Diffuse Irradiance

For terrestrial application there is always a considerable diffuse component of the solar irradiance even for clear sky conditions. Over a year the diffuse component amounts to 30% to 60% of the total irradiance (global irradiance). The spatial distribution within the sky’s hemisphere of the diffuse or scattered radiation is not homogenous. For an unscattered sun ray,

the probability to hit an air molecule or aerosol, and to be reflected, is a function of the air density and thickness of the atmosphere passed through. The reflected component itself is a function of the angle of incidence and the optical refractive indices of the media involved (Fresnel’s Law, see chapter 5.1.3.2). Additionally, a multiple scattering has to be considered. A model used for the angular sky irradiance as function of the position of the sun is DIN 5034 part 2 and is given below. An example of the distribution of the sky illuminosity at an elevation angle of the sun of у S = 30° is given in Figure 54 as a contour plot (projection of the sky’s hemisphere to the plane).

g

= 7.6752 + 6.1096-10“2-ys – 5.9344-lO’4^2 – 1.6018-10“4-Ys

LeZ

+ 3.8082- 10“6-Ys – 3.3126-10“8-Ys + 1.0343-10“10-Ys

Еен = °-5-£eo, sinYsCC – expC-T^-rn-^-) (26)

Po

6„-m =———————–

0.9 + 9.4-sinYs

LeP Luminosity of a point P at the sky hemisphere LeZ Luminosity of the zenith

TL Turbidity factor (function of the state of the atmosphere)

є angle between Zenith and point P (in °)

p angle between Sun and point P (in °):

p = arc cos (sinyS • cosє + cosyS • si^ • cos(aS-aP) ) у S Elevation angle of the Sun (in °) aS Azimuth angle of the Sun (in °)

aP Azimuth angle of point P (in °)

dR-m Product of the average optical density (of a pure, dry Rayleigh – atmosphere) and the relative optical air mass m.

Examples for average monthly turbidity factors TL in Germany are given in Table 7.2.

Table 7.2. Average monthly turbidity factors TL in Germany (DIN 5034 part 2) Month highest Monthly average of TL average lowest January 4.80 3.8 ± 1.0 3.20 February 4.60 4.2 ± 1.1 3.60 March 5.40 4.8 ± 1.5 4.30 April 5.70 5.2 ± 1.8 4.80 May 5.80 5.4 ± 1.7 4.90 June 7.40 6.4 ± 1.9 5.60 July 6.90 6.3 ± 2.0 5.70 August 6.90 6.1 ± 1.9 5.70 September 6.00 5.5 ± 1.6 5.20 October 4.90 4.3 ± 1.3 4.00 November 4.20 3.7 ± 0.8 3.30 December 4.10 3.6 ± 0.9 3.30 Yearly 5.40 4.9 ± 1.5 4.70 average

Spectral modeling of diffuse irradiance is based on the CIE publication No. 85 (1990), analogous to the modeling of the direct component. Figure 54 shows the spectra of the diffuse irradiance for AM 1, AM 1.5, AM 2 and for AM 5.6 under clear sky conditions.

Fig. 7.8. Distribution of illuminousity Lp(yP, aP) in W msr at the sky hemisphere, calculated according to DIN 5034 part 2 (as=120°; уj=30°; Zenith in center; North upwards).

Fig. 7.9. Spectra of diffuse irradiance for different air masses (AM), according to CIE Publication No. 85 (1990).