Actinic flux

TABLE 4.1 Relation between the Slant Path Optical Depth m and sec 0 for a Standard Rayleigh Atmosphere 

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 

FIGURE 4.8 Interception of radiation emanating from a solid angle dm on a surface element of area ds on an atmospheric layer of thickness dz. Pathlength through the layer is m(9). 

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  

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 

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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. 

The light available to a molecule in air for absorption and photodissociation includes both direct and scattered and reflected radiation coming from all directions as described earlier and depicted in Fig. 3.16. The term actinic flux or spherically integrated actinic flux, denoted by F( A), is used to describe the total intensity of this light and is the quantity of interest in calculating kp. 

There are several approaches to measuring actinic fluxes and photolysis rate constants. One approach is to measure the rate of decay of a species such as N02 directly, so-called chemical actinometry (e.g. see Madronich et al., 1983). Another approach is to measure the light intensity and convert this to an actinic flux. 

RELATIONSHIPS BETWEEN RADIANCE, IRRADIANCE, ACTINIC FLUX, AND PHOTOLYSIS RATE CONSTANTS... 

The actinic flux F( A) is the total incident light intensity integrated over all solid angles, given by... 

FIGURE 3.20 Schematic diagram of a In radiometer used to measure actinic fluxes (adapted from Junkermann et al., 1989). 

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. 

Madronich (1998) has calculated actinic fluxes using updated values of the extraterrestrial flux. In the 150-to 400-nm region, values from Atlas are used (see Web site in Appendix IV) whereas from 400 to 700 nm those of Neckel and Labs (1984) are used. In addition, the... 

The variation in the actinic flux with surface elevation is important because some of the world s major cities are located substantially above sea level. For example, Mexico City and Denver, Colorado, are at elevations of 2.2 and 1.6 km, respectively. 

Table 3.10 shows the calculated percentage increase in the actinic flux at the earth s surface for an elevation of 1.5 km and atmospheric pressure of 0.84 atm (corresponding approximately to Denver) as a function of zenith angle for four wavelength intervals. In this calculation, it was assumed that the vertical 03 and particle... 

TABLE 3.7 Actinic Flux Values F( A) at the Earth s Surface as a Function of Wavelength Interval and Solar Zenith Angle within Specific Wavelength Intervals for Best Estimate Surface Albedo Calculated by Madronich (1998) ... 

FIGURE 3.21 Calculated actinic flux centered on the indicated wavelengths at the earth s surface using best estimate albedos as a function of solar zenith angle (from Madronich, 1998). 

Figure 3.24 shows the relative changes in the total actinic flux as a function of altitude from 0 to 15 km at solar zenith angles of 20, 50, and 78° and at wavelengths of 332.5 (part a), 412.5 (part b), and 575 nm (part c), respectively. Again, since these are relative changes, these results of Peterson (1976) and Demerjian et al. (1980) are not expected to be significantly different from those that would be obtained with the Madronich (1998) actinic flux estimates. 

The calculated actinic flux typically increases significantly in the first few kilometers. This is partly due to scattering of light by particulate matter and to light absorption by tropospheric 03 close to the surface. The effect of 03 can be seen by comparing the total fluxes at 332.5 nm (Fig. 3.24a), where 03 absorbs, to those at 575 nm (Fig. 3.24b), where it does not. 

As discussed earlier, the net actinic flux incident on a volume of air is sensitive to a number of parameters,... 

Surface albedo In Table 3.11 the calculated actinic fluxes are given for a surface albedo of 80%, which might correspond to the situation over snow, for example. As expected, the higher surface reflectivity leads to substantially higher actinic fluxes and hence enhanced photochemistry (see Problem 11). 

TABLE 3.10 Percentage Increase in the Calculated Actinic Flux at a Surface Elevation of 1.5 km Using Best Estimate Albedos as a Function of Solar Zenith Angle and Selected Wavelengths"... 

Aerosol particles Table 3.13 shows the percentage change in the actinic flux calculated by Peterson (1976) and Demerjian et al. (1980) for two cases (1) a particle concentration of zero, corresponding to a very clean atmosphere, and (2) a total particle concentration doubled compared to the base case. The actinic flux is predicted to increase if the total particle concentration is zero and decrease if it doubles (note, however, as discussed later, the sensitivity to the vertical distribution of particles and the relative importance of light scattering compared to absorption). 

It is these contrasting effects of aerosol particles, combined with uncertainties in the contribution of absorption due to 03, that provide the largest uncertainties in calculations of actinic fluxes and photolysis rates in the boundary layer (e.g., Schwander et al., 1997). As a result, it is important to use the appropriate input... 

TABLE 3.12 Percentage Increase in Actinic Fluxes at the Earth s Surface for a 5% Decrease in Total Column... 

All the calculated actinic fluxes discussed so far refer to a cloudless sky. The effects of clouds are... 

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