Solar flux

The sun radiates approximately as a blackbody, with an effective temperature of about 6000 K. The total solar flux is 3.9 x 10 W. Using Wien s law, it has been found that the frequency of maximum solar radiation intensity is 6.3 x 10 s (X = 0.48 /rm), which is in the visible part of the spectrum 99% of solar radiation occurs between the frequencies of 7.5 X 10 s (X = 4/um) and 2 x 10 s (X = 0.15/um) and about 50% in the visible region between 4.3 x 10 s (X = 0.7 /rm) and 7.5 X 10 s (X = 0.4 /Ltm). The intensity of this energy flux at the distance of the earth is about 1400 W m on an area normal to a beam of solar radiation. This value is called the solar constant. Due to the eccentricity of the earth s orbit as it revolves around the sun once a year, the earth is closer to the sun in January (perihelion) than in July (aphelion). This results in about a 7% difference in radiant flux at the outer limits of the atmosphere between these two times. 

Specific solar radiation conditions are defined by the air mass (AM) value. The spectral distribution and total flux of radiation outside the Earth s atmosphere, similar to the radiation of a black body of 5,900 K, has been defined as AM-0. The AM-1 and AM-1.5 are defined as the path length of the solar light relative to a vertical position of the Sun above the terrestrial absorber, which is at the equator when the incidence of sunlight is vertical (90°) and 41.8°, respectively. The AM-1.5 conditions are achieved when the solar flux is 982 Wm2. However, for convenience purpose the flux of the standardized AM-1.5 spectrum has been corrected to 1,000 Wm2. 

R.L. Kurucz, I. Furenlid, J. Brault, L. Testerman Solar Flux Atlas from 296 to 1300 nm, Nat. Solar Obs. Atlas No. 1 (Smithsonian Astrop. Obs., Cambridge 1984)... 

The state-of-the-art solar concentrators can provide solar flux concentrations in the following ranges, depending on the type of the concentrator [26] ... 

The part of the Sun that we can see is called the photosphere and has a surface temperature of 5780 K. The solar flux from every square metre of the surface is then given by Equation 2.1 ... 

The calculation for flux arriving at the Earth requires the Sun s luminosity and the distance from the Sun. The total solar flux (FSun x total area of the Sun) gives solar luminosity LSun = 3.8 x 1026 W and the flux at the Earth, /, is given by ... 

Calculate the ratio of the photon flux from the Sun and the Full Moon on Earth and, using the measured solar flux on Earth, calculate the flux from the Full Moon on Earth. 

Energy arrives from the solar flux heating the surface of the nucleus, the amount depending on the distance from the Sun, the inclination towards the Sun and the rate of rotation of the object. 

The solar flux can be calculated via Stefan s law from the observed surface temperature of the Sun, and the level of radiation at a known distance is calculated via the inverse square law (Figure 7.6). 

Consider the amount of radiation arriving on the surface of the Earth at a distance of 1 AU or 1.5 x 1011 m. The total flux of the Sun is distributed evenly over a sphere of radius at the distance of the planet, d. From the luminosity calculation of the Sun, F, the solar flux at the surface of Earth, FEarth, is F/47t(1.5 x 1011)2 = 1370 Wm-2 from the least-square law of radiation discussed in Example 2.4 (Equation 2.4). Substituting this into Equation 7.6 with the estimate of the albedo listed in Table 7.2 gives a surface temperature for Earth of 256 K. 

The rates of reactions (8.149)—(8.152) vary with altitude. The rate constants of reactions (8.149) and (8.151) are determined by the solar flux at a given... 

The UV absorption spectrum of gaseous trifluoromethyl peroxynitrate (1) shows a continuous decrease of intensity from 185 nm to 340 nm. The reported absorption cross section (a/10 ° cm ) ranges from 370 at 190 nm, to 1.0 at 290 nm and to 0.014 at 340 nm. Using published solar flux data in the troposphere at sea level, and assuming a unity quantum yield, a half-life time of about 1 month can be estimated for compound 1, which makes it a potentially effective carrier of pollutants from industrial zones to remote unpolluted sites . ... 

Of more direct interest for atmospheric photochemistry is the solar flux per unit interval of wavelength. Values up to approximately 400 nm are provided by Atlas 3 (see Web site in Appendix IV) and from 400 nm on by Neckel and Labs (1984). Figure 3.12 shows the solar flux as a function of wavelength outside the atmosphere and at sea level for a solar zenith angle of 0° (Howard et al., 1960). 

Outside the atmosphere, the solar flux approximates blackbody emission at 5770 K. However, light absorption or scattering by atmospheric constituents modifies the spectral distribution. The attenuation due to the presence of various naturally occurring atmospheric constituents is shown by the hatched areas in Fig. 3.12. 

FIGURE 3.12 Solar flux outside the atmosphere and at sea level, respectively. The emission of a blackbody at 6000 K is also shown for comparison. The species responsible for light absorption in the various regions (Os, H2Q, etc.) are also shown (from Howard et at., 1960). 

To estimate the solar flux available for photochemistry in the troposphere then, one needs to know not only the flux outside the atmosphere but also the extent of light absorption and scattering within the atmosphere. We discuss here the actinic flux F(A) at the earth s surface the effects of elevation and of height above the surface are discussed in Sections C.2.d and C.2.e. 

There are a number of estimates of the actinic flux at various wavelengths and solar zenith angles in the literature (e.g., see references in Madronich, 1987, 1993). Clearly, these all involve certain assumptions about the amounts and distribution of 03 and the concentration and nature (e.g., size distribution and composition) of particles which determine their light scattering and absorption properties. Historically, one of the most widely used data sets for actinic fluxes at the earth s surface is that of Peterson (1976), who recalculated these solar fluxes from 290 to 700 nm using a radiative transfer model developed by Dave (1972). Demerjian et al. (1980) then applied them to the photolysis of some important atmospheric species. In this model, molecular scattering, absorption due to 03, H20, 02, and C02, and scattering and absorption by particles are taken into account. 

TABLE 3.8 Correction Factors for Extraterrestrial Solar Flux Values Depending on Earth - Sun Distance at Various Times of the Year... 

Jayaraman et al. (1998) measured the aerosol optical depth, aerosol size distribution, and the solar flux close to the coast of India, over the Arabian Sea, and then... 

A similar conclusion is reached using direct measurements of solar fluxes at the top of the atmosphere (TOA) and at surface sites under clear compared to cloudy conditions (e.g., Cess et al., 1995, 1996b Evans et al., 1995). Figure 14.51a shows the absorptance, defined as the fraction of the down-... 

---