Photochemistry and Photobiology, 2005, 81 : 154-1 62
Global Forecast Model to Predict the Daily Dose of the Solar Erythemally Effective UV Radiation?
Alois W. Schmalwieser*', Gunther Schauberger', Michal Janouch2, Manuel Nunez3, Tapani Koskela4, Daniel Berger5 and Gabriel Karamanian' 'Institute of Medical Physics and Biostatistics, University of Veterinary Medicine, Vienna, Austria 'Solar and Ozone Observatory Hradec Kralove, Czech Hydrometeorological Institute, Hradech Kralove, Czech Republic 3School of Geography and Environmental Studies, University of Tasmania, Hobart, Tasmania, Australia 4Finnish Meteorological Institute, Helsinki, Finland 5Solar Light Inc., Philadelphia, PA 'GAW Station-Ushuaia, Ushuaia, Argentina
Received 1 December 2003; accepted 24 September 2004.
A worldwide forecast of the erythemally effective ultraviolet (UV) radiation is presented. The forecast was established to inform the public about the expected amount of erythemally effective UV radiation for the next day. Besides the irradiance, the daily dose is forecasted to enable people to choose the appropriate sun protection tools. Following the UV Index as the measure of global erythemally effective irradiance, the daily dose is expressed in units of UV Index hours. In this study, we have validated the model and the forecast against measurements from broadband UV radiometers of the Robertson-Berger type. The measurements were made at four continents ranging from the northern polar circle (67.4"N) to the Antarctic coast (61.1's). As additional quality criteria the frequency of underestimation was taken into account because the forecast is a tool of radiation protection and made to avoid overexposure. A value closer than one minimal erythemal dose for the most sensitive skin type 1 to the observed value was counted as hit and greater deviations as underestimation or overestimation. The Austrian forecast model underestimates the daily dose in 3.7% of all cases, whereas 1.7% results from the model and 2.0% from the assumed total ozone content. The hit rate could be found in the order of 40 % .
INTRODUCTION The solar radiation reaching down to the earth's surface consists of only a few percentage of ultraviolet (UV) radiation. Despite being
YPosted on the website on 28 September 2004 *To whom correspondence should be addressed: Institute of Medical
Physics and Biostatistics, University of Veterinary Medicine, Veter- inaerplatz 1, A-1210 Vienna, Austria. Fax: 0043-1-25077-4390 e-mail: firstname.lastname@example.org
Abbreviations: asl, above sea level; EPTOMS, Earth Probe Total Ozone Mapping Spectrometer; MED, minimal erythemal dose; SED, standard erythemal dose; SPF, sun protection factor; TOC, total ozone content of the atmosphere; UV, ultraviolet; UVI, UV Index used as unit; UVIh, UV Index hours used as unit; WHO, World Health Organization; WMO, World Meteorological Organization.
0 200.5 American Society for Photobiology 0031 -8655/05
just a small fraction, the UV part is responsible for various effects on the humans. UV radiation is the main cause for many damaging effects by penetrating the skin and the eye. Sunburn, tanning, snow blindness and immune suppression are the acute and most obvious reaction to UV radiation overexposure. Cataracts and skin cancer are examples for latent damages.
Fair-skinned populations have associated tanned skin as a sign of good health and well-being during the past decades. This has resulted in excessive exposure to both sun and artificial sources (solaria) of UV to obtain and maintain a tan over the whole year. The exposure of humans to UV radiation depends strongly on the individual behavior. Schauberger et al. (1) have shown that in the case of the Austrian population, approximately 50% of UV radiation exposure is job related, whereas 36% occurs during leisure time, 13% through outdoor vacation activities and 1 % is caused by artificial UV sources in tanning devices. The UV radiation exposure of the skin can therefore be reduced greatly in many cases through public education and information addressing essential radiation protection.
Since 1995, International Commission on Nonionizing Radia- tion Protection, World Health Organization (WHO) and World Meteorological Organization (WMO) (2) jointly recommend the UV Index as the quantity for informing the public about the UV intensity. Following WMO (3) the UV Index should be defined as the global solar irradiance weighted by the Commission Inter- nationale de 1'Eclairage action spectrum (4) of the erythema. Thus, the UV Index is a unit of intensity, not alone the maximum value of the day. The UV Index is a dimensionless quantity normalized to unity by dividing the effective irradiance (W/m2) by 0.025 W/m2, which corresponds also to a multiplication by 40.
