Solar Radiation

This section reviews the properties of solar radiation on Earth and summaries well-known models which are used to estimate the amount of radiation falling on a tilted plane.

Extraterrestrial solar radiation falling on a surface normal to the sun’s rays at the mean sun earth distance is given by solar constant (Isc). The current accepted value of Isc is 1367 W/m2.

When solar radiation enters the Earth’s atmosphere, a part of the incident energy is removed by scattering or absorption by air molecules, clouds and particulate mat­ter usually referred to as aerosols. The radiation that is not reflected or scattered and reaches the surface straight forwardly from the solar disk is called direct or beam radiation. The scattered radiation which reaches the ground is called diffuse radia­tion. Some of the radiation may reach a panel after reflection from the ground, and is called the ground reflected irradiation. In the Liu and Jordon approach the dif­fuse and ground reflected radiations are assumed to be isotropic. The total radiation consisting of these three components is called global or total radiation as shown in Fig. 2.1.

In many cases it is necessary to know the amount of energy incident on tilted surface, as shown in Fig. 2.1. However, measured total and diffuse radiation on horizontal surface are given in most available solar radiation databases. There are many models to estimate the average global radiation on tilted surfaces.

In this section we present the isotropic model developed by Liu and Jordan (Liu and Jordan 1963) which also estimates the average hourly radiation from the average daily radiation on a tilted surface.

The daily total radiation incident on a tilted surface HT can be written as


where HT, Ньт, Hd, T and H, T are daily total, beam, diffuse and ground reflected radiation, respectively, on the tilted surface.

In this model, (Liu and Jordan 1963) assumed that the intensity of diffuse ra­diation is uniform over the sky dome. Also, the reflected radiation is diffuse and assumed to be isotropic. Consequently, the daily total radiation on a tilted surface is given by

1 + cos б 1 — cos в

Ht = HbRb + Hd 2 + Hp 2 (2.2)

where Hb, Hd and H are daily beam, diffuse, total radiation, respectively, on a hori­zontal surface. в represents a tilt angle, p the ground albedo and Rb the ratio of the daily beam radiation incident on an inclined plane to that on horizontal plane. For the northern hemisphere and south facing surfaces Rb is given by

cos (ф — в) cos 5 sin®( + (d’s sin (ф — в) sin 5 Rb (2.3)

cos ф cos 5 sin Щ + (Os sin Ф sin 5

where p, 5 and (os are the latitude, the declination and the sunset hour angle for the horizontal surface, respectively. (Ds is given by

cos = cos—1 (—tan ф tan S) (2.4)

(d’s is the sunset hour angle for the tilted surface; it is given by

co’s = min{cos— 1 (—tan^tanS),cos—1 (—tan(ф — в)tan5)} (2.5)

In the relation (2.3) (Ds and cd!. are given in radian.

The daily clearness index KT is defined as the ratio of the daily global radiation on a horizontal surface to the daily extraterrestrial radiation on a horizontal surface. Therefore,


Подпись: HQ Подпись: 21 Hc Подпись: 1 + 0.033cos Подпись: 2njd 365 Подпись: (cos ф cos 5 sin as + as sin^sinS) (2.7)

where H0 is the daily extraterrestrial radiation on a horizontal surface. H0 is given by (Sayigh 1977; Kolhe et al. 2003)

where jd is the Julian day of the year.

Outside the atmosphere there is neither diffuse radiation nor ground albedo. H0 is then assumed to be composed only of the beam radiation. Similarly, for tilted surfaces, the daily extraterrestrial radiation above the location of interest HT0 is constituted only of direct component. Then, according to the relation

Подпись:Подпись:HbT = HbRb

HT0 can be computed as follows

Ht q = HoRb

Updated: July 30, 2015 — 9:00 pm