ARTICLE IN PRESS
Renewable Energy 33 (2008) 1002–1010
www.elsevier.com/locate/renene
A simple formula for estimating global solar radiation in central arid
deserts of Iran
Ali A. Sabziparvar
College of Agriculture, Bu–Ali Sina University, Azadegan Blvd., Chrmsazi St., Hamedan 65174, Iran
Received 21 September 2006; accepted 12 June 2007
Available online 31 July 2007
Abstract
Over the last two decades, using simple radiation models has been an interesting task to estimate daily solar radiation in arid and semiarid deserts such as those in Iran, where the number of solar observation sites is poor. In Iran, most of the models used so far, have been
validated for a few specific locations based on short-term solar observations. In this work, three different radiation models (Sabbagh,
Paltridge, Daneshyar) have been revised to predict the climatology of monthly average daily solar radiation on horizontal surfaces in
various cities in central arid deserts of Iran. The modifications are made by the inclusion of altitude, monthly total number of dusty days
and seasonal variation of Sun–Earth distance. A new height-dependent formula is proposed based on MBE, MABE, MPE and RMSE
statistical analysis. It is shown that the revised Sabbagh method can be a good estimator for the prediction of global solar radiation in
arid and semi-arid deserts with an average error of less than 2%, that performs a more accurate prediction than those in the previous
studies. The required data for the suggested method are usually available in most meteorological sites. For the locations, where some of
the input data are not reported, an alternative approach is presented.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Solar energy estimation; Altitude; Number of dusty days; Mid-latitude arid deserts; Iran
1. Introduction
Solar radiation data are important tools for many areas
of research and applications in various engineering fields,
in particular for arid and semi-arid regions, where the
number of solar observation sites is poor. So far, a number
of formulas and methods have been developed to estimate
daily or monthly global radiation at different places in the
world. The availability of meteorological parameters,
which are used as the input of radiation models, is the
important key to choose the proper radiation models at
any location. Among all such meteorological parameters,
cloud cover and bright sunshine hours are the most widely
and commonly used ones to predict daily global solar
radiation and its components at any location of interest.
More sophisticated procedures such as the meteorological
radiation model (MRM) and the cloud radiation model
(CRM) have been developed by many authors (e.g. [1])
Tel.: +98 811 4227090; fax:+98 811 4227012.
E-mail address: swsabzi@basu.ac.ir
0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2007.06.015
since 1996. Gul et al. [1] tested the more common MRM
and CRM models for UK. Results showed that MRM has
some advantages over CRM, on account of its consistency
with measured data. New methods were also developed by
Chen et al. [2] for 45 stations in China, where sunshine
hours were unavailable. In another work [3], they revised
Angström and Bahel models at 86 stations in China. Using
visible data from the GOES satellite, Malik et al. [4]
prepared a set of solar maps for various places in Pakistan,
where ground-based meteorological data were unavailable.
Reddy [5] suggested the use of the number of rainy days,
bright sunshine hours, latitude and a geographical factor as
the inputs of his model. Using sunshine hours, maximum
air temperature, latitude and relative humidity, Sabbagh
et al. [6] estimated the global solar radiation at various
places. Their method was not capable of predicting the
direct and diffuse components of radiation. Rehman [7]
compared estimated daily radiation from 16 different
radiation models for 41 cities in Saudi Arabia. He used
latitude, altitude, sunshine hours and albedo in his work.
Other workers such as Al–Mohamad [8], Almorox [9] and
ARTICLE IN PRESS
A.A. Sabziparvar / Renewable Energy 33 (2008) 1002–1010
Nomenclature:
CF
(D)
DA
DN
cloud factor (see Appendix C)
Daneshyar method
day angle (rad)
day number in Julian Calendar (i.e. 1 for first of
January)
Idif
hourly diffuse radiation (MJ m2 h1)
Idir
hourly direct radiation (MJ m2 h1)
Kalt–dif height correction factor for diffuse radiation
Kalt–dir height correction factor for direct radiation
Kalt–glob height correction factor for global solar radiation
Kg
geographical factor of Sabbagh method as
suggested by Reddy [5]
L
Latitude of the location (rad)
m
total number of months in each year (i.e.
