Statistical Analysis and InterComparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus

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How to cite this article Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus. SM J Biometrics Biostat.
2017; 2(4): 1020.
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ISSN: 2573-5470
Introduction
UV radiation on the Earth’s surface varies widely and depends mainly on latitude, solar elevation,
ozone column and local atmospheric conditions. e emission of certain gases due to human
activity is known to alter the composition of the atmosphere. Some of the most serious damage
caused is the reduction of the ozone layer in the stratosphere, causing a corresponding increase in
ultraviolet radiation [1]. Measurements in Italy and England indicate that UV incidence increased
with decreasing ozone amount at xed solar zenith angles [2-3]. Ultraviolet (UV) radiation covers
wavelengths of the electromagnetic spectrum between 100 and 400 nm and it constitutes 8.73% of
the total extraterrestrial solar spectrum irradiance. Within the UV radiation spectrum three zones
are distinguished in relation to the eects that the radiation produces on living organisms: UVC
(100-280 nm), UVB (280-315 nm) and UVA (315-400 nm) [4].
UVC does not reach the earth surface since it is absorbed completely by the ozone layer in
the stratosphere. In the upper atmosphere, UVB irradiance amounts to 1.3% of the solar constant
[5]. is component disrupts proteins (DNA), causes skin sunburn, skin cancer and eye cataracts
in humans, losses of productivity and other destructive eects in plants [6-9]. Skin overexposure
produces severe sunburn that causes heat, erythema and other symptoms approximately 16 hours
aer exposure to natural sunlight [10]. On the other hand, the primary benet of human exposure to
UVB radiation is the need for UVB for synthesis of vitamin D in the skin. is synthesis is achieved
with very low doses of UVB radiation, such that a daily exposure of 10-15 min of the face, arms and
hands at the intensity of the radiation received in Northern Europe is sucient [11]. e ultraviolet
A (UVA) irradiance represents around 90-95% of the UV solar irradiance that reaches the Earth
surface and is the less energetic portion of the UV spectrum; it is only slightly absorbed by ozone
layer. e health-associated eects of UVA exposure include photo-aging of the skin, immuno-
suppression of the skin immune system and potential enhancement of the negative eects of UVB
exposure [12-13].
e enhanced UV irradiance due to global depletion of stratospheric ozone and the increased
cumulative sun exposure of the public are of major concern due to deleterious health-associated
eects of increased exposure to UV irradiance. Consequently, there is now added impetus to study
Research Article
Statistical Analysis and Inter-
Comparison of Solar UVA and Global
Radiation for Athalassa and Larnaca,
Cyprus
Pashiardis S1, Kalogirou SA1* and Pelengaris A2
1Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of
Technology, Cyprus
2Department of Cyprus Public Works, Ministry of Transport Communications and Works, Cyprus
Article Information
Received date: Nov 01, 2017
Accepted date: Nov 21, 2017
Published date: Nov 27, 2017
*Corresponding author
SA Kalogirou, Department of Mechanical
Engineering and Materials Science
and Engineering, Cyprus University of
Technology, Limassol, Cyprus,
Tel: +357-2500-2621; Fax: +357-2500-
2637; Email: soteris.kalogirou@cut.ac.cy
Distributed under Creative Commons
CC-BY 4.0
Keywords Broadband UVA irradiance;
Statistical analysis; Clearness index;
Frequency distribution; Transparency;
Statistical relationships; Cyprus
Abstract
A statistical analysis and inter-comparison of the broadband ultraviolet-A (UVA) radiation at two sites in Cyprus
representing two different climate regimes of the island (Athalassa-inland plain vs Larnaca-coastal location)
covering the period January 2013-December 2015 is presented. Mean annual and mean monthly daily totals of
the UVA irradiation and their frequency distribution at both sites are computed and discussed. Daily maximum of
hourly average irradiance values occur in July, 58W m-2 and minimum, 22 W m-2, in December at solar noon at
Athalassa. The respective values at Larnaca are slightly higher (68 W m-2 and 28 W m-2, respectively). UVA daily
values follow the pattern of the solar altitude angle; the total accumulated UVA irradiation along a mean year
reaches 385.8 MJ m-2 at Athalassa and 476.5 MJ m-2; maximum stability of UVA takes place at midday hours and
during the summer. Large uctuations of the daily UVA irradiation are observed in the winter and spring months,
which are mainly due to unstable meteorological conditions during the transition from cold to warm weather and
vice versa. During summer the daily UVA radiation exceeds the value of 1700 kJ m-2 at Athalassa and 2100 kJ m-2
at Larnaca, while during the winter season the lowest is about 250 kJ m-2 at both stations. The UVA potential and
extraterrestrial irradiation have also been calculated in order to estimate the attenuation of UVA radiation through
the atmosphere. The UVA transmittance, kUVA, is approximately 6 to 7% of the hemispherical transmittance for
the whole spectrum (kt). Statistical relationships between UVA and other radiation components were established
using linear or power relationships.