For quantifying biological effects, the radiant exposure (or dose) is the relevant parameter and not the irradiance. Under the assumption of the Bunsen-Roscoe law, the caused effect is proportional to the radiant exposure. Integration of the daily course of irradiance leads to the daily dose that can be expressed in units of UV Index hours (UVIh) following a suggestion of Saxebal(5). An advantage of the daily dose is that it is not dominated by short-term changes of atmospheric conditions, e.g. attenuation by clouds, like the UV Index, and it takes into account the length of the day.
In this article the global UV forecast model for the daily dose, expressed in units of UV Index hours (UVIh), is presented, which was developed and operationally used at the Institute of Medical
Photochemistry and Photobiology, 2005, 81 155
Physics and Biostatistics, University of Veterinary Medicine in Vienna, Austria. Model and forecast calculations of daily doses are validated by a comparison with measurements. These measure- ments were made at six sites on four continents ranging from 67"N to 60S, including extreme locations during periods up to 5 years. The validation is done with special attention to radiation protection and health care, using hit rate and underestimation of UV radiation as main quality criteria.
MATERIALS AND METHODS The forecast procedure was established to inform people about the expected daily dose for the next day. From the forecasted dose the user may choose the necessary sun protection tools. Therefore, the quality of such a forecast must be validated to prove its claim: radiation protection. In the first part of this section the model is described, as well as its input parameters and output. In the second part the methodology and data used for validation are presented.
Austrian forecast model. The core procedure of the Austrian forecast model is a fast spectral model, also called physical model with simple parameterization. The general idea traces back to a suggestion of Diffey (6): spectral measurements are parameterized to solar height and total ozone content of the atmosphere (TOC). The basing spectral measurements were made by Bener (7) over many years at the alpine observatory (46"48'N, 9"49'E, 1590 m above sea level [asl]) of Davos, Switzerland. Splines are introduced for parameterization. This procedure delivers the global spectral irradiance as the sum of the diffuse and direct component. From this the irradiance is calculated for 16 discrete wavelengths between 297.5 and 400 nm. To correspond to the altitude dependence of UV radiation, a wavelength-dependent factor gained by Blumthaler et al. (8) is applied. This factor leads to an increase in the erythemally effective irradiance of 15% per 1000 m. A further improvement was done by adding the eccentricity factor of the earth path following Sonntag (9). Also from Sonntag (9), formulas are taken for calculating the sun's zenith angle, correspondingly solar height. Cloudiness, aerosols and albedo can be handled by attenuation or enhancement factors.
Following the definition of the UV Index the spectral irradiance E(h) from the model has to be weighted by the action spectrum of the human erythema w ( 3 ) . Integration over the spectral range and normalization by 2.5 mW/mirYdeliver the dimensionless, erythemally effective irradiance E'uv" as the UV index:
Since the UV Index was introduced as minimum denominator for public information (2,3,10,11,12) in 1995, detailed research has already been done regarding measurements (13), models (14) and forecasts (15). The UV Index is therefore a well-determined measure of irradiance. But biological effects due to UV radiation depend on duration of exposure, the radiant exposure or dose O'uv'hl(At). The radiant exposure is calculated by the erythemally effective irradiance E[""'] and the exposure time At as
where f, and tb are starting and ending time of exposure, determining At = tb - ta. Following this, the daily dose DruVlhl(At) is calculated by integrating the daily course of erythema1 effective irradiance from sunrise (t, = tsunrise) to sunset (tb = t,,,,,t) and expressed in units of UV Index hours (UVIh).
Input parameters. The forecast is done for clear skies. Input parameters are time and date, geographical coordinates, elevation as1 and the TOC. Time and date determine the eccentricity factor and together with the geographical coordinates also solar height. Besides solar height the path length of irradiance through the atmosphere is determined by topography. For gridded data, we use a digital elevation model with high spatial resolution of 30 arcsec, respectively higher than 1 km. This data set is called GTOP030 and was built up by a collaborative effort led by the U.S. Geological Survey EROS Data Centre. Detailed description can be found in Gesch and Larson (16).
