#### 3.1. Weighted UV Irradiances as a Function of the Solar Zenith Angle

Although the 2018 summer solstice at Dortmund, Germany was on 21 June, examining several days around that date revealed that 1 July was the closest one to being cloudless. Thus, it was chosen to analyze the effect of different action spectra on the daily course of weighted UV irradiances as a function of SZA,

${E}_{X\left(\lambda \right)}\left(\mathsf{\Theta}\right)$, see

Figure 3. Due to its comparatively flat spectral distribution in the UVA and UVB region in comparison with other weighting functions, see

Figure 1,

${E}_{\mathrm{Setlow}}\left(\mathsf{\Theta}\right)$ is more than one order of magnitude higher than

${E}_{\mathrm{NMSC}}\left(\mathsf{\Theta}\right)$,

${E}_{\mathrm{CIE}}\left(\mathsf{\Theta}\right)$, and

${E}_{\mathrm{ICNIRP}}\left(\mathsf{\Theta}\right)$, but the latter three also vary significantly from each other reflecting differences in the wavelength dependences of their relative spectral sensitivities. The maxima, all located at that day’s minimum SZA of 28.4° (13:36), are given by 4.450 Wm

^{−2} (Setlow), 0.393 Wm

^{−2} (NMSC), 0.178 Wm

^{−2} (CIE), and 0.045 Wm

^{−2} (ICNIRP). The

${E}_{X\left(\lambda \right)}\left(\mathsf{\Theta}\right)$ curves resemble each other but

${E}_{\mathrm{Setlow}}\left(\mathsf{\Theta}\right)$ was flatter for most of the day, with the exception of the early morning and late afternoon. For example, while

${E}_{\mathrm{Setlow}}=$ 4% of its daily maximum for

$\mathsf{\Theta}=$ 85° (6:00),

${E}_{\mathrm{CIE}}$,

${E}_{\mathrm{NMSC}}$, and

${E}_{\mathrm{ICNIRP}}$ were below 1%. Note that

Figure 3 depicts weighted irradiances some time before sunrise and after sunset. The morning and afternoon data strongly overlapped for each

${E}_{X\left(\lambda \right)}\left(\mathsf{\Theta}\right)$ curve due to the high SZA symmetry.

In addition to 1 July 2018, two additional days are included in

Figure 3; however, solely focusing on erythemally weighted UV irradiances so as not to clutter the figure. The 18 September and 18 December were the closest cloudless days in 2018 to the autumn equinox (23 September) and the winter solstice (21 December), respectively.

${E}_{\mathrm{CIE}}\left(\mathsf{\Theta}\right)$ was also calculated for 25 March. The results were very similar to those for 18 September and are therefore not depicted, again in the interest of visual clarity. The general shapes of the SZA dependent

${E}_{\mathrm{CIE}}\left(\mathsf{\Theta}\right)$ remain much the same throughout the year, but the weighted UV irradiances for the autumn equinox and for the winter solstice vary on a much smaller SZA scale than it is the case for the summer solstice. The maximum values differ approximately by an order of magnitude: 0.178 Wm

^{−2} (1 July), 0.087 Wm

^{−2} (18 September), and 0.013 Wm

^{−2} (18 December). The SZA and temporal locations of these maxima shift from 1 July (

$\mathsf{\Theta}=$ 28.4° at 13:36) to 18 Sept (

$\mathsf{\Theta}=$ 49.7° at 13:18) and to 18 December (

$\mathsf{\Theta}=$ 75.0° at 12:06). Note the shift in the local maximum time for the 18 December that is caused by the biannual time change from UTC + 2 h to UTC + 1 h and vice versa at Dortmund, Germany (change to daylight saving time between end of March and end of October). For 25 March (data not shown), the maximum of 0.066 Wm

^{−2} is found at

$\mathsf{\Theta}=$ 49.7° (13:18); thus, matching the autumn equinox SZA.

To gain insights into the importance of latitude in this context, solar spectra from Bernhard et al. [

29] measured in Townsville, Australia (latitude 19.3° S) on 11 January 1996, and calculated ones for different latitudes from Gerstl et al. [

30] were biologically weighted as well. Data were available for only a few SZAs, but as is apparent from

Figure 3, the weighted irradiances are comparable to those obtained with the solar spectra measured at Dortmund, Germany. For example,

${E}_{\mathrm{CIE}}\left(\mathsf{\Theta}\right)$ for latitude 51.5° N agrees within 1–12% with the weighted irradiances based on Gerstl’s calculated spectra [

30] for latitude 50° N, but are about one third smaller than those determined with Bernard’s data for latitude 19.3° S. The latter match

${E}_{\mathrm{CIE}}\left(\mathsf{\Theta}\right)$ based on Gerstl’s calculated spectra for latitude 20° S within a range of (4 ± 6)% (data not shown). The difference between latitude 20° S and 50° N is probably due to the slightly lower stratospheric ozone concentration at lower latitudes [

29]. The agreement of weighted irradiances based on solar spectra of different origins is quite reassuring. It also demonstrates that the low-resolution spectra of Gerstl et al. [

30] are good enough for dose estimates under clear sky conditions.