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 2/16
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Copyright  Kalogirou SA
the temporal and spatial variability of both UVB and UVA irradiance.
In spite of the important role of UV, few radiometric stations measure
systematically the UV solar irradiance in the Mediterranean region.
A network of UV stations was established in Greece [14], Spain [15-
16], Israel [17] and Egypt [18]. In Cyprus, UV radiation is measured
currently at two locations: Athalassa (inland) and Larnaca (coastal
place) [19-20].
Various authors have analyzed the relation between solar UV
and global radiation. Martinez-Lozano et al. [21] studied UV (A+B)
irradiance values in Valencia in the period 1991-1994. Foyo-Moreno
et al. [22] analyzed UV and global irradiance in Granada. Canada et
al. [23] studied UV irradiance in Valencia and Córdoba in relation
to the clearness index, the relative optical air mass, the time of year
and the total irradiance on a horizontal surface. Mantis et al. [24],
Koronakis et al. [25], Kudish and Evseev [26-27], Jacovides et al.
[19-20,28] performed statistical analysis of various components of
UV radiation and global irradiances in Athens (Greece), Beer Sheva
(Israel) and Athalassa (Cyprus), respectively, Recently, Kalogirou et
al. [29] and Pashiardis et al. [30] performed statistical analysis on
temporal and spatial variability of erythemal and UVB solar radiation
components, respectively and compared two sites in Cyprus with
dierent climate regimes.
An assessment of the solar radiation climate of the Cyprus
environment was presented by Jacovides et al. in 1993 [31].
Kambezides [32] presented the ‘Typical Meteorological Year’ for
Nicosia. More recently, Kalogirou et al. [33] presented a statistical
analysis and inter-comparison of the solar global radiation at the
above two sites in Cyprus using measurements of 21 months at
both sites. e common feature of all the above studies is that they
rely mostly on measurements of solar radiation carried out in the
actinometric stations of Athalassa and Larnaca.
e present study is based upon broadband measurements of
UVA irradiance. e aim of the study is the statistical analysis of
the temporal and spatial variability of UVA irradiance at two sites
in Cyprus (inland and coastal). is is essential because of the fact
that the atmospheric conditions in the area favour dry summers
and cold winters, high air temperatures and low vapour pressure
values at midday in summer time which aect the transition of UVA
through the atmosphere. In this work we analyze hourly UVA and
global irradiance data on a horizontal plane and perform an inter-
comparison study between the two locations in Cyprus as well as
between other sites in the Mediterranean region.
Topography, Climatology, Measurements and Quality
Control
Topography and climate characteristics of the two sites
e radiation data on which this study is based are being
monitored at two meteorological stations: one located at Athalassa,
an inland plain location and the other one at Larnaca Airport which
is near the coast (Figure 1). e site parameters of the two stations are
listed in table1.
e climate of both stations is typical Mediterranean with mild
winters (mean seasonal air temperature of about 12 °C at Larnaca
and 10.5 °C at Athalassa) and warm summers (mean seasonal air
temperature of 27.5 °C at Larnaca and 29.5 °C at Athalassa). At
Larnaca Airport sea-breeze cells develop in late spring and summer.
Although Athalassa is an inland location, a westerly sea-breeze
is mainly noticeable during the summer time blowing from the
Morphou bay between the mountainous ranges of Pentadactylos and
Troodos (Figure 1). e annual rainfall is about 320 mm at Athalassa
and about 340 mm at Larnaca. Most of the rainfall occurs between
October and March; summer months are mostly dry. e two sites
are characterised by relatively high global and horizontal beam
radiation intensities. e average annual sunshine duration is 3332
hours for Athalassa and slightly higher at Larnaca (3368 h). All the
above climatic averages refer to the 1981-2010 period.
e annual average daily global radiations exceed 18.5 MJ m-2 at
the two sites, whereas the horizontal beam radiation is 13.1 MJ m-2 for
Athalassa and 14.2 MJ m-2 for Larnaca, respectively. Consequently,
the fraction of the beam component of the global radiation is
relatively high at both sites, viz., the annual average daily fraction
is >0.600 at the two sites. Comparing the two sites it seems that
Larnaca has slightly higher rates of global radiation than Athalassa,
since the average yearly cumulative global irradiation is 6835 MJ m-2
for Athalassa and 7183 MJ m-2 for Larnaca. e monthly average
frequency of days according to the classication of the magnitude
of the daily clearness index KT (daily global to daily extraterrestrial
radiation), showed that both clear and partially cloudy days exceed
90% annually (KT>0.35) [33].
Measurements and quality control processes
e period for presenting the data in both stations is January
2013 until December 2015 (3years), when both stations operated
simultaneously, so as to allow for comparison of the dierent
variables of solar and terrestrial radiation. Measurements of total
solar irradiance on a horizontal surface were taken with Kipp&Zonen
CM11 pyranometers whose spectral range is from 285 to 2800 nm.
Both stations are equipped with Kipp&Zonen UVS-AB-T broadband
radiometers with spectral range 280 to 315 nm (UVB) and 315 to 400
nm (UVA). e radiometers have directional response up to 700 solar
zenith angle (θz) less than 2.5%. All the sensors are factory calibrated,
Figure 1: Map of Cyprus showing the location of the two radiometric stations.
Table 1: Site parameters for the two meteorological stations.
Site Location Latitude Longitude Altitude (m,m.s.l)
Athalassa inland 35.1410 N 33.3960 E 165
Larnaca coastal 34.8730 N 33.6310 E 1

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 3/16
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Copyright  Kalogirou SA
in accordance with the World Radiometric Reference (WRR). Global
radiation instruments are calibrated outdoor against standard
references at irregular time intervals during the study period. e
errors involved in the radiation measurements are found to be no less
than ±2% for the normal incidence beam irradiance and ±3% for the
global irradiance.
A Campbell Scientic Instruments data-logger, located at each
site (Model CR10), monitors and stores the data at 10-min intervals
(the meters are scanned every 10-seconds and average, maximum,
minimum and instantaneous values at 10-min intervals are calculated
and stored). e stored data are downloaded to a desktop computer
periodically. e data refer to the Local standard Time (LST=GMT+2).
About 5% of the data values are missing because of some problems
with the instruments and some defects and maintenance in the data
acquisition systems. e validity of the individual measurements was
checked in accordance with WMO recommendations [34] and other
tests proposed by various authors [35-37]. Details about the quality
control procedures used in this study are given by Pashiardis and
Kalogirou [38]. All data that do not meet the conditions specied by
the suggested tests are not used in the study.
Regarding the UVA irradiance the following upper limit was
applied as suggested by Miguel et al. [39]:
(1)
Where, UVA is the measured value and
0
UVA
is the horizontal
extraterrestrial solar UVA irradiance. e measurements of both
stations were less than the horizontal extraterrestrial solar UVA
irradiance during the whole period of measurements (Figure 2). e
values of UVA irradiance during the night were close to zero. No
other errors were detected. Long missing data were detected during
the measurement period (2013-2015) at Larnaca due to instability of
the system.
Regarding the quality control of the daily UVA radiation data,
daily values were rejected in case of incomplete data during the day.
e time series plots of the daily values of UVA irradiation for both
stations are shown in gure 3. e gure indicates that the ascent
during the rst months of each year is very irregular with uctuations,
while the descent is smoother. During summer the daily UVA
radiation exceeds the value of 2000 kJ m-2 at Larnaca and 1800 kJ m-2
at Athalassa, while during the winter season the lowest daily value is
about 110 kJ m-2 at both stations. Comparing daily UVA and UVB
radiation it seems that UVA is about 50 times more than UVB in
mid-winter and about 30 times more in mid-summer at both stations.
Results and Discussion
Data variation
Global solar radiation and total UVA radiation have been analysed
and compared in this study. Figure 4a shows temporal evolution of
UVA and global solar radiation at Athalassa. A similar graph with
slightly higher values was obtained at Larnaca (Figure 4b). Data reveal
a common evolution shape with maxima in summer and minima
in winter, mainly due to the daily minimum solar zenith angle and
day-length (astronomical factors) variation during the year. Large
uctuations in the spring months and November are mainly due to
unstable meteorological conditions during the transition from cold
to warm weather and vice versa. e maximum of daily global solar
horizontal irradiation is reached in June or July and is around 31 MJ
m-2 at Athalassa and around 32 MJ m-2 at Larnaca.
Statistical analysis of hourly UVA irradiance
A statistical study of the most representative UVA indices for each
month of the year has been carried out and the UVA accumulated
values have been evaluated because they are very useful in the studies
of eects on human beings.
Table 2 shows the hourly statistical estimators for July for both
stations. e statistical parameters presented in the Table are: Number
of Data (N), Arithmetic Mean (Mean), Standard Deviation (StDev),
Coecient of Variation (CV in %), Minimum (Min), First Quartile
(Q1), median, third quartile (Q3), Maximum (Max), Interquartile
Range (IQR), percentile 5 (P5) and percentile 95 (P95) [20]. It can be
observed that the median values are slightly higher than the average
ones at least during the middle hours of the day.
e dierence between the Q3 quartiles and the maximum
values are low, with the highest ones not exceeding 2.20 W m-2 for
Athalassa and 3.86 W m-2 for Larnaca; this result shows that the
maximum values are representative of the UVA irradiance. On the
other hand the dierences between Q1 quartiles and minimum values
are relatively high (>5 W m-2) in most cases. Similarly, the dierence
between the minimum values (Min) and the percentile, P5, is very
high (>4 W m-2) at both stations, which suggests that the minimum
Figure 2: Daily values of UVA and UVB irradiation (kJ m-2) at Athalassa and
daily extraterrestrial UVA (UVAd0) irradiation (kJ m-2). Figure 3: Time series plot of daily UVA solar irradiation during the period
2013-2015 at Athalassa and Larnaca.
0
1.2*UVA UVA≤

