ANALYSIS
OF MONTHLY GLOBAL SOLAR RADIATION IN ERBIL-IRAQ
Hassan
S. Ibrahim*
Department
of Physics, College of Science, Salahaddin University-Erbil, Erbil, Kurdistan
Region-Iraq
Corresponding
Author Email: hassan.Ibrahim@su.edu.krd
ABSTRACT:
Solar
energy is a crucial and sustainable source of electricity that may be harnessed
for a long duration without causing pollution. Moreover, it reduces pollution,
thus improving the quality of life and reducing the cost of energy in the long
term. This study analyzes and uses the modified
Angstrőm–Prescott equation to estimate the monthly average global
solar radiation in the Erbil governorate depending on latitude
and daylight hours. The data is collected from the Agriculture Directorate
in Erbil for ten stations in different locations for the period (2016-2023).
Results show that the global solar energy in the region reaches a maximum of
8.4 kW.day-1.m-2 in the summertime and descends to a
minimum of 1.6 kW.day-1.m-2 in winter. The equation used
to estimate global solar energy is in strong agreement with measured data from
the ground base weather station, and to validate the results, mean absolute
percentage error (MAPE) and residual mean square error (RMSE) were used. They
found the value of MAPE = 4.34 -7.98 and RMSE= 0.183-0.426, indicating that the
model is suitable for estimating solar radiation.
KEYWORDS: Estimation,
Erbil, Extraterrestrial, Global, Solar energy.
1.
INTRODUCTION
Solar energy now seems more important than other forms of alternative energy
and has become a vital resource worldwide. Thus, solar energy can be considered
a major factor in air pollution reduction and environmental safety (Kassem et
al., 2018). The decline in other fuels led to a direction towards renewable
energy sources such as solar radiation because renewable energy, like solar
energy, is environment-friendly. Renewable energy is an alternative to fossil
fuels and nuclear energy. (Vecan, 2011). The solar radiation received at a
given location on the earth's surface depends on two main factors: external
solar radiation and atmospheric conditions. External solar radiation is the
amount of solar energy that reaches a horizontal surface at the top of the
atmosphere. The site's latitude determines this: the distance of the earth from
the sun and the time of year. The sun's daily cycle goes from zero at sunrise
to maximum noon light and back to zero in the evening and sunset. Angstrom made
the first attempt to calculate the total solar radiation, the monthly average
daily solar radiation, the average proportion of potential sunshine hours, and
precise day radiation at the site are all related to the original Angstrom-type
regression equation ( Duffie et al., 1980). Many researchers have attempted to
adapt or alter the original Angstrom model to estimate the amount of solar
radiation from other meteorological data at different locations worldwide due
to the absence of dependable solar radiation (Muhammad et al., 2014).
Five theoretical models that currently forecast global solar radiation in
Sokoto using relative humidity and maximum/minimum temperature as input factors
were assessed for accuracy by Aliyu and Sambo (Aliyu et.al., 1991).
If the coefficients of temperature-based empirical models were appropriately
modified, the models produced superior forecasts at all locations. Moreover,
the recently proposed models were the most precise in estimating temperature
for every station (Aksoy, 1997). AL-Salihi et al. Estimated global solar
radiation on horizontal surfaces using a model based on temperature and
relative humidity for different locations in Iraq and concluded that the
resulting models reasonably predict the global solar radiation received on
horizontal surfaces and the expected solar radiation behavior (AL-Salihi et
al., 2010). Values of extraterrestrial radiation and global solar radiation
were calculated (Abd et al.,2019) using the data on sunshine duration and
geographic location (latitude), applying the Angstrom equation. The FAO values
of the constant’s dependent on the station's location within Iraqi territory
were determined using the regression constants and b values.
