Action Spectra and Irradiance Trends

An action spectrum A(A) is a weighting function of wavelength A that estimates the relative strength of a process (e.g., biological process or material degradation) for each wavelength in a range from A1 to A2. The action spectrum is multiplied by the irradiance I(A, t) to obtain a production function PACT(t). A direct comparison of dose amounts for any causal effect is not given by A(A), but just indicates the relative effect of each wavelength. Frequently, what is wanted is the time integrated effect of the process EF over a specified time interval t1 to t2. The quantities PACT and Ef can be used to estimate the relative effect of exposure to solar radiation on different days at some specified time, or cumulatively over some portion of a day or longer (Eqs. (5.15) and (5.16)).

Typical action spectra have been estimated for skin reddening for Caucasian males, plant damage, vitamin D production, non-melanoma cancer production, and DNA damage, etc. The vitamin D action spectrum AVit-D is based on a digitization of the action spectrum graph presented by McLaughlin et al. 1988. The vitamin D production was obtained in the laboratory from "surgically separated skin." An accurate functional fit (Fig. 5.15(a)) to the published graph is given (250 nm<A<315 nm) in Table 5.2 along with functional fits to the graphs (Figs. 5.15(b), (c), (d)) for three other more common action spectra, Adna damage, plant growth Apla, and erythemal Aery.

300 320 340 360 380 400 280 300 320 340 360 380

Wavelength (nm) Wavelength (inn)

Figure 5.15 (a) Fit to vitamin D action spectrum (McLaughlin et al., 1982), 250 nm<A<314 nm; (b) Fit to DNA damage action spectrum from (Setlow, 1974), 290 nm<A<400 nm; (c) Fit to plant growth response action spectrum (Flint and Caldwell, 2003), 285 nm<A<390 nm; (d) Fit to erythemal action spectrum (McKinlay and Diffey, 1987), 250 nm < 1 < 400 nm

Figures 5.16 and 5.17 show the result of multiplying respective action spectra by the solar flux (Fig. 5.2) at the ground for an atmosphere with 300 DU of ozone and SZA = 0° (typical or the equatorial band with overhead sun). From a practical perspective, wavelengths below 300 nm have little effect at sites near sea level, because there are too few photons that are able to penetrate the atmosphere. Altitude must be taken into account at higher altitude sites, even though most of the short wavelength photons are absorbed by stratospheric ozone, but the numbers that do penetrate the stratosphere are not reduced as much by Rayleigh multiple scattering compared to the boundary layer atmosphere. The effect for DNA damage and vitamin D production decreases rapidly for longer wavelengths, especially for larger SZA typical of mid-latitudes. The erythemal effect persists into the UV-A

Normalized solar flux* action spectrum

285 290 295 300 305 310 315 320 325 330 Wavelength (nm)

Figure 5.16 Action spectra (DNA, vitamin D, and ERY) multiplied by the solar flux at the ground for 300 DU of ozone and SZA = 0°

Normalized solar flux* action spectrum

285 290 295 300 305 310 315 320 325 330 Wavelength (nm)

Figure 5.16 Action spectra (DNA, vitamin D, and ERY) multiplied by the solar flux at the ground for 300 DU of ozone and SZA = 0°

Plant grow tli

Normalized solar flux * action spectrum

280 300 320 340 360 380 400

Wavelength (nm)

Figure 5.17 Action spectrum (plant growth) multiplied by the solar flux at the ground for 300 DU of ozone and SZA = 0°

Plant grow tli

3 04

Normalized solar flux * action spectrum

280 300 320 340 360 380 400

Wavelength (nm)

Figure 5.17 Action spectrum (plant growth) multiplied by the solar flux at the ground for 300 DU of ozone and SZA = 0°

range, which is why it is important for sunscreen preparations to protect to as long a wavelength as is possible. Finally, the plant growth spectrum (Fig. 5.15(c)) spans both UV-B and UV-A, and extends into the VIS wavelengths.

