Tellus (2011), 63B, 1052–1058
C ?2011 The Authors
Tellus B C ?2011 John Wiley & Sons A/S
Printed in Singapore. All rights reserved
Application of an analytical formula for UV Index
reconstructions for two locations in Southwestern Spain
By M. ANT´ON1*, A. SERRANO2, M.L. CANCILLO2, J.A. GARC´IA2
and S. MADRONICH3,
2Departamento de F´ ısica, Universidad de Extremadura, Badajoz, Spain;3National Center for Atmospheric Research,
Boulder, Colorado, USA
1Departamento de F´ ısica Aplicada, Universidad de Granada, Granada, Spain;
(Manuscript received 17 January 2011; in final form 11 May 2011)
involves three independent variables: the solar zenith angle, the total ozone column and the clearness index. Regarding
the first application, daily UVI was estimated for more than 30 days when UV measurements were not available in
2007. For these cases, the missing UVI data were replaced by estimated values, thus affecting the UVI annual mean and
clear-sky cases (cloud and aerosol free conditions) using the COST 726 total ozone climatology. The linear UVI trends
for two periods (1957–1978 and 1979–2000) are calculated for summer months using linear least squares fits. Both
locations show statistically significant UVI trends for the most recent period 1979–2000, with values of +4.4 ± 1.6%
per decade for Badajoz, and +4.9 ± 1.8% per decade for Caceres. This result is mainly driven by the ozone decline at
northern mid-latitudes during this period. No significant trend is found for the other analysed period.
Although ultraviolet (UV) radiation (100–400 nm) represents
only 8% of the solar spectrum at the top of the atmosphere
(Iqbal, 1983), it plays a major role in the chemical processes
taking place in the atmosphere. In addition, the incident UV ra-
diation at the Earth’s surface has a strong biological influence
on human beings, and on terrestrial and aquatic ecosystems
(Diffey, 1991). It is well known that UV radiation can induce
detrimental effects on human health (particularly on the skin,
sight and immune system; World Health Organization (WHO),
1995; Lucas et al., 2006). Increases in the exposure of UV ra-
diation combined with more outdoor activities have favoured a
quick rise in those harmful effects. Therefore, the analysis of
long-term UV measurements and trend detection at different lo-
cations becomes a high priority in scientific research [United
Nations Environment Programme (UNEP), 2006].
The variable commonly used to inform the public about the
potentially harmful effects of UV radiation is the UV Index
(UVI; WMO, 1998). This informative variable is directly
derived from the ultraviolet erythemal radiation (UVER)
measured at surface which is quantified by weighting the solar
UV radiation with the erythemal spectral response (McKinlay
and Diffey, 1987).
10 years (Ant´ on et al., 2009a and references therein), which is
unfortunately too short for reliable climatology and trend anal-
ysis (Weatherhead et al., 1998). Thus, reconstruction methods
based on radiative transfer or empirical models are required
to build longer time-series of this variable (e.g. Bodeker and
McKenzie, 1996; Gantner et al., 2000; Kaurola et al., 2000;
Fioletov et al., 2001; Eerme et al., 2002; Diaz et al., 2003;
Engelsen et al., 2004; Trepte and Winkler, 2004; Lindfors
et al., 2003, 2007; Lindfors and Vuilleumier, 2005; den Outer
et al., 2005; 2010; Junk et al., 2007; Chuvaroba, 2008;
Rieder et al., 2008). The utility of those models is not only
focused on the reconstruction of past UV records, but also offer
the possibility of filling gaps in databases (Mateos et al., 2010).
In this framework, the main objective of this paper is
to reconstruct daily UVI time-series for two locations of
Southwestern Spain using an empirical model given by
Ant´ on et al. (2011) which relates the UVI to three inde-
pendent variables: total ozone column (TOC), clearness in-
dex (kt) and solar zenith angle (SZA). In this work, this an-
alytic method is applied for filling the data gaps in UVI
databases and for the reconstruction of clear-sky UVI values
1052Tellus 63B (2011), 5
P U B L I S H E D BY T H E I N T E R N AT I O N A L M E T E O RO LO G I C A L I N S T I T U T E I N S TO C K H O L M
ANALYTICAL FORMULA FOR UV INDEX RECONSTRUCTIONS 1053
during the period 1950–2000 using TOC values derived from
the COST 726 total ozone climatology (Krzy´ scin, 2008).
Although there are several works in the literature related to
the estimation of UV radiation values in the Iberian Peninsula
et al., 2009a, 2009b; Mateos et al., 2010), to our knowledge no
study on the reconstruction of past UV data in this region has
been published to date.
The instrumentation and the data used in this paper are de-
scribed in Section 2. Section 3 describes the analytical expres-
sion used in the reconstruction work. Section 4 presents and dis-
cusses the results obtained in this paper and, finally, Section 5
summarizes the main conclusions.
