relationship between the global solar radiation and the sunshine ...

Ozean Journal of Applied Sciences 5(3), 2012
Ozean Journal of Applied Sciences 5(3), 2012
ISSN 1943-2429
© 2012 Ozean Publication
RELATIONSHIP BETWEEN THE GLOBAL SOLAR RADIATION AND THE
SUNSHINE DURATION IN ABUJA, NIGERIA
Yakubu D.* and Medugu D. W.**
*Federal Ministry of Power, Abuja
**Department of Pure and Applied Physics, Adamawa State University, Mubi.
*E-mail address for correspondence: donald.yakubu@ymail.com
____________________________________________________________________________________________
Abstract: In this paper, Angstroms model have been developed to estimate global solar radiation at Abuja, Nigeria.
Correlation between measured and estimated values of global solar radiation was determined over the period of
fifteen years (1991 – 2005). A good agreement was observed between the measured and the predicted values. It was
found that utilizing only the relative sunshine hours and the location parameters gave the best overall estimate of the
predicted solar radiation. The regression coefficient a and b were found to be 0.30 and 0.53 respectively. The
dependency of the developed equation was tested in terms of mean bias error (MBE), and root mean square error
(RMSE) which were found to have low error values as expected. From the result obtained, the solar radiation in
Abuja varies between 16.73 MJm -2 day -1 in August to 25.02 MJm -2 day -1 in March throughout the seasons of the years
with the average value being 20.75 MJm -2 day -1 . This can be utilized very efficiently for predicting the performance of
solar devices in Abuja- Nigeria.
Keywords: Angstroms Model; Global Solar Radiation; Correlation; Regression Coefficient.
______________________________________________________________________________________________
INTRODUCTION
Renewable energy is considered as a key source for the future, not only for Abuja, Nigeria 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 like wind and biomass (Salaymeh, 2006).
All human cultures require the production and use of energy—that is, resources with the capacity to produce work or
power. Energy is used for transportation, heating, cooling, cooking, lighting, and industrial production (Offiong
2003). In fact, energy is the lifeblood of economies around the world and global economic growth depends on
adequate, reliable and affordable supplies of energy (Chineke at el, 2007).
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Ozean Journal of Applied Sciences 5(3), 2012
Solar energy occupies one of the most important places among the various possible alternative energy sources. It is
the energy provided by the sun. Nigeria receives abundant solar energy that can be usefully harnessed with an annual
average daily solar radiation of about 5250 Whm -2 day -1 . This varies between 3500 Whm -2 day -1 at the coastal areas
and 7000 Whm -2 day -1 at the northern boundary. The average amount of sunshine hours all over the country is about
6.5 hours (Chineke and Igwiro, 2008).
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. Information on global solar radiation received at any site
(preferably gained over a long period) should be useful not only to the locality where the radiation data is collected
but also for the wider world community (Akpabio et al, 2002). A global study of the world distribution of global
solar radiation requires knowledge of the radiation data in various countries and for the purpose of worldwide
marketing, the designers and manufacturers of solar equipment will need to know the average global solar radiation
available in different and specific regions (Medugu et al, 2011).
Obviously, measured data is the best form of this knowledge. Unfortunately, there are very few meteorological
stations that measure global solar radiation, especially in developing countries. For such stations where no measured
data are available, the common practice is to estimate global solar radiation from other measured meteorological
parameters like relative sunshine duration. Some works used the sunshine duration (Menges, 1998) others used the
relative humidity and temperature (Layi et al,1994), while others used the number of rainy days, sunshine hours and
a factor that depends on latitude and altitude (Lewiw et al, 1992).There are several correlations available for such
estimation in developing countries (Burari and Sambo, 2001).
The objective leading to this paper is to continue in the effort to develop predictive techniques for as many regions as
possible to provide a basis for future regional (sub-saharan) iso-radiation maps. The correlation developed in this
paper is that suggested by angstroms models type regression equation and will then be used to estimate global solar
radiation for places where only sunshine records are available. Since facilities of recording global solar radiation data
are not easily available probably because of lack of maintenance culture or lack of trained personnel to take
measurements or delay in repair in case of instrument failure. Abuja has been chosen for this paper due to its climatic
condition which varies significantly with the season of the year.