Atmospheric absorption results mainly from the total ozone content. Because of showing both, spatial and temporal variability, appropriate TOC values have to be provided to ensure high accuracy of UV model
calculations (17). As shown by Schmalwieser et al. (18), TOC measure- ments from satellites can be prepared to deliver TOC values appropriate for a forecast of the erythemally effective UV radiation. For the presented forecast, the basis is TOC data from National Aeronautics and Space Adminstration's Earth Probe Total Ozone Mapping Spectrometer (EP- TOMS) (19). Details on this simple global TOC forecast scheme can be found in Schmalwieser et al. (18). By its use, daily mean TOC values for the day of forecast, for certain sites or on a global grid were gained. The latter consists of 360 X 180 values, which correspond to a spatial resolution of 1.0" in latitude and longitude.
Output. The Austrian forecast model generates a global forecast of the erythemally effective UV radiation as maximum irradiance around solar noon (UVI) and as daily dose (UVIh), both for clear sky. The forecast is made daily at 0O:OO h, for up to 36 h in advance. Data visualization is done by maps, showing the geographical distribution of the expected UV radiation. According to the recommended labels of the WHO (12) for the UV Index, 11 levels of intensity were used, indicated by colors between green, yellow, orange, red and purple. Values are also assessed verbally following the suggestion of the WHO. Verbal assessment and colors are adopted for dose levels. Besides the presentation by maps the forecast is also made for selected sites. This forecast is done using TOC values prepared by the TOC forecast scheme mentioned above, and for certain geographical coordinates and altitudes.
Validation of the Austrian forecast model. The quality of the forecast model is estimated by comparisons with measurements. Deviations AD:" are defined as
(3) mpak = D Y - DdC
Whereas denotes the measurements of daily dose made at day i and the Dfalc the corresponding calculated value, which may result either from the model DTd or from the forecast Of".
Further, the deviations ,fa1' of the calculated daily dose from the measurements can be divided into three groups depending on their sign: (1) hits, where -E 5 ALI;" 5 +& with E describing the preselected accuracy; (2) overestimation, where < - E; ( 3 ) underestimation, where AD;dc > + E.
Occurring deviations can be divided into two types of errors. One error type is the pure model error myd. This error results from parameter- izations and approximations within the chosen radiation model. The other error type is the total error of the forecast AD:, which is the sum of the pure model error and the error due to uncertainties of the forecasted input parameters, in our case the forecast error of the TOC and the uncertainties related to atmospheric aerosols and surface albedo.
The statistical description of deviations was done using quartiles (minimum [Min], first quartile [Ql], median [Med], third quartile [Q3] and maximum [Max]) and the mean deviation (MD) defined as:
1 " MD = . ( AD?") i=1
whereas n is the number of measurements. Measurements for validation. The measurements for validation were
taken from broadband UV radiometers of the Robertson-Berger type (20) at six different sites (Table 1) in four continents. The spectral sensitivity of these devices (UV-Biometer model SL501, Solar Light Inc., Philadelphia, PA ; hereafter, UV-Biometer) is similar to the sensitivity of the human skin for the acute effect of the erythema (13). The measurements were stored as mean values over a certain period ranging from 1 to 60 min. Their sum from sunrise to sunset delivers the daily dose. The measured values are observed in the upper panels of Figs. 1-6; a statistical description for each station is given in Table 1. These doses are used to validate the model and the forecast on all days, cloudy or not.
The first data set was obtained from a site north of the polar circle, Sodankyla (67.367"N, 26.650"E 179 m asl), Finland, where the sun does not rise above horizon for a week in December and does not set from the end of May till the middle of July. The operational measurements were carried out there since 1993, with a temporal resolution of 1 min. In absolute scale, the measurements at the observatory are traceable to the WMO intercomparison of 1995 (22). At Sodankyla the lowest values in dose were measured. During summer the daily dose values reach up to 37 UVIh. These result from high TOC values during summer (-370 DU) and the northern location. During spring, short-term increases in TOC can be measured, forcing decreases in UV radiation.
