## Radiative Flux In The Atmosphere

Consider a beam of radiation of radiance L crossing a surface dS with the beam axis making an angle 0 to the normal to dS (Figure 4.6). dS projects as dS cos 0 perpendicular to the beam axis of the radiation, and the radiant flux density dF on dS is

The radiant flux density, or irradiance, on the surface dS is obtained by integrating the radiance over all angles: When the radiance L is independent of direction, the radiative field is called isotropic. In this case, (4.13) can be integrated over the half-space, fi = 2n, and the relation between the irradiance and the radiance is E = nL.

The irradiance on a horizontal surface is obtained from the incoming radiance by integrating the radiance over the spherical coordinates 0 and <j)

where the direction of the incoming beam is characterized by the angle 0 (see Figure 4.7).

The spectral radiant flux density, F(X), is the radiant flux density per unit wavelength interval, expressed in watts per square meter per nanometer (Wm~2 nm 1). Equivalently, when considering radiation incident upon a surface, the spectral irradiance, E(X), is expressed as Wm-2 nm-1.

Sometimes the spectral radiant flux density is expressed as a function of frequency v, that is, F(v). Because the frequency v of radiation is related to its wavelength by (4.1), v = c/X, F(X) and F(y) can be interrelated. Since the flux of energy in a small interval of FIGURE 4.7 Coordinates for radiative calculations.

FIGURE 4.7 Coordinates for radiative calculations.

wavelength dX must be equal to that in a small interval of corresponding frequency dv, then

Generally we will deal with wavelength as the variable rather than frequency, although they can easily be interrelated as indicated in (4.16). 