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 4/16
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Copyright  Kalogirou SA
values are not representative of the UVA irradiance at the station level
and correspond to unusual extreme values, particularly in summer.
Similar results have been obtained by Martinez-Lozano et al. [21]
Foyo-Moreno et al. [22] and Bilbao et al. [15] for a number of stations
in Spain. On the other hand the dierence between the maximum,
Max and the percentile, P95, is quite small. In July the dierences are
lower than <1 W m-2 at both stations. e absolute maximum values
of the two stations were 61.03 W m-2 for Athalassa and 72.78 W m-2
for Larnaca.
e UVA variability has been studied by means of the Coecient
of Variation (CV). As it can be seen in table 2, the CVs in July are low
during the midday (3-9%) at both stations, indicating a high stability
along these hours in summer. Furthermore, CVs uctuate between 3
and 15% at Athalassa, while at Larnaca is slightly higher (3-22%). e
standard deviation is lower along midday hours and symmetrically
distributed around solar noon during the summer months. is
could be explained by a minor presence of clouds in the summer
months that lead to a high stability.
Analysis of monthly average hourly UVA irradiance
e daily variation of the average hourly UVA irradiance is
shown in gure 5. e gure shows that UVA irradiance uctuates
between 22.28 W m-2 in December and 52.53 W m-2 in July at solar
noon at Athalassa. e values at Larnaca are higher than in Athalassa
and they uctuate between 28.51 W m-2 in December and 68.56 W
m-2 in June at solar noon. A high symmetry is also observed around
the months of June or July when the irradiance reaches its maximum,
while it decreases in spring and autumn and reaches its minimum in
winter months. e results can be explained by taking into account
the symmetry relation between the summer and winter solstices.
Table 2: Statistical estimators of the mean hourly UVA irradiance (W m-2) in July, under all sky conditions, for the period 2013-2015, for a) Athalassa and b) Larnaca.
a) Athalassa
Hour N Mean StDev CV (%) Min Q1 Median Q3 Max IQR P5P95
6 93 5.06 0.75 14.92 2.32 4.61 5.13 5.55 6.56 0.94 3.60 6.26
7 93 12.22 1.54 12.60 6.59 11.37 12.47 13.20 15.04 1.84 9.17 14.54
8 92 23.89 1.91 8.01 18.13 23.01 24.26 25.07 27.24 2.06 20.19 26.74
9 92 36.01 1.81 5.01 30.10 34.89 36.23 37.24 39.44 2.35 32.85 38.76
10 92 46.49 1.98 4.25 37.07 45.51 46.70 47.69 49.72 2.18 43.48 49.19
11 92 54.03 1.82 3.36 47.29 53.13 54.16 55.41 57.06 2.27 50.87 56.53
12 92 57.53 1.89 3.29 51.62 56.64 57.75 58.83 61.03 2.19 53.40 60.21
13 92 56.68 3.30 5.83 38.67 56.10 57.50 58.56 60.24 2.46 48.51 59.56
14 92 51.30 4.90 9.55 29.86 51.02 53.05 53.99 55.45 2.97 39.47 55.14
15 92 42.51 6.86 16.14 16.69 43.03 45.23 46.03 47.75 3.01 23.26 47.06
16 92 33.44 4.26 12.74 6.82 33.28 34.67 35.57 37.22 2.29 23.84 36.38
17 92 22.52 2.03 9.02 11.11 22.11 22.97 23.63 25.24 1.52 18.78 24.49
18 92 11.41 0.98 8.63 7.06 10.88 11.52 12.08 13.17 1.20 9.78 12.96
19 92 5.48 0.57 10.37 2.92 5.15 5.48 5.82 6.63 0.67 4.67 6.36
b) Larnaca
Hour N Mean StDev CV (%) Min Q1 Median Q3 Max IQR P5P95
6 77 5.10 1.12 21.97 2.07 4.38 4.99 5.97 7.45 1.60 3.57 7.04
7 77 13.15 2.72 20.65 9.26 10.93 12.17 15.72 19.00 4.79 9.73 17.91
8 77 26.71 3.73 13.96 19.32 23.91 25.71 30.16 34.02 6.25 20.40 32.71
9 77 40.83 3.96 9.70 29.57 37.98 41.01 44.29 47.93 6.31 34.12 46.97
10 77 53.43 3.62 6.77 41.50 50.76 53.84 56.23 59.78 5.47 47.99 58.98
11 77 62.77 3.09 4.92 52.36 60.51 63.14 64.76 68.21 4.25 57.95 67.48
12 77 68.13 2.66 3.90 61.45 66.27 68.77 69.87 72.78 3.60 63.24 72.19
13 77 68.56 2.27 3.32 63.38 67.14 68.72 70.19 72.59 3.06 63.77 71.71
14 77 63.78 2.36 3.70 59.38 61.78 63.72 65.84 68.00 4.06 59.62 67.40
15 77 54.35 4.05 7.46 25.56 52.97 54.21 56.65 59.82 3.68 51.33 58.51
16 77 41.50 3.83 9.23 24.05 40.01 41.85 43.61 47.73 3.60 31.63 40.10
17 77 27.42 2.89 10.54 16.38 24.80 27.34 29.72 32.60 4.92 23.64 31.77
18 77 13.35 1.98 14.79 5.08 11.63 13.47 14.77 16.76 3.14 10.98 16.33
19 68 6.95 0.87 12.47 4.53 6.39 7.01 7.71 8.38 1.33 5.63 8.15

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 5/16
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Copyright  Kalogirou SA
Analysis of accumulated UVA irradiation
In the studies on the biological eects of UVA irradiation or the
availability of solar energy for technological applications, we require
the accumulated UVA solar irradiation (kJ m-2) through a period of
time. Figure 6 shows the accumulated hourly UVA irradiation values
for an average day of each month and the last value is the total daily
amount. It can be seen that the highest value for UVA irradiation was
produced in July, with a daily average of 1650.8 kJ m-2 for Athalassa,
while at Larnaca the highest is recorded in June (2000.9 kJ m-2).
On the other hand, in December the average energy received was a
minimal 467.5 kJ m-2 at Athalassa and 609.4kJ m-2 at Larnaca. e
accumulated irradiation received in an average year is 385.8 MJ m-2
for Athalassa and 476.5 MJ m-2 for Larnaca.
Monthly mean hourly UVA/G ratio
e increase of UVA/G ratio with the cloud cover is signicantly
higher for low solar elevation. e monthly mean of the hourly
UVA/G ratio is given in table 3. e monthly mean hourly ratio is
almost constant throughout the year at both stations. e annual
mean hourly ratio is 0.0587 at Athalassa and slightly higher at Larnaca
(0.0667).
Inuence of solar elevation on UVA irradiance
e most important factor which aects the solar radiation is the
solar elevation. is variable determines the optical path of solar rays
from the top of the atmosphere until they reach the Earth’s surface.
e solar elevation is related to the optical air mass, that is dened
as the ratio between the relative optical air mass in a given direction
and the optical mass in a vertical direction and is calculated using the
equation suggested by Kasten and Young, [40]:
1.6364
1/ (cos 0.050572(96.07995 ) )
z z
m
θ θ
−
= + −
(2)
Where
z
θ
is the zenith angle of the Sun (complementary angle of
the solar elevation).
Figure 4: Co-variability of daily measured UVA values (UVAd) and daily
global horizontal solar radiation (Gd) during the period 2013-2015 at a)
Athalassa and b) at Larnaca. Figure 5: Daily evolution of the monthly mean hourly UVA irradiance (W m-2)
for the period 2013-2015 at a) Athalassa and b) Larnaca.
Table 3: Mean monthly of the hourly UVA/G ratio for Athalassa and Larnaca
during the period 2013-2015.
Month Ath Lca
1 0.0579 0.0682
2 0.0578 0.0649
3 0.0574 0.0661
4 0.0574 0.0661
5 0.0594 0.0672
6 0.0617 0.0658
7 0.0585 0.0656
8 0.0583 0.0655
9 0.0596 0.0635
10 0.0613 0.0682
11 0.0567 0.0672
12 0.0574 0.0721
Year 0.0587 0.0667

