
Research Article


Estimation of Global Solar Radiation on Horizontal Surface Using Routine Meteorological Measurements for Different Cities in Iraq 

Ali M. ALSalihi,
Maylaa M. Kadum
and
Ali J. Mohammed



ABSTRACT

In this study, global solar radiation received on horizontal surfaces, maximum temperatures, sun shine duration and relative humidity for Baghdad, Mosul and Rutba are presented, analyzed, tabulated and plotted on graphs and discussed for three selected locations which represents different weather condition of Iraq. Mosul in the North, Baghdad in the middle, Rutba in the West of Iraq. A correlation between the measurements of global solar radiation and meteorological parameters were given for the considered location. The correlation and regression coefficients, standard errors of estimation, mean bias error, root mean square error and tstatics are calculated. The values of correlation coefficients vary from 89% for Rutba station to 97% for Baghdad station and the error of estimation are between 0.035 and 0.063, tstatics varied between 1.2 and 2.06 for Baghdad and Rutba, respectively. It can be concluded that the presented models reasonably predict the global solar radiation received on horizontal surfaces and the expected solar radiation behavior.







INTRODUCTION
Renewable energy is considered as a key source for the future, not only for
Iraq but also for the world. This is primarily due to fact that renewable energy
resources have some advantages if compared to fossil fuels. They are, in fact,
complementary to each other and can be used effectively alone or in combinations
of two or more renewable energy sources (e.g., wind and biomass) (Salaymeh,
2006). The global radiation is an important parameter necessary for most
ecological models and an input for different solar systems. It is the ultimate
energy for all ecosystems. Although, solar radiation data are available at most
meteorological stations, but still there are stations in many region in our
country suffers from a shortage concern the solar radiation records, therefore
we present simple model with high accuracy depend on data which available in
all meteorological stations. Various models have been proposed to estimate solar
radiation by Salaymeh (2006), Jibril
(1999), Ulgen and Hepbasli (2002) and Shaltout
and Fathy (2001), several investigation (UDO, 2002;
Akpabio and Etuk, 2003; Safari and
Gasore, 2009) have demonstrated the predictive ability of the Angstrom type
oneparameter equation correlating the global solar radiation to the percentage
of bright sun shine hours in a simple linear regression form (Angstrom,
1924). In order to estimate monthly global solar radiation the maximumlikelihood
quadratic fit was employed by Poltrneanu et al. (2002).
There are many empirical formulae have been developed to estimate the solar
radiation using different meteorological parameter (Yag,
1994; Gopinathan, 1988; Ksakal
and Shafiq, 1999). Iraq geography and climate is well position for solar
energy potential and its potential is about 2600 hour per year with average
daily solar radiation is 501 W m^{2} (ALRiahi
and ALKayssi, 1998). Although, Iraq has high solar potential, the uses
of solar energy in different life sectors are very limited.
Several empirical models were development by many researchers to predict the
solar radiation for various location of the world, among these models (Kenisarian
and Tkachenkova, 1990). Also, Dincer et al. (1995)
presented the most simple model, the data in these models were correlated with
their respective ambient temperature for estimating the monthly average of daily
global solar radiation. Kenisarian and Tkachenkova (1990)
noticed that the global solar radiation and ambient temperature changes have
periodical character, although the amplitude of these changes in each location
can differ from each other significantly. They proposed relation using Fourier
series for estimating global solar radiation depending on the ambient air temperature.
Empirical models are classified in three categories: sunshine based models,
