Extraterrestrial solar radiation

The sun is an almost spherical radiation source with a diameter of 1.392 106 km. It lies in one of the foci of the elliptical orbit of the earth. The solar radiation flow, which reaches the earth is inversely proportional to the square of the distance r between the sun and the earth. The mean distance is r0 = 149.6 106 km this distance is called one astronomical unit (AU)7. The smallest distance lies at 0.983 AU and occurs on 3rd January, the largest separation between the sun and 

The large distance between sun and earth means that solar radiation forms a quasi-parallel bundle of rays. The radiation that is not yet weakened by scattering and absorption in the earth s atmosphere is called extraterrestrial radiation. If it is perpendicularly incident on a surface just outside the earth s atmosphere, at a distance r0 = 1 AU from the centre of the sun then the irradiance of the extraterrestrial solar radiation is called the solar constant E0. By evaluating more recent measurements, C. Frohlich and R.W. Brusa [5.33] determined the value 

The irradiance of extraterrestrial radiation, that falls perpendicularly onto a surface that is at the same distance r as the earth is from the sun, is given by 

The sun s polar angle / s depends on the position and the orientation of the irradiated surface. This dependence is reproduced by trigonometric equations that can be found in books about solar radiation and its uses, e.g. in [5.30] and [5.34]. 

The spectral irradiance Es n of extraterrestrial solar radiation, that falls perpendicularly on a surface at a distance r0 = 1 AU from the sun, has been determined by several series of experiments using stratospheric aircraft. Their evaluation by C. Frohlich and C. Werli at the World Radiation Centre in Davos, 

The Sun is primarily composed of hydrogen and helium, along with smaller amounts of heavier elements such as calcium, iron, magnesium, aluminum, nickel, etc. The temperature in its interior is believed to be as high as 2 x 107 K, due to a chain of nuclear reactions which convert H into He. This energy is radiated to the upper convective levels, undergoing a series of absorption and emission processes. 

Most of the energy reaching the Earth s atmosphere originates from a relatively thin layer (about 1000 km thick) called the photosphere. This layer defines the visible volume of the Sun, and although the entire star is 

The emission of the photosphere is a continuum, superimposed with relatively dark lines called the Fraunhofer lines. These are produced by selective absorption and reemission of radiation in the upper photosphere where the temperature is as low as 4000 to 5000 K. Some of these lines 

The layer above the photosphere extends to 5000 to 10000 km, and is called the chromosphere. This layer can sometimes be seen during total solar eclipses. Its temperature is 105 - 106 K at the upper levels. Radiation originating from the chromosphere is composed predominantly of emission lines (H, He, Ca), and the visible emission is weak. 

The region above the chromosphere is called the corona, which extends outward for several solar diameters. Its temperature is about 106 K. Several emission lines are associated with this region. Its free electrons scatter photospheric light. 

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The Earth s elliptical orbit causes the distance between the Earth and the Sun (the Earth s radius vector) to vary by 3.39% from perihelion (closest) to aphelion (farthest). These variations in distance cause the intensity of solar radiation at the top of the atmosphere to vary as 1/R2, where R is the radius vector. Thus the solar input at the top of the atmosphere varies from 1414 Wm 2 (in December) to 1321 Wm 2 (in July). Additional variations in solar intensity, or brightness, result from the solar sunspot cycle, and even solar oscillations. These slight variations in the solar output are usually accounted for in the calculation of solar energy available at the top of the atmosphere, or the total extraterrestrial solar radiation, referred to as ETR. The ETR has only been monitored from space since the early 1970 s, or almost three solar sunspot cycles. Excellent histories of ETR measurements and analysis are provided in Frohlich3 and Gueymard.4... 

I extraterrestrial solar radiation shall be considered to be black body radiation. Under these assumptions determine the emissive power Ms of the sun and its surface temperature Ts. What proportion of the radiation leaving the sun falls within the region of visible light (0.38 fim < A < 0.78 /an) ... 

As a first approach, extraterrestrial solar radiation can be taken to be radiation from a black body at this temperature, see also section 5.3.5. 

Fig. 5.39 Extraterrestrial solar radiation on a surface, whose normal forms the polar angle /3s with the direction of the solar rays...

Fig. 5.40 Spectral irradiance of extraterrestrial solar radiation falling perpendicularly on an area at a distance ro = 1AU from the sun...

Switzerland, yielded the spectrum reproduced in Fig. 5.40. The numerical values upon which this diagram is based can be found in M. Iqbal [5.34]. The maximum of EfAn lies in the visible light region at A pa 0.45 /tm. 99 % of the irradiance falls in the wavelength band A < 3.8 fim. Fig. 5.40 also shows the spectral irradiance EXa of the radiation emitted by a black sun at Ts = 5777 K. The areas under the two curves (up to A —> oo) are equal — they each yield the solar constant E0 —, but the spectrum of the extraterrestrial solar radiation deviates significantly at some points, in particular at A < 0.6//.in, from the spectrum of radiation from a black body. 

Example 5.6 Determine the irradiance of extraterrestrial solar radiation on a horizontal area in Berlin (latitude i > = 52.52° North, longitude

[Pg.557]

We will now apply (5.108) to solar radiation, Fig. 5.43. The path s of the bundle of rays is slightly curved because of refraction in the atmosphere. It begins, at large distance away, with Lx(l0) = Lx(s — oo) = Lsx the spectral intensity of extraterrestrial solar radiation, and ends at the earth s surface (s = 0) with the intensity Lx(s = 0). It therefore follows from (5.108), taking into account d/ = — ds, that... 

The spectral transmissivity rA from (5.110) also gives the ratio of the spectral irradiance EXn of an area located on the ground and oriented perpendicular to the direction of radiation, to the spectral irradiance Esx by extraterrestrial solar radiation. It therefore holds that... 

Fig. 5.48 Spectral irradiance EBX J, of extraterrestrial solar radiation and Ex,a of direct solar radiation at the ground for a pure, cloudless atmosphere with mr l = 1-5. The curve indicated by rA,R-E A°n represents the attenuation caused by Rayleigh scattering alone. The dark areas indicate the absorption by each of the gases written on the graph (/io3 = 0.30 cm, w = 2.0cm)...

Table 2.15 Spectral distribution of extraterrestrial solar radiation definition according to WMO (1986).

Table 3.1 Extraterrestrial solar radiation flux (average sun-earth distance) (per 5 mn, base e)...

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