The CIE, NMSC, and ICNIRP curves are essentially parallel, while

${E}_{\mathrm{Setlow}}\left(\mathsf{\Theta}\right)$ is decidedly flatter for most of the SZA range. In their daily courses between SZAs of 20° and 70°, CIE, NMSC, and ICNIRP weighted irradiances vary by a factor of 12–15, whereas

${E}_{\mathrm{Setlow}}\left(\mathsf{\Theta}\right)$ changes only by a factor of about 4. This is due to the flatness of the Setlow action spectrum in the UVA region, which gives much more weight to wavelengths above 310 nm region compared to the other action spectra. As mentioned in

Section 2.2, our weighting procedure disregards spectral contributions above 400 nm. For the CIE, NMSC, and ICNIRP action spectra, this is sufficient, because no spectral sensitivities are defined at longer wavelengths. Additional calculations with the solar spectra by Bernhard et al. [

29] showed, however, that in the case of Setlow’s action spectrum the weighted irradiances including spectral contributions up to 550 nm are by a factor of 2.6–3.0 higher than those given in

Figure 3. This factor is essentially independent of the SZA.

In summary, similar SZA dependences were found for CIE, NMSC, and ICNIRP weighted irradiances with absolute values varying by an order of magnitude, whereas irradiances weighted with Setlow’s action spectrum for melanoma increased less steeply with decreasing SZA for most of the day. Calculations based on literature data showed consistent SZA dependences virtually irrespective of season and latitude when compared with those based on solar spectra measured at Dortmund, demonstrating the usefulness even of low-resolution data.

#### 3.2. Annual Course of Cumulative Weighted UV Doses

Annual biologically relevant UV doses were calculated according to Equation (2) with the CIE, NMSC, ICNIRP, and Setlow weighting functions. It is important to note that not all 365 days of 2018 were analyzed but only the 1st, 5th, 10th, 15th, 20th, and 25th of each month and some additional days, for example, being close to summer and winter solstice. Furthermore, due to this selection of roughly every 5th day, no longer just cloudless days could be used for the analysis, and the cumulative UV dose, ${H}_{X\left(\lambda \right)}\left({j}^{\prime}\right)$, must be regarded as an approximation, albeit a sufficiently appropriate one.

The similarity found for the daily courses (1 July 2018) of SZA dependent UV irradiances,

${E}_{X\left(\lambda \right)}\left(\mathsf{\Theta}\right)$, weighted either by the CIE, NMSC, or ICNIRP action spectrum, see

Figure 3, reappears for their cumulative annual UV doses, see

Figure 4, which are peak normalized (31 December) for better comparison. These three

${H}_{X\left(\lambda \right)}$ curves are hardly distinguishable because of their strong overlap. In contrast, Setlow’s melanoma action spectrum attributes a higher relative carcinogenicity to solar UVR in the first months of the year (February to June) and a lower one between August and November. Due to the comparably flat spectral distribution of Setlow’s weighting function above 310 nm,

${H}_{\mathrm{Setlow}}\left({j}^{\prime}\right)$ closely matches the radiometric (unweighted) annual UV doses with a percentage deviation of −2.5–0.1% throughout the whole year. By the end of March, both the radiometric and the Setlow-weighted solar spectra reach about 13% of their annual UV doses, whereas for all other weighting functions only about 8% is accumulated. This is due to the fact that the SZA dependences of the radiometric and Setlow-weighted irradiances are generally flatter than those with the CIE erythema and NMSC or ICNIRP action spectra, see

Figure 3. Consequently, the UVR doses accumulated at higher SZAs during the first quarter of the year are more significant for the radiometric and Setlow-weighted annual doses than is the case with the other three weighting functions.

