. This work has been partly funded
by the following projects: UBACYT X135, ANPCYT
BID 1728/OC-AR PICT 38273, and the European
Project of the Sixth Framework Programme
CLARIS-A Europe–South America Network for Climate Change Assessment and Impact Studies (GOCECT-2003-001454). We also thank Eric Gilleland and
Richard W. Katz for the extRemes toolkit used in this
analysis (http://www.isse.ucar.edu/extremevalues/
evtk.html) and the anonymous reviewers who helped to
improve the manuscript.
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