A study using Artificial Neural Networks (ANNs) to forecast the daily average
solar radiation (DASR) and examine the impact of meteorological factors on DASR
in Duhok City, Iraq, was conducted. The input variables utilized were the daily
average of the relative humidity (RH), lowest temperature (T min), maximum
temperature (T max), wind speed (WS), cloud layer (CL), atmospheric pressure
(AP), and ultraviolet (UV) levels in order to determine DASR. For certain
models, the reported findings demonstrate superior predictive accuracy compared
to others. The study suggests that different meteorological conditions might
greatly impact the prediction of solar radiation (Mahdi et al., 2020). The
solar direct irradiance in Iraq was forecasted for three locations (Erbil,
Bagdad, and Basra) using an artificial neural network. The prediction was based
on seven input variables: Temperature, Precipitation, Humidity, Wind speed,
Wind direction, Sunshine duration, and Date. They reported a Root Mean Square
Error (RMSE) ranging from 2.5 to 3 (Saleem et al.,2021). The solar data
obtained from meteorological stations and satellite-derived models were
examined and compared using the PVGIS-5 geo-temporal irradiance database. The
findings unveiled substantial regional disparities in sun radiation throughout
the Iraqi Kurdistan Region. The solar radiation map indicated places with
abundant solar potential, particularly in the southern and western regions,
while also highlighting areas with limited solar energy availability, such as
mountainous or forested regions (Keya et al., 2022).
There are many weather stations in Erbil governorate, but most do not measure
solar radiation; the ones that suffer from significant records gaps and missing
data are common among them. Therefore, we suggest a simple model to estimate
data depending on latitude and sunlight duration. The global solar radiation
data estimated here can benefit solar power designers, researchers, and any
field that uses solar energy data.
2. METHODOLOGY
2.1 Study area
Erbil is a governorate located in the Kurdistan region of Iraq, situated in the
northern part of the country. The Geographical location shown in Fig.1 is
between latitudes (35o 25'N - 37o 18'N) and longitudes
(43o 19'E - 45o 08'E). The governorate consists of three
regions starting from south to northeast (a broad plane, low mountains, and a
high mountain) areas that affect the amount of rainfall that increases as it
moves north-eastward in the region as altitude increases.
Erbil is hot and dry in summer with plenty of sunshine, daylight reaching 13
hours, and cold and wet in winter, with daylight decreasing to around 4.5
hours, with short spring and autumn seasons compared to summer and winter.
2.2 Data and
Software
The solar energy recording of 10 stations
in Erbil governorate was obtained from the Directorate of Agriculture in Erbil
from 2016-2023. All calculations and plots were performed with Microsoft Excel
and map drawing with GIS Pro 3.5.
Figure 1: Map of
Erbil-Iraq governorate.
2.3 Solar Radiation
The theoretical extraterrestrial solar radiation Io
on a horizontal surface can be calculated from the following equation (Duffieet.
al., 1980):
… (1)
Where Isc is the solar constant and equal to 1367 W.m-2
(Frolich et al., 1981), n is the day of the year from January 1 to December 31,
is the latitude of
the location, 
is solar
declination angle, and ws the hour angle for the horizontal
surface is given as (Duffieet. al., 1980):
… (2)
Declination
is calculated as (Cooper, 1969):
… (3)
The day length N is the number of hours of sunshine or darkness within
24 hours on a given day. For a horizontal surface, it is given by (Duffieet. al,
1980):
= 
) … (4)
Empirical relations have been developed to forecast the monthly average global
radiation using various meteorological data. In many countries, sunshine
duration data are readily available among existing correlations. Several
algorithms have been developed based on these data to calculate solar radiation
from sunshine duration. Angstrťm created the most frequently used
approach, while Prescott later made modifications. The most practical and
extensively used correlation for estimating worldwide radiation has been the modified Angstrőm–Prescott version. The formula
is (Duffie et al., 1994):
… (5)
Here, dn is the actual monthly average daily number of hours
of bright sunshine, and Ig and Io are the
monthly average daily global and extraterrestrial radiation on a horizontal
surface, respectively, measured in kWm-2day-1, a and b
are Angstrom coefficient (also called regression
coefficient) The values of a and b are obtained from monthly
averaged data of all months of the year for a location. There are many models
that use different values of regression coefficients and equations that are
suitable for different locations and altitudes; in this research, we calculated
our own values of the regression coefficient for each location based on solar
radiation data recorded in our region that proved to be more accurate and
suitable for our purpose as will be seen in the results.
