The solar energy which reaches Earth’s surface is much smaller than that which reaches a surface situated outside the atmosphere. This happens because of the phenomenon of diffusion and absorption of solar radiation by components of the atmosphere. The collision with molecules of air, steam and atmospheric dust results in scattered reflection because of which a part of the radiation is sent back to outer space. Absorption, instead, is principally due to ozone (O3), steam (H2O) and carbon dioxide (CO2). O3 absorbs mainly in the ultraviolet region while H2O absorbs in the infrared region.

Figure 7 shows the spectral distribution of solar radiation when the Sun is at the zenith.

The part of the solar radiation which reaches the Earth’s surface following the direction of the solar rays without being absorbed and reflected is called directed radiation (on soil), while the part that reaches the Earth’s surface from all direc­tions (because of the scattering) is called scattered radiation. Global radiation on soil refers to the sum of directed and scattered radiation.

Diffuse radiation can be picked up almost entirely by flat panels since glass is actually transparent to all solar radiation which arrives with an angle of incidence i (i. e. the angle between a solar ray and a normal surface) smaller than the maxi­mum value of reflection (70-80°). On the other hand, concentrators, assuming that they work in conformity with the rules of geometrical optics, have to be oriented towards directed radiation; they do not pick up diffuse radiation.

If we do not consider horizontal surfaces, which are inclined in any manner, besides directed and diffuse radiation, it is necessary to take into consideration a third kind of radiation: the reflected solar radiation, the radiation reflected from the soil or from the objects near the given surface; its intensity is influenced by the albedo of those objects. Albedo is the fraction of solar radiation that is received

and suddenly reflected by a surface. Every kind of soil and vegetation has its own value of albedo [1-3].

Albedo can also be defined as a transmission coefficient of the atmosphere, which depends on the wavelength and the route of the solar rays in the atmosphere, besides depending on atmospheric composition, which varies with local weather conditions. In the case of clear sky days, the transmission coefficient of directed radiation, given by the ratio between directed radiation on the soil and extraterrestrial radiation on the orthogonal surface, can be calculated using the following equation:

ть = 0.5{exp[ -0.65m(z, a)] + exp[ -0.95m(z, a)]} (9)

We can assume:

m(z, a) = m(0,a)p(z )/p (0) (10)

where p(z) and p(0) are the atmospheric pressures at level z and sea level, respectively.

The adimensional parameter m(z, a) is the air mass for an altitude z above the sea level. This parameter is defined as the ratio between the effective route length of solar rays and their shortest route length, with the Sun at the zenith; a is the angle formed by solar rays with a horizontal plane (see Fig. 8).

The air mass m(0,a) for the sea level can be calculated using the approximated equation:

m(0,a) = 1/sen a = cosec a (11)

which gives an error percentage of 1% per a > 15°, or it can be calculated with the exact formula, taking into consideration the Earth’s and the atmosphere’s bending:

m(0,a) = [1229 + (614sen a)2]05 -614sena (12)

The angle a determines the Sun’s position in space at any time; the relative air mass m has a certain value; therefore, we calculate tb.

Directed radiation is then given by:

I = 11

bn 10 b (13)

Hottel’s model is the second way to calculate the radiation on soil during clear sky days. This model estimates direct radiation on clear sky days for a standard atmosphere with 23 km visibility and four kinds of climate.

The transmission coefficient of normal direct radiation (7bn//0) is calculated using these relations/equations, which are valid for altitudes lower than 2.5 km:

tb = a0 + a^xp( — k/ sena) a0 = r0[0.4237 — 0.00821(6 — Z )2] a1 = r1[0.5055 + 0.00595(6.5 — Z )2] k = rk [0.2711 + 0.01858(2.5 — Z )2]

where Z is the observer altitude expressed in km and r0, r1 and rk are adimensional corrective coefficients.

To achieve global radiation on soil it is also necessary to determine diffuse radi­ation. Liu and Jordan developed an empirical relation between the coefficient of direct radiation tb and that of diffuse radiation td during clear sky days:

td =0.2710 — 0.2939tb (15)

td is the ratio between diffuse radiation on soil over a horizontal plane and extra­terrestrial radiation over a horizontal plane (I0 sen a) [1, 3].