Phorochemivtry and Phorobiology Vol. 5 2 , No. 5 , pp. 102%1032. 1990 Printed in Great Britain. All rights reserved

003 1-865.5190 $03.0()+0.00 Copyright 0 1990 Pergamon Press plc

MODEL FOR THE GLOBAL IRRADIANCE OF THE

RADIATION ON INCLINED SURFACES SOLAR BIOLOGICALLY-EFFECTIVE ULTRAVIOLET-

GUNTHEK SCHAUBEKCEK Institut fur Medizinische Physik, Veterinarmedizinische Universitst Wicn, A-1030 Vienna, Austria

(Received 4 April 1990; accepted 1 Jwie 1990)

Abstract-The body surface area of man is the relevant receiving surface for solar UV radiation. To consider this body surface geometry, the biologically-effective UV radiation of the solar global radiation was measured. This was done at 26 differently aligned measuring points whose orientation was determined by the angle of inclination (vertical) and the azimuth (horizontal). Approximately eight hundred sets of measurement series were carried out at 33 different sites. A simple model, developed from the data obtained, made i t possible to calculate relative irradiance as a function of the angle of inclination and the ground reflection ( U V albedo). Thus relative risk o f solar UV exposure t o different regions of the body can be assessed.

In addition to this, if the irradiance on a horizontal plane (measured or calculated by a corresponding model) is taken into consideration. the absolute values f o r UV irradiancc on tilted planes can be determined.

INTRODUCTION

The surface of man is the relevant receiving surface for solar biologically-effective UVR. To determine the U V dose received by the skin, and thereby the U V load, the topography of man has to be taken into consideration. The majority of radiation measurements of the sun are marked on horizontal surfaces. The advantage of this approach is that measurements can be standardized at different re- cording stations. Also this approach is not dependent on the azimuthal orientation of the receiving surface for astronomical and geographical factors, ground cover and meteorological parameters. Its disadvan- tage lies in the limited transferability of measure- ments to the human body surface which, due to its complex topography, has very few uncovered horizontal surfaces (Diffey et al., 1988).

To determine the solar U V load of different areas of the body, irradiance of the solar global UVR was measured on various receiving surfaces at different measuring sites and conditions.

MATERIALS AND METHODS

The technique used measured the radiation intensity at 26 differently aligned receiving surfaces. The 26 measuring points were arranged on a horizontally coordinated sys- tem, which was directed towards geographic north. The position of each measuring point was determined by its azimuth (horizontal angle), which is measured clockwise starting at geographic north, and its angle of inclination. The latter is measured positively from the horizontal plane towards the zenith and negatively towards the nadir. The following measuring points were chosen: horizontal against

*Abhreviutions: A . correction factor; 01, angle of incli- nation; E , relative irradiance of the global UV radi- ation; MED, minimal erythema1 dose; r , ground reflection; UVR, ultraviolet radiation.

the zenith (angle of inclination 90"); 8 points (4s" horizon- tally apart from each other) at an angle of inclination of +45": 8 points at an angle of inclination of 0" (receiving surface perpendicular to the horizontal plane); 8 points at an angle of inclination of -45"; and the nadir (horizontal receiving surface), pointed towards the ground at -90".

The U V sensor was attached to a tripod which allowed flexibility of movement. A compass was used to determine geographic north and the horizontal was verified with an inclinometer. The accuracy of the angle adjustment was approx. 3". Measurements were made with a Berger sun- burn meter (Solar Light Co.). Its spectral sensitivity corre- sponds approximately with the erythema action spectrum proposed by Parrish et al . (1982). The measuring device indicates the measurements in minimal erythema doses per hour (MED/h)*.

The sensor was shown to have an adequate cosine- weighted response: this was tested at an optical bench using a UV point source. Because all measurements were to be made in outdoor conditions, the sensor and its associated radiometer were both tested for response to any influence of temperature. Measurements carried out in a climatic chamber with a temperature range from 0 to 25°C did not produce any changes in sensitivity.

The measurements of 800 series were taken at 33 differ- ent measuring sites. Date and time of the measurements, a description of the location and the prevailing conditions were recorded. The conditions were determined by a com- bination o f ground cover, cloud cover (octals) and the cloud intensity ( 3 grades).

