**7.1 Total (global) solar radiation prediction formulae**

Some prediction formulae for the radiation fluxes generated by the author include:

$$\text{H/H}\_{\text{0}} \text{=} 0.329 \text{+} 0.315 \text{(s/S}\_{\text{m}}) \tag{10}$$

where:

10 Solar Radiation

done in the shortwave regions, 0.2 to 4.0µm wavelengths, which includes the photo

The measurement is done to date, for example, at BSRN station, Physics Department University of Ilorin using Eppley Precision Spectral Pyranometer (PSP), serial number, SN17675F3 and 28866F3 with calibration constant of 8.2 x 10-6 V/ Wm-2 and well documented calibration history. Data quality is ensured by eliminating spurious errors that could arise from incidental and shading or partial un-shading of sensor by discarding all observations for which the insolation is less than 20Wm-2. The data assembled on minute –

The direct solar irradiance or solar beam **Hb**, is the component of the total solar irradiance H, which comes directly from the top of the atmosphere, through the atmosphere, to the ground surface not deviated, nor scattered nor absorbed. The ratios of it to the total H i.e Hb/H and to the extraterrestrial radiation Ho, i.e Hb/Ho, are very important atmospheric radiation parameters in the radiative property of the atmosphere. Hb/H can be used to indicate the clearness of the atmosphere while Hb/Ho may be used to indicate the cleanness

The direct solar irradiance is similarly measured like the global solar irradiance. It is measured using the Eppley solar tracker(NIP) with calibration constant 8.42 x 10-6V/ Wm-2. Unfortunate the incessant power outage prevented the continuous functioning of this radiation sensor in many developing nations.Therefore the data of direct solar irradiance is

This radiation flux is also known as the sky radiation. It is short wave radiation, coming from the sky covering angular directions of 1800 to the sensor. It is incident on the ground surface as a result of scattering and reflection by particles in the atmosphere. Its ratio to the total flux H, i.e Hd/H measures the cloudiness and turbidity of the sky and its ratio to the extraterrestrial radiation Ho i.e Hd/Ho is expected to measure the scattering co-efficient of

This radiation flux is measured in same manner as those above. An Eppley Black and White Pyranometer model 8-48 with calibration constant 9.18 x 10-6 V/Wm-2, with a shadow ring across the sensor, is used for the measurement. Unfortunately and inevitably the shadow ring may cut off some diffuse radiation, thus making the measurement to be inaccurate. This is why eqn.6 may not be valid or suitable to obtain the correct direct solar irradiance Hb .

As part of measurements, formulas for generating the different radiation fluxes: global (total) solar irradiance, H and its components, direct solar irradiance Hb, diffuse solar irradiance Hd, are developed to generate the required data of these radiation fluxes where they are required and are not regularly measured. Some of the expressions were developed in terms of other easily measured radiation and meteorological parameters. Numerous of

by – minute basis was used to generate the hourly, daily and monthly averages.

of the atmosphere and to determine the transmittance property of the atmosphere.

here, as in many other stations, obtained by computation.

synthetically Active Radiation (PAR).

**6.1.2 Direct solar irradiance, Hb** 

**6.1.3 Diffuse sky irradiance, Hd** 

**7. Radiation fluxes formulae** 

the atmosphere.

H is the global (total) sw - solar irradiance been predicted. Ho is the extraterrestrial at the top of the atmosphere of the site. s/Smis the fraction of sun shine hours at the site.

Eqn.10 is of the Angstrom type obtained by the author in 1995 at the BSRN station University of Ilorin (Babatunde,1995). Another is a multivariate one given by

$$\rm H/H\_{o} = 0.0189 + 0.2599(s/S\_{m}) + 0.0027V + 0.0101T \tag{11}$$

where:

Ho and s/Sm are already defined in eqn 10.

V is the average visibility and T is the average ambient temperature at the location.

