Angle, zenith

Because of the tilt of the earth s axis by 23.5° with respect to the plane of the earth s revolution around the sun, the north pole is tilted toward the sun on June 22 and away from the sun on December 21 (Fig. 17- 2). This tilt causes the solar beam to have perpendicular incidence at different latitudes depending on the date. The zenith angle Z is determined from ... 

Figure 14. Principle of an astatic levers support system. The mirror rests on three fixed points but the total weight is distributed on a number of levers, which, by design, apply reaction forces proportional to the cosine of the zenithal angle.

Now for the photon flux. As the altitude increases, the atmosphere looks thinner so the light has to pass through a smaller amount of atmosphere dependent on the zenith angle, which is related to the latitude on the planet and the angle that its axis of rotation makes with the plane of the solar system, the season of the year and hence the position of the planet in its orbit. The depth of atmosphere through which the Sun s rays pass is given by dz sec0. Hence the optical absorption is ... 

Analytic representation of dependence of albedo on daily average zenith angle... 

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. 7-1. The annual average insolation and average zenith angle as a function of the sine of latitude. The zenith angle has been multiplied by a factor of 10 so that its variation can be seen. The sine of latitude is used as the ordinate in all of these plots because it reflects the relative surface area at each latitude.

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...

Fig. 7-3. The albedo as a function of temperature at a solar zenith angle of 75°, comparing clear and cloudy ocean and land. The temperature effect results from the large albedo of ice and snow. The sensitivity is small for cloud-covered land and...

Latitude Relative area Land fraction Land clouds Ocean clouds Insolation Zenith angle... 

Seasonal variation of insolation and zenith angle from subroutine SEASON... 

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

I modify the program to simulate the effect of permanent ice at high latitudes by setting the albedo for the two highest latitudes in each hemisphere equal to 0.7, independent of season, temperature, or solar zenith angle. These values are set at the end of subroutine SWALBEDO. The modified program is listed as DAV10. 

Seasonal variation of insolation and zenith angle from subroutine SEASON This program uses the new solver GAUSSD and SLOPERD All ice is suppressed in SHALBEDO nrow = 18 the number of equations and unknowns ncol = nrow + 1... 

Of more direct interest for atmospheric photochemistry is the solar flux per unit interval of wavelength. Values up to approximately 400 nm are provided by Atlas 3 (see Web site in Appendix IV) and from 400 nm on by Neckel and Labs (1984). Figure 3.12 shows the solar flux as a function of wavelength outside the atmosphere and at sea level for a solar zenith angle of 0° (Howard et al., 1960). 

The path length L for direct solar radiation traveling through the earth s atmosphere to a fixed point on the earth s surface can be estimated geometrically using Fig. 3.14. This flat earth approximation is accurate for zenith angles < 60°. One can approximate L... 

With reference to Fig. 3.14, for zenith angles less than 60°,... 

Table 3.5 shows values of the air mass at various zenith angles 9, either estimated using m = sec 9 or corrected for curvature of the atmosphere and for refraction it is seen that only for 9 > 60° does this correction become significant. 

FIGURE 3.14 Definition of solar zenith angle 8 at a point on the earth s surface. 

---