RESULTS

The distribution of the irradiance, dependence on the azimuth, and the angle of inclination, was calculated for an initial descriptive analysis. In order to be able to compare the approx. 800 measure- ments from each of the 26 measuring points, values were standardized with the irradiance of the hori- zontal receiving surface. The results were shown by the contour lines of the relative irradiance in percentages. On the basis of this normalization, the

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1030 G ~ N T H E R SCHAUBERGER

receiving surface has a value of 100% and the sur- face facing the ground gives the ground reflection (UV albedo). The distance between the contour lines is 10%. In Figs. 1 and 2, two typical situations are shown. Figure 1 demonstrates the distribution of the relative UV irradiance over ground cover with very limited reflectivity (grass). For Fig. 2 a distribution over snow-covered ground (old snow) was selected. The influence of the ground reflection on the distribution is evidence that ground reflection increases the intensity of UVR on receiving surfaces facing the ground.

Because of the importance of ground cover on the distribution of UVR, an investigation of ground reflection was carried out. Different ground covers were categorized. For each category the calculated values of the ground reflection are shown in the form of notch boxes (Fig. 3).

The distribution of UVR (Figs. 1 and 2) is based on all of the 26 values and is clearly influenced by many different parameters. For the determination of the actual UV-exposure on the skin, a quantita-

90-100 100

-60 4

0 60 120 180 240 300 360

Azimuth (deg)

Figure 1. Contour diagram of the relative irradiance of the global UV-radiation in percentages (biologically effective, normalized by the horizontal irradiance) over grass as a function of the azimuth and angle of inclination a (ground reflection: 0.014; sun elevation: 66"; sun azimuth: 182").

90-100 I -100-

-90 I , , . , . , , , . , 0 60 120 180 240 300 360

Azimuth (deg)

Figure 2. Contour diagram of the relative irradiance of the global UV-radiation in percentages (biologically effective, normalized by the horizontal irradiance) over old snow as a function of the azimuth and angle of inclination a (ground reflection: 0.485; sun elevation: 65"; sun azimuth: 176").

1 .o,

Ground cover

Figure 3 . Notch boxes of the ground reflection of solar UV-radiation for different surfaces (notch boxes: median * quartil * extreme value, the notch represents the con- fidence interval of the median). [ l asphalt; 2 grass; 3 old snow; 4 new snow; 5 soil; 6 gravel; 7 concrete; 8 rubble;

9 water surface; 10 metal grating.]

tive model is required. For the development of such a model a reduction of the data set is possible.

Man is constantly moving at random around a vertical axis. That is why the mean over the azimuth is a useful simplification (Diffey et al., 1988). The reduction of data enables the calculation of the relative U V irradiance as a function of the angle of inclination of the receiving surface. Taking the azimuth into consideration would only be useful for objects which are fixed towards geographic north, e.g. houses. For the purpose of better comparison the normalization was done in the same way as above by the horizontal value.

The model describes the distribution of solar UVR according to two parameters. The first par- ameter defines the measuring site by the ground reflection; the second parameter defines the geometry by the angle of inclination. The large number of sets of measurements allowed us to verify the model by the measurements.

E(a,r) = 112 (l+sin a ) + r 1/2 (I-sin a ) (I)

[relative irradiance of the global UVR E(u , r ) = Ei(a,r)/Eh with irradiance of the global UVR on inclined surfaces Ei(a,r) and irradiance of the global UVR on a horizontal plane Eh, angle of inclination a (angle between the horizontal and the normal to the receiving surface), ground reflection (UV albedo) r , arbitrary correction factor A].

The first term describes the irradiance of the upper half space as a function of the angle of incli- nation only when the direct radiation of the sun is zero. In other cases, there is no strict description of the distribution of the radiation. This would only be possible if global radiation is divided into diffuse (sky) radiation and direct radiation. The second term describes the direct and diffuse radiation, reflected by the ground, assuming isotropic behav- iour.

To reduce the influence and error within this assumption and to consider direct radiation in the

- A (1 - r ) COS' a

Model for the global UVR 103 I

model, a third term was introduced as a function of the angle of inclination a and the ground reflection r (Steven and Unsworth, 1980). A comparison between the model and the measured values shows that, through the use of the third term, both fit together well. Five hundred and twenty-nine sets of measurements were selected in which the global irradiance on the horizontal plane is greater than 0.5 MED/h to evaluate the model. The constant A of this term was selected as -0.18 so that the mean of the residual, i.e. the difference between model values and measurements, was zero for the vertical receiving surface (angle of inclination is 0'). The mean value of the residuals for all angles of incli- nation where measurements were made are summa- rized in Table 1. For the angle of inclination of +90° (horizontal facing the zenith) and -90" (horizontal facing the ground), there were no deviations from the model.

