**3.1 Monthly variation of extraterrestrial and terrestrial solar radiation**

In order to obtain the pattern variation of monthly mean values of extraterrestrial (GO) solar radiation, equation (2.3) is used in calculating it for various locations for which the measured global insolation is available. The calculated values are without any atmospheric effects. Based on the calculated values of extraterrestrial horizontal insolation for locations and the measured global insolation on a horizontal surface for the same locations. Also Terrestrial solar radiations (G) obtained from Eq. 2.2 are plotted with Latitudes (selected stations) and months of the year are plotted using the same axes (Figures 3.1 and 3.2).


Table 3.1. Geographical coordinates and altitudes of studied stations

Fig. 3.1. Monthly variation of extraterrestrial solar radiation (GO) for selected stations (Ikeja, Ilorin, Ibadan, Port Harcourt and Benin).

Fig. 3.2. Monthly variation of terrestrial solar radiation (G) for selected stations (Ikeja, Ilorin, Ibadan, Port Harcourt and Benin).

#### **3.2 Monthly variation of Clearness Index**

Clearness index (KT) is defined as the ratio of the observation/measured horizontal terrestrial solar radiation (G), to the calculated/predicted horizontal extraterrestrial solar radiation (Go). Clearness index is a measure of solar radiation extinction in the atmosphere, which includes effects due to clouds but also effects due to radiation interaction with other atmospheric constituents. To develop the model for the clearness index, the insolation on a horizontal surface for a few locations is measured over a period of time encompassing all seasons and climatic conditions. Different values of the clearness index at different stations may be as a result of different atmospheric contents of water vapour and aerosols. It can be seen from the above expressions that the extra-terrestrial horizontal insolation is a function of latitude and the day of year only. Hence, it can be calculated for any location for any given day. However, the calculated insolation does not take any atmospheric effects into account

$$K\_T = \frac{G}{G\_0} \tag{3.1}$$

1 2 3 4 5 6 7 8 9 10 11 12

Months

Fig. 3.2. Monthly variation of terrestrial solar radiation (G) for selected stations (Ikeja, Ilorin,

Clearness index (KT) is defined as the ratio of the observation/measured horizontal terrestrial solar radiation (G), to the calculated/predicted horizontal extraterrestrial solar radiation (Go). Clearness index is a measure of solar radiation extinction in the atmosphere, which includes effects due to clouds but also effects due to radiation interaction with other atmospheric constituents. To develop the model for the clearness index, the insolation on a horizontal surface for a few locations is measured over a period of time encompassing all seasons and climatic conditions. Different values of the clearness index at different stations may be as a result of different atmospheric contents of water vapour and aerosols. It can be seen from the above expressions that the extra-terrestrial horizontal insolation is a function of latitude and the day of year only. Hence, it can be calculated for any location for any given day. However, the calculated insolation does not take any atmospheric effects into

*T*

*<sup>G</sup> <sup>K</sup>*

*O*

*G* (3.1)

10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21

G

5

Ibadan, Port Harcourt and Benin).

**3.2 Monthly variation of Clearness Index** 

6

Latitudes

account

7

Fig. 3.3. Monthly variation of clearness index for selected stations (Ikeja, Ilorin, Ibadan, Port Harcourt and Benin).

#### **3.3 Monthly variation of relative sunshine duration**

The term sunshine is associated with the brightness of the solar disc exceeding the background of diffuse sky light, or, as is better observed by the human eye, with the appearance of shadows behind illuminated objects. According to WMO (2003), sunshine duration during a given period is defined as the sum of that sub-period for which the direct solar irradiance exceeds 120 Wm–2. A new parameter describing the state of the sky, namely the sunshine number has been defined in Badescu (1999). The sunshine number is a Boolean quantity stating whether the sun is covered or not by clouds. Using the sunshine number, it strongly increases the models accuracy when computing solar radiation at Earth surface (Badescu, 1999). Relative sunshine duration is a key variable involved in the calculation procedures of several agricultural and environmental indices.

The relative sunshine duration is expressed as

$$R\_s = \frac{S}{S\_O} \tag{3.2}$$

Where S is the measured sunshine duration hours and So the potential day length astronomical length. A high number of outliers in the data sets signify that the observation has high degree of variability or a large set of suspect data. Figure 3.3 shows that RS is low between the months of June through October in Nigeria.

Fig. 3.4. Monthly variation of relative sunshine duration for selected stations (Ikeja, Ilorin, Ibadan, Port Harcourt and Benin).