m ¼ 12 for each year)
MABE mean absolute bias error (MJ m2 day1)
MBE mean bias error (MJ m2 day1)
(MD) modified Daneshyar method
(MP) modified Paltridge method
MPE mean percentage error (%)
(MS) modified Sabbagh method
n
monthly average daily real sunshine duration
(h); measured by Campbell–Stokes sunshine
recorders
N
monthly average of daily maximum possible
sunshine duration (h)
Zhou [10] employed mainly sunshine hours to predict
surface global solar radiation for different places in the
world. Paltridge and Proctor [11] employed cloud factor
(see Appendix C) and latitude in a model which was able to
predict the direct and diffuse daily solar radiation at the
Earth’s surface. Using the above model, Daneshyar [12]
proposed his method to predict daily global radiation for
Tehran (Iran). Jafarpour and Yaghoubi [13] estimated
monthly and annual radiation for only one location in
Shiraz (Iran). In another work, Samimi [14] developed a
model by the use of Meinel and Meinel’s [15] work. To
predict the daily radiation for different places in Iran, he
applied a Sun–Earth correction factor, cloud factor and
bright sunshine hours as the main input parameters.
Following his work, Yaghoubi and Sabzevari [16] used
bright sunshine hours in order to calculate monthly
clearness Index (CI) for Shiraz, Iran. Although the
suggested models [12–14,16] can easily be used for any
location in Iran, the effects of water vapor, altitude and
dust on solar radiation are not considered in their work.
Due to the shortage of experimental radiation data in
central deserts of Iran, it seems necessary to use reliable
radiation models for the prediction of solar radiant energy.
In this work, several methods are tested against real solar
observations and the most suitable method is introduced.
1003
(NCD)
(NDD)
(P)
Qic
monthly mean total number of cloudy days
monthly mean total number of dusty days
Paltridge method
calculated monthly averaged daily radiation in
month (i) in each year
Qim
observed monthly averaged daily radiation in
month (i) in each year
Rdif
total daily diffuse radiation (MJ m2 day1)
Rdir
total daily direct radiation (MJ m2 day1)
Rest
estimated total daily radiation on horizontal
surface (MJ m2 day1)
Rext
monthly average of extraterrestrial daily solar
radiation (MJ m2 day1)
Rm
calculated total monthly global radiation on
horizontal surface (MJ m2 month1)
Ryear
calculated total annual global radiation on
horizontal surface (MJ m2 year1)
RMSE root mean square error (MJ m2 day1)
RH
relative humidity (%)
(S)
Sabbagh method
Tmax
monthly average of daily maximum air temperature (1C)
A:
Sun–Earth distance correction factor
y
solar zenith angle (deg)
f
latitude of the location (deg)
os
sunshine hour angle (deg)
cm
seasonal factor in month (m) as suggested by
Reddy [5]
It should be mentioned that the average total number of
clear-sky days in the central deserts is 242 days per year
(with maximum in summer), while the number of overcast
days is fewer than 30 days per year.
2. Data and methodology
To calculate the daily radiation for central arid deserts of
Iran, 22 meteorological stations were selected (Fig. 1) and
their meteorological data were used as the input of the
radiation models. Model validation was employed by
means of daily solar measurements observed at 6 solar
radiation sites (Table 1). For each location, the climate
types were identified according to Köppen climate classification (Table 1).
2.1. Data
Having conducted quality control and necessary statistical tests, we used different observed meteorological data
as the input of the employed radiation models (see
Nomenclature). Measured data were taken mainly from
the Islamic Republic of Iran Meteorological Office
(IRIMO) data centre [17]. The quality control of daily
global solar radiation was employed using statistical tests
ARTICLE IN PRESS
A.A. Sabziparvar / Renewable Energy 33 (2008) 1002–1010
1004
40
38
Latitude (degrees N)
36
34
32
30
28
26
46
48
50
52
54
Longitude (degrees E)
56
58
60
62
Fig. 1. Geographical location of the central arid desert meteorological sites (shown inside the dotted polygon).