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 6/16
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Copyright  Kalogirou SA
To quantify the eect of solar elevation on UVA irradiance, the
optical air mass, m, was calculated at the midpoint of each hour. Figure
7 shows the relationship between UVA irradiance and optical air mass
for three dierent classes of hourly clearness index (kt), (the ratio of
global irradiance at the Earth surface to the global solar extraterrestrial
irradiance both measured on a horizontal surface),i.e., (kt)>0.65
(clear hours), 0.35<kt≤0.65 (partly cloudy hours) and kt<0.35 (cloudy
hours). It can be seen that, despite the wide dispersion of data, the
highest values of UVA irradiance decrease with the optical air mass.
erefore, the solar elevation plays an important role on the levels
of UVA irradiance, since it is an important factor in the calculation
of the optical air mass (Equation 2). e range of dispersion of the
data for the case of clear hours is smaller comparing to the other two
classes. e equations which describe the above relationships for each
class of hourly clearness index are presented in table 4. e equations
can be used for the estimation of the hourly UVA irradiance. e
relationships have the following form:
*b
UVA a m=
(3)
Analysis of UVA daily time series
Daily and monthly average daily UVA irradiation values have
been calculated and gure 8 shows the results for both stations. e
daily values present a greater uctuation in spring season. It can
be seen that the variation of the monthly mean values (continuous
smooth line) is quite regular, with the maximum values taking
place in June and July and the minimum in December. Daily UVA
increases in spring to summer shown by the slope which is smaller
than the decrease in autumn.
Table 5 shows the statistical characteristics of daily UVA data
for all-sky conditions. e median values are mainly higher than
the average ones and the maximum of the standard deviation occurs
in May; the coecient of variation shows the lowest values in the
summer months, which means that the highest stability is observed
in these months. e dierences between the minimum, (Min) and
the percentile, P5 are quite high and therefore, the minimum values
correspond to unusual extreme values. On the other hand, the
dierences between the maximum, (Max) and the percentile P95 are
small. e observed daily maximum is occurred in June at Athalassa
(1797 kJ m-2) and in July at Larnaca (2140 kJ m-2). e denition of
frequency distribution types is a function of the range of kurtosis (K)
and skewness values (As) as suggested by Kudish and Evseev [27].
Table 4: Relationship between UVA irradiance (W m-2) and optical air mass (m)
for three different classes of clearness index (kt) at Athalassa and Larnaca.
Hourly
Clearness
Index (kt)Equation
kt> 0.65
0.35 <kt≤ 0.65
kt< 0.35
kt> 0.65
0.35 <kt≤ 0.65
kt< 0.35
1.227
_ 58.144*UVA Ath m−
=
1.169
_ 44.075*UVA Ath m−
=
0.853
_ 18.776*UVA Ath m−
=
1.217
_ 69.534*UVA Lca m−
=
1.138
_ 50.766*UVA Lca m−
=
0.991
_ 24.921*
UVA Lca m−
=
Figure 7: Dependence of hourly UVA irradiance (W m-2) on optical air mass
(m) for three different classes of clearness index (kt) at a) Athalassa and b)
Larnaca.
Figure 6: Accumulated hourly UVA values for a mean day of each month (kJ
m-2), during the period 2013-2015 at a) Athalassa and b) Larnaca.

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 7/16
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Copyright  Kalogirou SA
e most frequent distribution of the monthly daily irradiation at
Athalassa is Type IV (almost normal with negative tail) and occurred
on 6 occasions. e second frequent type is V (narrow peak with
negative tail) and is recorded in 5 months. February is characterized
by Type I normal distribution. At Larnaca, the most frequent
distribution of the monthly daily irradiation is Type V (7 months),
with the second one of Type IV (4 months). November is characterized
by Type I normal distribution. Generally, the distribution types of the
daily UVA irradiation for each of the month of the year are similar to
those in Israel [27].
Table 6 shows the monthly average daily values of UVA and Global
irradiation as well as the daily average ratio UVA/G at both stations.
e monthly average ratios are relatively constant throughout the
year. e mean annual ratio UVA/G is 0.0570 at Athalassa and
0.0655 at Larnaca. Figure 9 compares the monthly mean daily values
of the two stations in Cyprus with two stations in Israel. UVA values
at Athalassa are comparable with those in Israel during most of the
Table 5: Statistical estimators of the daily UVA irradiation values (kJ m-2) at a) Athalassa and b) Larnaca, during the period 2013-2015.
a) Athalassa
Month N Mean CV (%) Min Q1 Median Q3 Max IQR As K P5P95 Distr. Type
1 93 515.4 27.22 106.5 411.6 551.0 622.5 732.1 210.9 -0.72 -0.18 233.5 700.5 IV
2 84 718.1 21.68 348.8 651.8 740.2 821.7 1020.8 169.9 -0.62 -0.05 390.6 945.0 I
3 93 973.2 23.78 146.1 856.7 994.4 1158.3 1353.2 301.5 -0.85 0.87 522.5 1282.9 V
4 90 1249.7 19.60 628.5 1101.3 1300.1 1414.7 1599.7 313.4 -0.76 -0.05 720.3 1568.2 IV
5 90 1407.6 20.71 321.7 1262.9 1521.2 1600.9 1742.7 338.0 -1.64 3.05 793.9 1711.7 V
6 89 1612.6 10.37 1125.1 1513.6 1673.2 1745.7 1796.8 232.1 -1.13 0.45 1264.0 1785.3 IV
7 92 1650.9 5.38 1306.6 1608.1 1665.8 1711.1 1774.4 103.0 -1.35 2.23 1468.3 1756.6 V
8 93 1467.9 6.93 1184.8 1412.7 1479.2 1532.5 1693.9 119.8 -0.51 0.28 1249.2 1628.5 IV
9 90 1140.2 14.28 590.0 1060.8 1163.2 1262.0 1439.6 201.3 -0.90 0.84 809.9 1354.3 V
10 93 869.7 19.36 363.5 764.1 906.9 990.5 1137.5 226.4 -0.82 0.40 536.2 1101.6 IV
11 89 595.7 18.69 215.2 543.1 611.8 647.7 833.2 104.6 -0.52 1.22 372.9 801.4 V
12 91 467.6 26.42 112.0 401.9 509.6 568.6 605.5 166.7 -1.14 0.54 197.3 595.2 IV
Year 1087 1056.9 42.12 106.5 638.2 1045.2 1478.8 1796.8 840.7 -0.01 -1.28 396.4 1713.8 VI
b) Larnaca
Month N Mean CV (%) Min Q1 Median Q3 Max IQR As K P5P95 Distr.
Type
1 31 676.1 22.41 206.6 583.8 706.7 766.6 930.3 182.8 -1.28 2.33 280.0 885.8 V
2 38 984.1 16.83 445.0 929.4 1011.7 1106.4 1234.7 177.1 -1.50 3.39 494.5 1218.7 V
3 62 1212.5 22.64 555.3 994.0 1235.5 1454.4 1628.0 460.4 -0.45 -0.60 707.6 1612.1 IV
4 54 1551.0 18.74 657.1 1413.4 1628.9 1772.4 1900.4 359.0 -1.27 1.42 807.0 1884.3 V
5 49 1790.9 12.23 1217.3 1664.5 1878.8 1959.4 2057.1 294.9 -1.10 0.52 1292.2 2030.3 IV
6 30 1995.8 5.86 1606.4 1991.5 2038.5 2067.7 2108.8 76.2 -2.14 4.37 1656.8 2095.6 V
7 77 1962.8 4.85 1593.0 1909.2 1964.6 2024.5 2140.2 115.3 -0.74 1.78 1803.5 2103.1 V
8 66 1798.1 5.25 1581.7 1742.1 1810.4 1872.0 1942.9 129.9 -0.46 -0.73 1626.3 1927.5 IV
9 35 1400.3 14.56 824.0 1342.0 1423.9 1501.5 1693.7 159.5 -1.15 1.82 862.6 1685.5 V
10 74 1082.8 17.24 540.2 982.3 1093.4 1229.9 1372.7 247.5 -0.70 0.42 714.6 1343.1 IV
11 82 745.2 18.72 331.2 661.8 767.8 820.1 1036.4 158.4 -0.27 0.19 485.3 974.7 I
12 62 592.3 26.61 124.6 511.0 650.2 712.2 769.5 201.3 -1.29 1.08 213.4 754.6 V
Year 660 1305.6 39.83 124.6 811.2 1292.7 1822.6 2140.2 1011.4 -0.07 -1.34 543.3 2036.3 VI
Figure 8: Annual evolution of daily and monthly UVA irradiation values (kJ
m-2) at Athalassa and Larnaca, during the period 2013-2015.