156 Alois W. Schmalwieser et a/.
Table 1. Specifications of measuring sites and statistical description of TOC measurements (maximum [03,,], mean [03,,,] and minimum [03,,,]) and maximum measured daily dose(D,,,)*
Altitude 03,,, 03,, 03,i, D,,, Station Latitude Longitude (masl) (DU) (DU) (DU) (UVIh)
Finland 67.367"N 26.650"E 179 513.5 336.8 230.8 37.0
Austria 48.258"N 16.434"E 153 512.5 334.3 198.2 50.6
USA 40.050"N 75.130"W 20 475.9 325.0 225.9 61.2
Australia 42.444's 147.904"E 33 445.5 316.0 231.3 70.2
Argentina 54.850"s 68.310'W 17 416.9 300.5 180.1 63.7
Antarctica 60.1OO0S 58.080"W 10 428.0 288.3 144.2 60.8
*03 represents ozone.
The second data set was measured at the University of Veterinary Medicine in Vienna (48.258"N; 16.434"E 153 m asl), Austria. The UV-Biometerispart of the Austrian UV monitoring network (23), calibrated twice per year within a ring trial of this cooperating network (24). At Vienna, significantly higher daily doses up to a level of 50 UVIh can be found. The shortest days have a length of 8 h, the longest 16 h. TOC values are as high as at Sodankyla, reaching up to 510 DU during spring, whereas during summer, values range from 350 to 300 DU. During winter time, Vienna was found to be under so- called ozone miniholes (25), which occur regularly throughout the mid- latitudes of both hemispheres (26). During these episodes, TOC values fall to a level of 200 DU. These phenomena are relatively short lived, caused by horizontal and vertical advection in the middle atmosphere (27,28,29). Their increased number may account for up to a third of the ozone trends (30) during late winter. Because of the low solar elevation and high cloud frequency, these low values in TOC cannot be recognized in the UV data set.
The third data set on the Northern Hemisphere originates from a UV- Biometer maintained by Solar Light Co., Inc. in Philadelphia (40.050N, 75.130"W; 20 m asl).
On the Southern Hemisphere the Department of Geography and Environmental Studies of the University of Tasmania at Hobart (42.4443, 147.904"E; 33 m asl), Australia, has delivered a further data set.
Philadelphia and Hobart have similar latitudinal locations, but differences in daily dose are significant (Table 1). The differences are caused by the different annual courses of TOC. Whereas for Philadelphia, TOC values near the solstice are close to the annual mean (325 DU), TOC values over Hobart are close to the minimum at solstice (-280 DU). When the annual decrease of TOC starts over Antarctica, high TOC values occur over Hobart.
At Ushuaia GAW station (54.850"s. 68.310"W; 17 m asl) in Argentina an instrument of the National Meteorological Service, which is part of WMO's Southern Cone Ozone Project, was installed in 1997 to monitor the UV radiation in this southem part of the world. Ushuaia is influenced by the Antarctic ozone hole. In 1998 and 2000, but not in 1999, TOC values dropped below 200 DU. Because of the general low TOC values, daily dose during summer reaches 55 UVIh at noon. For days with extremely low TOC, the measurements climb up to 70 UVIh.
Henrik Arctowski Station is the most southern station of our sample, situated on the King George Island, South Shetlands Archipelago (6O.10O0S, 58.O8O0W, 10 m asl). The deployed device was brought through the Czech Antarctic scientific program to the Polish Antarctic Station (19961998). After a duty cycle of 24 months the device was sent to the Solar and Ozone Observatory at Hradec Kralove (Czech Republic). By comparison with measurements of Spectrophotometer (Brewer MKIV, No. 96) as well as with measurements of the Czech national standard UV- Biometer (SL 501), no noticeable changes in spectral and angular response were detectable. Values of daily dose at Arctowski reflect the lack in ozone in an impressive way. As TOC values decrease by 50% within a few days, UV radiation increased by a factor of 2, reaching values of 80 UVIh. Solar elevation combined with TOC values that are close to the mean for the corresponding time of the year would have caused values between 20 and 40 UVIh for these days.
Figure 1. Validation of model and forecast calculations for Sodankyla (67.367'N, 26.650"E 179 m ad), Finland. Plotted are TOC (a), measure- ments D y and model calculations ADyd of daily dose (b). Frequency distributions (c) indicate deviations in daily dose for the model ADyd (white) and the forecast AD? (gray).
