1. Introduction |
Energy generated by the sun is radiated outwards in all directions, and only two thousand-millionths of it is intercepted by the earth as light and infrared (heat) radiation. The intensity of the sun's radiation (irradiance) at the top of the earth's atmosphere at the mean distance of the earth from the sun is roughly constant (solar constant) with an observed value of 1366 Watts/m2 ± 0.3%. However, on average, only about half of this energy reaches the earth's surface [1].
The total quantity of short wave radiant energy emitted by the suns disc as well as that scattered diffusively by the atmosphere and cloud, passing through a unit area in the horizontal in unit time is referred generally as global solar radiation. Monitoring the daily global solar radiation will help in assessing the total solar energy at any location considering diurnal and seasonal variations. The global solar radiation reaching the earth’s surface is made up of two components, direct and diffuse. The sum of the direct and diffuse components reaching a horizontal surface is global radiation. Direct radiation is the part, which travels unimpeded through space and the atmosphere to the surface; and diffuses radiation is the part scattered by atmospheric constituents such as molecules, aerosols, and clouds. In simple terms, direct radiation causes shadows, and diffuse is responsible for skylight [1].
Approximately 30% is reflected back to space, and clouds, dust, and “greenhouse” gasses such as water vapor, carbon dioxide, and ozone absorb the remaining 20%. The annual global radiation in India varies from 1600 to 2200 kWh/sq.m which is comparable with radiation received in the tropical and sub-tropical regions. The equivalent energy potential is about 6,000 million GWh of energy per year [2].
1. 1. Characteristic of the solar radiation
Solar radiation is made up of electro-magnetic waves (Es), which travels from the sun to the earth with the speed of light (c). Wavelength (?) of the wave is related to the frequency (?), and is given in Eq. 1.
| C = ? ? | (1) |
The electro-magnetic waves of solar radiation (Es, cal/min) emitted into the space and its part intercepted by the earth (Ee, cal/min) is given by:
where, ro, re, Io are the mean distance between sun and earth, the radius of the earth, and solar constant, respectively. The part of solar radiation intercepted by the earth depends mainly on the insolation of the earth’s outer atmosphere.
1. 2. Insolation at the outer atmosphere
Insolation is the rate at which energy reaches the earth surface. It is the absorption of solar radiation by the earth surface [3]. If the earth were represented as a sphere, then at the equator a horizontal surface at a point immediately under the sun would receive 1.36 kW/sq.m continuously. Horizontal surface on the same longitude but different latitude would receive correspondingly less. The earth rotates about an axis, which is inclined at an angle (231/3)o to it. This modifies the solar radiation to give rise to a seasonal variation of solar radiation and due to this, more radiation falls on the polar region in the summer than at the equator. An important feature is the absence of seasons at the tropics and the extremes of 6 month summer and 6-month winter at the poles.
T. V. Ramachandra / Energy Education Science & Technology 18 (2007) 101-114 103 Another feature of significance is the 12 hour day, 12 hour night in the tropics compared to the shorter night/longer day summer cycle in temperate areas and the reverse in the winter. Other than the insolation at the outer atmosphere the atmosphere inside the earth surface also has an effect on radiation.
1. 3. Effects of the earth’s atmosphere
It is seen that about 30% of the incident solar radiation is reflected by the atmosphere, a further 20% is absorbed on passing through the atmosphere and the remaining arrives to the earth’s surface, where as 2% is reflected and the remaining is absorbed. For the most favored region the average flux density is as high as 300w/sq.m the average for the tropics is about 250w/sq.m and in more temperate region the figure is about half this value. In order to study the effects of solar radiation on the earth, it is necessary to determine the amount of radiation reaching the earth's atmosphere and surface.
The quantity of short wave radiant energy emitted by the sun passing through a unit area in the horizontal in unit time is referred generally as global solar radiation (G) [4]. The computation of daily sums of global solar radiation at sites where no radiation data’s are available, can be done through various probable relationships among the parameters such as from (a) sunshine and cloudiness, (b) extra terrestrial radiation allowing for it’s depletion by absorption and scattering in the atmosphere. There is a relationship between solar radiation received on earth’s surface and sunshine. Hence earlier researchers like Kimball (1919), Ångström (1924) and others used sunshine data for solar radiation estimation [5].
The statistical relation formulated between the daily duration of sunshine N and the daily total global solar radiation G is of the form,
| (G/Go) = a + (1-a) (n/N) | (4) |
where, Go is daily global solar radiation with cloud free atmosphere, a is mean proportion of radiation received on a completely overcast day, and N: maximum possible duration of sunshine (with solar elevation < 5o), h.
Due to the difficulties in the precise evaluation of Go in the above equation, Go was replaced by the extra terrestrial radiation (ETR) on a horizontal surface, and the relation is given by,
| (G/ETR) = a + b (n/N) | (5) |
where, ETR is extra terrestrial radiation, kWh / m2 / day. ETR on a horizontal surface for any place for any day / month can be estimated by the following relation,
| ETR = 10.39 K (cosfcosdsin? + ?sinfsind) | (6) |
10.39 is solar constant (assumed equal to 1.36kw/sq.m. x 24/p), K is correlation factor for varying earth sun distances, f is Angle of latitude, d is angle of declination and ? is sun set hour angle in radians
To compute (n/N) at a place where only cloud cover data are available with out mean sun shine data the inverse relation between the sunshine n/N and cloud cover C is used, which is given by,
| C = 1 – (n/N) | (7) |
Since (n/N’) is used for deriving G the relation between (n/N’) and C is given by,
| 1 – (n/N’) = 1C + 0.310 + 0.476C3 + 0.100C4 | (8) |
where, N’ is maximum possible duration of sunshine (with solar elevation >= 5o), h. Hay correlated n/N’ with G’/ETR, where G’ is the global solar radiation that first strikes the ground before undergoing multiple reflections. The numerical relation between G and G’ is given by,
| G – G’ = GR[(0.25n/N’) + 0.60(1-n/N’)] | (9) |
where R is surface albedo.
where RH is relative humidity; f1, f2, f3, and f4 are empirical constants, which vary with geographical location, respectively.
1. 5. Diffused solar radiation (D)
It is the part of short wave radiation scattered by the atmosphere reflected diffusely and transmitted by clouds and passing through unit horizontal area in unit time [4]. For average conditions, D can be determined with reasonable accuracy from G and ETR through a linear regression equation connecting D/G in one hand and G/ETR on the other [5]. The general regression equation is of the form,
| (D/G) = c + d(G/ETR) | (20) |
where, D is diffused solar radiation, c is regression constant and d is regression constant, always negative.
To secure better accuracy D should be replaced by D’ and G by G’, where D’ is given by,
| D’ – D = G R [(0.25 n /N’) + 0.60 (1-n/N’)] | (21) |
The linear regression equation used to derive D takes the form,
| D’/G’ = c + d (G’/ETR) | (22) |
1. 6. Direct Solar Radiation (IH)
It is the quantity of solar radiation emitted from the solid angle subtended by the visible disk of the sun and passing through a unit area in horizontal in units of time [4].
| IH = G – D | (23) |