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 8/16
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Copyright  Kalogirou SA
seasons with the exception of the summer months. Larnaca shows
the highest values throughout the year. As it was indicated in the
section of the quality control the sensor is relatively unstable with
long periods of missing records. erefore, it requires recalibration.
Frequency distribution of daily UVA irradiation
e annual histogram of the frequency distribution (PDF) of
the daily UVA irradiation of both stations is displayed in gure 10,
while the cumulative frequency distribution of the same variables is
shown in gure 11. As indicated in gure 10, the type of the annual
distribution of the daily UVA irradiation is bimodal for both stations.
e PDF graphs show similarities with the highest frequencies
occurring at around 600 kJ m-2 of UVA irradiation at both stations
and a second highest in the range of 1500-1800 kJ m-2. Figure 11,
indicates that in 60% of the year, the daily sums of UVA irradiation at
Athalassa are below 1250 kJ m-2, while at Larnaca for the same value
the probability is about 50%.
Relationship between UVA and other radiation components
It can be useful to estimate UVA irradiance based on the global
irradiance ranges. e correlation between the data have been
analysed by assuming relations of the following forms:
(4)
(5)
Table 7 shows the values of the t parameters for Equations (4)
and (5) as well as the coecient of determination,
2
R
, for the hourly
(W m-2) and daily values (kJ m-2) for both stations. e characteristic
of these relationships is that the coecients of determination are
close to 1. For the model of the Equation (5) the t of the result is
given by the parameter S which is the standard error of the regression.
S is measured in the units of the response variable and represents
the standard distance the data values fall the regression line, or the
standard deviation of the residuals. For a given study, the better the
equation predicts the response, the lower the value of S. From the
table 7a, it is indicated that the results are satisfactory for estimating
UVA using both the above equations. Figure 12 shows the relationship
between UVA irradiance and global irradiance based on the Equation
(5) for Athalassa. Similar results were obtained for the estimation of
Table 6: Average daily UVA and Global irradiation (kJ m-2) and monthly mean
ratio UVA/G at Athalassa and Larnaca (2013-2015).
Daily UVA (kJ m-2) Daily Global (kJ m-2) Daily Ratio (UVA/G)
Ath Lca Ath Lca Ath Lca
Month Mean Mean Mean Mean Mean Mean
1 515.4 676.1 9358 10012 0.0551 0.0675
2 718.1 984.1 13267 14345 0.0541 0.0686
3 973.2 1212.5 17535 18573 0.0555 0.0653
4 1249.7 1551.0 22273 23921 0.0561 0.0648
5 1407.6 1790.9 24053 26383 0.0585 0.0679
6 1612.6 1995.8 27780 29527 0.0580 0.0676
7 1650.9 1962.8 27961 29261 0.0590 0.0671
8 1467.9 1798.1 24913 26300 0.0589 0.0684
9 1140.2 1400.3 20088 21679 0.0568 0.0646
10 869.7 1082.8 15511 16723 0.0561 0.0647
11 595.7 745.2 11367 11449 0.0524 0.0651
12 467.6 592.3 8784 9439 0.0532 0.0628
Year 1056.9 1305.6 18529 19926 0.0570 0.0655
UVAd_Lca Gd_Lca 0.98
UVAd_Ath Gd_Ath S=53.29
UVAd_Lca Gd_Lca S=62.21
66.202y x=
1.066
46.537y x=
1.049
56.636y x=
Table 7: a) Relationships between hourly UVAh irradiance (W m-2) and global
(Gh) irradiance (W m-2) at both stations. b) Relationships between daily UVAd
irradiation (kJ m-2) and Global (Gd) (MJ m-2) irradiation at both stations.
Variable y Variable x Equation R2 / S
UVAh_Ath Gh_Ath 0.98
UVAh_Lca Gh_Lca 0.98
UVAh_Ath Gh_Ath S=2.364
UVAh_Lca Gh_Lca S=2.789
UVAd_Ath Gd_Ath 0.96
0.0667y x=
57.266y x=
0.057y x=
1.093
0.031y x=
1.092
0.036y x=
Figure 10: Annual histogram of the frequency distribution of the daily UVA
irradiation (kJ m-2) at a) Athalassa and b) Larnaca.
Figure 9: Comparison of monthly mean daily UVA irradiation (kJ m-2) at the
two sites in Cyprus (CY) and two sites in Israel (IS).
Y aX=
b
Y aX=

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 9/16
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Copyright  Kalogirou SA
Table 8: Statistics of daily UVA irradiation (kJ m-2) based on various thresholds of daily global radiation (MJ m-2) for the period of measurements, for a) Athalassa and
b) Larnaca.
a) Athalassa
Athalassa-Daily Global Radiation Athalassa-Daily UVA radiation (kJ m-2)
Bin Endpoints (MJ m-2) Occurrences Mean Median Min Max Std. Dev.
Lower Upper
0 2 4 120.2 116.4 106.5 146.1 17.73
2 4 14 227.8 211.1 180.1 321.7 39.97
4 6 25 334.0 340.1 276.9 412.1 32.35
6 8 41 414.9 416.0 336.9 469.6 32.29
8 10 59 507.6 501.8 442.8 628.5 38.31
10 12 119 600.6 585.7 509.6 756.7 52.09
12 14 90 687.6 686.0 571.5 899.4 59.05
14 16 72 820.5 826.0 590.0 975.8 66.77
16 18 81 947.3 945.7 756.3 1131.9 67.40
18 20 64 1053.4 1058.3 859.4 1185.8 69.19
20 22 76 1193.1 1208.5 997.0 1349.2 70.29
22 24 79 1318.4 1313.9 1184.1 1487.7 75.14
24 26 91 1445.8 1458.2 1277.9 1581.3 67.59
26 28 110 1577.2 1583.1 1433.0 1693.9 57.48
28 30 106 1688.2 1696.8 1497.0 1783.8 52.77
30 32 18 1769.5 1774.4 1725.9 1796.8 18.55
b) Larnaca
Larnaca-Daily Global Radiation Larnaca-Daily UVA radiation (kJ m-2)
Bin Endpoints (MJ m-2) Occurrences Mean Median Min Max Std. Dev.
Lower Upper
0 2 2 153.4 182.1 124.6 182.1 40.66
2 4 6 261.0 263.8 206.6 331.2 57.17
4 6 4 393.4 408.3 343.0 422.2 34.82
6 8 25 510.8 497.2 445.0 621.3 47.36
8 10 28 605.1 596.3 542.9 701.2 41.92
10 12 63 709.8 706.6 602.6 871.7 48.82
12 14 68 811.8 799.6 555.3 996.6 75.66
14 16 43 967.7 967.1 852.7 1064.2 50.95
16 18 50 1078.0 1076.6 807.2 1269.0 88.04
18 20 42 1219.4 1221.4 872.2 1372.7 92.86
20 22 43 1368.6 1364.0 1182.9 1501.5 82.75
22 24 29 1506.5 1501.4 1348.0 1660.6 77.52
24 26 53 1651.2 1650.2 1518.6 1849.0 67.03
26 28 76 1818.1 1820.3 1650.3 1955.1 65.98
28 30 84 1950.2 1949.3 1821.3 2052.4 60.51
30 32 44 2041.9 2057.1 1916.2 2140.2 56.68