RESULTS Presentation and dissemination
The forecast of the erythemally effective UV radiation has been done operationally since 1995 at the Institute of Medical Physics and Biostatistics, University of Veterinary Medicine, Vienna, Austria. The products are maps showing the distribution over selected areas and tables with selected sites. They are available for the public via the www server of the University of Veterinary Medicine, Vienna (http://www-med-physkvu-wien.ac.at/uv/
Photochemistry and Photobiology, 2005, 81 157
Figure 2. Validation of model and forecast calculations for Vienna (48.258N, 16.434E; 153 m asl), Austria. Plotted are TOC (a), measure- ments D Y and model calculations AD$od of daily dose (b). Frequency distributions (c) indicate deviations in daily dose for the model AD$d (white) and the forecast hDfc (gray).
uv-online.htm). The products are further disseminated daily to mass media via file transfer protocol (newspapers, radio, television, video text) and additionally delivered also to some other health care-related web servers. Figure 7, as an example, shows the distribution of the daily dose for the whole globe for 12 November 2003. In this map as well as all other the assignment between the four classes of cloud cover (symbols for clear sky, partly cloudy, cloudy and covered) and the color is used to observe the geographical distribution. Verbal categories are given also. For this the suggestion of the WHO (13) for the labels of the UV Index
Figure 3. Validation of model and forecast calculations for Philadelphia (40.05OoN, 75.130W; 20 m ad), USA. Plotted are TOC (a), measurements DY and model calculations ADyd of daily dose (b). Frequency distributions (c) indicate deviations in daily dose for the model AD$od (white) and the forecast AD? (gray).
is converted to daily dose. Dose within 0 and 15 UVIh is denoted as low (0-2 UVI), within 16 and 33 UVIh as moderate (3-5 UVI), within 34 and 45 UVIh as high (6-7 UVI), within 46 and 63 UVIh as very high (8-10 UVI) and values higher than 63 WIh as extreme (> 11 UVI).
The model error ADPd is the difference between measurements D Y and model calculations Dyd. For this, the calculations have
158 Alois W. Schmalwieser et a/,
Figure 4. Validation of model and forecast calculations for Hobart (42.4443, 147.904%; 33 rn ad), Australia. Plotted are TOC (a), measurements D y and model calculations ADyd of daily dose (b). Frequency distributions (c) indicate deviations in daily dose for the model m m o d , (white) and the forecast Df" (gray).
to be done with well-known input parameters, which means that the uncertainty of these input parameters was minimized. TOC was taken from EPTOMS and prepared following the scheme of Schmalwieser et al. (18). With that the model calculations were done for clear sky and are shown in the second panels of Figs. 1 4 . The deviations in daily dose were calculated following Eq. 3 using all available measurements. A statistical description of these deviations is given separately for each station in Table 2. The annual courses of deviations are shown, as well as their frequency distributions, in the lower panels of Figs. 1-6. For the validation,
Figure 5. Validation of model and forecast calculations for Ushuaia (54.850"5, 68.310"W 17 m ad), Argentina. Plotted are TOC (a), measurements DYw and model calculations myd of daily dose (b). Frequency distributions (c) indicate deviations in daily dose for the model
(white) and the forecast AD: (gray).
the class width was chosen to be 22.5 UVIh because this dose corresponds to the minimal erythema1 dose (MED) for skin type 1. For the daily dose the frequency of hits ( t2 .5 UVIh) is within 27.2% (Hobart) and 58.7% (Ushuaia) where the mean for all is 41.2%. Underestimation in daily dose greater than 7.5 UVIh occurs only at two stations (Philadelphia and Ushuaia) with a frequency less than 0.8%. The total frequency of underestimating the daily dose is less than 2% for all. The upper quartile (43) is less than zero for all stations and within the hit class. All medians (Med) can be found in the hit or the first class of overestimation (-2.5 to -7.5
Photochemistry and Photobiology, 2005, 81 159
Figure 6. Validation of model and forecast calculations for Arctowski (6O.10O0S, 58.080"W; 10 m ad), Antarctica. Plotted are TOC (a), measurements D Y and model calculations myd of daily dose (b). Frequency distributions (c) indicate deviations in daily dose for the model m m o d I (white) and the forecast ADfc (gray).
