Empirical model for estimation of global radiation from sunshine duration of Ijebu-Ode

Development of solar energy research program must always start with a study of solar radiation data at a site or region of interest. Measurement of solar radiation exists for only relatively few Meteorological stations and a place where it is not directly measured. It can be estimated by using models and empirical equations (Duffie and Beekman,1994). Global solar radiation has a fundamental importance for life on earth. It is used in various types of calculation such as, the estimation of reference evaporation. However, its measurement is costly and time consuming. For the utilization of solar energy and balance studies, it is desirable to measure the diffuse global radiation and direct solar radiation (Sodha et al., 1986). Hence, Global solar radiation is the sum of diffuse solar (sky) radiation and direct solar radiation, while Global solar irradiance is the irradiance produce by solar radiation on a horizontal surface on the earth. The knowledge of daily and hourly record of the amount of sunshine is necessary for estimating global solar radiation using regression equation and for optimising the design of a particular solar collection. In


INTRODUCTION
Development of solar energy research program must always start with a study of solar radiation data at a site or region of interest.Measurement of solar radiation exists for only relatively few Meteorological stations and a place where it is not directly measured.It can be estimated by using models and empirical equations (Duffie and Beekman,1994).Global solar radiation has a fundamental importance for life on earth.It is used in various types of calculation such as, the estimation of reference evaporation.However, its measurement is costly and time consuming.For the utilization of solar energy and balance studies, it is desirable to measure the diffuse global radiation and direct solar radiation (Sodha et al., 1986).Hence, Global solar radiation is the sum of diffuse solar (sky) radiation and direct solar radiation, while Global solar irradiance is the irradiance produce by solar radiation on a horizontal surface on the earth.
The knowledge of daily and hourly record of the amount of sunshine is necessary for estimating global solar radiation using regression equation and for optimising the design of a particular solar collection.In order to homogenise the data on the world wide network for sunshine duration, a special design of the Campbell-Stokes sunshine recorder was recommended by World Meteorological organisation (WMO, 1962).The solar constant (I sc ), is the irradiance produced by the extraterrestrial solar radiation on the surface perpendicular to the sun's ray to the mean yearly sun-earth distance (150million km).According to the World Radiation Centre (WRC), the most acceptable value of solar constant is 1367W/m 2 .Hence the direct correlation between global solar radiation and sunshine duration for a particular station is the regression equation between the solar global radiation and the temperature observed.In this study, the determination of correlation between the sunshine duration and global solar radiation is described by (1) called ANGSTROM FORMULA.

METHODOLOGY
The data sets for Ijebu-Ode used in this study include monthly daily observed solar radiation (Gunn-Bellani distillate) and monthly average of sunshine duration in hours for a period of five years.The data for Ijebu-Ode were obtained from the archives of Nigeria meteorological Agency, Oshodi, Lagos State.The geographical location of Ijebu-Ode is on latitude and longitude .
ANGSTROM FORMULA was used to investigate the correlation between the sunshine duration and global solar radiation as described by equation 1. (1) By re-writing (1), we have The sunset hour angle is given as: (5) The declination angle is given as (6) (Rao et al., 1984;Reitveld, 1983).
Maximum hours of insulation which is the maximum possible duration of sunshine is given as:

STATISTICAL ANALYSIS
The validity of the model was tested using the statistical tools proposed by Stone (1993) which are analysed into two namely; the