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 10/16
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Copyright  Kalogirou SA
Figure 11: Annual cumulative frequency distribution of daily UVA irradiation
at both stations.
the daily values of UVA (Table 7b). Generally, the constants of the
equations of the two stations are comparable.
e relationships of the UVA variables between the two stations
are shown below. e coecient of determination is high for both
relations.
Hourly data (W m-2):
_ 1.023 0.778 _
h h
UVA Ath UVA Lca= +
20.91R=
(6)
Daily data (kJ m-2):
_ 25.35 0.830 _
d d
UVA Ath UVA Lca= − +
2
0.95R=
(7)
It is also interesting to know the statistics of the daily UVA
radiation obtained from dierent daily global radiation thresholds,
since most of the stations measure global radiation. Table 8 presents
the results of the above classication. At Athalassa, the most frequent
cases occurred in the bins of 10-12 (MJ m-2) of daily global irradiation
following by the bins of 26-28 and 28-30 (MJ m-2). At Larnaca, the
values of both global and UVA irradiation are higher and the most
frequent cases occurred in the bins of 10-12 and 12-14 (MJ m-2) of
daily global irradiation following by the bins of 26-28 and 28-30 (MJ
m-2). e mean and the median values of UVA irradiation are almost
similar at both stations. It is estimated that UVA irradiation is about
Figure 12: Relationship of hourly UVA and global irradiances based on
Equation (5) at Athalassa.
5.7% of global irradiation at Athalassa (inland location) and about
6.7% at Larnaca (coastal location).
Relationships between hemispherical transmittances
In this section the relationships between the clearness
index (global hemispherical transmittance) (
t
k
) and the UVA
hemispherical transmittance (kUVA) will be examined. e clearness
index is dened as:
0
/
t
k G G=
, G being the measured global irradiance
and G0 the extraterrestrial solar irradiance, both measured on
horizontal surface and for the same interval of time [5]. In the same
way the UVA hemispherical transmittance (
UVA
k
) is dened as:
0
/
UVA
k UVA UVA=
, where UVA is the measured irradiance and
UVA0 is the extraterrestrial UVA irradiance, both measured on a
horizontal surface during the same time interval. e small ‘k’ refers
to hourly values, while the capital letter ‘K’ denotes daily values.
e daily extraterrestrial (UVAd0) irradiation is estimated from the
following equation:
0(24/ )* * [sin sin (( ) /180) cos cos sin ]
s s
scUVA
d
UVA G
π ε φ δ πω φ δ ω
= +
(8)
Where ε is the eccentricity, φ is the latitude, δ is the solar
declination, ωs is the sunset hour angle and GscUVA is the UVA solar
constant (70.64 W m-2) and it was obtained from Gueymard [41].
Figure 13 shows the histograms with the hourly values of kt. Most
of the data are concentrated in the 0.7-0.8 range at both stations. e
clearness index is mostly aected by the presence of clouds. Figure 14
shows the histograms with the hourly values of kUVA. Most of the data
are concentrated in the 0.4-0.8 range at both stations.
Figure 13: Frequency distribution of hourly clearness index (kt) at a)
Athalassa and b) Larnaca.

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 11/16
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Copyright  Kalogirou SA
Figure 14: Frequency distribution of hourly UVA hemispherical transmittance
(kUVA) at a) Athalassa and b) Larnaca.
e above results suggest that relationships can be established
between the indexes kt and kUVA. Two dierent models were
implemented. Firstly, a linear t was applied, without intercept of
the form:
t
UVA
k ak=
. Secondly, a model of the form of Equation (5)
was applied. e above models were applied for both the hourly and
daily values of the said transmittances (Table 9). As it is indicated
from the constant of the linear t, the hemispherical transmittance
kUVA is approximately 6 to 7% of the hemispherical transmittance
for the whole spectrum (kt). In the case of the linear regression, the
coecient of determination (R2) is 0.97 for the hourly values and 0.99
for the daily values, suggesting that the linear t is better than the
other models. e standard error of the regression (S) of the third
model is also low which suggests that the model could be also used
for the prediction of the kUVA transmittance. Generally, the values of
the constants of the three models of the two stations are comparable.
Table 10 shows the levels of the daily UVA irradiation based on
the classication of the daily clearness index (KT), i.e., KT>0.65 clear
days, 0.35<KT≤0.65 partly cloudy days and KT<0.35 cloudy days. e
median values of the daily UVA irradiation at Athalassa, are lower
than the mean values for the cases of cloudy and partly cloudy days,
while for the clear days they are higher. At Larnaca, the median values
on cloudy days are slightly higher than the mean values, reversing
during partly cloudy days and again higher during the clear days.
Attenuation of the UVA radiation
Table 9a: Relationships between hourly transmittance kUVA of UVA irradiance and
the clearness index (kt) of global irradiance (W m-2) at both stations.
Variable y Variable x Equation R2 / S
kUVA_Ath kt_Ath 0.97
kUVA_Lca kt_Lca 0.97
kUVA_Ath kt_Ath S=0.083
kUVA_Lca kt_Lca S=0.116
0.881y x=
1.033y x=
0.655
0.766y x=
0.720
0.932y x=
Table 9b: Relationships between the daily transmittance (
UVA
K
) and the daily
transmittance (
T
K
) at both stations.
Variable y Variable x Equation R2 /S
KUVA_Ath KT_Ath 0.99
KUVA_Lca KT_Lca 0.99
KUVA_Ath KT_Ath S=0.029
KUVA_Lca KT_Lca S=0.046
0.549y x=
1.406y x=
0.945
0.536y x=
0.771
1.261y x=
e daily UVA irradiation during the clear days is the highest
expected on the Earth’s surface and is dened as the potential UVA
irradiation (UVAp). From the monthly mean daily values of UVA
potential (UVAp), extraterrestrial (UVA0) and measured (UVA)
radiation, the ratios between these variables were estimated. e
ratio UVA/UVAp represents information about the percentage
of energy which, on the average, is transmitted by the atmosphere
and may be considered as the atmospheric transparency under
average conditions, i.e., including hydrometeors and aerosols. e
ratio of UVA potential to UVA extraterrestrial, UVAp/UVA0, gives
information about the atmospheric transparency on clear days, i.e,
without clouds but with aerosols, though in low proportion. e ratio
of UVA/UVAp, represents the observed UVA irradiation fraction
which corresponds to cloud-free sky, i.e., this attenuation is due to
cloudiness and aerosols [42-43].
Figure 15 shows the monthly average daily values of extraterrestrial
(UVA0), the potential (UVAp) and measured UVA irradiation at
Athalassa. e graph shows that the maximum of (UVA0) and (UVAp)
variables is recorded in June, but the maximum of the measured
UVA is recorded in July. e dierence between the UVAp and UVA
measured values is greater in the spring and winter time, while during
the summer the dierence is small. is is attributed to the fact that
during the summer almost all days are clear [33].
Figure 16 shows the monthly mean of the above ratios for
Athalassa. e greatest variability is shown in the ratio of UVA/UVA0.
e evolution of these ratios increases from spring to summer and
decreases from summer to winter. e maximum of UVA/UVA0 is
0.9, while the ratio UVA/UVAp is close to one in the summer.
Inter-Comparison of the Two Sites
e inter-comparison of the broad-band solar radiation intensity
measurements at both sites are reported in table 11 for the global,
UVB and UVA radiation. e solar radiation intensities are reported
as monthly average daily values, the number of days of each variable
for the period of measurements and the relative attenuation reported
for each one, which is dened as:

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 12/16
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Copyright  Kalogirou SA
Table 10: Statistics of daily UVA irradiation (kJ m-2) based on various thresholds of daily clearness index (KT) for the period of measurements, for a) Athalassa and b)
Larnaca.
a) Athalassa
KT Bin Endpoints Occurrences Daily UVA irradiation (kJ m-2)
Lower Upper Mean Median Min Max Std. Dev.
0 0.05 0
0.05 0.1 5 160.5 116.4 106.5 321.7 91.4
0.1 0.15 4 231.5 211.1 180.1 332.7 68.7
0.15 0.2 6 212.2 209.4 197.4 243.1 16.5
0.2 0.25 10 337.8 363.5 197.9 439.2 83.2
0.25 0.3 20 401.9 348.8 276.9 735.1 136.5
0.3 0.35 18 463.3 424.5 297.5 842.0 158.4
0.35 0.4 35 557.4 538.2 336.9 975.8 183.4
0.4 0.45 38 702.4 672.2 401.4 1157.4 238.4
0.45 0.5 53 716.6 688.2 398.6 1261.9 226.2
0.5 0.55 71 765.3 613.4 442.8 1378.5 298.1
0.55 0.6 103 919.1 898.3 481.7 1508.9 297.6
0.6 0.65 145 1039.6 1071.4 509.6 1590.2 343.2
0.65 0.7 328 1226.9 1369.6 534.4 1741.2 392.4
0.7 0.75 210 1390.8 1526.0 571.9 1796.8 353.1
0.75 0.8 3 1691.7 1751.0 1564.1 1760.0 110.6
b) Larnaca
KT Bin Endpoints Occurrences Daily UVA irradiation (kJ m-2)
Lower Upper Mean Median Min Max Std. Dev.
0 0.05 0
0.05 0.1 1 124.6 124.6 124.6 124.6 0.0
0.1 0.15 4 206.0 211.6 182.1 223.8 17.5
0.15 0.2 3 308.0 329.0 263.8 331.2 38.3
0.2 0.25 3 481.7 445.0 343.0 657.1 160.3
0.25 0.3 3 643.3 583.3 540.2 806.3 142.8
0.3 0.35 9 511.6 492.4 400.1 701.2 103.3
0.35 0.4 11 567.9 507.9 447.1 834.9 141.4
0.4 0.45 17 675.9 595.6 455.9 1256.1 212.9
0.45 0.5 24 798.1 745.7 489.8 1335.8 273.8
0.5 0.55 34 922.7 934.3 542.9 1479.7 265.2
0.55 0.6 44 979.4 918.0 576.7 1660.6 332.6
0.6 0.65 62 1057.4 976.6 602.6 1866.5 365.0
0.65 0.7 132 1273.9 1288.9 627.4 1995.7 454.1
0.7 0.75 273 1613.0 1774.0 647.7 2120.2 416.3
0.75 0.8 40 1660.3 1768.4 967.2 2140.2 335.0
Re (%) (( ) / )*100
Lca Ath Ath
lativeAttenuation X X X= −
(9)
where X refers the type of solar radiation, i.e., either global, UVB
or UVA. e subscripts refer to the two sites.
As indicated in table 11, the magnitudes of the monthly average
daily values of the three types of solar radiation components are
higher at Larnaca than at Athalassa. Generally, the percentages of
relative attenuation are lower during the summer period for all the
three variables. e % relative attenuation is < 10% for all months. e
dierences in altitude between the two stations are not signicant and
therefore the daily values are almost similar. However, the percentage
of relative attenuation of UVB is higher than that of UVA since the

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 13/16
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Copyright  Kalogirou SA
Table 11: Monthly average daily solar global, UVB and UVA at Athalassa and Larnaca and their relative differences.
Ath (Gd) Lca (Gd) Ath (UVBd) Lca (UVBd) Ath (UVAd) Lca (UVAd)
Month N Mean N Mean % Rel. N Mean N Mean % Rel. N Mean N Mean % Rel.
MJ m-2MJ m-2atten. kJ m-2kJ m-2atten. kJ m-2kJ m-2atten.
1 93 9.36 92 10.01 6.99 93 9.95 62 14.68 47.56 93 515.4 31 676.1 31.18
2 84 13.27 66 14.35 8.13 84 15.64 66 22.96 46.85 84 718.1 38 984.1 37.04
3 93 17.54 93 18.57 5.92 93 23.39 93 32.11 37.27 93 973.2 62 1212.5 24.59
4 90 22.27 90 23.92 7.40 90 31.84 90 43.63 37.03 90 1249.7 54 1551.0 24.11
5 77 24.05 93 26.38 9.69 90 38.87 90 52.38 34.76 90 1407.6 49 1790.9 27.23
6 82 27.78 90 29.53 6.29 89 47.97 89 60.73 26.59 89 1612.6 30 1995.8 23.76
7 92 27.96 93 29.26 4.65 92 50.59 93 60.37 19.33 92 1650.9 77 1962.8 18.89
8 93 24.91 93 26.30 5.57 93 43.77 69 52.22 19.32 93 1467.9 66 1798.1 22.49
9 84 20.09 90 21.68 7.92 90 31.66 69 42.46 34.09 90 1140.2 35 1400.3 22.81
10 93 15.51 93 16.72 7.81 93 21.12 93 28.73 36.02 93 869.7 74 1082.8 24.50
11 78 11.37 90 11.45 0.72 89 12.31 90 16.93 37.52 89 595.7 82 745.2 25.10
12 91 8.78 93 9.44 7.46 91 8.71 93 12.89 47.95 91 467.6 62 592.3 26.67
Year 1050 18.53 1076 19.93 7.54 1087 28.04 997 37.11 32.37 1087 1056.9 660 1305.6 23.53
Figure 15: Annual variation of monthly mean values of daily extraterrestrial
(UVA0), potential (UVAp) and measured UVA irradiation at Athalassa.
Figure 16: Monthly mean values of the ratios UVA/UVAp, UVAp/UVA0 and
UVA/UVA0 at Athalassa.
Mo nth 121110987654321
50
40
30
20
10
0
Rel ative A ttenuatio n (% )
Glob al
UVB
UVA
Vari able
Figure 17: Relative attenuation of solar global, UVB and UVA radiation for
Athalassa and Larnaca.
Table 12: Inter-comparison of the two sites with respect to global and UVA
radiation.
Variable Athalassa Larnaca
Location inland coastal
Annual daily average global irradiation (Gd) (MJ m-2) 18.53 19.93
Annual total global irradiation (MJ m-2) 6835 7183
Annual daily average UVA irradiation (UVAd) (kJ m-2) 1056 1316
Annual total UVA irradiation (MJ m-2) 12.74 15.95
Accumulated daily UVA irradiation in July (kJ m-2) 1650.8 2000.9
Accumulated daily UVA irradiation in December (kJ m-2) 467.5 609.4
Mean annual daily ratio of UVA/G 0.0569 0.0661
Maximum Hourly Average UVA irradiance in July (W
m-2)61.03 72.78
Maximum Hourly Average UVA irradiance in December
(W m-2)29.73 37.02
Mean annual Ratio of daily UVA/UVAp 0.886 0.923