UVER data were measured on a plane and horizontal surface in
Badajoz(38.99◦N,7.01◦W, 199ma.s.l.),andCaceres (39.48◦N,
ground-based stations are characterized by a high frequency of
cloud-free days during the year, particularly during the summer
ters was sampled every 10 s and its 1-min average was recorded
on a Campbell CR10X data acquisition system.
The spectral and angular characterization of these two in-
struments was performed during the first Spanish calibration
campaign of ultraviolet broad-band radiometers at the ‘El
Arenosillo’ INTA station in Huelva (Spain), from 20 August to
15 September 2007 (Vilaplana et al., 2009). This campaign also
included the absolute calibration of the radiometers which was
performed through the outdoor intercomparison with respect to
a well-calibrated Brewer spectroradiometer. All this informa-
tion is utilized for converting the raw signal of broadband UV
radiometers into erythemal units (expressed in W m−2) using
the expression proposed by Webb et al. (2006). This new cali-
bration method (two-step method) leads to a great improvement
relative to the previous procedure (one-step method) which only
consists in the direct comparison between the output signal of
the broadband radiometers and the erythemally integrated spec-
(Cancillo et al., 2005). Although the calibration factors obtained
with the one-step method are only valid for the total ozone and
SZAs recorded during the outdoor intercomparison, the calibra-
tion factors derived from the two-step method account for the
total ozone and SZA dependence along the complete ozone and
angle ranges (Bais et al., 1999). Therefore, the two-step method
is recommended by several organizations responsible for cal-
ibration protocols, because of its higher accuracy (Bais et al.,
1999; Webb et al., 2003).
It is well known that the spectral response of the broadband
UV radiometers changes with time, mainly attributable to the
aging effect of these instruments. For this reason, and to work
corresponding to each UVER value is calculated by multiplying
these values by 40 (WMO, 1998).
developed within the scope of European Union’s Action COST
over Europe’. This European ozone climatology is derived from
a statistical model which was trained on satellite data over the
period 1979–2004 (NIWA assimilated total column ozone data
base) and over the period 2005–2009 (OMI total ozone data
base). The total ozone values were calculated from the recon-
from the result of the training with satellite data, and time-series
of meteorological variables and atmospheric circulation indices.
The COST 726 ozone data base consists of daily total values for
a rectangular area with longitude from 25.625◦W to 35.625◦E
and latitude from 30.5◦N to 80.5◦N. The spatial resolution is
1◦in the latitudinal and 1.25◦in the longitudinal direction. De-
tailed description of this COST 726 ozone climatology and its
validation can be found in the work of Krzy´ scin (2008). The
trend analysis of the total ozone values derived from this cli-
matology can be found in the paper of Krzy´ scin and Borkowski
In this work, the atmospheric clearness is characterized by
the transmissivity of solar total horizontal irradiance in the at-
mosphere. This variable, also named clearness index (kt), is
obtained as the ratio of the total solar irradiance on a horizon-
tal surface to the extraterrestrial total irradiance on a horizontal
surface. Total solar irradiance (310–2800 nm) is measured by
a pyranometer Kipp & Zonen CM-6B collocated in each sta-
tion. The clearness index is mainly associated with cloudiness,
characterizing the absorption and scattering processes of total
solar irradiance in the atmosphere. In addition, the attenuation
processes related to the aerosols and the molecular constituents
of the atmosphere show also significant effects on the clear-
ness index, that is this index is smaller than 1 for a completely
Ant´ on et al. (2011) proposed the following general analytic for-
mula for the estimation of UVI under all sky conditions:
where μ0is the cosine of the SZA, TOC is the total ozone col-
umn in Dobson Units (DU) and ktis the clearness index. The
coefficient a represents the UVI value for the following specific
conditions in Southwestern Spain: the smallest SZA (summer
solstice; μ0= 0.96), TOC equal to 315 DU (annual mean value)
UVI = a
Tellus 63B (2011), 5
1054 M. ANT´ON ET AL.
a multiple regression analysis using the least squares approach.
Daily data were selected for the period between January 2006
and December 2007. The UVI and ktdata correspond to values
recorded at solar noon (maximum daily μ0). In addition, TOC
corresponds to the daily value provided by the COST 726 ozone
climatology. Values of a, b, c and d were found to be respec-
tively 9.63 ± 0.07, 2.24 ± 0.02, 1.14 ± 0.04 and 0.75 ± 0.01 for
Badajoz; and 9.85±0.06, 2.35 ± 0.01, −1.30 ± 0.03 and
expression 1 to fill gaps in UVI databases and the reconstruction
of past UVI records.