Half of the CIE, NMSC, and ICNIRP weighted annual UV doses were accumulated until 28 June (day 179, $\mathsf{\Theta}=$ 28.7°) or until 25 June (day 176, $\mathsf{\Theta}=$ 28.6°) for ${H}_{\mathrm{Setlow}}\left({j}^{\prime}\right)$, both days being close to the middle of the year (182.5 days). There exist rough symmetries regarding 25% and 75% of the total cumulative weighted UV doses, which were found at −44 and +40 days (NMSC, CIE, ICNIRP: day 135, $\mathsf{\Theta}=$ 33.3° and day 219, $\mathsf{\Theta}=$ 35.4°) or at −52 and +46 days (Setlow: day 124, $\mathsf{\Theta}=$ 36.1° and day 222, $\mathsf{\Theta}=$ 36.3°). Without further analysis it remained unclear if the discrepancies between 25% and 75%, 4 and 6 days, respectively, result from the limited number of days for which calculations were carried out or from specific conditions during 2018 (cloudiness, ozone levels, etc.). The absolute annual UV doses amount to 18.1 MJm^{−2} (Setlow), 1.0 MJm^{−2} (NMSC), 484 kJm^{−2} (CIE), and 113 kJm^{−2} (ICNIRP). The differences between these values are substantial with, for example, a nine times higher annual ${H}_{\mathrm{NMSC}}$ compared to ${H}_{\mathrm{ICNIRP}}$.

The main notion here is that throughout the year, the cumulative UVR doses weighted with the CIE, NMSC, or ICNIRP action spectra are practically identical (when normalized to their value at the end of the year). Therefore, if necessary, they can be converted into each other by means of constant factors. In contrast, the annual SZA course of normalized Setlow weighted doses agrees with that for radiometric values.

#### 3.3. UV Doses Measured by Detectors Mimicking Erythema Sensitivity

In the last decades, quite a number of measurement devices have been developed aiming to mimic the skin’s UVR sensitivity, more particularly the wavelength dependence of erythema induction. A selection of detector responsivities is presented in

Figure 2 with additional information listed in

Table 1. In order to assess the accuracy of these detectors to reflect erythema response, but also for an easier comparison between them, the standardized CIE erythema action spectrum and the associated weighted UV irradiances and doses were used for reference. Instead of more “sophisticated” ways of analysis, we decided to focus on the simple ratio of

${E}_{X\left(\lambda \right)}$ to

${E}_{\mathrm{CIE}}$ or

${H}_{X\left(\lambda \right)}$ to

${H}_{\mathrm{CIE}}$, hereafter referred to as

${r}_{X\left(\lambda \right),\mathrm{CIE}}$, because of its higher practical benefit.

Figure 5a shows this ratio in the course of 1 July 2018 for six detecting systems. All depicted ratios have more or less pronounced minima in the early morning (before 6:00) and late afternoon (after 21:00), i.e.,

$\mathsf{\Theta}>$ 85°, except for

${r}_{\mathrm{VioSpor},\mathrm{CIE}},$ which is smallest for a SZA of approximately 70°. The associated measured irradiances, however, do not contribute significantly to the daily UV doses because more than 90% of them are accumulated for

$\mathsf{\Theta}\le $ 60°. None of the detectors shows a substantial difference between morning and afternoon, i.e., both

${r}_{X\left(\lambda \right),\mathrm{CIE}}$ curves overlap strongly. The SZA dependences of the ratios are rather small with mean values and standard deviations of 15 ± 2 (PSF), 7.4 ± 0.8 (RBM), 5.0 ± 0.9 (Genicom), 1.9 ± 0.2 (501-UV), 1.11 ± 0.04 (VioSpor), and 0.94 ± 0.07 (JEC1-IDE). Very similar values were found when calculations were based on solar spectra from Bernhard et al. [

29], namely 13 ± 2 (PSF), 7.3 ± 0.8 (RBM), 5.5 ± 0.3 (Genicom), 2.0 ± 0.1 (501-UV), 1.15 ± 0.06 (VioSpor), and 1.00 ± 0.04 (JEC1-IDE). This demonstrates the need for a careful handling of data from weighting UVR detectors. For example, PSF detectors, which have been the most frequently applied accumulating UVR dosimeters for decades, overestimate erythemally weighted UVR exposures by a factor of about 15; thus, these values must be corrected downwards. It is also obvious that PSF has a somewhat different dependence on SZA than the CIE erythema sensitivity curve, so that the precise correction factor is 17 at 60° but 14 at 30°. For RBM, this variation is between 8 at 60° but 7 at 30°. Other devices, for example, the VioSpor or the JEC1-IDE system, are able to mimic the convolution of UVR with the CIE action spectrum quite well as both of their ratios are close to 1.