The accuracy of action spectra are usually not specified since they are meant to convey the response that occurred during a particular set of experiments that are highly specific to the particular samples that were examined. This is particularly true for the three spectra that pertain to human response to UV light. None of these spectra apply to any specific individual or group of people, but are just indicative of a process. The spectra can be used to give an idea of how a process would change if there were a change in the UV irradiance for a sample that had an approximate average response that was similar to the above spectra. The best-known example of this is the use of the UV index based on the erythemal action spectrum. Here the accuracy of the UV index is limited to no better than 10% (i.e., an integer scale from 0 to 10), but nonetheless, the index is useful for estimating when conditions are likely to cause harm from exposure to UV irradiance. All of the action spectra should be considered in a similar manner.

As discussed in Section 5.3.1, the behavior with respect to ozone change of action spectrum weighted summed irradiances is not the same as for monochromatic irradiances. The fractional change is approximated by a power law in RAF described in Section 5.3.2, which has been demonstrated to hold for a wide range of ozone values Q with constant RAF for each SZA. Rearranging Eq. (5.3) in terms of fractional differences,

However, the RAF(#), where d = SZA, must be empirically derived for each action spectrum and each SZA. This has been done for the erythemal irradiance Fery using measurements from Mauna Loa, Hawaii (Bodhaine et al., 1997). The resulting variation of RAF(#) with SZA is shown in Fig. 5.18, along with a theoretical calculation based on Eq. (5.4) applied to each wavelength and summed with erythemal weighting. This shows that the empirical power law behavior F1/F2 = (Q^IQ 1)RAF(0) can be explained by application of the physically based Beer's Law for absorption in the atmosphere. The behavior with SZA is as expected from a mix of UV-B and UV-A wavelengths, as the importance of UV-B decreases with increasing SZA. In addition to standard action spectra, a recent WMO report (Seckmeyer et al., 2005) has developed an RAF(#,.ß) analysis for the specific response of particular types of broadband instruments that are intended to approximate the erythemal response function. They also present an analysis of RAF(#,.ß) for the exact erythemal weighting function ^ERY (Table 5.4) for the ozone range from 100 DU to 600 DU. In all of the work discussed here RAF(#,.ß) = RAF(#) by limiting the range of Q to 200 DU <n < 600 (see Appendix 5.1).

Figure 5.18 RAFery(^) variation with 0 <0< 85° for the erythemal action spectrum from data obtained at Muana Loa, Hawaii (Bodhaine et al., 1997) compared with a theoretical calculation based on summation over wavelengths using ^4ery and Eq. (5.4) yielding the form of Eq. (5.17), which is fitted by Eq. (5.18a) for erythemal irradiance (Herman, 2009)

Figure 5.18 RAFery(^) variation with 0 <0< 85° for the erythemal action spectrum from data obtained at Muana Loa, Hawaii (Bodhaine et al., 1997) compared with a theoretical calculation based on summation over wavelengths using ^4ery and Eq. (5.4) yielding the form of Eq. (5.17), which is fitted by Eq. (5.18a) for erythemal irradiance (Herman, 2009)

Table 5.4 Function fit to four UV action spectra of Fig. 5.8

Fit to vitamin D spectrum (McLaughlin et al., 1988) A-v-lt_D 250 nm <A< 314 nm logio(AVlt_D) = (A + CA05 + EA + GAL5)/(1 + BA05 + DA + Fl1'5)

A = -0.9601647127133382 B = -0.1771944277419561 C = 0.1798847906875285 D = 0.01044079180885732 E = -0.01118449188229313 F = -0.00020464360877287360

G = 0.0002309087838152358_

Fit to DNA damage spectrum (Setlow, 1974) Adna 290 nm <A< 400 nm log10(ADNA) = (A + CA05 + EA)/(1 + BA05 + DA + FA15)