4. Results and discussion
4.1. Application to fill data gaps
The broadband UV radiometers belonging to the Extremadura
UV radiometric network suffer from some periods without
for example, both UV radiometers were sent to the manufac-
turer in the Netherlands during the period March to May 2004
to measure their spectral response. In addition, the instruments
have been moved to the ‘El Arenosillo’ ESAT/INTA station
every two years for outdoor intercomparison with respect to a
well-calibrated Brewer spectroradiometer #150 (Cancillo et al.,
2005; Vilaplana et al., 2009). The mentioned calibration field
campaigns lasted for about 1 month.
The empirical models can be used for filling existing gaps in
the database whenever the information about the independent
variables is available during these periods. This is the case for
pyranometers for measuring the total solar irradiance, which
continued recording data in Badajoz and Caceres during the
absence of the UV radiometers in these locations. Thus, the
clearness index is available for those periods without UVI data,
model (eq. 1).
Figure 1 shows two plots with the measured and estimated
Two vertical dashed lines mark the limits of the period without
experimental data due to the participation of the UV broad-band
instruments in the calibration campaign at El Arenosillo Sta-
tion from 20 August to 15 September 2007. The mean absolute
UVI data (UVImod−UVImea/UVImea) for the year 2007 is 5.8%
and 4.6% for Badajoz and Caceres, respectively. This excellent
agreement when UVI observations are available supports the
reliability of the reconstructed time-series.
The original 319 daily UVI measurements during 2007 in
Badajoz have increased up to 352 values using the empirical
model (the reconstructed data represents 9.4% of all). In Cac-
values when UVI was reconstructed by the model (the recon-
structed data represents 11.9% of all). These notable differences
in the number of data between both time-series affect the an-
nual statistical parameters of the UVI at the two locations. For
example, for Badajoz, the mean (median) annual value changes
from 4.40 (4.17) for the measured dataset to 4.52 (3.80) for the
reconstructed data set.
4.2. Application to reconstruct past data for
The empirical model proposed in this paper (eq. 1) allows us to
clearness index is only available for our locations after 2000, the
reconstruction of the past UVI data must be performed for clear-
Thus, a constant clearness index equal to 0.91 was considered in
the empirical models for Badajoz and Caceres. This value was
obtained as the 99? of all daily clearness indexes during the
period of available measurements (2001–2008) at each location.
The temporal evolution of the reconstructed UVI data for
the whole period 1950–2000 is shown in Fig. 2 for Badajoz
and Caceres separately. Each point in the plot represents the
annual summer mean value of the reconstructed UVI data cal-
culated as the average of the four months around the summer
solstice (May to August). These months were selected as the
period of the year when the highest UVI values are recorded
(Ant´ on et al., 2009a). In addition, the prevailing cloud-free
situation in Southwestern Spain during these months (Serrano
et al., 2006) allows the clear-sky reconstructed UVI values to
be considered very close to the real past UVI values. From the
two plots of Fig. 2, similar reconstructed UVI values can be
seen for the two ground-based stations during the whole period.
Thus, the relative difference between the reconstructed values
(UVICaceres−UVIBadajoz/UVIBadajoz) for the period 1950–2000 is
only about 4%.
This reconstructed UVI values are derived assuming a con-
stant clearness index (99? of daily clearness index values
between 2001 and 2008) as explained earlier. The variability
of this index is mainly related to cloudiness and atmospheric
depth (e.g. Cheymol and De Baker, 2003; Kazadzis et al., 2007;
mier, 2005; Rieder et al., 2008; den Outer et al., 2010) have
been reported since early 1990s in Europe. In addition, it is well
known that the maximum atmospheric turbidity was reached in
Europe during the period 1970–1990 (e.g. Tegen et al., 2000).
western Spain between 2001 and 2008 may be higher than the
Tellus 63B (2011), 5
ANALYTICAL FORMULA FOR UV INDEX RECONSTRUCTIONS 1055
Jan. Mar.May Jul.Sep. Nov.
Fig. 1. Evolution of the measured and estimated daily UVI data at Badajoz (top) and Caceres (bottom) for the year 2007. The time between the
vertical dashed lines represents the period without experimental UVI data.
same percentile for the 1990s and previous decades. This fact
could likely result in slightly overestimated reconstructed UVI
values between the 1970s and 1990s.
The linear long-term trends were obtained as least squares
fits of the annual summer mean values (calculated as detailed
above). Figure 2 shows a high interannual variability of summer
UVI values, which makes the trend analysis notably sensitive
to the length of the data set (Weatherhead et al., 1998). In this
sense, we work with two subperiods of 22 years: from 1957 to
1978, and from 1979 to 2000. The linear trends were calculated
for each interval at the two locations. The trends for the second
period 1979–2000 have been added to the figure. It can be seen
that the summer trends for the period 1979–2000 are clearly
positive in the two locations, suggesting a possible connection
to the ozone decline at middle-latitudes which started about the
late 1970s and stopped about middle 1990s (Krzy´ scin, 2006;
Harris et al., 2008).
