2 Solar Radiation

Dr. Sunayan Saha

1. Introduction

The energy in the sun is produced by nuclear fusion reaction and it maintains a high temperature at the surface. The radiated heat energy from the sun is called solar energy or solar radiation. This radiation is the fundamental part of all the biotic and abiotic processes on the earth. The energy and various gaseous cycles between terrestrial and atmospheric continuum depends on solar radiation. The water cycle, local weather and climate, circulation of wind are also controlled by the solar radiation. The photosynthesis is possible in the presence of solar radiation and hence it is important for plants and to animals.

2. Solar radiation spectrum

The sun is considered as a black body having high surface temperature (5,800oC). The electromagnetic spectrum of solar radiation ranged from gamma rays (100 nm) to radiowaves (1 mm). The solar radiation spectrum (Fig 1) consists of emission at various wavelengths but more at short wavelengths.

The maximum emissive power of the radiation takes place at wavelength of 0.48um. The average time taken by solar radiation to reach the surface of the earth from Sun is about 8 minutes.

Source: Krondratjev, 1969

Fig 1 Solar radiation spectrum

The solar radiation spectrum represents continuous spectra of electromagnetic waves. About 95 percent of the total energy lies in the short wave length region of 0.3-2.4 μm and about 99 percent is within 0.25-4 μm range. The long waves in the spectrum ranged greater than 4 μm accounts only to 1 percent. And the radiation spectrum from the earth consists mainly of long wavelengths and maximum emission takes place at 10um.

3. Irradiance and irradiation

Irradiance is the rate at which radiant energy is incident on a unit surface area. It is the measure of power density of sun light falling per unit area and time. It is measured in watt per square meter. Heat energy is measured in joules and while watt or joules per second is unit of power.

Irradiation is solar energy per unit surface area which is striking a body over a specified time. Hence it is integration of solar illumination or irradiance over specific time (usually an hour or kilowatt a day). It is measured in kilowatt-hour or kilowatt day per square meter.

Irradiation = irradiance x time period

For example, if irradiance is 20 k W/m2 for 5 h, irradiation is 20 × 5 = 100 k W/m2.

The earth revolves around the sun in an elliptical orbit as shown in figure 1. The earth is closest to the sun on 21 March and 23 September. The earth is farthest from the sun on 21 June and 22 December. The mean distance of the earth from the sun is 1.495 × 1011 m.

Fig 2. Elliptical orbit of earth around sun

The intensity of solar radiation outside the earth’s atmosphere reduces with distance and it is dependent on the distance between the earth and the sun. In fact, the intensity of solar radiation reaching outside the earth’s atmospheric varies with the square of the distance between centers of the earth and the sun. This is the reason why earth receives 7 % more radiation on 21 March and 23 September as compared to 21 June and 22 December. The intensity of solar radiation keeps on attenuating as earth propagates away from the surface of the sun, but the content of wave length in the radiation spectrum does not change.

The earth axis is tilted about 23.45̊ with respect to earth’s orbit around the sun as shown in figure(2) owing to this tilting of earth’s axis, the northern hemisphere of the earth points towards the sun in the month of June and it point away from the sun in the month of December. However, earth’s axis remains perpendicular to the imaginary line drawn from the earth to sun during the month of September and March. The sun- earth’s distance varies during earth’s rotation around the sun, thereby varying the solar energy reaching its surface during revolution, which bring about seasonal changes. The northern hemisphere has summer in the month of September and March, both the hemisphere are at the same distance from the sun and receive equal sunshine. During the summer, the sun is higher in the sky, while the sun is lower in the sky during winter for the northern hemisphere.

Fig 2. Inclination of earth’s axis

4. Extraterrestrial radiation

Solar radiation incident on the outer atmosphere of the earth is called extraterrestrial radiation. The extraterrestrial radiation varies based on the change in sun- earth’s distance arising from earth’s elliptical orbit of rotation. The extraterrestrial radiation is not affected by changes in atmospheric condition.

5. Solar constant: it is defined as the energy received from the sun per unit time on a unit surface area perpendicular to the direction of propagation of solar radiation at the top of earth’s atmosphere when earth is at its mean distance from the sun. The value of solar constant is taken as 1367W/m2.

This includes all types of solar radiation. It has a fluctuation of about 6.9% during a year. It means solar constant varies from 1,412 W/m² in early January to 1,321 W/m² in early July. This is because of the difference in earth’s distance from the Sun. So solar constant of 1367 W m-2 is with a range of standard deviation of 1.6 Wm-2 to ±7 Wm-2

The extraterrestrial radiation is determined by using solar constant

Iext = Isc x (Rav/R)2 W/m

Where

Iext  is extraterrestrial radiation

Isc is solar constant (1367 W/m2)

Rav is mean distance between sun and earth

R is actual sun-earth distance

It can aso be expressed as Iext =                ] W/m2

6. Terrestrial radiation

When radiation passes through earth’s atmosphere, it is subjected to the mechanism of atmospheric absorption and scattering depending on atmospheric conditions. Earth’s atmosphere contains various constituents, suspended dust and solid and liquid particles, such as air molecules, oxygen, nitrogen, carbon dioxide, carbon monoxide, ozone, water vapour and dust. Therefore, solar radiation or intensity of radiation is depleted during its passage through the atmosphere. The solar radiation that reaches earth’s surface after passing through earth’s atmosphere is called terrestrial radiation.

