X

28.23MJ/m2

A list of definitions that includes those related to solar radiation is found in Appendix 2. The reader should familiarize himself or herself with the various terms and specifically with irradiance, which is the rate of radiant energy falling on a surface per unit area of the surface (units, watts per square meter [W/m2] symbol, G), whereas irradiation is incident energy per unit area on a surface (units, joules per square meter [J/m2]), obtained by integrating irradiance over a specified time interval. Specifically, for solar irradiance this is called insolation. The symbols used in this book are H for insolation for a day and I for insolation for an hour. The appropriate subscripts used for G, H, and I are beam (B), diffuse (D), and ground-reflected (G) radiation.

2.3.6 Atmospheric Attenuation

The solar heat reaching the earth's surface is reduced below Gon because a large part of it is scattered, reflected back out into space, and absorbed by the atmosphere. As a result of the atmospheric interaction with the solar radiation, a portion of the originally collimated rays becomes scattered or non-directional. Some of this scattered radiation reaches the earth's surface from the entire sky vault. This is called the diffuse radiation. The solar heat that comes directly through the atmosphere is termed direct or beam radiation. The insolation received by a surface on earth is the sum of diffuse radiation and the normal component of beam radiation. The solar heat at any point on earth depends on

1. The ozone layer thickness

2. The distance traveled through the atmosphere to reach that point

3. The amount of haze in the air (dust particles, water vapor, etc.)

4. The extent of the cloud cover

The earth is surrounded by atmosphere that contains various gaseous constituents, suspended dust, and other minute solid and liquid particulate matter and clouds of various types. As the solar radiation travels through the earth's atmosphere, waves of very short length, such as X rays and gamma rays, are absorbed in the ionosphere at extremely high altitude. The waves of relatively longer length, mostly in the ultraviolet range, are then absorbed by the layer of ozone (O3), located about 15-40 km above the earth's surface. In the lower atmosphere, bands of solar radiation in the infrared range are absorbed by water vapor and carbon dioxide. In the long-wavelength region, since the extraterrestrial radiation is low and the H2O and CO2 absorption are strong, little solar energy reaches the ground.

Therefore, the solar radiation is depleted during its passage though the atmosphere before reaching the earth's surface. The reduction of intensity with increasing zenith angle of the sun is generally assumed to be directly proportional to the increase in air mass, an assumption that considers the atmosphere to be unstratified with regard to absorbing or scattering impurities.

The degree of attenuation of solar radiation traveling through the earth's atmosphere depends on the length of the path and the characteristics of the medium traversed. In solar radiation calculations, one standard air mass is defined as the length of the path traversed in reaching the sea level when the sun is at its zenith (the vertical at the point of observation). The air mass is related to the zenith angle, $ (Figure 2.27), without considering the earth's curvature, by the equation:

Therefore, at sea level when the sun is directly overhead, i.e., when $ = 0°, m = 1 (air mass one); and when $ = 60°, we get m = 2 (air mass two).

B Earth

B Earth

FiGuRE 2.27 Air mass definition.

Similarly, the solar radiation outside the earth's atmosphere is at air mass zero. The graph of direct normal irradiance at ground level for air mass 1.5 is shown in Appendix 4.

2.3.7 Terrestrial Irradiation

A solar system frequently needs to be judged on its long-term performance. Therefore, knowledge of long-term monthly average daily insolation data for the locality under consideration is required. Daily mean total solar radiation (beam plus diffuse) incident on a horizontal surface for each month of the year is available from various sources, such as radiation maps or a country's meteorological service (see Section 2.4). In these sources, data, such as 24 h average temperature, monthly average daily radiation on a horizontal surface H (MJ/m2-d), and monthly average clearness index, KT, are given together with other parameters, which are not of interest here.2 The monthly average clearness index, KT, is defined as

Ho where

H = monthly average total insolation on a terrestrial horizontal surface (MJ/m2-d).

Ho = monthly average daily total insolation on an extraterrestrial horizontal surface (MJ/m2).

The bar over the symbols signifies a long-term average. The value of Ho can be calculated from Eq. (2.79) by choosing a particular day of the year in the given month for which the daily total extraterrestrial insolation is estimated to be the same as the monthly mean value. Table 2.5 gives the values of Ho for each month as a function of latitude, together with the_recommended dates of each month that would give the mean daily values of Ho. The day number and the declination of the day for the recommended dates are shown in Table 2.1. For the same days, the monthly average daily extraterrestrial insolation on a horizontal surface for various months in kilowatt hours per square meter microns (kWh/ m2^m) for latitudes -60° to +60° is also shown graphically in Figure A3.5 in Appendix 3, from which we can easily interpolate.