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 14/16
Gr up
SM
Copyright  Kalogirou SA
attenuation is inversely proportional to the wavelength and therefore
greater for the shorter UVB wavelengths. e high values of relative
attenuation of the UVA radiation could be also attributed to the fact
that long periods of missing data were detected in the time series of
UVA at Larnaca. e percent relative attenuation is also presented
graphically for the three solar radiation types in gure 17.
e summary of the inter-comparison of the two sites with
respect to UVA radiation is presented in table 12.
Conclusion
Measured data at 10 min intervals, obtained by UV Kipp&Zonen
radiometers installed at two locations in Cyprus, one at Athalassa
(inland location) and the other at Larnaca (coastal location) during
the period January 2013 and December 2015, have been used to
dene the statistical characteristics of both hourly UVA irradiance
and daily UVA irradiation values.
Large uctuations in the spring and winter months are mainly
due to unstable meteorological conditions during the transition
from cold to warm weather and vice versa. During summer the
daily UVA radiation exceeds the value of 1700 kJ m-2 at Athalassa
and 2100 kJ m-2 at Larnaca, while during the winter season the lowest
maximum is about 600 kJ m-2 at Athalassa and about 770 kJ m-2 at
Larnaca. Slightly lower values were recorded in the year 2015 at both
stations which can be attributed to the higher amounts of aerosols in
the atmosphere. e year 2015 is characterized as an extremely dry
year with more frequent dust episodes over the island (dust from the
deserts of Middle East and Sahara), increasing therefore the aerosols
in the atmosphere which aect the absorption of the UVA radiation.
e accumulated UVA irradiation received in an average year is
385.8 MJ m-2 for Athalassa and 476.5 MJ m-2 for Larnaca. UVA daily
values at Athalassa are comparable with those in Israel during most
of the months. Larnaca shows the highest values throughout the year.
Furthermore, the distribution types of the daily UVA irradiation for
each of the month of the year are similar to those in Israel. e type
of the annual distribution of the daily UVA irradiation is bimodal for
both stations.
e UVA variability has been studied by means of the Coecient
of Variation (CV). It was demonstrated that the CVs in July are low
during the midday (3-9%) at both stations, indicating a high stability
along these hours in summer.
Regarding the hourly values, UVA irradiance uctuates between
22 W m-2 in December and 53 W m-2 in July at solar noon at Athalassa.
e values at Larnaca are slightly higher than in Athalassa and they
uctuate between 29 Wm-2 in December and 69 W m-2 in July at solar
noon. Solar elevation plays an important role on the levels of UVA
irradiances.
With respect to the estimation of UVA irradiance, it is indicated
that the results were satisfactory for estimating UVA from the global
irradiance values, either using linear relationships or relations of the
power form (Equation (5)). Similar results were obtained for the
estimation of the daily values of UVA. Generally, the constants of the
equations of the two stations are comparable.
e dierence between the potential UVA (UVAp) and the
measured UVA values is greater in the spring and winter time, while
during the summer the dierence is small. is is attributed to the
fact that during the summer almost all days are clear.
Two dierent models were implemented to estimate the UVA
transmittance. Firstly, a linear t was adopted, without intercept of
the form:
t
UVA
k ak=
. Secondly, a power model based of the form of
Equation (5). e above models were applied to both the hourly and
daily data. As it is indicated from the constant of the linear t, the
hemispherical transmittance kUVA is approximately 6 to 7% of the
hemispherical transmittance for the whole spectrum (kt). In the case
of the linear regression, the coecient of determination (R2) is 0.97
for the hourly values and 0.99 for the daily values, suggesting that the
linear t is better than the other models.
As indicated from the analysis, the magnitudes of the monthly
average daily values of the three types of solar radiation components
(global, UVB and UVA) are higher at Larnaca than at Athalassa.
Generally, the percentages of relative attenuation are lower during
the summer period for all the three components. e % relative
attenuation is < 10% for all months. e dierences in altitude
between the two stations are not signicant and therefore the daily
values are almost similar. However, the percentage of relative
attenuation of UVB is higher than that of UVA since the attenuation
is inversely proportional to the wavelength and therefore greater for
the shorter UVB wavelengths. e high values of relative attenuation
of the UVA radiation could be also attributed to the fact that long
periods of missing data were detected in the time series of UVA at
Larnaca.
Nomenclature
As Skewness coecient
CDF Cumulative probability density function
CV Coecient of variation (%)
G Global solar irradiance [Wm-2]
0
G
Extraterrestrial irradiance [Wm-2]
0d
G
Daily Extraterrestrial Irradiation (ETR) [MJ m-2]
Gd Daily global irradiation [MJ m-2]
Gsc Solar constant [1367 Wm-2]
GscUVA Solar constant of UVA irradiance [70.64 Wm-2]
IQR Interquartile range
K Kurtosis
t
k
Hourly clearness index (
0
/
t
k G G=
)
UVA
k
Hourly UVA transmittance (
0
/
UVA
k UVA UVA=
)
T
K
Daily clearness index (
0
/
Td d
K G G=
)
Max Maximum
Min Minimum
N Non missing observations
N* Missing observations
n Julian day number (1..365)
P5 Percentile 5%
P95 Percentile 95%

Citation: Pashiardis S, Kalogirou SA and Pelengaris A. Statistical Analysis and Inter-
Comparison of Solar UVA and Global Radiation for Athalassa and Larnaca, Cyprus.
SM J Biometrics Biostat. 2017; 2(4): 1020. Page 15/16
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Copyright  Kalogirou SA
PDF Probability density function
Q1 First Quartile
Q3 ird Quartile
S Standard error of the regression or standard deviation of
the residuals
StDev Standard deviation
UVC Ultraviolet radiation in the range of 100 to 280 nm
UVB UVB irradiance [Wm-2] / UVB irradiation [kJm-2]
UVA UVA irradiance [Wm-2] / UVA irradiation [kJm-2]
UVA0 Extraterrestrial UVA irradiance [Wm-2]
UVAp Potential UVA irradiance [Wm-2]
UVAd Daily UVA irradiation [kJ m-2]
UVAd Daily UVA irradiation [kJ m-2]
UVER UV erythema irradiance [Wm-2] / UV erythema
irradiation [kJ m-2]
UV UV irradiance [Wm-2] / UV irradiation [kJ m-2] (UV(A+B))
Greek:
z
θ
Solar zenith angle (SZA) [degrees]
δ Solar declination [degrees]
ε eccentricity correction
φ Latitude [degrees]
s
ω
Sunset hour angle [degrees]
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