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" The authors are grateful to Dr. Sasha Madronich for generously providing these calculations.
h This column lists the power of 10 by which all entries should be multiplied. For example, at d = 0° the total actinic flux in the wavelength interval from 306 to 308 nm is 2.0 X 1014 photons cm s .
other molecules in air, most commonly N2 or Oz, and return to the ground state:
Only reaction (7) leads to the removal of NOz via photochemistry and hence the quantum yield for reaction (7) is needed to calculate the photolysis rate. Data on both primary quantum yields and absorption cross section (f>(\), characteristic of each molecule, are found in Chapter 4.
It must again be stressed that the absorption cross sections, cr(A), used to calculate photolysis rates are to the base e, not base 10, even though the latter is what has often been measured and reported in the literature in the past.
The actinic flux F( A), describing the intensity of light available to the molecule for absorption, depends on many factors, including geographical location, time, season, presence or absence of clouds, and the total amount of 03 and particles in the air which scatter light as it passes through the atmosphere. At the earth's surface, however, the actinic flux estimates and associated data of Madronich (1998) in Table 3.7 are commonly used to estimate rates and lifetimes of species with respect to photolysis under cloudless conditions.
(as opposed to a photophysical process such as fluorescence or energy transfer). For example, once N02 has absorbed light and is in an electronically excited state, it can either dissociate or energy transfer to
FIGURE 3.32 Calculated actinic fluxes as a function of altitude for a solar zenith angle of 30° and a surface albedo of 0.3. (From DeMore et a!., 1997.)
FIGURE 3.32 Calculated actinic fluxes as a function of altitude for a solar zenith angle of 30° and a surface albedo of 0.3. (From DeMore et a!., 1997.)
Because the actinic flux data are reported as averages over certain wavelength intervals, rather than integrating over Eq. (OO) in a continuous manner, in practice one calculates the sum of the product <f>(\)cr(\)F(A) over discrete wavelength intervals AA. The intervals are chosen to match the available flux data; for example, in Table 3.7, actinic fluxes are reported as averages over 2nm intervals from 290 to 320 nm, which is important for the 03 absorption, 5nm intervals from 320 to 420 nm, 10nm intervals from 420 to 580 nm, and 20nm intervals from 580 to 700 nm. Since the primary quantum yield, (f>( A), and the absorption cross section, a(A), are not normally reported over identical intervals, representative averages of these parameters over the same intervals for which the actinic flux data are reported must be calculated from the literature data.
In the most commonly used form, then, Eq. (OO) becomes:
A = 290 nm where <£av(A) is the primary quantum yield for the photolysis of the molecules averaged over the wavelength interval A A, centered at A, crav(A) is the absorption cross section, base e, averaged over the wavelength interval A A, centered at A, and Fav( A) is the actinic flux in photons cm~2 s_1 summed over the wavelength interval A A, centered at A, at a solar zenith angle 6 (Table 3.7) corrected for season (Table 3.8). If desired, corrections for surface elevation, altitude, etc. can be included. Note that the values in the tables are the total actinic fluxes over the wavelength intervals given. They are not per nm.
The sum (or integral if Eq. (OO) is used) is carried out from the lower limit of wavelengths in the troposphere, 290 nm, to some wavelength A; at which either the primary quantum yield or the absorption cross section becomes negligible.
Experimentally, while the determination of absorption cross sections is fairly straightforward, measuring primary quantum yields is not, due to interference from rapid secondary reactions. As a result, in cases where quantum yield data are not available, calculations of maximum rates of photolysis are often carried out in which it is assumed that (f>( A) = 1.0. It should be emphasized in such cases that this represents only a maximum rate constant for photolysis; the true rate constant may be much smaller, even zero, if photophysical fates of the excited molecule such as fluorescence or quenching predominate.

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