In addition to the Stokes vector, there are two other important radiant quantities: irradiance and mean radiance.

Irradiance, or vector irradiance, is defined as the integral over the
entire spherical solid angle of the normal component of the radiance,
relative to some surface.
Irradiance follows the cosine law in that a collimated beam of photons
intercepting a plane surface produces an irradiance that is proportional
to the cosine of the angle between the photon direction and the
surface normal. It has units of Wcm
nm^{-1}
and may be written as,

where is the position vector, is the surface normal unit vector, is the solid angle differential expressed in polar coordinates with being the polar angle and being the azimuthal angle.

In a plane-parallel atmosphere (see section 2.6),
only the irradiance along the -direction
is relevant so the vector representation is not necessary.
The irradiance in polar coordinates is,

(3.15) |

which is also the difference between the downwelling, , and the upwelling, , irradiances. Irradiance is also the first moment of the radiation field. In terms of the fields, the irradiance is equivalent to the monochromatic Poynting vector. Irradiance is used in the calculation of heating rates and is usually used in determining the radiance reflected by a surface.

The mean radiance, *F*, also referred to as actinic flux, mean intensity,
flux density, or flux (Madronich, 1987), describes the number
of photons converging upon a volume element per unit time, area and
wavelength.
The mathematical expression for mean radiance is equivalent to
the zeroth moment of the radiation field,

(3.16) |

and hence is analogous to a flux density. The units usually used for mean radiance are photonss cm nm sr