**4. Factors affecting the amount of solar radiation received on the earth surface**

#### **4.1 Astronomical factor**

6 Solar Radiation

two angles in this expression are related to the location of a site on the earth's surface with

The amount of solar energy received per unit area per second at the outer edge of the earth's atmosphere above a site is known as Extraterrestrial radiation, and is about 3.0 x 1026 Joules. The extraterrestrial radiation being received at the normal incidence (i.e. Sun – earth average distance) at the outer edge of the atmosphere of a site is known as the solar constant Isc

where **m** is mass and **c** is velocity of light, the energy therefore, radiated by the sun, is

**m=3x1026/c2 =3.3x109 kgs-1**  If the Sun thus loses mass at this rate, it can be estimated that the Sun may extinct in about 2x104 b years. Hence the energy of the Sun can be said to be in-exhaustible by the earth, i.e.,

However the amount of the energy reaching the earth's surface is about 1.00 x 103Wm-2 at noontime at the equator. The depletion of the Sun's energy as it passes through the atmosphere to the earth's surface, coupled with the seasonal, night and weather interruptions, constitutes the major impediment to the full realization of solar energy utilization. This notwithstanding, solar energy is proving by far the most attractive

Solar energy is pollution free, communitarian, conservational, decentralizable, adaptable, and the related devices to utilize it require very little or no maintenance, safe and cost effective. Solar energy utilization has come to stay as the possible future long–term energy resource. It can be argued that it is the only recurrent source, large enough to meet mankind demands of energy supply if properly harnessed. All other renewable energy sources

The sun emits energy in form of electromagnetic waves which are propagated in space without any need of a material medium and with a speed, c = 3 x 108 ms-1. Electromagnetic radiation emitted by the Sun reaching out in waves extends from fractions of an Angstrom

Electromagnetic radiations are usually divided into groups of wavelengths. The wavelength

**E = mc2** (2)

If the Sun emits energy as said above, in form of electromagnetic radiation given by

equivalent to a mass loss by the sun every second and can be evaluated to be:

respect to the sun:

which is about 4921kJm-2h-1.

the Sun is with us for some time to come.

alternative source of energy for mankind.

**3. Solar radiation fundamentals** 

**3.1 Electromagnetic spectrum of the sun** 

to hundreds of meters, from x – ray to radio waves.

An angstrom is a unit of length given by 1A = 10-8 cm = 10-4 μm.

regions of principal importance to the earth and its atmosphere are the;

depend directly or indirectly on the Sun for their existence.

Φ, the latitude, and **δ**, the declination angle of the Sun.

As said above, only a tiny portion of the energy of the sun reaches the earth's surface. The sun-earth distance constitutes one of the factors affecting the amount of solar energy available to the earth. The earth is known to be orbiting round the sun once in a year and at the same time rotates about its own axis once in a day. The two motions determine the amount of solar radiation received on the earth's surface at any time at any place. The path or the trajectory of the earth round the Sun is an elliptical orbit with the Sun located at one of the foci of the ellipse. The implication of this is that the distance of the earth from the sun is variant; hence the amount of radiation received on the earth surface varies. For example, the shortest distance of the Sun from the earth is called the perihelion, and is 0.993AU. (Astronomical unit of distance(AU)=1.496 ×108km). It takes place on December 21st.

On 4th of April and 5th of October the earth is just at 1AU from the sun, while on 4th of July, the earth is at its longest distance, 1.017AU from the sun; this position is called Aphelion. The path of the sun's rays thus varies with time of the day, season of the year, and position of the site on the earth's surface. It becomes shorter towards the noon time, it decreases towards the perihelion position and increases towards aphelion. Thus the variation in the sun-earth distance causes variation in the amount of solar radiation reaching the earth surface. The path of the sun's ray through the atmosphere is perhaps the most important factor in solar radiation depletion. It determines the amount of radiation loss through **scattering** and **absorption** in the atmosphere.

The eccentricity (**Eo**) of the elliptical orbit is expressed in terms of the sun-earth distance (**r**) and the average, **r0** of this distance over a year. It is given by

$$\mathbf{E\_o = (r\_0/r)^2 = 1 + 0.033 \cos(2 \text{nd}\_\eta / 365)}\tag{3}$$

where **dn** is the Julian day number in the year. For example **d1=1** on January 1 and **d**365 =365 on December 31.

The elliptical motion of the earth round the sun gives rise to the seasons we experience on earth, and its rotation about its own axis determines the diurnal variation of the amount of radiation received. The amount of solar radiation received on a unit horizontal surface area per unit time at the top of the atmosphere is known as the **Extraterrestrial** radiation Ho, and is given by

$$\mathbf{H}\_0 = 24 \text{\textquotedblleft n } \mathbf{I}\_{\text{cc}} \to\_{\text{o}} \mathbf{o} \text{ } \mathbf{o} \text{ } \text{cos } \mathbf{\delta} \text{ (sinəə- (n/180) } \boldsymbol{\alpha}\_{\text{s}} \cos \alpha\_{\text{s}} \text{)}\tag{4}$$

This equation gives the average daily value of extraterrestrial radiation, **H**o on a horizontal surface at the top of the atmosphere, while

**Io=Isc Eo cos ф cos δ (cosωi-cos ωs)** (5)

gives the average hourly value of the extraterrestrial radiation. where **ф** is the latitude of the site, **δ** is the declination angle of the sun **ωi** is the hour angle **ωs** is the sun set hour angle