Microsoft Excel is used to calculate Io for each day
(365 days of the year). The procedure is applied on all stations; the only
difference is the latitude variable that changes each station's outcome (higher
latitudes receive less solar radiation than lower latitudes). Moreover, the
theoretical day length N is calculated from Eq. (4). Then, the monthly
average extraterrestrial solar radiation is determined. Two measurements were
taken from the station's data: the monthly average solar radiation and the
monthly average daily number of hours of bright sunshine. To find the monthly
regression coefficients for the selected station, Eq. (5) is used by plotting
between Ig/Io versus dn/N; the linear
fitting equations can be added to the scatter plot to find regression constants
a and b; Excel also provides the regression coefficient R2. The
regression constants a and b calculated from the previous step
can now be used to estimate the solar radiation at each station.
2.4 Model Validation
To evaluate the model's accuracy, we compared our model's estimated solar
radiation values with the measured solar radiation Ig values
for each station in order to evaluate the accuracy of the model. We validated
the models using the methods of residual mean square error (RMSE), mean
absolute percentage error (MAPE), and coefficient of determination (R2).
To compare estimated and measured values of solar radiation, the acceptable
ranges for Mean Absolute Percentage Error (MAPE) and Root Mean Square Error
(RMSE) are 0% to 10% for MAPE and 0 kW/m2 to 10 MJ/m2 for
RMSE. The evaluation methods commonly employed to analyze empirical models are
those described by (Nwokolo et. al. 2022) and (Ghazouani
et. al. (2022).
A good precision model is indicated by MAPE values of less than 10% (Djoman et
al., 2021) and (Zirebwa et al., 2014). The model is more accurate when its RMSE
values are closer to zero, and the optimal value is when RMSE equals zero.
The mean absolute
percentage error (MAPE) can be determined from the equation (Ghazouani et al.
(2022):
… (6)
Where Sc and Sm are the values of predicted and measured
global solar radiation, respectively and N is the total number of
values.
And the residual
mean square error (RMSE) can be determined from the equation (Ghazouani et al.
(2022):
… (7)
3. RESULTS AND
DISCUSSION
The fitting curve between vs for each station is shown in Fig. (2); the linear
equation fits are acceptable, with regression coefficients R2
ranging from 0.68 to 0.9; the purpose of these graphs in Fig. (2) is to
reconstruct Eq. (5) with custom equations for each station to be used later to
estimate the solar energy.
The monthly regression coefficients for the chosen sites are displayed in Table
1. These coefficients were derived from each station's monthly clearness index versus
sunshine duration fractions using Eq. (5), which expressed the regression
coefficients, a and b, as the linear y-intercept and gradient of
each line, respectively. The value of a, which is the intersection with
the y-axis or Ig/Io, is quite small, ranging from
-0.2772
to +0.0038, while coefficient b, or the slope of the line, ranges from 0.75 to
1.17. Differences in the values of a and b can be due to the
location factors of each station, such as altitude and neighboring buildings
and trees, in some cases, to instrument accuracy.
The use of the estimated equation listed in Table (1) enables us to calculate
the solar energy at each station location and compare it with measured values; these
graphs are useful to show how close our results are close to real values, which
can be seen in Fig. (3). The compression is made for the year of each station
for the years that have best and complete data. We can see from the graphs that
the best results are obtained in months that have low values of solar energy,
such as the months of (Oct, Nov, Dec, Jan, Feb, and Mar) where solar energy is
most affected by cloud cover while in other months when the solar energy is
high, the estimated values become less accurate but within reasonable ranges.