UVIh). Values for the lower quartile (Ql) vary between -5.2 and -12.8 UVIh. Overestimation reaches down between -31.3 and 4 7 . 5 UVIh, depending on the maximal measured daily dose.
To estimate the total error AD:, the 36 h forecast values for clear sky were compared with all available measurements of daily dose for all stations. The results are shown as filled bars in the histograms of Figs. 1 4 and statistically described in Table 2. A slight broadening
of the error distribution relative to the error distribution of the pure model can be noticed. The mean hit rate for the forecasted daily dose is 36.8% for all cases. Maximum values of overestimation reach -3 1.7 to -68.0 WIh and are therefore 0.5 UVIh lower than those of the model. The median tends also to be slightly lower and was estimated to be -3.85 UVIh. The underestimation on the other hand has increased also. The frequencies of overestimation and un- derestimation have grown relatively to those of the model by around 2%, reaching 59.4% and 3.7%, respectively.
DISCUSSION Forecast concept and validation
To aid people in sun protection, the Austrian UV model is developed for worldwide calculations of the erythema1 effective UV radiation under clear sky. Because it is a tool of sun protection and health care, the forecast values should be as close as possible to the real values but should not underestimate them to avoid health damage. Model calculations are called unsatisfactory if the forecast value is lower than the observation. An error distribution symmetrically around zero would therefore be insufficient because the UV forecast has to be seen as an aspect of radiation protection.
Our presented forecast underestimates the measured daily dose in only 3.7% of all days, hits occur with a frequency of 36.8%, and in 59.4% of all days, the measured daily dose is overestimated by the forecast. The error in the predicted TOC values cause a slight broadening of the error distribution compared with the pure model. More than half (2%) the overestimation results from the uncertainties in TOC. The other half (1.7%) comes from the radiation model itself and missing input data like albedo. The highest underestimation occur at the most southern stations, Ushuaia and Arctowski. At Arctowski the maximum underestima- tion of the model is 3.43 UVIh, whereas for the forecast it is 25.75 UVIh. This deviation occurs while Arctowski is under the ozone hole and the difference between calculated and measured TOC is high. The highest underestimation at Ushuaia appears also when this station is influenced by the ozone hole.
In 41% of all cases the measurements are close to the modeled values for clear sky. Overestimation (57.1%) is mainly caused by cloudiness and aerosols, because we assume clear sky. The introduction of a cloud cover forecast could increase the hit rate. Unfortunately, recent cloud cover forecasts do not satisfy the requirements, which are necessary for the erythemally effective radiation (31). In addition, the hit rate of recent cloud cover forecasts on a European or regional scale is rather poor as shown by Schmalwieser et al. (32). Even for the prediction of the total cloud cover, the hit rate ( 1 octa) was found to be below 30%. And further, as several authors (e.g. 33) have shown, transmission factors for clouds show high variability even if more parameters are available than cloud cover like cloud type and base height. To include the cloudiness in the forecast we have chosen a way that involves the user actively. The observation is done using colors. The legends are made for four classes of cloud cover, which are represented as symbols, ranging from cloud free to overcast skies. This enables the user to include the actual weather situation and urges not to take values blindly, for example, in the case of a rainy day.
Finally, it should be noted that the forecast was compared with measurements made with UV broadband meters, which may also affect the error distribution. The devices are mounted horizontally so that the elevation of the horizon influences the measurements
160 Alois W. Schmalwieser et a/.
Figure 7. Global distribution of the daily dose in units of UV Index hours as delivered from the operational fore- cast.
especially at low solar elevations (34). Furthermore, the cosine response of the devices is quite well but for low solar elevations, deviations may become larger (13). In addition, the spectral error increases with decreasing solar height and may exceed the cosine error. However, at low solar height the irradiance is rather low and therefore also the absolute values of uncertainties.