The corresponding expressions for computing the extraterrestrial radiation on a tilted surface toward the equator at any latitude in the northern hemisphere are given by Igbal (1983). For the daily average, we have

$$\mathbf{H}\_{\mathrm{o\bar{\mathfrak{p}}}} = 24/\mathfrak{n} \,\mathrm{I\\_E}\_{\mathrm{o}} \left[ (\mathfrak{n}/180) \,\mathrm{o}\,\mathrm{i}\,\mathrm{sin}\,\mathrm{6sin}(\mathfrak{d}\cdot\mathfrak{p}) + \cos\mathrm{6cos}(\mathfrak{d}\cdot\mathfrak{p})\sin\mathrm{o}\,\mathrm{s} \right] \tag{6}$$

And for the hourly average, we have

$$\mathbf{I}\_{\mathsf{o}\mathfrak{f}} = \mathbf{I}\_{\mathsf{sc}} \mathbf{E}\_{\mathsf{o}} \left[ \sin \mathsf{δ} \sin(\mathsf{d} \mathfrak{p} \mathfrak{f}) + \cos \mathsf{δ} \cos(\mathsf{d} \mathfrak{p} \mathfrak{f}) \mathbf{cos} \mathbf{o}\_{\mathsf{i}} \right] \tag{7}$$

where **β** is the angle of tilt toward equator

$$
\alpha\_s^\perp \equiv \min \{ \alpha\_\nu \cos^{-1} [\tan \delta \tan(\Phi \cdot \beta)] \}\tag{8}
$$

#### **4.2 The atmospheric factor**

The extraterrestrial radiation mentioned above is the maximum solar radiation available to us at the top of our atmosphere. The variable quantities affecting its amount at the ground surface are the astronomical factors mentioned above and the atmospheric factors.

Solar radiation however has to pass through the atmosphere to reach the ground surface, and since the atmosphere is not void, solar radiation in passing through it is subjected to various interactions leading to **absorption, scattering** and **reflection** of the radiation. These mechanisms result in depletion and extinction of the radiation, thus reducing the amount of solar radiation we receive at the ground surface of the earth. Several atmospheric radiation books describe and discuss these radiation depletion mechanisms.

### **5. Other radiation and atmospheric related parameters**

The knowledge of radiation parameters, such as cloudiness index, clearness index, turbidity, albedo, transmittance, absorbance and reflectivity of the atmosphere through which the solar rays pass to the ground surface is very necessary for the utilization of solar energy. Also the knowledge of the meteorological parameters such as number of **sun shine hours** per day, **relative humidity, temperature, pressure, wind speed, rainfall** etc is desirable and important for accurate calculation of parameters of some solar energy devices. For example it is needed to know the average number of sun shine hours per day for accurate calculation of PV (photovoltaic) power needed in sizing solar power electrification for any location. In Nigeria, for example, we have an average of 4.5 hours of sunshine in a day. In detailed work, however, this value varies with geographical locations. Because of these, the

This equation gives the average daily value of extraterrestrial radiation, **H**o on a horizontal

The corresponding expressions for computing the extraterrestrial radiation on a tilted surface toward the equator at any latitude in the northern hemisphere are given by Igbal

The extraterrestrial radiation mentioned above is the maximum solar radiation available to us at the top of our atmosphere. The variable quantities affecting its amount at the ground

Solar radiation however has to pass through the atmosphere to reach the ground surface, and since the atmosphere is not void, solar radiation in passing through it is subjected to various interactions leading to **absorption, scattering** and **reflection** of the radiation. These mechanisms result in depletion and extinction of the radiation, thus reducing the amount of solar radiation we receive at the ground surface of the earth. Several atmospheric radiation

The knowledge of radiation parameters, such as cloudiness index, clearness index, turbidity, albedo, transmittance, absorbance and reflectivity of the atmosphere through which the solar rays pass to the ground surface is very necessary for the utilization of solar energy. Also the knowledge of the meteorological parameters such as number of **sun shine hours** per day, **relative humidity, temperature, pressure, wind speed, rainfall** etc is desirable and important for accurate calculation of parameters of some solar energy devices. For example it is needed to know the average number of sun shine hours per day for accurate calculation of PV (photovoltaic) power needed in sizing solar power electrification for any location. In Nigeria, for example, we have an average of 4.5 hours of sunshine in a day. In detailed work, however, this value varies with geographical locations. Because of these, the

surface are the astronomical factors mentioned above and the atmospheric factors.

**Io=Isc Eo cos ф cos δ (cosωi-cos ωs)** (5)

**ssinδsin(ф-β) + cosδcos(ф-β)sinω<sup>ǀ</sup>**

**Ioβ = Isc Eo [sinδsin(ф-β) + cosδcos(ф-β)cosω<sup>i</sup>** (7)

**s = min{ωs, cos-1[tanδtan(ф-β)]}** (8)

**s]** (6)

surface at the top of the atmosphere, while

where **ф** is the latitude of the site, **δ** is the declination angle of the sun

(1983). For the daily average, we have

And for the hourly average, we have

**4.2 The atmospheric factor** 

where **β** is the angle of tilt toward equator

**ωi** is the hour angle **ωs** is the sun set hour angle

gives the average hourly value of the extraterrestrial radiation.

**Ho<sup>β</sup> = 24/π Isc Eo [(π/180) ω<sup>ǀ</sup>**

**ωǀ**

books describe and discuss these radiation depletion mechanisms.

**5. Other radiation and atmospheric related parameters** 

measurement of solar radiation amount and its spectral distribution under all atmospheric conditions is undertaken at many radiation networks around the world (Babatunde and Aro, 1990).

The knowledge of the spectral distribution of solar radiation available is also important for development of semiconductor devices such as photo detectors, light emitting diodes, power diodes, photo cells, etc; it is also essential in the design of some special solar energy devices for the direct conversion of solar energy to electricity.