Finally, to evaluate our results, mean absolute
percentage error (MAPE) and residual mean square error (RMSE) are used. The
value of MAPE ranges from 4.34 to 7.98; as mentioned earlier, MAPE values less
than 10 % indicate good precision; therefore, according to our results which
are much less than 10% our estimation can be considered in good accordance with
the real values, to validate our estimate the values of RMSE is calculated
which ranges from 0.183 to 0.426 as shown in Table (2) these values are close
enough to zero to indicate the good agreement with measured values.
Table
1: Monthly regression equations and coefficients developed for selected
locations.
|
Station
|
Long.
|
Lat.
|
Altitude
|
Equation
|
R2
|
|
1
|
Balisan
|
44.5333
|
36.3959
|
885
|
y = 0.7905x - 0.0430
|
0.800
|
|
2
|
Banslawa
|
44.0900
|
36.1571
|
530
|
y = 1.1768x - 0.2772
|
0.807
|
|
3
|
Taqtaq
|
44.5830
|
35.8830
|
387
|
y = 0.7148x + 0.0038
|
0.875
|
|
4
|
Harir
|
44.3550
|
36.5475
|
655
|
y = 0.9083x - 0.1030
|
0.684
|
|
5
|
Dibaga
|
43.8050
|
35.8737
|
348
|
y = 0.9695x - 0.1772
|
0.796
|
|
6
|
Shaqlawa
|
44.3214
|
36.4056
|
980
|
y = 0.7494x - 0.0183
|
0.724
|
|
7
|
Shorsh
|
44.3828
|
36.1797
|
760
|
y = 0.8446x - 0.0772
|
0.886
|
|
8
|
Bastora
|
44.1636
|
36.3336
|
663
|
y = 0.8554x - 0.0995
|
0.856
|
|
9
|
Shamamk
|
43.9210
|
36.0246
|
345
|
y = 0.8493x - 0.0595
|
0.901
|
|
10
|
Choman
|
44.1267
|
36.6371
|
1174
|
y = 0.8561x - 0.0630
|
0.906
|
Table
2: Validating the estimated results with MAPE and RMSE.
|
Station
|
MAPE
|
RMSE
|
|
1
|
Balisan
|
5.420
|
0.223
|
|
2
|
Banslawa
|
6.481
|
0.426
|
|
3
|
Taqtaq
|
5.628
|
0.248
|
|
4
|
Harir
|
7.652
|
0.363
|
|
5
|
Dibaga
|
5.136
|
0.250
|
|
6
|
Shaqlawa
|
7.983
|
0.325
|
|
7
|
Shorsh
|
4.340
|
0.228
|
|
8
|
Bastora
|
5.076
|
0.279
|
|
9
|
Shamamk
|
5.141
|
0.183
|
|
10
|
Choman
|
6.638
|
0.350
|
Figure
2: Fitting curve between Ig/Io vs dn/N to
find the regression coefficients a and b of all stations.
Figure
3: Measured global solar energy versus estimated.
CONCLUSION
This study uses a modified Angstrőm–Prescott model for global solar
radiation at selected stations in the Erbil governorate with a calculated Angstrom coefficient suitable for each station in the
study area. The main parameters used were latitude and daylight hours for each
station. The
effectiveness of the model was assessed using two common parameters, namely
MAPE and RMSE. The values of MAPE varied between 4.34 to 7.98, whereas RMSE
ranged from 0.183 to 0.426. This indicates that the model is of high accuracy
in the estimation of solar radiation in the area.
It is also noteworthy that the Erbil governorate has high solar radiation
energy of up to 8.4 kW.day-1.m-2, which may occur in
summer and is as low as 1.6 kW.day-1.m-2 in winter. The modified Angstrőm–Prescott model, with its
calculated Angstrom coefficient that suits the study region in particular, can
be applicable to nearby regions also, with consideration of site environments
that can affect the solar energy available, such as vicinity to mountains,
buildings, trees, and such barriers that reduce the amount of solar energy
received at site location. The model can be effectively used in the design,
analysis, and performance estimation of solar energy systems and may contribute
to its enhancement and optimization in the area.
Acknowledgement
The author would like to thank Salahaddin University-Erbil for their financial
support.
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