In the simplest case, let us assume there is an overcast sky with a layer of uniform optical thickness. Figure 1 shows the impact of increasing optical thickness on the amount of UV reaching the surface relative to the clear sky dose for three solar zenith angles (0°, 30°, and 60°), and a total column ozone amount of 450 Dobson Units (DU). There is a nonlinear relationship between UV dose and increasing optical depth; the rate of change of UV as a function of increasing optical depth decreases. These results are in good agreement wlith previous work in this area (e.g. Frederick and Snell, 1990).
Figure 1. Variation of surface UV dose as a function of cloud optical depth for overcast sky conditions.
A sensitivity study of surface irradiance at 305 nm and 320 nm with varying boundary layer aerosol extinction was carried out for two different solar zenith angles, assuming clear sky conditions and a total column ozone amount of 305 Dobson Units (DU). The modeled irradiance at 305 nm and 320 nm relative to the value with zero aerosol extinction is shown in Figures 2 and 3, respectively. The zenith angles correspond to a near-horizon sun position (81.3°) and near-peak zenith angle (37.3°) for this day. The extinction coefficient values shown here are reasonable to expect in a region that is not highly polluted, and indicate that UV irradiance at these wavelengths can change by a few percent for conditions that are typically experienced in a non-urban environment.
Figure 2. Effect of aerosol extinction coefficient on surface irradiance at 305 nm relative to case with no aerosol extinction.
Figure 3. Effect of aerosol extinction coefficient on surface irradiance at 320 nm relative to case with no aerosol extinction.
The effect of ozone absorption is also seen in these figures. In the 305 nm case where ozone absorption is still relatively strong, there is little variation in surface irradiance with changing aerosol extinction for the two zenith angles due to the high ozone mass path. At 320 nm where ozone absorption is much weaker, the aerosol extinction mass path becomes more important as indicated by the variation in relative irradiance with solar zenith angle.
Figure 4. UV-B dose relative to dose calculated with a boundary layer ozone concentration of 10 ppb.
(power
rule) (6)
where UV and DU are the dose and ozone column density, and [[Delta]]UV and [[Delta]]DU are the changes in these quantities. The subscripts on these terms in the power rule formula indicate initial (1) and final (2) quantities of UV dose and ozone amount. This parameter must be treated with caution, however, as values can vary significantly depending on the wavelength interval and action spectrum used in calculating UV dose. This parameter also varies with respect to solar zenith angle and vertical ozone distribution. The RAF is limited in validity to small changes in total column ozone on the order of a few percent (Madronich, 1993). Using the erythema action spectrum of McKinlay and Diffey (1987) in the wavelength range 290 nm to 400 nm, RAFs calculated using this model range from 1.1 to 1.3 using varying solar zenith angles and total column ozone amounts, in good agreement with previously published results (e.g. Madronich et al., 1994).
Figure 7 shows the relative sensitivity of integrated UV-B dose amount to total column ozone abundance at solar zenith angles of 0°, 30°, and 60°. Note that the sensitivity is greatest at low ozone levels; increasing column abundance by a given percentage will have a greater impact on attenuating UV-B than will an equal percentage increase in ozone at higher column amounts. The effect of solar zenith angle in this case is similar to increasing the total column ozone depth as path length increases nonlinearly with increasing zenith angle, effectively increasing the ozone column depth needed to penetrate to the surface.
Figure 8 shows the wavelength-dependent irradiance for a portion of the UV-B regime for total column ozone amounts of 250, 300, 350, and 390 Dobson Units calculated at a solar zenith angle of 30°. The wavelength dependence of ozone absorption cross sections are easily observed in this diagram; changes in irradiance for different ozone amounts are greatest at shorter wavelengths and become negligible beyond 320 nm.
Figure 7. UV-B dose relative to dose amount at 250 DU.
Figure 8. UV-B irradiance as a function of wavelength for total column ozone amounts of 250 DU (topmost curve), 300 DU, 350 DU, and 400 DU (lowest curve).
Brühl, C. and P. J. Crutzen, On the Disproportionate Role of Tropospheric Ozone as a Filter Against Solar UV-B Radiation. Geophysical Research Letters, Vol. 16, pp. 703-706, 1989.
Charache, D. H., V. J. Abreu, W. R. Kuhn, and W. R. Skinner, Incorporation of Multiple Cloud Layers for Ultraviolet Radiation Modeling Studies. Journal of Geophysical Research, Vol. 99, pp. 23,031-23,040, 1994.
Frederick, J. E., and H. E. Snell, Tropospheric Influence on Solar Ultraviolet Radiation: The Role of Clouds. Journal of Climate, Vol. 3, pp. 373-381, 1990.
Frederick, J. E., A. D. Alberts, and E. C. Weatherhead, Empirical Studies of Tropospheric Transmission in the Ultraviolet. Journal of Applied Meteorology, Vol. 32, pp.1883-1892, 1993.
Liu, S. C., S. A. McKeen, and S. Madronich, Effect of Anthropogenic Aerosols on Biologically Active Ultraviolet Radiation. Geophysical Research Letters, Vol. 18, pp. 2265-2268, 1991.
Madronich, S., Chapter 2, UV radiation in the natural and perturbed atmosphere, in UV-B Radiation and Ozone Depletion: Effects on Humans, Animals, Plants, Microorganisms, and Materials, M. Tevini, ed., Lewis Publishers, Boca Raton, Florida, 1993.
Madronich, S., R. L. McKenzie, M. M Caldwell, and L. O. Björn, Changes in Ultraviolet Radiation Reaching the Earth's Surface. Chapter 1 in Environmental Effects of Ozone Depletion: 1994 Assessment, United Nations Environment Programme, pp. 1-22, November 1994.
McKinlay, A. F., and B. L. Diffey, A Reference action spectrum for ultra-violet induced erythema in human skin, in Human Exposure to Ultraviolet Radiation, Risks and Regulations, W. F. Passchier and B. F. M. Bosnjakovic, ed., International Congress Series 744, pp. 83-87, 1987.
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