Irradiance on a Horizontal Plane

As described above, solar radiation is scattered and reflected when passing through the atmosphere. Rays of extraterrestrial sunlight are virtually parallel. Terrestrial sunlight, on the other hand, consists of direct and diffuse components (see Figure 2.6). Direct solar radiation casts shadows, because it is directional, coming directly from the sun; diffuse irradiation, on the other hand, has no defined direction. The total irradiance on a horizontal surface on Earth is also called global irradiance EG,hor. It is the sum of the direct irradiance Edirhor and the diffuse irradiance Ediffhor on the horizontal surface:

Table 2.6 shows the monthly average daily direct and diffuse irradiation in Berlin and Cairo. In Berlin the diffuse irradiation dominates, whereas the direct irradiation is much higher in Cairo, even in winter.

The annual diffuse irradiation does not have to vary greatly between locations despite high differences in the annual global irradiation (see Table 2.7). Upington in South Africa and London in the UK have annually about the same amount of diffuse irradiation even though the annual global irradiation in Upington is more than twice that of London. Regions with high air pollution or tropical regions have a significantly elevated contribution of diffuse irradiation. However, differences in annual direct irradiations are much higher. For example, the annual direct irradiation in Upington is almost five times that of London.

Direct Reflected Irradiance
Figure 2.6 Sunlight Passing Through the Atmosphere

Days with low global irradiation have a high percentage of diffuse irradiation, sometimes approaching 100 per cent; however, the contribution of diffuse irradiation decreases to less than 20 per cent on days with very high global irradiation values. Figure 2.7 shows the variation of direct and diffuse irradiation throughout one year in Berlin as an example of a location with relatively low annual irradiation. Figure 2.8 shows irradiation values for Cairo as an example for a location with relatively high annual irradiation. There are significant differences between these locations. In Berlin, variation of both diffuse and direct irradiation is much higher throughout the year than in Cairo.

Table 2.6 Monthly Average Daily Direct and Diffuse Irradiation in kWh/(m2 day) in Berlin and Cairo

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Average

Berlin Direct 0.17 0.40 1.03 1.42 2.13 2.58 2.29 2.05 1.38 0.54 0.22 0.10 1.20 Diffuse 0.44 0.74 1.41 2.07 2.64 2.86 2.97 2.53 1.67 1.05 0.54 0.35 1.61 Cairo Direct 1.74 2.37 3.07 3.78 4.56 5.16 4.93 4.57 3.86 3.07 1.96 1.58 3.39 Diffuse 1.35 1.63 2.08 2.49 2.47 2.40 2.41 2.19 2.01 1.62 1.49 1.28 1.95

Table 2.7 Annual Average Daily Direct and Diffuse Irradiation in kWh/(m2 day)

Bergen Berlin London Rome LA Cairo Bombay Upington Sydney

Direct 0.86 1.20 0.99 2.41 3.03 3.39 2.75 4.70 2.42 Diffuse 1.29 1.61 1.47 1.78 2.07 1.95 2.39 1.47 2.13

Diffuse Solar Radiation Kairo
Figure 2.7 Daily Direct and Diffuse Irradiation in Berlin

Many meteorological stations measure global irradiance only. However, most calculations for solar energy systems need a separation into direct and diffuse irradiance. Empirical functions found by statistical investigations can split the global irradiation into direct and diffuse irradiation (Reindl et al, 1989). Hourly values of the global irradiance EGhor, the extraterrestrial irradiance E0 and the sun height 7S (which is calculated in the following section) define the factor kj as follows:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 2.8 Daily Direct and Diffuse Irradiation in Cairo

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 2.8 Daily Direct and Diffuse Irradiation in Cairo

B0 B0 40 20

B0 B0 40 20

Sun height yS

Figure 2.9 Diffuse Irradiance Component as a Function of kT and ys

Sun height yS

Figure 2.9 Diffuse Irradiance Component as a Function of kT and ys

With this factor, the diffuse irradiance Ed;ff hor can be calculated easily using the global irradiance EGhor and the sun height 7S:

Ediff,hor = EG,hor • (1.020 - 0.254 • kT + 0.0123 • sin 7S) for kT ^ 0.3

Ediff,hor = EG,hor • (1.400 - 1.749 • kT + 0.177 • sin 7S) for 0.3 < kT < 0.78

Ediff,hor = EG,hor • (0.486 • kT - 0.182 • sin 7s) for kT £ 0.78.

Figure 2.9 shows this correlation graphically. It is obvious that the diffuse irradiation component is very low if the global irradiance values are high on clear days however, the diffuse irradiation component is rarely below

20 per cent. If it is very cloudy and the global irradiance is low (^^0), the diffuse irradiance component can reach 100 per cent. The following section describes methods to calculate the solar altitude angle, or sun height 7s.

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Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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