In general, ratios similar to

${r}_{X\left(\lambda \right),\mathrm{CIE}}$ can be calculated for the same detectors but with other action spectra than the CIE erythema standard curve as reference. However, the weighting function for melanoma induction proposed by Setlow [

27] is the only one that has a markedly different spectral sensitivity; thus, one would expect an altered daily course to that presented in

Figure 5a only for

${r}_{X\left(\lambda \right),\mathrm{Setlow}}$. Indeed, these ratios are not more or less independent of the position of the sun as it was found for

${r}_{X\left(\lambda \right),\mathrm{CIE}}$ but decrease with increasing SZA. For 30°

$\le \mathsf{\Theta}\le $ 70° of 1 July,

${r}_{\mathrm{PSF},\mathrm{Setlow}}$ and

${r}_{\mathrm{RBM},\mathrm{Setlow}}$ are roughly halved (factors of 1.8 and 2.1), whereas the ratios of the Genicom (2.6), the 501-UV (2.5), the JEC1-IDE (2.7), and the VioSpor detectors (2.7) are reduced somewhat more. These values were calculated with the spectral UV irradiances measured at Dortmund, but again, very similar values were found with the solar spectra published by Bernhard et al. [

29], namely 1.7 and 2.0 for PSF and RBM, 2.4 for Genicom, 2.5 for 501-UV, 2.7 for JEC1-IDE, and 2.9 for VioSpor.

In addition to UVR detectors, which are applied for a certain period like a few hours, days or weeks to record an individual’s personal exposure, other devices are permanently installed, for instance on roofs, to continuously monitor the solar spectrum in a particular locality and to calculate erythemally weighted UVR exposure. Therefore, it makes sense to take a closer look at the variation of the dose ratios, i.e.,

${H}_{X\left(\lambda \right)}\left({j}^{\prime}\right)$ to

${H}_{\mathrm{CIE}}\left({j}^{\prime}\right)$, in the course of the year 2018, see

Figure 5b, but with the focus on a temporal and not on a SZA dependence. All ratio curves are virtually flat, and they stabilize by 1 July at the latest to their annual mean values as given in

Table 3. The Genicom detecting system has the highest percentage standard deviation with 7% followed by PSF with 5%. As expected from their daily

${r}_{X\left(\lambda \right),\mathrm{CIE}}$ courses, the VioSpor dosimeter’s and the JEC1-IDE radiometer’s 2018 ratios are close to 1. Overall, the annual standard deviations demonstrate that the mean ratios can be applied as correction factors the better the longer the devices are measuring.

None of these detectors has been intended to mimic relative spectral sensitivities other than the CIE standard erythema curve, but additional ratios can be calculated regarding the NMSC, ICNIRP, and Setlow weighting function to provide insights in their comparability with each other. The mean annual ratio values

${r}_{X\left(\lambda \right),\mathrm{NMSC}}$,

${r}_{X\left(\lambda \right),\mathrm{ICNIRP}}$, and

${r}_{X\left(\lambda \right),\mathrm{Setlow}}$ are presented in

Table 3. Although irradiances measured by the 501-UV biometer are disproportionately high by a factor of approximately 2 regarding

${E}_{\mathrm{CIE}}$, they are appropriate to describe

${E}_{\mathrm{NMSC}}$ without any correction. In contrast, the VioSpor and JEC1-IDE detectors underestimate

${E}_{\mathrm{NMSC}}$. A constant factor of ~0.5 is present for all

${r}_{X\left(\lambda \right),\mathrm{NMSC}}$ when compared to

${r}_{X\left(\lambda \right),\mathrm{CIE}}$ because of their annual UV doses, which are given by 1.0 MJm

^{−2} (NMSC) and 484 kJm

^{−2} (CIE). For UV doses weighted with the ICNIRP and Setlow action spectrum, these factors are 4.3 and 0.02, respectively.

Overall, the annual ratios are mean values taking all SZAs into account. Consequently, where the ratio strongly varies with the position of the sun, as we have mentioned above for the Setlow action spectrum, the averaged values do not adequately represent each daily situation, for example, at noon (minimum SZA) or in the early morning/late afternoon (maximum SZA). This mean nature is also apparent from the relatively high standard deviations in the case of the Setlow action spectrum (19–25% instead of 2–12% for the other weighting functions).

We conclude that the ratios of UV irradiances (or doses) from several detectors and erythemally weighted ones are practically constant throughout the day and the year. The detectors can therefore provide accurate risk estimates for erythema and NMSC when corrected with constant factors supporting the comparability of differently recorded data in the literature. They are not suitable to predict melanoma risk (if Setlow’s action spectrum is correct).