(i.e. run-test; higher limits of daily sunshine hours and daily
limits of extra-terrestrial daily solar radiation of the
location).
The run-test and limit check were carried out on the
daily observed total solar radiation (TSR) data to make
sure that the data are homogeneous and the variations of
daily observed TSR are caused only by climatic influences
and not by other sources of errors (e.g. systematic errors
caused by instruments, calibration problems, data transferring, etc.).
Astronomical and geographical data were determined as
follows:
(a) the monthly average of daily maximum possible
sunshine duration (N) from Cooper [18];
(b) monthly average of extraterrestrial daily solar radiation
(Rext) and sunshine hour angle (oS) from Iqbal [19];
(c) solar constant from the Royal Meteorological Institute
of Belgium [20];
(d) and solar declination angles (d) from Spencer [21].
In calculation of solar declination angle (d) and
Sun–Earth distance correction factor, the day angles
(DA, see Nomenclature) is usually determined for the start
of the day. In this work, we modified the DA formula for
ARTICLE IN PRESS
A.A. Sabziparvar / Renewable Energy 33 (2008) 1002–1010
1005
Table 1
Geographical information and climate types of cities located at central part of Iran
No.
City
Latitude
(1N)
Longitude.
(1E)
Alt. (m)
Climate typec
Regional site code
Remarks
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Abadeh
Anar
Baft
Bam
Birjand
Esfahan
Ferdos
Garmsar
Ghom
Gonabad
Kabootar-Abad
Kashan
Kashmar
Kerman
Khoor-Biabanak
Miandeh-Jiroft
Semnan
Shahr-Babak
Sirjan
Tabass
Tehran
Yazd
31.18
30.88
29.23
29.10
32.86
32.67
34.02
35.20
34.70
34.35
32.52
33.98
35.33
30.25
33.78
28.58
35.55
30.10
30.47
33.60
35.68
31.90
52.67
55.25
56.58
58.35
59.20
51.87
58.17
52.27
50.85
58.68
51.85
51.45
58.47
56.97
55.03
57.80
53.55
55.13
55.68
56.92
51.32
54.40
2030
1409
2280
1067
1491
1601
1250
825
877
1056
1545
982
1110
1754
845
601
1171
1834
1739
711
1190
1230
BWhf
BWh
BSke
BWh
Md
BWkg
BWh
BWh
BWk
M
BWk
BWh
M
BWh
BWh
BWh
BWh
M
BWh
BWh
M
BWh
40818
40839
40853
88179
40809
40802
40792
40758
40770
40778
40803
40785
40763
40841
40789
–
40757
40849
88175
40791
40754
40721
SSa
SS
SS
SS
(*)b
(*)
SS
SS
SS
SS
SS
SS
SS
(*)
(*)
SS
SS
SS
SS
(*)
(**)h
(*)
a
SS: synoptic station.
(*): Solar radiation site.
c
Based on Köppen’s climate classification.
d
M: marginal climate.
e
BSk: semi-arid Steppe.
f
BWh: hot arid desert.
g
BWk: cold arid desert.
h
(**): because of the marginal climate, this station was not considered in calculation of the errors.
b
mid–day (real solar time of 12:00), where the major total
daily radiation is received [22]:
DA ¼ 2p ðDN 0:5Þ=365.
(1)
2.2. Methods
2.2.1. Method1. Sabbagh method (S)
This model which is described in [6] might be applicable
to dry arid and semi-arid regions such as Iran.
n RH0:333
1
Rest ¼ 0:06407ðK g Þ exp L
,
(2)
12
T max
100
where Rest is the estimated total daily global radiation
(MJ m2 day1) at a horizontal surface and (Kg) is the
geographical and seasonal factor described in Appendix
A.5 [5]. Though the Sabbagh model is able to take into
account the effect of relative humidity on the diffuse
radiation, it is incapable of considering the effect of dust on
incoming solar radiation. In addition, the model is only
reliable for locations with an average mean sea level of
about 300 m [6] and needs to be modified for arid regions
with higher altitudes.