RESULT AND DISCUSSION
The value of solar global radiation measured on the ground surface depends on the clarity or transparency of the atmosphere to the incident radiation; hence the value of the ratio of will depend on the clearness of the atmosphere (Babatunde, 2005).The value of extra-terrestrial solar radiation ( ) and relative sunshine duration were computed as given by Duffie and Beckman (1994) and Sodha et al.,(986) using equation 4 and 8 (Tables 1 and  2).
From Table 1, the highest extra-terrestrial solar radiation H 0 occurs in the month of December (49.145587MJmThe ratio of the terrestrial solar radiation to the extraterrestrial solar radiation (H/H 0 ), which is the clearness index K T varies throughout the months of the year.It was observed that from Table 2 the highest values occurred in the month of May with the value 0.57843 while the least is found in the month of August with the value 0.31152 both in the monsoon period due to the fact that it is tropical region and radiation will be higher in sunny season than the rainy season.Based on the definition,sunshine duration is referred to as the cloudy nature of the atmosphere.It is clearly observed from Table 2 that the least value occurred in the month of August with the value of 0.1748 which show that the sky will be prevailed by clouds.However, the highest value occurred in the month of February with the value of 0.5796 which from all indication show that the sky would be quite clear and very much less cloudy since it is around the harmattan period.
Comparing the clearness index with relative sunshine duration, It can be seen from Table 3a and b that the correlation co-efficient for the whole year is low having the correlation co-efficient as low as 0.30166 with the degree of fitness of 9.1% which is also low.But taking cognisance of the monsoon period, there is vivid rise in correlation co-efficient having the value 0.8913 with the degree of fitness 79.4% which is high compared to the former.Hence, seasonal correlation co-efficient most especially that of rainy season is most appreciable.
Also from the statistical analysis there is remarkable agreement between the clearness index and relative sunshine duration due to the low value of RMSE of the value, , which indicates that there is good correlation between the clearness index and relative sunshine duration.RMSE is always positive, however, a low or few values are ideal or desirable for tropical region (Iqbal, 1983;Halouani et al., 1993).The test of RMSE provides information on the short term performance of the studied model.On the other hand, the test on MBE provides information on the long term performance of the model.A positive MBE value gives the average amount of over-estimation in the calculated value.Hence, low MBE is appreciable (Almorox et al., 2005;Che et al., 2007).

Conclusion
The monthly average global solar radiation and sunshine duration for Ijebu -Ode has been used to determine the applicability of the Angstrom -type regression model for estimating the global irradiance from sunshine duration.The model developed has been found to be applicable in the seasonal period (rainy season) than the whole year for the station with (i) Harmattan period: this is one of the seasons in Nigeria characterised by extreme dryness, dust and cold weather.It lowers humidity, dissipates cloud cover, prevents rainfall formation and creates big clouds of dust resulting in duststorm or sandstorm; it also limits visibility and blocks the sun for several days.This is usually observed between December and January.Wind from the Sahara desert blows over the area and its environ are is heavily overcast with dust for many days with hazy and cloudy free weather condition.(ii) The cloudy and dust free period: This is observed around November, February and March.
Carrying out the analysis based on the season, dry season led to the poor correlation coefficient (October-March) probably due to the large characteristic of the sky condition during the period.
The corresponding equation for the rainy season with respect to correlation coefficient is given as: Ogunsanwo et al. 39 The aforementioned model could be employed in the estimation of global radiation for location that lies within the rainforest climatic zone of Southern Nigeria.Hence, in this study, rainy season model was considered to be quite satisfactory.
the clearness index and is defined as the ratio of global horizontal irradiance to the extra-terrestrial horizontal irradiance.Extra-terrestrial solar radiation is the solar radiation incident on the outer limit of the earth's surface.S=, is the corresponding sunshine duration.are regression constants which have to be determined monthly.The monthly global solar radiations which were obtained using Gunn-Bellani distillate were converted and standardized after Folayan (1988) expressed as, (3) is the global solar radiation in and is the raw data obtained using Gun-Bellani distillate.*Gun-Bellani distillate is the raw solar radiation data observed directly by the Nigeria meteorological agency.EXTRA-TERRESTRIAL SOLAR RADIATION Extra-terrestrial solar radiation is the radiation that is incidence on the terrestrial surface.It is known as the top of atmospheric irradiance.could be computed using equation 4 below: =monthly mean daily extra terrestrial radiation = global solar constant = sunset hour angle for the typical day n of each month = latitude angle for the location in degree.= declination angle for month in degree =is the Julian day number of the year from January 1 to December 31.
type regression model equation has been used to estimate for the global solar radiation for various stations in Nigeria.The equation is proposed byAngstrom (1924)  which was later modified byPage (1964).
sunshine duration, S is the hours of bright sunshine, and are regression constants which are dependent on latitude and other meteorological parameter.
is the calculated value from the model is the observed value is the total number of observation

- 2 )
which is of dry season while the least occur in month of June (24.872968MJm -2) which is rainy season (Figures1 to 7).
season at Ijebu -Ode consists of two main distinct periods:

Table 1 .
The computed value of the extra-terrestrial solar radiation .

Table 2 .
Computed values of relative sunshine duration and clearness index.
mean bias error (MBE) and Root mean square error (RMSE).The mean bias error and Root mean square error were evaluated using the following equations for the station.

Table 3a .
Statistical tools and regression constants: RMSE and MBE value for Ijebu-Ode.
 

Table 3b .
Correlation analysis for different period of the year.