Table 1 shows the results of the summer trend analyses, to-
gether with their standard errors, expressed in UVI units and in
percentage with respect to the average UVI value for the months
May to August during each period. The trends for the period
1.8% per decade for Caceres, being both statistically significant
at the 95% confidence level. It should be emphasized that these
results together with the prevailing cloud-free conditions dur-
ing summer in Southwestern Spain suggest that the increase in
UVI in this region has been real between 1979 and 2000 during
summer. The empirical model used in this work for the recon-
struction of past clear-sky UVI data involves two inputs: the
solar zenith angle and the total ozone column. Thus, the signif-
icant positive UVI trends obtained for the period 1979–2000 at
Badajoz and Caceres are related to the decline of the total ozone
data for the same period (about −3.6% per decade in the two
Tellus 63B (2011), 5
1056 M. ANT´ON ET AL.
1950 19601970 19801990 2000
1950 1960 19701980 19902000
Fig. 2. Evolution of the annual mean value (May to August) of the reconstructed clear-sky UVI data at Badajoz (top) and Caceres (bottom) for the
period 1950–2000. Linear trend over the period 1979–2000 is also shown.
The results of the UVI trend analysis for Badajoz and Cac-
eres are in broad agreement with the results found in the liter-
ature. Among of them, Fioletov et al. (2001) calculated linear
trends in reconstructed cloud-free UVER for three locations in
Canada, showing values between +3.3% and +5.4% per decade
summer (May to August) over two periods (1957–1978 and
1979–2000) in Badajoz and Caceres
Linear trends (±standard error) in UVI units per decade for
−0.09 ± 0.13
(−1.1 ± 1.7)
−0.21 ± 0.16
(−2.7 ± 2.1)
+ 0.33 ± 0.12
(+ 4.4 ± 1.6)
+ 0.38 ± 0.14
(+ 4.9 ± 1.8)
Note: Results in percent per decade are shown in parentheses.
for summer (May to August) during 1979–1997. The work of
den Outer et al. (2005) showed that the annual UVER dose re-
ceived at Bilthoven (the Netherlands) for cloud-free conditions
was 3.1 ± 0.8% per decade over the period 1979–2003. Kaurola
et al. (2000) found a statistically significant increasing trend of
5.4 percent per decade in the yearly reconstructed UV doses at
Jokioinen (Finland) for the period 1979–1997. Lindfors et al.
(2007) analysed the past clear-sky UVER values at four stations
period 1983–2005. Krzy´ scin et al. (2010) found positive UVER
trends (5.5 ± 1.0% per decade) at Belsk (Poland) for the period
year (April–October). Chubarova (2008) performed a long-term
analysis (1968–2006) of reconstructed UVER data at Moscow
(Russia), reporting linear statistically significant positive trends
ysed by den Outer et al. (2010) for eight sites in Europe, show-
ing linear trends from +0.3 ± 0.1% to +0.6 ± 0.2% per year
Tellus 63B (2011), 5
ANALYTICAL FORMULA FOR UV INDEX RECONSTRUCTIONS 1057
for the period 1980–2006. Our results also agree with the
works of Gantner et al. (2000) and Trepte and Winkler (2004),
which analysed the UV levels at Hohenpeissenberg (Germany),
showing statistically significant increasing trends in clear-
sky noontime UVER values for the months between March
and September over the periods 1968–1997 and 1968–2001,
1957–1978 were slightly negative. Nevertheless, these trends
were not statistically significant at the 95% confidence level.
This result shows the high impact that the applied time range
has on the trends and their uncertainties.
The application of a simple analytic model to the reconstruction
of UVI data has allowed filling short gaps in UVI measurement
series for two locations in Southwestern Spain under all sky
conditions. Thus, the UVI has been estimated for more than
30 days with missing data during 2007. In addition, the recon-
struction of past UVI time-series values (1950–2000) has been
performed using the model for clear-sky conditions. Statisti-
cally significant UVI trends were found for Badajoz (+4.4% per
decade) and Caceres (+4.9% per decade) for summer months
during the period 1979–2000. These results suggest that the
UVI values in summer increased during this period in South-
western Spain. No significant trends were found for the period
UV data using reliable instruments are necessary. Nevertheless,
allow extension of the UV information to periods when direct
measurements are not available.
The authors thank COST Action 726 and Dr. J.W. Krzyscin
for the total ozone climatology used in this paper. This work
has been partially supported by the Spanish Ministerio de Cien-
cia e Innovaci´ on under project CGL2008-05939-C03-02/CLI.
Manuel Ant´ on thanks Ministerio de Ciencia e Innovaci´ on and
de la Cierva).
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