2.2.2. Method 2— Paltridge method (P)
This model is able to determine the instant and total
daily radiation at any location of interest. This model,
which takes the solar zenith angle (y), daylength (N ) and
cloud factor (CF) as inputs, was suggested by Paltridge and
Proctor [11]. Their model assumes that the effect of albedo
and aerosol optical air mass on surface radiation is small
(less than 5%). In their model, the total daily global
radiation was computed from Eqs. (3) and (4):
Rest ¼ Rdir þ Rdif ,
Z
(3)
Z
sunset
sunset
I dir ðyÞ cos y dt þ
Rest ¼ ð1 CFÞ
sunrise
I dif ðyÞ dt.
sunrise
(4)
In this work, the time interval for integrating the daily
global radiation is 15 min and the units of Rest for all
equations are in (MJ m2 day1). The details of Eq. (4) are
described in [11].
2.2.3. Method 3— Daneshyar method (D)
Following Paltridge and Proctor’s [11] work, Daneshyar
[12] proposed his method by defining new coefficients for
diffuse radiation adjusted for the climate conditions of
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A.A. Sabziparvar / Renewable Energy 33 (2008) 1002–1010
1006
Tehran (Iran):
I dir ¼ 3:42286½1 exp ð0:075ð90 yÞÞ,
(5)
I dif ¼ 0:00515 þ 0:00758ð90 yÞ þ 0:43677CF:
(6)
The hourly direct and diffuse radiation is calculated
from Eqs. (5) and (6). Accordingly, the total daily radiation
estimated, using time steps of 15 min, is
Z sunset
½3:42286½1 exp ð0:075 ð90 yÞÞ
Rest ¼ ð1 CFÞ
sunrise
Z sunset
½0:00515 þ 0:00758 ð90 yÞ
cos y dt þ
sunrise
þ0:43677CFdt.
ð7Þ
2.2.4. Method 4— modified Sabbagh method (MS)
In method 4, we made the following modifications to the
Sabbagh model:
(1) height correction factor, (2) Sun–Earth distance
correction factor and (3) inclusion of monthly total number
of dusty days. In this research, the reference height (href) is
taken as 0.265 km (the average altitude of the cities where
the model was tested by Sabbagh et al. in 1977) and the
height correction factor was determined according to
Rehman [7]. For this work, an annual mean height
gradient of 2% per km is used (1.5% per km for summer
time and 2.5% per km for winter time due to the larger
optical air mass).
Therefore, the height correction factor (kaltglob) for any
location with (h) km above sea level is defined as
K altglob ¼ ½1 þ 0:02ðh href Þ.
(8)
To employ the seasonal variations of the Sun–Earth
distance, the Sun–Earth distance factor of Duffie and
Beckman [23] was adopted. Although the day-to-day
changes in the Sun–Earth distance factor are less than
0.5%, we replaced (DN) by (DN-0.5) because a large
percentage of solar energy is received during mid-day
(Eq. (9)):
K ¼ 1 þ 0:033 cos ð2pðDN 0:5Þ=365Þ
(9)
Though the mean annual astronomical daylength (N ) is
similar everywhere (i.e. 12 h), above the subtropical
latitudes (i.e. lat.4301) the seasonal variation of daylength
could be significant during the year [19], suggesting that for
the mentioned latitudes, application of (n/12) in Sabbagh
formula may lead to overestimation of solar energy in
summer and underestimation in winter months. For this
reason, in MS method, (n/12) was replaced by the relative
sunshine hour (n/N),
Rest ¼ 0:06407ðK Þ ðK altglob Þ ðK g Þ
n RH0:333
1
.
exp L
N
T max
100
ð10Þ
To consider the effect of dust on incoming solar
radiation, we applied the monthly mean total number of
dusty days (NDD) in Eq. (10) as follows:
a
ðK Þ ðK altglob Þ ðK g Þ
Rest ¼ 0:06407 1 þ
NDD þ 1
n RH0:333
1
b NDD .
exp L
N
T max
100
ð11Þ
To determine the coefficients of (a) and (b) in Eq. (11),
we fitted the model results to the observed experimental
data at each solar site so that the least discrepancies
between the model results and the experimental data were
obtained. This procedure was accomplished for the daily
radiation for each solar site (i.e. each set of data contains
up to 13 years, 12 months and 365 days measured and
the model predicted radiation data) and the mean values
of (a) and (b) for all solar sites were determined.