temperature based models, cloud based models (Firoz and Intikhab,
2004; Myers, 2005; Yang et
al., 2006; Muneer et al., 2007; Ridha
and Ammar, 2008). Recently, some researches on modeling solar radiation
have done in developing countries (Bashahu and Nkundabatware,
1994; Museruka and Mutbazi, 2007), but yet comparative
researches on techniques and approaches used and results are still needed.
In this study, multi linear correlation have been developed for estimation global solar radiation on horizontal surface in different cities in Iraq from a long term records of monthly mean daily maximum temperatures, sun shine duration and relative humidity for Baghdad, Mosul and Rutba. MATERIALS AND METHODS
In order to evaluate the performance of the proposed solar radiation models
for Baghdad, Mosul and Rutba for the period (20042008) a statistical comparison
is performed using the indicators, proposed by Stone (1993),
a tstatistic (t_{s}). This indicator is used with two wellknow parameters
Mean Bais Error (MBE) and Root Mean Square Error (RMSE). Both MBE and RMSE have
been employed as adjustments of solarradiation models (Soler,
1990; Halouani and Ngguyen, 1993; Mac
and Iqbal, 1984). The RMSE and MBE are defined as shown in statics quantities.
The test of MBE provides information on the long term performance of models
studied. A positive MBE value gives the average amount of overestimation in
calculated values and vice versa. The test on RMSE provides information on the
shortterm performance of the models as it allows a termbyterm comparison
of the actual deviation between calculated and measured value (Iqbal,
1983). Thus, each test by itself may not be an adequate indicator of models
performance because it is possible to have a large value of the RMSE and at
the same time, a small value for the MBE and vice versa, therefore, Stone
(1993) introduced the tstatistic as a new indicator of adjustment between
calculated and measured data, this statistical indicator allows models to be
compared and, at the same time, can induced whether or not a models estimates
are statistically significant at a particular confidence level. It can be computed
using RMSE and MBE and takes in to account the dispersion of the result. The
tstatics is defined as shown in statistics quantities.
RESULTS AND DISCUSSION
The monthly mean of daily solar radiation, sun shine duration, maximum temperature
and relative humidity, were obtained from the archives of Iraqi meteorological
office. The data covered a period of five years of daily data for Baghdad city
with latitude and longitude (33.22N°, 44.23E°), Mosul (36.32N°,
43.15E°) and Rutba (33.03N°, 40.28E°) which represented Middle,
North and West of Iraq. Unfortunate there are no data of solar radiation for
Southern region, which is represented by Basrah station. The monthly average
of daily solar radiation have been presented and employed in present paper for
each model in multi linear regression for in the following equation:
G/G_{o}= a+ b (S/S _{max})
+c T_{max}+ d RH 
(1) 
Where:
G 
= 
Monthly mean of daily global solar radiation (Mj/m^{2}/day) 
G_{0} 
= 
Monthly mean of daily global extraterrestrial solar radiation on (Mj/m^{2}/day),
this value were computed from following equation: 
From Table 13, we can summarize that the
Global solar radiation measurements (G) on horizontal surfaces have the maximum
values at all considered locations appear in June, while the minimum values
were in December, the annual average daily values for the global solar radiation
on horizontal surface at Baghdad is 18.57 M J/m^{2}/day, at Mosul is
14.75 M J/m^{2}/day and at Rutba is 18.53 M J/m^{2}/day, The
maximum temperature has higher values in July and lower in December and January
at all places.
Table 1: 
The monthly mean daily global solar radiation (G), extraterrestrial
radiation (G_{o}), clearness index (G/G_{o}), bright sunshine
(S), day length (S_{o}), ratio of bright sunshine duration to day
length, maximum temperature (T_{max}), relative humidity (RH %),
for Baghdad station 

