Actinic Flux

Sunlight drives the chemistry of the atmosphere by dissociating a number of molecules into fragments that are often highly reactive. Whether a molecule can be dissociated in the atmosphere depends on the probability of an encounter between a photon of appropriate energy and the molecule. The radiative quantity pertinent for photochemical reactions is the photon flux incident on the molecule from all directions, since it does not matter to the molecule from which direction a photon comes. The radiative flux from all directions on a volume of air is called the actinic flux (actinic means "capable of causing photochemical reactions"). We use the symbol I for the actinic flux to distinguish it from the irradiance E\ I is usually expressed in units of photons cm-2 s-1. The spectral actinic flux, I(X), expresses the wavelength dependence of the actinic flux; I(X) has units of photons cm 2 s_i nm "'. Whereas the spectral irradiance is expressed per square meter of area, the actinic flux is usually expressed per square centimeter; the different area units, m~2 versus cm'2, arise because molecular absorption cross sections are expressed in terms of cm2, and the photodissociation rate of a molecule will be seen shortly to be a product of the spectral actinic flux and the molecular absorption cross section.

To compute atmospheric photochemical reaction rates it is necessary to determine the total light intensity incident on a given volume of air, from all directions. The light

3The TOA radiative flux can be estimated by measuring E(X) on a surface at ground level for various solar zenith angles 80 and plotting In E(X) versus m and extrapolating torn = 0. The slope of the best-fit straight line is z(k). This method of calculating Ex(X) is called the Bouguer-Langley method. Integrating Ex (k) overall wavelengths produces the solar constant S0.

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FIGURE 4.8 Interception of radiation emanating from a solid angle da on a surface element of area ds on an atmospheric layer of thickness dz. Pathlength through the layer is m(0).

FIGURE 4.8 Interception of radiation emanating from a solid angle da on a surface element of area ds on an atmospheric layer of thickness dz. Pathlength through the layer is m(0).

intensity impacting a volume of air includes not only direct solar radiation, but light, either direct from the Sun or reflected from the Earth's surface, that is scattered into the volume by gases and particles, as well as light reflected directly from the Earth's surface.

The actinic flux is related but not equal to the irradiance. The relation between the two quantities has been illustrated carefully by Madronich (1987). Consider an atmospheric layer of infinitesimal vertical thickness dz, illuminated from above (Figure 4.8). The quantity of light incident on the top surface of the layer depends on the direction of incidence of the light, as defined by the spherical coordinates 9, c|>. This dependence is specified by the spectral radiance L(X, 0, 4>), expressed in units of photons cm-2 s"1 nm 1 sr 1. The number of photons entering the layer (through ds, in time dt, from solid angle rfco) is

To determine the spectral actinic flux in the layer in Figure 4.8 resulting from the spectral radiance L(X, 0, <f>), we need to jump ahead a bit. The rate of photodissociation of a species A is written as dnA dt

where nA is the molecular number concentration (molecules cm-3) and jt\ is the photodissociation rate coefficient (s '). jA depends on the available light and the nature of the molecule A, expressed in terms of the product of the probability a photon will be absorbed and the probability of dissociation following absorption of a photon. After entering the layer in Figure 4.8, photons may interact with molecules of A in the layer and be absorbed. For an infinitesimally thin layer, the Beer-Lambert law can be used to compute the number of photons absorbed in time dt in wavelength range dX as aA(X)nAm(Q)L(X, 0, <))) cos QdsdadtdX

where cta(A.) is the absorption cross section (cm-2) of a molecule of A and m(Q) is the pathlength shown in Figure 4.8. m(Q) = dz/cos 0. For each photon absorbed, the probability that the molecule will dissociate is <t>A (A,). (This is called the quantum yield.) Thus the number of molecules dissociated in time dt in wavelength range dX is

§A(X)aA(X)nAL(X, 0, §)dsdzd(i)dtdX

The total number of dissociations dNA occurring in the volume in a time interval dt is obtained by integrating over all solid angles, over the upper surface of the layer, and over all wavelengths:

dNA = -idz Jdsj(nAdt) J <$>A{X)oA{X)( J L{X,Q,<\>)da\dX

The first factor on the right-hand side (RHS) is just the total volume of the layer, which can be brought to the left-hand side (LHS) along with dt to produce

d^=-nAJ^ $A{X)vA{X) ^ jf L(X, 0, <J>)</a> jdX

As indicated, the quantity on the RHS multiplying nA is jA. The spectral actinic flux is then the radiative quantity that drives the photodissociation, that is, the quantity that multiplies c|)a(/~)cta(a) to produce a product that when integrated over all wavelengths produces the photodissociation rate coefficient. The spectral actinic flux l(X) is then

It is important to distinguish the actinic flux from the spectral irradiance. The spectral irradiance E(X) is the radiant energy crossing a surface (per unit surface area, time, and wavelength) and is calculated from L(X, 0, <j>) by (4.14),

E(X)= / L(X, 0, <(>) cos 0 sin 6 dQ (4.33)

The factor cos 0 reflects the change in the projected area of the surface as the angle of incidence is varied. This factor does not appear in the expression for the actinic flux because the projected area and the pathlengths offset exactly. As the angle of incidence is changed from overhead (0 = 0°) to nearly glancing (0 —> 90°), the energy (irradiance) incident on the layer decreases, but the actinic flux remains unchanged because the lower intensity is exactly compensated for by the longer pathlength of light through the layer.

Continue reading here: Atmospheric Photochemistry

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  • Margaret
    What is called actinic flux?
    3 years ago
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    What is flux atmospheric chemistry?
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  • kevin hartmann
    How to calculate actinic flux?
    10 years ago
  • griffo
    What is the symbol for actinic flux?
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