Comparing Weighting Functions for Erythema and Vitamin D

The weighting functions for erythema (McKinlay and Diffey, 1987) and for vitamin D production (Bouillon et al., 2006), as published by the International Commission on Illumination (CIE), are compared in Fig. 2.5 (upper panel). Each of these is arbitrarily normalized to unity at its maximum value. The figure also includes typical global solar irradiance spectra measured at a mid-latitude site at local noon on cloudless days close to the summer and winter solstices. The resolution of the spectra is approximately 0.9 nm at full-width half-maximum (fwhm), and the detailed structure is mainly due to absorption in the sun's atmosphere. The sharp decrease at wavelengths shorter than 315 nm is due to absorption by atmospheric ozone. All of these curves are plotted on a logarithmic vertical scale. Although the erythemal weighting function extends to longer wavelengths, the vitamin D weighted irradiance for the summer spectrum is about twice as large as for erythema because of its increased contribution between 300 nm and 315 nm. The weighted integrals for erythema (UVEry) and vitamin D (UVVitD1) are compared in the middle panel of Fig. 2.5, with a linear vertical scale. In all cases, the contribution from UVA is small, especially in the case of vitamin D-weighted UV. For the summer spectrum shown, the weighted irradiances, which are given by the integrated areas under these curves, are: UVEry = 0.28 W m and UVVitD = 0.54 W m-2 (UVVitD is reduced by ~5% if the weighting function is cut at 315 nm, see discussion below). For the winter spectrum, the weighted irradiances are: UVEry = 0.026 W m-2 and UVVitD = 0.027 W m-2 (UVVitD is reduced by ~10% if the weighting function is cut at 315 nm). The lower panel of Fig. 2.5 shows the same weighted irradiances, but focuses on the wavelength region from 290 nm to 330 nm only. There are substantial differences in the spectral shape of these weighted irradiances between summer and winter. In the winter, the contribution from longer wavelength components has a greater relative importance.

1 UV radiation weighted by the action spectrum for production of pre-vitamin D.

Figure 2.5 Upper panel: Weighting functions for erythema and vitamin D production, along with sample spectra measured at Lauder New Zealand at noon in the summer and winter. Middle panel: Weighted irradiances for the spectra shown in the upper panel. Lower panel: Detail of the weighted irradiances between 290 nm and 330 nm, with winter values (dashed curves) scaled up by a factor of 10

Figure 2.5 Upper panel: Weighting functions for erythema and vitamin D production, along with sample spectra measured at Lauder New Zealand at noon in the summer and winter. Middle panel: Weighted irradiances for the spectra shown in the upper panel. Lower panel: Detail of the weighted irradiances between 290 nm and 330 nm, with winter values (dashed curves) scaled up by a factor of 10