Table 2: 
The monthly mean daily global solar radiation (G), extraterrestrial
radiation (Go), clearness index (G/G_{o}), bright sunshine (S),
day length (S_{o}), ratio of bright sunshine duration to day length,
maximum temperature (T_{max}), relative humidity (RH %), for Mosul
station 

Table 3: 
The monthly mean daily global solar radiation (G), extra terrestrial
radiation (G_{o}), clearness index (G/G_{o}), bright sunshine
(S), day length (S_{o}), ratio of bright sunshine duration to day
length, maximum temperature (T_{max}), relative humidity (RH %),
for Rutb station 

 Fig. 1: 
Monthly mean variation of global solar radiation, clearness
index, bright sunshine and S/S_{max} for Baghdad station 
 Fig. 2: 
Monthly mean variation of maximum temperature, relative humidity
for Baghdad station 
The annul mean of the maximum temperatures decrease towards the North (Mosul
station), where these values are 30.45, 28.5 and 27.8°C at Baghdad, Rutba
and Mosul, respectively. The relative humidity has the maximum in January at
all considered stations. Monthly variation of (maximum temperature and relative
humidity, global solar radiation and sunshine duration), (G/G_{o} and
S/S_{o}) are shown by Fig. 1, 3
and 5 for all considered stations, from the results is clear
that:
 Fig. 3: 
Monthly mean variation of global solar radiation, clearness
index, bright sunshine and S/S_{max} for Rutba station 
 Fig. 4: 
Monthly mean variation of maximum temperature, relative humidity
for Rutba station 
 Fig. 5: 
Monthly mean variation of global solar radiation, clearness
index, bright sunshine and S/S_{max} for Mosul station 
The monthly variation of global solar radiation and sunshine duration have
same trends where the maximum values each mentioned parameter were in June and
the minimum in January and the clearness index (G/G_{o})and (S/S_{o})have
the same behavior for all stations. Figure 2, 4
and 6 clarify that monthly variation of maximum temperature
and relative humidity has opposite behavior with all considered locations. From
Table 4, the formulae of empirical models investigated in
present study can be written as the follows:
 Fig. 6: 
Monthly mean variation of maximum temperature, relative humidity
for Mosul station 
Table 4: 
Geographic location of the selected stations and correlation
coefficients, regression coefficients, standard errors, mean bias error,
root mean square error and tstatics 

Baghdad Model:
G/G_{o}= 10.78+0.071(S/S_{0})+0.0026T_{max}0.00078RH 
(3) 
Rutba Model:
G/G_{o}=15.07+0.104(S/S_{0})+0.00139T_{max}0.00112RH 
(4) 
Mosul Model:
G/G_{o}=8.86+0.301(S/S_{0})+0.0035T_{max}+0.00157RH 
(5) 
From Table 4, we can notice that the Correlation Coefficient
(CC) at Baghdad is the best, where it is value is (97%) with standard error
(SE) of estimation is 0.035. The lowest value of CC is (89%) at Rutba and SE
is 0.0653. The values of global solar radiation estimated using the proposed
models (Eq. 57) and compared with the corresponding
measured values. The results are shown Fig. 7ac
for considered stations. The models performance examined using mean error (MBE)
and Root Mean Square Error (RMSE). The test RMSE provides in for motion on the
short term performance of the proposed model as it allows a termby term comparison
of the actual deviation between calculated and measured value. Iqbal
(1983), Halouani and Ngguyen (1993), Almorox
(2005) and Che et al. (2007) have recommended
that a Zero value for MBE is ideal and low RMSE is very desirable. According
to these supposition and from Table 4 we can considered that
Baghdad station which has the lowest values of MBE (0.002), RMSE (0.014) and
tstatics (1.2) is the better among the presented models in this study and the
indicate that Baghdad station model give the lowest overestimation for estimated
values.
 Fig. 7: 
Comparison of the measured and estimated global solar radiation
values. (a) Baghdad, (b) Rutba and (c) Mosul models, respectively 
CONCLUSION
The results of this study, clearly indicate the primary importance of developing
empirical approaches for formulating the global solar radiation on horizontal
surface reaching the earth at different geographical sites in Iraq. Baghdad
model shows a good agreement between calculated and measured values of the monthly
mean of daily global solar radiation, from the above results and considerations,
the values of the correlation coefficients vary between 97% at Baghdad and 89%
at Rutba and the standard error did not exceed 0.063. Equation
35 are used with high accuracy to estimate the global
radiation on horizontal surfaces at the selected sites using common meteorological
parameters.
NOMENCLATURE
Astronomical Quantities and Solar Quantities
δ=(23.5π/180)sin(2π284+J)/365 
: 
Solar declination (radian) 
J=1 to 365 
: 
Julian day 
φ=(2π/360)xLatitude 
: 
Latitude of the place (radian) 
ω_{s=arccos(tanφtanδ)} 
: 
Sunset hour angle (radian) 
π =4xarctan (1.0) 
: 

I_{0} =1367 W m^{2} 
: 
Solar constant 
G_{0} 
: 
Monthly average daily Extraterrestrial solar radiation (MJ/m^{2}/day) 
G 
: 
Monthly average daily global solar radiation on horizontal surface (MJ/m^{2}/day) 
S_{0}=2/15ω_{s} 180/π 
: 
Day length 
S 
: 
Daily sunshine duration (hour) 
Statistics Quantities
A, b, c, d 
: 
Coefficients of regressions 
Qmes 
: 
Measured value 
Qest 
: 
Estimated value 
N 
: 
No. of observations 
Mean bias error:
Root mean square error:
tstatics:

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