Whereas for the erythemal effective irradiance the recommended (2 ) unit is the UV Index, for the erythemal effective dose there are several units in use. The MED is commonly used for observational studies in humans and other animals to describe the individual erythemal effect due to exposure to UV radiation. The value of 1 MED is defined as an UV dose that causes a just noticeable reddening of a previously unexposed skin. It is a subjective measure and depends on many variables, e.g. individual sensitivity to UV radiation, skin pigmentation, anatomic site, etc. The value of 1 MED varies in human populations roughly within the range of
200-500 J/mz for white-skinned people. Opposed to the MED, the standard erythemal dose (SED) is a standardized measure of the erythemogenic UV radiation (35). The value of 1 SED is equivalent to an erythemal effective radiant exposure of 100 J/m2.
Our proposal is to introduce the quantity daily dose (in UVIh, like proposed by Saxeb@l), defined by the integral of irradiance from sunrise to sunset. The advantage is that the estimation of objective doses received during outdoor activities would be easy and straightforward and closely related to the measure of irradiance. The subjective MED and SED can be converted to UVIh, by using 1 UVIh = 90 J/m2, depending on the photobiological skin type. For the melanocomprised skin types 1 and 2 , the subjective MED is 2.5 rt 1 UVIh, respectively, between 3.5 -C 1 UVIh. For the melanocompetent skin types 3 and 4 the MED are 4.5 ? 1 UVIh and 5.5 ? 1 UVh. For the purpose of sun protection, the knowledge of the individual minimal erythemal dose MEDj in units of UVIh connected with a forecasted dose Dfc can lead easily to a recommended sun protection factor SPF; for a whole-day stay outdoor, which is defined as:
Table 2. Deviations of model ADmod (model error) and forecast calculations ADfc (total error) from measurements (in UVIh). Frequency distribution of deviations is described by mean (Mean), minimum (Min), lower quartile (Ql), median (Med), upper quartile (Q3) and maximum (Max). Deviations were also grouped into three classes (overestimation, hits and underestimation) and their frequency (%) is given in the last three columns
Station Parameter Mean Min Q1 Med Q3 Max Overestimation (%) Hit rate (%) Underestimation (%)
-4.81 -4.70 -7.09 -9.07 -8.35 -8.24 -8.55 -8.39 -4.47 -4.37 -6.65 -6.57 -6.65 -6.89
-31.3 -31.7 -41.1 -54.1 -48.4 -46.0 -62.8 -57.0 -67.5 -68.0 -53.8 -55.8 -67.5 -68.0
-7.70 -7.88 -9.60
-13.2 -12.8 - 12.9 -10.9 -11.9 -5.19 -5.59 -9.89 -9.69 -9.34
-3.08 -2.91 -4.50 -6.26 -5.14 -5.39 -4.67 -4.55 - 1.33 - 1.45 -2.53 -2.58 -3.54 -3.85
-0.43 -0.28 -1.87 -2.67 - 1.08 - 1.04 -2.16 -1.63 -0.43 -0.37 -0.53 -0.54 -1.09 -1.09
4.16 7.43 3.13 7.80 8.33
11.00 3.29 7.26
13.14 19.41 3.43
25.75 13.14 25.15
53.0 52.5 67.3 76.1 64.2 67.3 71.3 69.1 37.8 41.4 50.1 49.8 57.1 59.4
45.8 44.6 32.4 22.9 31.9 26.0 27.2 28.4 58.7 50.7 51.0 48.1 41.2 36.8
1.2 2.9 0.2 0.9 3.9 6.7 1.2 2.5 3.5 7.9 0.5 1.8 1.7 3.7
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Df" SPFP = -
by using the MED, values from above, depending on the sensitivity. This estimation gives an upper limit. Whereas sunbathers spend most of their stay in a horizontal position, the irradiance for a vertical-orientated receiving surface above snow- free ground is reduced by about two-thirds with respect to the horizontal one following Schauberger (36). Another study by Boldeman et al. (37) showed that playing children receive only 15% of the horizontal dose, on average.
The sun protection factor (SPF) is a well-known quantity because of the advertising strategies for sunscreens and cosmetics. Nowadays, also the SPF for clothing is given. However, there is only little information for the public about which SPF should be used. Taking into account all the problems when dealing with the SPF, the forecasted daily dose could be a first approach in supporting the public in selecting sun protection tools.
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