Solar zenith angle calculation

Figure IX-B-18. Approximate photolysis frequencies versus solar zenith angle calculated for 3-methylbutanal for a cloudless day in the lower troposphere with an overhead ozone column of 350 DU. The solid curve for y(Total) was calculated to fit the EUPHORE data point the thin black curve for j l) was calculated using

Photolysis frequencies representative of the lower atmosphere were calculated using the measured cross sections and with the extrapolations shown in the figure IX-F-19. The numerical listing of the values of totai and cross sections used are summarized at 1 nm intervals in table IX-F-7. The results of the calculations of /(Total) values versus solar zenith angle, calculated for a cloud-free troposphere with an overhead ozone column of 350 DU, are given in figure IX-F-20. 

Figure IX-H-21. Photolysis frequencies for (CHs jNNO as a function of solar zenith angle. Calculations were made for clear-sky conditions in the lower troposphere with an overhead ozone column of 350 DU.

Figure IX-I-3. Comparison of photolysis frequencies for HONO2, HOONO2, and several organic nitrates versus solar zenith angle calculated for a cloud-free lower troposphere with an overhead ozone colurtm of 350 DU.

The albedo depends on surface properties—whether ocean, land, or ice—on the presence or absence of clouds, and on the zenith angle of the sun. The formulation I use is based on a detailed study by Thompson and Barron (1981). I have fitted to the results of their theory the analytical expressions contained in subroutine SWALBEDO. Figures 7-2 and 7-3 illustrate the calculated albedos for various conditions Figure 7—2 shows the variation of albedo for clear and cloudy skies over land and ocean as a function of the daily average solar zenith angle, results that were calculated using subroutine SWALBEDO. The temperature was taken to be warm enough to eliminate ice and snow. The most important parameter is cloud cover, because the difference between land and ocean is most marked... 

Fig. 7-2. The albedo as a function of the daily average solar zenith angle comparing clear and cloudy land and ocean. The temperature for these calculations was taken as +15°C to suppress ice and snow. In this formulation, the albedo is...

Also calculates daily average solar zenith angle for use in SWALBEDO day = tvar 365.2422... 

The solar zenith angle can be calculated in the following manner for any particular location (i.e., latitude and longitude), day of the year (dn), and time of day as described by Spencer (1971) and Madronich (1993). First, one needs to calculate what is known as the local hour angle (th), which is defined as the angle (in radians) between the meridian of the observer and that of the sun ... 

The second derived parameter that is needed for calculating the solar zenith angle at a particular time... 

For other latitudes, dates, and times, the solar zenith angle can be calculated as described by Madronich (1993) and summarized earlier. 

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). 

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"... 

FIGURE 3.24 Calculated relative actinic flux using best estimate albedos as a function of height above the earth s surface for solar zenith angles 8 of 20, 50, and 78°, respectively, at (a) 332.5, (b) 412.5, and (c) 575 nm [from Peterson (1976) and Demerjian et al. (1980)]. 

From Peterson (1976) and Demerjian et al. (1980) although these are based on actinic fluxes different from those in Table 3.7, the relative changes calculated here should be similar to those that would be derived using the model from which the data in Table 3.7 were derived the changes in the particle concentration are relative to the base case shown in Table 3.7. h Solar zenith angle. 

Calculated for typical winter conditions of a solar zenith angle of 70° and a surface reflectivity of 80% for a collimated incident light beam. 

Under the typical summertime conditions, the thinner cloud shows an increase of 65% in the actinic flux above the cloud whereas the thicker cloud shows an increase of almost a factor of three, the maximum theoretically possible. This is due to scattering of diffuse light from the top of the cloud, as well as from the ground. As expected, below the thicker cloud, the total actinic flux is reduced, in this calculation, to 19% of the clear-sky value. However, for the thinner cloud of optical density 8, the actinic flux below the cloud is actually calculated to be greater than for the cloudless case. This occurs in the case of a small solar zenith angle and direct (rather than diffuse) incident light because the direct incident light is diffused as it traverses the cloud as discussed earlier for the case of the actinic flux above a Lambertian surface, conversion of a direct to diffuse source leads to an enhancement in the actinic flux. 

Similarly, Fig. 3.30 shows measurements of i(N02) at an altitude of 7-7.5 km as a function of solar zenith angle compared to a multidirectional model calculation (Volz-Thomas et al., 1996). The agreement in this case is generally good. However, this is not always the case. For example, Fig. 3.31 shows some measurements of 7(N02) as a function of solar zenith angle made by different groups at different locations and using different techniques (Kraus and Hofzumahaus, 1998). 

FIGURE 3.30 Values of 7(N02) at 7- to 7.5-km altitude as a function of solar zenith angle (0) measured using 2ir radiometers (circles) compared to a model calculated photolysis rate (solid line). (Adapted from Volz-Thomas et al., 1996.)... 

Figure 3.32 shows some calculated actinic fluxes in the stratosphere at 20-, 30-, 40-, and 50-km altitude at a solar zenith angle of 30° (DeMore et al., 1997) as well as at ground level. The surface albedo was assumed to be 0.3 and the aerosol concentrations typical of moderate volcanic conditions. ... 

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 al 1997.)... 

Following the procedure outlined in Section 3.C.la, calculate the solar zenith angle for your city or town at the following times (a) noon on January 1 (b) 8 00 a.m. on March 15 ( Beware the ides of March... ) (c) noon on June 21 (d) 3 30 p.m. on September 1 (e) 9 00 a.m. on December 21. The latitudes and longitudes for various locations can be found, for example, in the Rand McNally International Atlas. 

Use the data in Tables 3.7 and 3.11 to calculate the ratio of the actinic flux at the earth s surface for an 80% surface albedo compared to the best estimate albedo at solar zenith angles of 0 and 78° for the following wavelength regions 298-300, 318-320, and 400-405 nm. Comment on the expected effects on photochemistry in the boundary layer. 

The surface albedo can have a large effect on the total light available for photolysis in the troposphere. Calculate the factor by which the photolysis of H202 would increase at a solar zenith angle of 60° on December 1 over snow with a surface albedo of 80% compared to a normal best estimate surface albedo. 

Crowley et al. (1994) have measured the absorption cross sections of CH3OCl and calculate a lifetime with respect to photolysis under stratospheric conditions of 4 h at a solar zenith angle of 80°. The rate of the heterogeneous reaction (38) is not known. 

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