A = -0.1090717334891702 B = -0.1578036701734071 C = 0.01546956801974633 D = 0.008268275171175154 E = -0.000529417616572146 F = -0.0001436582640327567 Fit to plant growth response action spectrum (Flint and Caldwell, 2003) Apla log10(APLA) = (A + CA05 + EA)/(1 + BA05 + DA+ Fl1'5) 285 nm <A< 390 nm

A = -2.747265993518105 B = -0.1791860260727771 C = 0.4772684658484249 D = 0.01068302156756403 E = -0.02764643975624155 F = -0.0002119599411078172

G = 0.0005339842703179307_

Fit to erythemal action spectrum (McKinlay and Diffey. 1987) AERY log10(AERY) 250 nm <A< 400 nm log10(AERY) = 0 250 nm <A< 298 nm log10(AERY) = 0.094(298 -A) 298 nm<A<328 nm log10(AERY) = 0.015(139 -A) 328 nm<A<400 nm

Theoretically calculated RAF(#) values for all four action spectra in Fig. 5.15 are given in Fig. 5.19, and the fitting functions for each RAF in Table 5.5,

Eqs. (15.8a~15.8d), for the ozone range from 200 DU to 600 DU, which gives an RAF(#) that is independent of the ozone value. If the range is extended to 100 DU, the RAF(#,A depends on the ozone amount and SZA. The behavior of some action spectra RAFs with SZA (e.g., DNA) is similar to single wavelength RAFs for relatively narrow action spectra mostly contained in the UV-B region; namely, increasing RAF with SZA. More broadly-based spectra have RAF values that are nearly constant for SZA < 40°, and decrease for larger values of SZA. Very wide spectra, such as the Plant Growth spectrum, decrease for all SZA > 0.

Figure 5.19 The variation of RAF with SZA for the four spectra in Fig. 5.15. Note that RAFery and RAFVIT look similar because of different scales (200 DU < n < 600 DU)

The reason that scattering can be neglected when calculating change in irradiance is that the scattered radiance is linearly proportional to the direct solar beam when stratospheric ozone is the primary absorber. The calculation may not be accurate for strongly absorbed wavelengths at large SZA when the direct solar beam is very small compared to the scattered irradiance. When this happens, the path through the atmosphere to the ground is the expected slant path through the stratosphere, which changes to a nearly vertical path for scattered irradiance that occurs lower in the atmosphere (Umkehr effect). This shortens the optical path and reduces the sensitivity to ozone change that occurs in the troposphere. If ozone changes in the stratosphere are much larger than in the troposphere, FiIF2 = (A/A)RAF(0) is still a good approximation, since scattering can be neglected for estimations of irradiance change.

Table 5.5 Fitting functions for the action spectra RAF of Fig. 5.19

RAFERY = (A + C005 + E0)/(1 + B005 + D0 + F015)

(5.18a)

A

= 1.253034387380404 B = -0.1893942742785442

C

= -0.2374988749526192 D = 0.008753703248421607

E

= 0.01109085001133105 F = 2.163425112458424D-05

RAFdna = (A + C02 + E04)/(1 + B02 + D0a)

(5.18b)

A

= 2.006603342348651 B = -0.000222243468041799

C

= -0.0004040537916876323 D = 1.23788082612675D-08

E

= 1.861486615239331D-08

RAFVIT = (A + C005 + E0 + G015)/(1 + B005 + D0 + F015)

(5.18c)

A

= 1.300000361376985 B = -0.2561979971919163

C

= -0.3331173671966876 D = 0.02040664839011024

E

= 0.02657302492632673 F = -0.0004560385514125725

G

= -0.0006221828632328866

RAFPLA = (A + C005 + E0)/(1 + B005 + DO)

(5.18d)

A

= 0.4073412230744607 B = -0.1992738307220675

C

= -0.08017040437930313 D = 0.01140308620531996

E

= 0.004045533964044966

The percent change in zonal average clear-sky erythemal irradiance as a function of latitude can be estimated from the 30-year monthly and zonal averaged ozone time series by using Eqs. (5.17) and (5.18a) (Fig. 5.20). The estimations are restricted to latitudes between 53 °S to 53 °N because the estimation of the RAF was for SZA<80".During the winter solstice, at 53° latitude, the noon SZA is 76°.The estimation of RAFs for large SZA > 80° could be done with a spherical geometry corrected radiative transfer analysis.