7. Types of solar radiation

Insolation is the downward solar energy flux at the ground surface in the shortwave region of electromagnetic spectrum. The solar radiation reaches earth’s surface in two ways from extraterrestrial region:

7.1 Beam radiation – a part of sun’s radiation travels through earth’s atmosphere and its reaches directly, which is called direct or beam radiation. The solar radiation along with the line joining the receiving point and the sun is called beam radiation. This radiation has any unique direction

7.2 Diffuse radiation –the remaining major part of the solar radiation is scattered, reflected back into the space or absorbed by earth’s atmosphere. A part of this radiation may reach earth’s surface. This radiation reaching earth’s surface by the mechanism of scattering and reflecting, that is, radiation, is called diffuse or sky radiation. The solar radiation which is scattered by the particles in earth’s atmosphere and this radiation dose not have any unique direction. The diffuse radiation takes pace uniformly in the all direction and its intensity does not change with the orientation of the surface.

Total or global radiation at any location on earth’s surface

= beam radiation + diffuse radiation.

However, direct or beam radiation depends on the orientation of the surface. The beam radiation depends on the angle of incident on the surface and its intensity is maximum when the solar radiation is falling normal to the surface. The solar radiation propagating normal to its direction is specified by In.

8. Air mass (m)

The radiation reaching earth surfaces depend on (i) atmospheric condition and depletion and (ii) solar altitude. Air mass is the ratio of the path length through the atmosphere which the solar beam actually traverses up to earth’s surface to the vertical path length through the atmosphere (minimum height of terrestrial atmosphere). At sea level, the air mass is unity when the sun is vertically is in the sky (inclination angle 90̊ ).

9. Basic Sun-Earth Angles

9.2 Longitude:9.1 Latitude or angle of latitude (λ): the latitude location of earth’s surface is the angle made by the radial line joining the specified location to the centre of earth with the projection of this line on the equatorial plane. The latitude equator is zero and it is 90 ̊at poles. On a globe of the earth, lines of latitude are circles of different size. The largest one is the circle at equator (circle at equator with centre at earth’ centre) whose latitude is taken as zero. The circles at the poles have latitude of 90̊ north and 90 ̊south (or 90 ̊) where these circles shrink to a point.

On the globe, vertical lines of constant longitude (meridians) extend from pole to pole similar to the segment boundaries on peeled orange. Every meridian has to cross the equator and equator is circle. Like any circle, it has 360 degrees or division. Hence, longitude of a point is the marked value of that division where its meridian meets the equator circle. The meridian passing through the royal astronomical observatory at Greenwich, UK had been chosen as zero longitude. The meridian passing through this location is called prime meridian. The prime meridian or longitude is considered zero longitude and there are 180 longitude lines or degrees at cast (+ 180 ̊) of Greenwich. The longitude lines meet at poles and these have wide separation at the equator (about 111 km).. Solar noon is the time when the sun is at the longitude of the place.

9.3 Declination angle (δ): it is the angle made by the line joining the centres of sun and earth with equatorial plane.

Fig 4. Declination angle

The angle of declination varies when earth revolves around the sun. it has maximum value of 23.45 ̊ when earth achieves a position in its orbit corresponding to 21 June and it has minimum value of – 23.45 ̊when earth is in orbital position corresponding to 22 December. the northern hemisphere. The angle of declination can be given by

9.4 Hour angle ( ) : the hour angle at any instant is the angle through which the earth has to turn to bring the meridian of the observer directly in line with sun’s rays. It is an angular measure of time.

It is the angle in degree traced by the sun 1 h with reference to 12 noon of the (LAT) is positive in afternoon and negative in forenoon as shown in fig(5).

The earth completes one rotation (360 ̊) in 24 h. Hence, 1 h corresponds to 15 ̊of earth rotation. As at solar noon the sun rays is in the line with local meridian or longitude, the hour angle at that instant is zero.

The hour angle can given as follows:

= [Solar time -12] x 15 o

9.5 Zenith angle ( z)

It is the angle between sun’s ray and normal to horizontal plane as shown in fig 6..

9.6 Solar azimuth angle ( s): it is the angle between the projection of sun’s ray to the point on the horizontal plane and line due to south passing through that point. The value of the azimuth angle is taken positive when it is measure from towards west.

9.7 Angle of incidence ( ):Angle of incidence for any surface is defined as the angle formed between the direction of the sun ray and the line normal to the surface as shown in the fig 6.

Tilt or slope angle (β): the tilt angle is the angle between the inclined slope and the horizontal plane

Surface azimuth angle ( ): it is the angle is horizontal plane between the line due south and the horizontal projection of normal to the inclined plane surface. It is taken as positive when measured from south towards west.

Example 3: Find the solar altitude at 2 h after local solar angle on 1 June for place located at 26.75o N latitude. Determine sunrise and sunset hours as well as day length?

Solution

12. Intensity of terrestrial radiation

The normal intensity (IN) is the intensity normal to horizontal surface, beam radiation (Ib) and diffuse radiation (Id) on horizontal surface is given by

14. Measurement of solar radiation data

The following instruments are used to measure duration and quantifying solar radiation.

Sunshine Recorder : It measures the duration of Bright Sunshine (BSS) Hours in any given day.

Pyranometer : Measures the total or Global radiation i.e. the summation of direct and diffuse radiation

Pyrheliometer or Tube Solarimeter : Measures direct solar beam i.e. radiation falling on a plane surface at normal (perpendicular) incidence angle.