## Calculating RAF0

If the RAF is calculated directly from the power law definition F1/F2 = (A/A)RAF or RAF = ln(F1/F2)/ln(.^2/^i), the result will have a dependence on ozone amount for any range of Q\ relative to the reference amount (Fig. 5.A1).

In this study, the RAF is calculated as the best fit to the function i)RAF

with the requirement that U is approximately 1 (Fig. 5.A2). This approximation works well for the entire range of SZA (Fig. 5.A3), the ozone range 200 DU to 600 DU, and for all four action spectra discussed in this study. The result is a small error in the estimation of action spectra irradiance change, if the ozone independent RAF is used in the power law formula. If more accuracy is needed for the erythemal spectrum, the parameter U(d) is given by UERY = (A + CO ' + E9)/(1 + B90-5 + D9+ F915) with the coefficients given in Table 5.A1. 0.95 < Uery(#) < 0.99. Similar functions can be derived for other action spectra.

If the range is extended to 100 DU < W < 600 DU, then the functional form changes (Fig. 5.A4) for SZA < 50° and the form U(n2m 1)RAF with an RAF value independent of Q can no longer be used.

1.24

SZA=ltf

Figure 5.A1 RAF computed from its definition, RAF = ln(F1/F2)/ln(.ß2/ß1) Figure 5.A2 RAF computed as best fit to irradiance ratios F1/F2 (gray squares) using U(n2/n1)RAB (black line) Figure 5.A3 F1/F2 for 0° <SZA<80° for 200 DU< W <600 DU

1.25

1.25 0,2 0,4 0,6 0,8 1.0 Figure 5.A4 Irradiance ratios when the ozone range is extended 100 <Q < 600

Table 5.A1 UeRY = (A + C005 + E0)/(1 + B005 + DO + F0ls)

A = 0.9893339422829114 B = -0.2091512249939112

C = -0.2065389508416529 D = 0.01116628089647472

E = 0.01084565669362034 F = -0.00001740267964926986