METHODOLOGY
Abuja, the capital of Nigeria, is located in the middle of the country. Situated on latitude 8°23'N of the Equator,
longitude 6°12‘E of the Green witch Meridian and elevation of about 70m above sea level. Abuja is in tune with
nature with abundant hills, highlands and other distinguishing features that make it a delight to behold.
The global solar radiation and sunshine duration data presented in this paper were supplied by the Nigerian
Meteorological Agency (NIMET), Abuja, Nigeria for the period of fifteen years (1991 – 2005).
Various climatic parameters have been used in developing empirical relations for predicting the monthly average
global solar radiation (Massaquoi, 1988). Among the existing correlations, the following relation is the generally
accepted modified form of the Angstrom-type regression equation, relating the monthly average daily global
radiation to the average daily sunshine hours (Duffie et al, 1994):
H
H
0
a b
S
S o
Regression Equation (1) has been found to accurately predict global solar radiation in several locations (Rietveld,
1978). Here, the monthly average daily global radiation on a horizontal surface (MJm -2 day -1 ), is the
monthly average daily extraterrestrial radiation on a horizontal surface (MJm -2 day -1 ),
is the monthly average daily
1
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Ozean Journal of Applied Sciences 5(3), 2012
number of hours of bright sunshine,
(or day length) and a; b are regression constants to be determined.
is the monthly average daily maximum number of hours of possible sunshine
The extraterrestrial solar radiation on a horizontal surface was calculated from the following equation (Duffie et al,
1994)
H
o
24x3600
I
sc
dn
2
s
1
0.033cos360
sin
sin cos
cos sin s
365
360
2
where dn is the Julian day number, I SC = 1367 Wm -2 is the solar constant, is the latitude of the location, is the
declination angle given as
and
284 dn
23.45sin360
3
365
is the sunset hour angle given as
cos 1 tan
tan
The maximum possible sunshine duration is given by (Akpabio, 1992):
2
2
S cos
1
o
tan
tan
5
15
15
In this paper, and were computed for each month by using Equations (2) and (5), respectively. The regression
coefficients a and b in Equation (1) have been calculated from values of and . The values of the monthly
average daily global radiation
and the average number of hours of sunshine were obtained from daily
measurements covering a period of 15 years. The regression coefficient a and b have been obtained from the
relationship given as (Tiwari et al, 1997):
a 0.110
0.235cos
0.323( S / S
b 1.449 0.553cos
0.694( S / S
To compute estimated values of the monthly average daily global radiation, e , the values of a and b were used in
Equation (1).The deviation between the estimated and measured values was determined using the following
statistical parameters (Nguyen et al, 1997):
o
)
o
)
H
4
6
Mean Bias Error (MBE);
MBE
Root Mean Bias Error (RMBE);
N
i
1
H
m
H
N
e
8
9
RMBE
N
i
1
H
m
H
N
e
2
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Ozean Journal of Applied Sciences 5(3), 2012
Where i = 1, 2, 3,……..,N and N was the total number of observation points;
monthly average daily global radiation .
H
m
, is the measured values of the
The calculated and measured valued of average daily global radiation on the horizontal surface were compared. The
results are as shown in Tables 1.
RESULTS AND DISCUSSION
The average numbers of hours of sunshine were obtained from daily measurements covering a period of 15 years.
From Table 1, the overall average clear index ( ) was computed and substituted into equation 6 to obtained the
values of the regression coefficients a and b as 0.30 and 0.53 respectively. The values of a and b were substituted
into equation 1 which gives the model for computing the estimated global solar radiation shown in Table 1.
The RMSE, which is a measure of accuracy of estimation, was found to be 3.58% as low as expected. The
correlation between measured and estimated global solar radiation at Abuja is shown in Table 1. It is indicated that
our model is suitable for the estimation of monthly average daily global radiation, from monthly average daily
sunshine hours in the guinea savannah climatic zone of Nigeria. It is observed from the results that the percentage
error between the measured and predicted values rarely exceeds 11.16% and, in general, is very low as expected.