#### **3.4 Monthly variation of Clearness Index, relative humidity and temperature for Iseyin**

There are other methods to estimate solar radiation. Satisfactory result for monthly solar radiation estimation was obtained by using atmospheric transmittance model, while other authors have used diffuse fraction and clearness index models. Parametric or atmospheric transmittance model requires details atmospheric characteristic information. Meteorological parameters frequently used as predictors of atmospheric parameters since acquiring detail atmospheric conditions require advance measurement. Meteorological parameters used in this section clearness index, sunshine duration, temperature and relative humidity data have been used to study monthly variation of atmospheric transmittance coefficient in parametric model. This kind of model is called meteorological model.

Fig. 3.5. Monthly variation of clearness Index and temperature for Iseyin

Fig. 3.6. Monthly variation of clearness Index and temperature for Iseyin

### **4. Variation of diffuse solar radiation**

124 Solar Radiation

1 2 3 4 5 6 7 8 9 10 11 12

Months

Fig. 3.4. Monthly variation of relative sunshine duration for selected stations (Ikeja, Ilorin,

**3.4 Monthly variation of Clearness Index, relative humidity and temperature for Iseyin**  There are other methods to estimate solar radiation. Satisfactory result for monthly solar radiation estimation was obtained by using atmospheric transmittance model, while other authors have used diffuse fraction and clearness index models. Parametric or atmospheric transmittance model requires details atmospheric characteristic information. Meteorological parameters frequently used as predictors of atmospheric parameters since acquiring detail atmospheric conditions require advance measurement. Meteorological parameters used in this section clearness index, sunshine duration, temperature and relative humidity data have been used to study monthly variation of atmospheric transmittance coefficient in

1 2 3 4 5 6 7 8 9 10 11 12

Months

parametric model. This kind of model is called meteorological model.

Fig. 3.5. Monthly variation of clearness Index and temperature for Iseyin

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6

KT

0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72

RS

5

Ibadan, Port Harcourt and Benin).

24

25

26

27

Temperature

28

6

Latitudes

7

Several models for estimating the diffuse component based on the pioneer works of Angstrom (1924) and Liu and Jordan (1960) and developed by Klein (Klein, 1977). These models are usually expressed in either linear or polynomial fittings relating the diffuse fraction (Hd) with the clearness index and combining both clearness index (KT) and relative sunshine duration (Orgill and Hollands, 1977; Erbs et al., 1982; Trabea, 1992; Jacovides, 2006; Hamdy, 2007, Falayi et al., 2011) established hourly correlations between KT and Hd under diverse climatic conditions. Ulgen and Hepbasli (2002) correlated the ratio of monthly average hourly diffuse solar radiation to monthly average hourly global solar radiation with the monthly average hourly clearness index in form of polynomial relationships for the city of Izmir, Turkey. Oliveira et al., (2002) used measurements of global and diffuse solar radiations in the City of Sao Paulo (Brazil) to derive empirical models to estimate hourly, daily and monthly diffuse solar radiation from values of the global solar radiation, based on the correlation between the diffuse fraction and clearness index

The diffuse solar radiation Hd can be estimated by an empirical formula which correlates the diffuse solar radiation component Hd to the daily total radiation H. The ratio, Hd/H, therefore, is an appropriate parameter to define a coefficient, that is, cloudiness or turbidity of the atmosphere. The correlation equation which is widely used is developed by Page (Page, 1964).

$$\frac{H\_d}{H} = 1.00 - 1.13 K\_T \tag{4.1}$$

Another commonly used correlation is due to Liu and Jordan (1960) and developed by Klein (Klein, 1977) and is given by

$$\frac{H\_d}{H} = 1.390 - 4.027K\_T + 5.53 \left(K\_T\right)^2 - 3.108 \left(KT\right)^3 \tag{4.2}$$

We engaged both Page (1964) and Klein (1977) models to study the variation of diffuse solar radiation for Ikeja, Ilorin, Ibadan, Port Harcourt and Benin. Large variations in the intensities of diffuse radiation due to cloudiness have been indicated as stated earlier.

Fig. 4.1. Monthly variation of diffuse solar radiation using Klein model for selected stations (Ikeja, Ilorin, Ibadan, Port Harcourt and Benin)

Fig. 4.2. Monthly variation of diffuse solar radiation using Page model for selected stations (Ikeja, Ilorin, Ibadan, Port Harcourt and Benin).

The results of the variation are plotted in Figures 4.1 and 4.2 exhibit the trend variation of diffuse solar radiation. The maxima of diffuse radiation for the month of July - September are quite appreciable. This means that there was a high proportion of cloudy days and relatively low solar energy resource in July –September across the locations, and there was high proportion of sunshine days and relatively abundant solar energy resource between the month of April and October across the stations. This wet season is expected due to poor sky conditions caused atmospheric controls as the atmosphere is partly cloudy and part of solar radiation are scattered by air molecules. The presence of low values of diffuse solar radiation in Figures 4.1 and 4.2 will be very useful for utilizing it for solar concentrators, solar cookers and solar furnaces etc.