To predict the performance of a solar system, hourly values of radiation are required. Because in most cases these types of data are not available, long-term average daily radiation data can be utilized to estimate long-term average radiation distribution. For this purpose, empirical correlations are usually used. Two such frequently used correlations are the Liu and Jordan (1977) correlation and the Collares-Pereira and Rabl (1979) correlation.

2 Meteorological data for various locations are shown in Appendix 7.

Latitude

Jan 17

Feb 16

Mar 16

Apr 15

May 15

June 11

July 17

Aug 16

Sept 15

Oct 15

Nov 14

Dec 10

60°S

41.1

31.9

21.2

10.9

4.4

2.1

3.1

7.8

16.7

28.1

38.4

43.6

55°S

41.7

33.7

23.8

13.8

7.1

4.5

5.6

10.7

19.5

30.2

39.4

43.9

50°S

42.4

35.3

26.3

16.8

10.0

7.2

8.4

13.6

22.2

32.1

40.3

44.2

45°S

42.9

36.8

28.6

19.6

12.9

10.0

11.2

16.5

24.7

33.8

41.1

44.4

40°S

43.1

37.9

30.7

22.3

15.8

12.9

14.1

19.3

27.1

35.3

41.6

44.4

35°S

43.2

38.8

32.5

24.8

18.6

15.8

17.0

22.0

29.2

36.5

41.9

44.2

30°S

43.0

39.5

34.1

27.2

21.4

18.7

19.8

24.5

31.1

37.5

41.9

43.7

25°S

42.5

39.9

35.4

29.4

24.1

21.5

22.5

26.9

32.8

38.1

41.6

43.0

20°S

41.5

39.9

36.5

31.3

26.6

24.2

25.1

29.1

34.2

38.5

41.1

42.0

15°S

40.8

39.7

37.2

33.1

28.9

26.8

27.6

31.1

35.4

38.7

40.3

40.8

10°S

39.5

39.3

37.7

34.6

31.1

29.2

29.9

32.8

36.3

38.5

39.3

39.3

5°S

38.0

38.5

38.0

35.8

33.0

31.4

32.0

34.4

36.9

38.1

37.9

37.6

0

36.2

37.4

37.9

36.8

34.8

33.5

33.9

35.7

37.2

37.3

36.4

35.6

5°N

34.2

36.1

37.5

37.5

36.3

35.3

35.6

36.7

37.3

36.3

34.5

33.5

10°N

32.0

34.6

36.9

37.9

37.5

37.0

37.1

37.5

37.0

35.1

32.5

31.1

15°N

29.5

32.7

35.9

38.0

38.5

38.4

38.3

38.0

36.5

33.5

30.2

28.5

20°N

26.9

30.7

34.7

37.9

39.3

39.5

39.3

38.2

35.7

31.8

27.7

25.7

25°N

24.1

28.4

33.3

37.5

39.8

40.4

40.0

38.2

34.7

29.8

25.1

22.9

30°N

21.3

26.0

31.6

36.8

40.0

41.1

40.4

37.9

33.4

27.5

22.3

19.9

35°N

18.3

23.3

29.6

35.8

39.9

41.5

40.6

37.3

31.8

25.1

19.4

16.8

40°N

15.2

20.5

27.4

34.6

39.7

41.7

40.6

36.5

30.0

22.5

16.4

13.7

45°N

12.1

17.6

25.0

33.1

39.2

41.7

40.4

35.4

27.9

19.8

13.4

10.7

50°N

9.1

14.6

22.5

31.4

38.4

41.5

40.0

34.1

25.7

16.9

10.4

7.7

55°N

6.1

11.6

19.7

29.5

37.6

41.3

39.4

32.7

23.2

13.9

7.4

4.8

60°N

3.4

8.5

16.8

27.4

36.6

41.0

38.8

31.0

20.6

10.9

4.5

2.3

According to the Liu and Jordan (1977) correlation, n 24

sin(hss)

Ms 36G

where rd = ratio of hourly diffuse radiation to daily diffuse radiation. hss = sunset hour angle (degrees). h = hour angle in degrees at the midpoint of each hour.

According to the Collares-Pereira and Rabl (1979) correlation,

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