Eqns. 10 and 11 are formulae for estimating or generating global (total) solar radiation fluxes. Eqn.11 however is a multivariate expression. The magnitude of contributions by the meteorological variables in the expression to the amount of radiation obtainable at the location are indicated by their coefficients. The amount of global solar radiation predicted at the location depends, as can be observed from the equation, strongly on the variant, s/Sm, the number of sun shine hours, less on the ambient temperature T and much less on visibility V. The equation was developed by Babatunde and Aro (1996).

When tested, the value of global radiation flux predicted by eqn.10 was within 2.5% while that of eqn.11 was within 0.6%. Thus an equation developed in terms of multivariate metrological variables, although cumbersome, gives a better value of the radiation flux than the one in terms of one single variable. However for estimating values of the flux, H, for engineering purposes, the two equations are found to be adequate and reliable.

#### **7.2 The diffuse radiation prediction formulas**

Some formulas for computing the diffuse sky radiation were developed at various times and also in terms of related radiation and meteorological parameters by Babatunde (1995 ; 1999). Three of them, two of which are Angstrom type, are presented.

$$\rm H\_{4}/H \rightleftharpoons 0.4949 \ -0.1148 S\_{h} \tag{12}$$

$$\mathbf{H} \sqrt{\mathbf{H}} \equiv 0.945 \mathbf{\hat{s}} - 0.971 \mathbf{K}\_{\varepsilon} \tag{13}$$

$$\mathbf{H}\_{\mathsf{q}} / \mathbf{H} \equiv \mathbf{1} \ - \ \mathbf{K}\_{\mathsf{c}} \tag{14}$$

where Hd/H is known as the cloudiness index. Sh is the fraction of sunshine hours. Kc is the clearness index H/Ho.

When they were tested on the year 2000 radiation data, the values predicted by eqn.12 were within 18% while that of eqn.13 was within 11% and that of eqn.14 was within 19%. Therefore it can be said of these equations that they will adequately produce diffuse sky radiation data with reasonable accuracy. Eqn.13 is however the best of the three. It is of the Angstrom type, obtained as a result of experimental analysis and not as a result of regression analysis like others.

#### **7.3 Direct radiation prediction formulas**

Direct radiation component data is the most difficult to acquire because of the nature of the equipment for measuring it. Estimation of its values has therefore been relied upon to provide the data when needed.

The following formulas by the author for computing it were developed at various times (Babatunde, 1999; 2000)

$$\mathbf{H}\_{\rm b} \equiv \mathbf{H}^2 / \mathbf{H}\_0 \tag{15}$$

$$\text{H}\_{\text{b}}\text{/H} \equiv 0.308 + 0.424 \text{ H} / \text{H}\_{\text{0}} \tag{16}$$

The two equations were developed in terms of the total radiation H and extraterrestrial radiation Ho. The two radiation fluxes, the predictors, are easily measured and computed respectively with very reasonable accuracy. Eqn.15, in particular, is a unique equation, developed purely from experimental results, Eqn.15 and eqn.16 will produce dependable values of the direct radiation data in all atmospheric conditions.

Some other equations developed for predicting Hb for specific atmospheric conditions are:

$$\text{H}\_{\text{V}}\text{/H} = 0.341 + 0.571 \text{ K}\_{\text{c}} \tag{17}$$

and

$$\text{H}\_{\text{b}}\text{/H} \rightleftharpoons 0.247 + 0.415 \text{ K}\_{\text{c}} \tag{18}$$

They have been tested and proven to be much more suitable for clear – sky conditions and cloudy – sky conditions respectively. They are equally as good as eqns. 15 and 16 above but only at the atmospheric conditions specified.

#### **8. Solar energy applications**

The major areas of application of solar energy are in the provision of low and high grade heat, direct conversion to electricity through Photovoltaic cells and indirect conversion to electricity through turbines.

Thus solar energy is utilizable through the principle of energy conversion from one form of energy to another. In this case, the thermal and electrical conversions of sun's energy make realizable, the various applications of solar energy. The various applications feasible and in practice are enumerated as follow.