Table 1: Monthly Mean Values of Daily Global Solar Radiation and the Meteorological Parameters
for Abuja for the Period of ten years (1991 – 2005)
Month (hr) (hr)
Error %
(MJm -2 day -1 ) (MJm -2 day -1 ) (MJm -2 day -1 )
Jan
6.62
11.52
0.57
32.02
21.78
19.35
11.16
Feb
7.71
11.55
0.67
32.13
23.14
21.01
9.2
Mar
9.63
11.69
0.82
33.96
25.61
25.02
2.32
Apr
8.17
11.91
0.69
36.06
23.53
23.93
-1.7
May
7.23
12.15
0.60
37.08
21.67
22.82
-5.31
Jun
6.32
12.35
0.51
36.85
19.46
21.05
-8.17
Jul
4.44
12.47
0.36
36.47
15.74
17.82
-13.21
Aug
3.61
12.45
0.29
36.87
14.92
16.73
-12.13
Sep
4.39
12.30
0.36
37.80
18.04
18.49
-2.49
Oct
5.71
12.08
0.47
37.97
19.69
20.9
-6.15
Nov
6.20
11.84
0.52
37.47
22.43
21.64
3.52
Dec
6.53
11.64
0.56
33.90
21.22
20.25
4.57
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Ozean Journal of Applied Sciences 5(3), 2012
Figure 1: Monthly Average Global Radiation; Comparison Between and for Abuja (1991 – 2005).
Figure 2: Monthly Average Global Radiation; Variation of Estimated Global radiation for Abuja (1991 –
2005).
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Ozean Journal of Applied Sciences 5(3), 2012
Figure 3: Monthly Average Sunshine Duration; Variation of Sunshine Hours for Abuja (1991 – 2005).
Figure 1 shows that in the overall average years (1991 - 2005), there were two maxima (major and minor) and two
corresponding minima (major and minor). The major maximum occurred between February-April during the dry
season and the minor maximum occurred between November-January. In the rainy season (May-October), we have
the major minima in the months of July-August. While the minor minima was in the month of January due to the
harmattan dust haze that covers the atmosphere at that period of the year.
The peak month, March, with of 25.02 MJm -2 day -1 contributed 10.05% and the least month, August, with of
16.73 MJm -2 day -1 contributed 6.72% of the annual total of the estimated global radiation. The result also shows that
the global solar irradiation value for Abuja-Nigeria is between 16.73 MJm -2 day -1 and 25.02 MJm -2 day -1 as observed
in Figure 2.
Figure 2 also indicates the trend of global solar irradiation at Abuja, with high values during the dry season. While
minimum irradiation is obtained during the rainy season, as the rain bearing clouds pervade the sky.
Finally, in Figure 2 and 3, the monthly variation of global solar radiation and sunshine duration have same trends
where the maximum values each mentioned parameter were observed in March and the minimum in August. From
Table 1, the formulae of empirical models investigated in the present paper can be written as follows:
H
H
0
0.30 0. 53
S
S o
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Ozean Journal of Applied Sciences 5(3), 2012
CONCLUSION
The Angstrom related form of correlation equations have been developed for Abuja - Nigeria. This equation will in
no small measure help in predicting the solar radiation in this area. It will go a long way in estimating the solar
radiation in any part of the guinea savannah climatic zone of Nigeria because of its agreement with measured data.
Since facilities of recording global solar radiation data are not easily available probably because of lack of
maintenance culture or lack of trained personnel to take measurements or delay in repair in case of instrument
failure, this equation can be used with ease and trust.
The global solar radiation at Abuja exhibits monthly and seasonal variation, with two maxima (major and minor) in
February, March, April, and November and December, respectively. While in the months of July, August and
January, we have the minima (major and minor) variations, respectively.
This gives credence to two types of global solar radiation at the location. First, the high irradiation values in the dry
season associated with long duration of sunshine hours (above 6 hours/day) and less cloudy skies. Second, the low
irradiation values are in the rainy season (when the rain bearing clouds pervade the sky) associated with least
sunshine hour (less than 5 hours/day).
Finally the monthly average of global solar radiation in Abuja varies between 16.73 MJm -2 day -1 in August to 25.02
MJm -2 day -1 in March throughout the seasons of the years (rainy and dry season) with the average value being 20.75
MJm -2 day -1 . This can be utilized very efficiently for predicting the performance of solar devices in Abuja- Nigeria.
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