The results in Fig. 5.20 show that there have been large changes in potentially damaging UV-B radiation at all wavelengths. The monochromatic changes were estimated from Eq. (5.4) because some of the ozone changes were sufficiently large as to result in a small error using the differential form in Eq. (5.1). The high latitude values may have a very small error caused by neglecting the spherical geometry correction to sec(SZA) for winter conditions at 52.5° latitude when the noon SZA reached 75.8°.The effect would be to slightly reduce the optical path and the estimated change in irradiance. At lower latitudes, the effect is negligible.

Since the DNA damage RAF, which is dominated by the behavior between 300 nm and 310 nm (Fig. 5.16), is similar in shape with respect to SZA to the monochromatic RAF, the percent increase will be much larger for DNA damage than for the erythemal spectrum. Figures 5.21 and 5.22 present the monthly percent change of 100 dF12/F2 in 305 nm irradiance and the DNA damage weighted irradiance PDNA(Month, d) from 1979 to 2008. As expected, the change in percent is similar for low latitudes where the ozone change is fairly small. For larger Q

Figure 5.20 The percent change in annual clear-sky erythemal irradiance (ERY solid black) for 30 years during the period 1979 to 2008, based on Eqs. (5.17) and (5.18a), and the monthly and zonal averaged ozone time series. The change in monochromatic 305, 308, 310, 315, 320, and 325 nm irradiance from Eq. (5.4) are also shown (gray)

Figure 5.20 The percent change in annual clear-sky erythemal irradiance (ERY solid black) for 30 years during the period 1979 to 2008, based on Eqs. (5.17) and (5.18a), and the monthly and zonal averaged ozone time series. The change in monochromatic 305, 308, 310, 315, 320, and 325 nm irradiance from Eq. (5.4) are also shown (gray)

changes at high southern latitudes, the behavior is somewhat different because of increased contribution to PDNA (Eq. (5.15)) from wavelengths smaller than 305 nm for the summer months. The same summer effect is smaller at high northern latitudes because the ozone change is less (annual ozone change 3.5% compared to 7%, Fig. 5.22).

Figure 5.21 Percent change in clear-sky 305 nm irradiance from 1979 to 2008 as a function of month and latitude calculated from Eq. (5.4) and the monthly zonal average ozone data

Lalilude

Figure 5.21 Percent change in clear-sky 305 nm irradiance from 1979 to 2008 as a function of month and latitude calculated from Eq. (5.4) and the monthly zonal average ozone data

Latitude

Figure 5.22 Percent change in clear-sky DNA damage spectrum weighted irradiance from 1979 to 2008 as a function of month and latitude calculated from Eq. (5.17), Table 5.2, and the monthly zonal average ozone data

Latitude

Figure 5.22 Percent change in clear-sky DNA damage spectrum weighted irradiance from 1979 to 2008 as a function of month and latitude calculated from Eq. (5.17), Table 5.2, and the monthly zonal average ozone data

From the viewpoint of population in the higher latitudes of the Northern Hemisphere, the increases in clear-sky PDNA have been 5% - 8% during most of the spring and summer months when the solar UV irradiance exposure is at a maximum (more clear days as well as seasonally declining ozone going into the summer). The changes have been much larger in the higher latitudes of the Southern Hemisphere during the spring and summer months, ranging from 12% to over 20%, and extend to lower latitudes (a 12% to 15% increase between 30°S and 40°S and 18% to 22% between 40°S and 50°S). These are serious increases in damaging UV irradiance that likely would have been much worse in the absence of the chlorine limiting agreement contained in the Montreal Protocols and subsequent agreements.

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