Consequently, the final formulation for the MS method is
suggested as
0:066
Rest ¼ 0:06407 1 þ
ðK Þ ðK altglob Þ ðK g Þ
NDD þ 1
n RH0:333
1
0:011:NDD .
exp L
N
T max
100
ð12Þ
2.2.5. Method 5— modified Daneshyar method (MD)
In this work, we made the following modifications to the
Daneshyar method. (1) In methods (P) and (D), solar
constant of 1353 (W/m2) has been used by the workers.
Since the new suggested average value of solar constant is
about 1367 (W/m2) [20], the total daily global radiation
(Rest) was multiplied by a factor of 1.01. (2) For each
month, the monthly mean global radiation was modified by
the Sun–Earth distance correction factor (Ke), the same as
method 4. (3) Height effect was also applied separately on
direct and diffuse radiation. For calculation of the height
correction factor in the MD method, Tehran (where
Daneshyar calibrated his suggested model) is taken as the
reference (Eqs. (13) and (14)).
For the central deserts of Iran, in which the bright
sunshine hours are high and annual mean ratio of direct-toglobal radiation is large (0.67 for winter and 0.82 for
summer), the annual mean values of 7% (per km) and 10%
(per km) were defined as height gradients (Eqs. (13) and
(14)) for direct and diffuse radiation, respectively [24].
These values are applicable for regions classified as arid
and semi-arid climates, with altitudes less than 4 km [25].
As a result, in this method, the following altitude factors
were applied to the direct and diffuse radiation:
K altdir ¼ ½1 þ 0:07ðh href Þ at l ¼ 400 nm;
(13)
K altdif ¼ ½1 0:10ðh href Þ
(14)
at l ¼ 400 nm;
where (h) is the height of the location and (href) is
the reference height (altitude of Tehran) in km. Therefore,
in the MD method, the final formulation for estimation of
ARTICLE IN PRESS
A.A. Sabziparvar / Renewable Energy 33 (2008) 1002–1010
monthly average total daily global radiation in arid
deserts is
Rest ¼ ð1:01Þ ðk Þ ðð3:42286Þ ð1 CFÞ ðK altdir ÞÞ
Z sunset
½1 exp ð0:075ð90 yÞÞ cos y dt þ ðK altdif Þ
sunrise
Z sunset
½0:00515 þ 0:00758ð90 yÞ þ 0:43676CFdt .
sunrise
ð15Þ
2.2.6. Method 6— modified Paltridge method (MP)
Similar to method 5, the same modifications were made
to the modified Paltridge–Proctor method. As a result, the
final formulation suggested for the estimation of daily
radiation by (MP) method is presented by
Rest ¼ ð1:01Þðk Þ ð3:42286ÞðK altdir Þ ð1 CFÞ
Z sunset
½1 expð0:075ð90 yÞÞ cos y dt þ ðK altdif Þ
sunrise
Z sunset
½0:00912 þ 0:01252ð90 yÞ þ 0:72320CF dt
sunrise
ð16Þ
Please see Appendix B and Table 2 for calculations of
monthly mean radiation.
3. Results and discussion
Using different revised radiation models, we estimated
the monthly mean daily global solar radiation for 22
locations (Fig. 1) in central arid and semi-arid deserts of
Iran. The predicted solar data have been compared against
a long-term (up to 13 years) experimental daily radiation
observed at 6 solar sites. Model validation was made by
Table 2
Representative days in each month used for monthly mean calculations
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Day
17
15
16
15
15
11
17 16
16
16
15
11
1007
means of mean bias error (MBE), RMSE, mean percentage
error (MPE) and MABE (see Appendix A) statistical
criteria [7]. MBE and MPE show the deviations between
the measured and the simulated radiation, which have to be
kept as minimum as possible to select the best method.
For each method, the averages of errors (MABE, MBE,
RMSE, MPE) between the model results and the observed
data were computed (Table 3). As shown in Table 3, the
new suggested formula MS, yields the best estimation for
arid and semi-arid deserts (MPE error of less than 2% on
average). The magnitudes of other errors (MBE, MABE,
RMSE) for the MS method are also the least. Furthermore,
the differences (residuals) between the solar radiant energy
predicted by the suggested formula and the actual
measurements show a nearly normal distribution (not
shown here), compared with other methods. In contrast,
the MP method with MPE error of more than 11% yields
the worst estimation. According to the errors presented in
Table 3, if RH and Tmax are not available to be employed
in the MS method, the MD method can be a good
alternative for modeling the global solar radiation in desert
regions.
Table 4 shows the total monthly solar energy for the
selected sites. The predicted total annual energy varies
between 6730 (Semnan) and 7788 MJ m2 yr1 (Bam). This
suggests a meridional global radiation gradient of about
2.4% per latitude degree for the central deserts, which is
less than those determined for humid and mountainous
climates [25].
The annual distribution of solar energy (Table 5) implies
that about 35% of total energy is received in summer,
which is very different from that in winter (16%). As
illustrated in Table 5, on average, the ratio of incoming
summer to winter energy is about 2.2. This emphasizes
that, owing to significant temperature differences between
summer and winter, electric energy consumed by cooling
and heating appliances in summer and winter of midlatitudes arid deserts can be significant, unless renewable
solar or wind energy is replaced. This is in consistence with
the work of Ardehali [26] who suggested the development
of solar energy plants for the central desert plateaus of
Iran.
Table 3
Minimum, maximum, and mean values of errors for central deserts of Iran obtained from 6 methods
Models
Sabbagh
Paltridge
Daneshyar
Modified Sabbagh
Modified Paltridge
Modified Daneshyar
RMSE
MBE
MABE
MPE(%)
Min
Max
Mean
Min
Max
Mean
Min
Max
Mean
Min
Max
MMean
1.41
2.58
1.13
1.55
4.44
0.98
2.60
3.77
1.77
4.82
4.79
0.61
1.78
3.28
1.46
0.80
4.29
0.94
0.45
0.87
1.56
1.52
1.38
1.37
1.41
2.75
0.17
1.08
3.37
0.06
1.21
1.94
0.59
0.18
2.57
0.40
1.49
2.15
0.87
1.24
3.36
0.74
2.08
2.94
1.55
3.99
3.73
0.80
1.66
2.55
1.22
0.52
3.40
0.81
1.9
3.9
7.3
6.9
6.7
-0.6
7.3
13
1.9
6.4
16.5
-6.2
5.4
8.9
3.7
1.1
11.8
2.4
Units of RMSE, MBE and MABE are in MJ m2 day1.
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1008
Table 4
Best estimation of total monthly global solar radiant energy (MJ m2 month1)a received on horizontal surface
No.
City
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Abadeh
Anar
Baft
Bam
Birjand
Esfahan
Ferdos
Garmsar
Ghom
Gonabad
Kabootar-Abad
Kashan
Kashmar
Kerman
Khoor-Biabanak
Miandeh-Jiroft
Semnan
Shahr-Babak
Sirjan
Tabass
Tehran
Yazd
429.5
423.3
411.8
436.1
382.2
376.8
362.4
361.4
357.7
345.9
388.6
348.0
353.7
404.0
384.5
402.3
346.0
417.2
424.6
378.0
342.7
384.5
442.8
433.4
435.3
445.1
390.8
399.9
377.4
366.6
367.1
357.7
415.0
367.1
357.0
418.9
398.8
398.0
359.7
398.5
438.4
390.2
357.8
409.1
520.7
511.8
480.1
526.6
479.1
497.9
468.3
456.5
456.9
455.6
490.9
450.9
439.4
503.5
500.3
487.1
446.1
501.9
505.8
486.5
446.4
486.1
573.0
585.4
573.9
586.0
554.7
554.7
554.5
526.3
517.7
520.2
549.7
523.2
522.1
573.8
576.3
590.8
514.3
576.5
592.9
559.2
518.5
547.1
731.4
742.4
754.2
753.6
728.3
702.8
706.5
665.3
668.0
700.1
694.2
651.5
681.2
736.2
715.2
735.4
646.0
757.9
752.7
710.1
673.4
706.9
862.6
853.7
845.7
858.5
840.7
834.1
841.4
743.3
828.0
804.7
809.1
767.6
768.5
855.3
825.5
831.1
784.3
882.5
870.1
821.7
812.9
839.1
898.5
936.6
854.3
910.8
854.0
900.5
908.2
799.1
757.9
900.5
889.4
847.1
879.1
929.7
914.1
857.5
843.9
918.4
899.2
889.4
871.7
893.0
858.2
929.3
861.9
905.7
898.2
854.2
890.2
836.6
785.7
860.4
854.7
807.1
852.2
898.8
874.9
832.8
810.9
876.6
867.7
861.1
835.8
875.6
793.5
821.1
775.0
813.8
798.4
785.9
790.1
734.7
761.4
773.3
743.7
776.9
753.8
831.3
791.6
758.2
735.1
789.6
813.3
781.5
754.7
806.7
589.5
611.1
601.7
637.8
610.9
581.2
560.5
534.8
540.9
554.7
549.5
527.4
560.8
624.4
597.6
616.2
529.5
621.7
626.9
589.4
558.5
597.0
449.6
463.8
465.8
491.9
447.6
425.1
427.2
390.5
394.3
416.4
417.7
385.8
414.0
476.7
433.1
476.0
388.8
468.4
473.6
427.0
392.7
437.1
393.1
387.2
383.8
422.0
366.0
352.2
332.9
331.3
329.8
337.1
346.2
329.7
333.7
389.3
364.1
384.0
325.8
381.5
375.5
355.2
324.2
367.7
a
Unit conversion: (cal. cm2) ¼ (MJ m2) (23.88).
Table 5
Seasonal distribution (in percent) of global solar radiation in central deserts of Iran
No.
City
Winter (%)
Spring (%)
Summer (%)
Autumn (%)
Sum/wint (ratio)
Spr/Aut (Ratio)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Abadeh
Anar
Baft
Bam
Birjand
Esfahan
Ferdos
Garmsar
Ghom
Gonabad
Kabootar-Abad
Kashan
Kashmar
Kerman
Khoor-Biabanak
Miandeh-Jiroft
Semnan
Shahr-Babak
Sirjan
Tabass
Tehran
Yazd
16.8
16.2
16.5
16.7
15.5
15.5
14.9
15.7
15.6
14.8
16.1
15.4
15.1
15.9
15.6
16.1
15.3
15.8
16.2
15.5
14.9
15.8
24.2
23.9
24.3
24.0
24.0
24.2
24.0
24.4
24.3
23.9
24.3
24.0
23.8
23.7
24.3
24.6
23.9
24.2
24.2
24.2
23.8
23.7
34.7
35.3
34.4
34.3
35.3
35.6
36.6
35.3
35.1
36.5
35.7
35.7
36.1
35.1
35.4
34.2
36.2
35.3
34.5
35.5
36.6
35.5
24.3
24.6
24.8
25.0
25.3
24.7
24.6
24.6
25.1
24.8
23.9
24.9
25.0
25.3
24.7
25.1
24.6
24.8
25.0
24.8
24.8
25.0
2.07
2.19
2.08
2.05
2.28
2.29
2.46
2.25
2.25
2.47
2.22
2.32
2.39
2.21
2.28
2.13
2.36
2.24
2.13
2.29
2.46
2.25
1.00
0.97
0.98
0.96
0.95
0.98
0.97
0.99
0.97
0.96
1.01
0.96
0.95
0.94
0.98
0.98
0.97
0.98
0.97
0.98
0.96
0.95
The last two columns are the ratio of summer to winter and spring to autumn solar energy.
4. Conclusions
The results show that the inclusion of altitude and dusty
days in simple radiation models can reasonably improve
the solar radiation prediction (by up to 12% in the short
term) in mid-latitude arid deserts. The evaluation of the
model results against the experimental data shows that the
modified Sabbagh method (MS) performs the best estimation (mean error of about 2%) in arid and semi-arid
regions if the number of dusty days (NDD) is included in
the model. The model results also indicate that in midlatitude desert regions, the summer time incoming solar
ARTICLE IN PRESS
A.A. Sabziparvar / Renewable Energy 33 (2008) 1002–1010
radiation is by a factor of 2 higher than the radiation
received during winter. Furthermore, the geographical
variation of global solar radiation of about 2% per
100 km (estimated in this work for the arid deserts)
suggests that in such regions, a dense network of expensive
solar radiation observation sites is not very necessary for
climatological studies.
Because of the dependence of relative humidity (RH) to
ambient air temperature, radiation models such as MS and
S methods may not show the actual effect of water vapor
on incoming solar radiation. Further investigations are
necessary for replacing RH with some independent (i.e.
dew point temperature, mixing ratio, etc.) meteorological
parameters. According to Table 3, for the locations where
sunshine duration (n) are not observed, prediction by the
modified Daneshyar method (MD) that only requires cloud
data (are available easily by satellites and ground-based
measurements) can be a good alternative for the similar
regions. The new height-dependent radiation model MS,
which is suggested in this work, is only valid for arid and
semi-arid climates (BWk, BWh and BSk) and may not be
suitable for other types of climates. To test the models in
other climates, future work is needed.
Acknowledgments
The author thanks the Iranian Meteorological Office
(IRIMO) Data Centre for providing the requisite data. The
author also thanks Dr. Ann Webb from the University of
Manchester, School of the Environment, UK, Dr. Sun
Zhian from Bureau of Meteorology Research Centre,
Melbourne (Australia) and the anonymous reviewers for
their useful comments before the final submission. This
work was funded as a part of a National Research Project
by the IRIMO Research Department under Contract No.
IRIMO/DB/ 1503-26-14.
1009
Appendix B. Calculation of monthly mean daily solar
radiation
To reduce the CPU time in calculating the monthly mean
daily solar radiation, normally, the mid-month (i.e. day 15)
of each month is selected as the representative mean of that
month. Since the variation of solar parameters during the
course of the year is not linear, in the present work, a day is
defined as the representative of the monthly mean
according to the seasonal variations of solar declination
angle (d), daylength (N) and daily extraterrestrial solar
radiation (Rext). The results which are presented in Table 2
show 1–2 day differences in some months with those
previously presented by Klein [27]. With the exception of
June and December periods, taking the mid-month (i.e.
15th or 16th ) as the representative of the monthly mean
can be reasonable for the model calculations.
Appendix C. Calculation of cloud factors (CF)
Cloud factors (CF) are not directly reported by Iranian
meteorological office (IRIMO). This parameter could be
obtained by using numbers of cloudy days in each month
and cloud cover. The monthly mean cloud cover is
observed in three different ranges: 0–2 octas, 3–6 octas
and 7-8 octas. To convert the cloud cover to cloud fraction
(CF), the following relationship is used [14]:
CF ¼
ðNCD02 Þ þ 4:5 ðNCD36 Þ þ 7:5 ðNCD78 Þ
,
8 ðNCD02 þ NCD36 þ NCD78 Þ
(C.1)
where NCD02, NCD3–6 and NCD7–8 are the total number
of days in each month, with zero to 2/8, 3/8–6/8 and 7/8–8/
8 cloud cover, respectively.
References
Appendix A
MABE ¼
m X
Q Q =n,
ic
im
(A.1)
i¼1
MBE ¼
m
X
ðQic Qim Þ=n,
(A.2)
m
X
Q Qim
ð ic
100Þ=n,
Qim
i¼1
(A.3)
i¼1
MPEð%Þ ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
m
X
ðQic Qim Þ2 =n,
RMSE ¼
(A.4)
i¼1
K g ¼ 100ðlN þ cm cos LÞ,
(A.5)
l ¼ 0:2=ð1 þ 0:1LÞ.
(A.6)
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