An easy application of the model for the assess- ment of the U V load in relation to the orientation of the skin surface is possible by using Fig. 4. The graphs show the relative irradiance of global UVR for selected values of ground reflection.

DISCUSSION

The description of the solar irradiance as a func- tion of the azimuth and angle of inclination requires many, differently oriented measuring points. This had not been carried out for UVR before. Blum-

Table I . Rcsidual of the calculated values [Eq. ( I ) ] and the measured values (mean i SD)

Angle of inclination (a) Residual (mean t- SD)

90" 45" 0"

-45" -YO"

0 0.017 ? 0.035 0.000 * 0.064 0.028 2 0 . 0 6 7

0

r = 0 8 0 r = 0 6 0 r = 0 4 0 r = 0 2 0 r = u 15 r = 0 10 r = 0 0 5 r = 0 0 7

60 1

90

Angle of inclination a (deg)

Figure 4. Relative irradiance of the global UV-radiation E calculated by Eq. ( 1 ) as a function of the angle of inclination (Y and for different values of the ground reflec-

tion r .

thaler and Ambach (1985) and Diffey et al. (1988) limited their interest to solar UVR on vertical receiving surfaces. Valko (1980, 1988) investigated the whole spectral range but predominantly the upper half space.

The graphical presentation of the measured data in Figs. 1 and 2 shows the distribution of the UV- irradiance on a sphere, where the sphere has a fixed orientation to north. The mean value of the 26 measured points is equivalent to the value obtained from an ideal spherical response receiver (Holmes, 1989).

Ground reflection is the dominant influence on the measuring site. The results of the descriptive studies (notch boxes in Fig. 3) show that the meas- ured values lie very close together, although the measurements were carried out under different con- ditions (i.e. sun elevation, cloud cover, cloud inten- sity, atmospheric turbidity, etc). There is only one exception to this and that is snow. Due to different structure, consistency (age) and pollution, the values of the ground reflection of snow varies between 0.5 and 1.0 (Ambach and Eisner, 1986). The measured ground reflection of different ground covers (Fig. 3) corresponds well to results obtained by Blumthaler and Ambach (1988). The small devi- ation of the ground reflection from the mean values makes it possible to use these figures from Fig. 3, hence a measurement is not necessary.

There are some models describing the solar irradiation as a function of the angle of inclination. All of these models describe only the diffuse radi- ation, because for direct radiation it is not necessary to set up a model. To determine the UV exposure to a person it is not appropriate to divide the global radiation into diffuse and direct components.

The model presented here has two parameters. The ground reflection is the dominant parameter of the measuring site; the angle of inclination describes the geometry (topography of the receiving surface). The application of this model to man has the advan- tage that the random motion around a vertical axis is taken into account.

The first and second terms of the model [Eq. ( l ) ] correspond to the model published by Bird and Riordan (1986). which, however, included circum- solar radiation. Both models make the same assumption: both diffuse (sky) radiation and ground reflection behave isotropically. Factor A [Eq. (1)) of the third term is equivalent to the figure used by Steven and Unsworth (1979). This is in the same range as the residual between the isotropic and anisotropic assumption for a vertical receiving sur- face.

The comparison between the model and the mea- sured values demonstrates that the model fulfills its purpose of calculating the relative UV irradiance for inclined planes. Assessments of the relative UV load on different regions of the body can be made in a way similar to those made in the experimental works of Diffey et al. (1979, 1987). The results there

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can be compared directly with the results of the model. They show considerable agreement. By the use of this model the UV load on inclined planes can also be calculated as an absolute value. For this, the irradiance on the horizontal plane Eh is necessary [Eq. (l)]. It does not matter if this value is a measured one or one calculated by a published model (e.g. Bjorn, 1989). The combination of the irradiance on a horizontal plane with the model gives the irradiance as a function of ground reflec- tion and angle of inclination Ei(a,r). This value corresponds to the skin dose proposed by Slaper and van der Leun (1987) for describing the effective UV load.

Acknowledgement-This work was supported by the fund “200 Jahre Veterinarmedizinische Universitat Wien” founded by the Wiener Handelskammer.

REFERENCES

Ambach, W. and H. Eisner (1986) Albedo verschiedener Schneeoberflachen fur erythemwirksame solare Strah- lung. Wetter und Leben 38, 1-4.

Bird, R. E. and C. Riordan (1986) Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth’s surface for cloudless atmospheres. J . Clim. Appl. Meteorol. 25, 87-97.

Bjorn, L. 0. (1989) Computer programs for estimating ultraviolet radiation in daylight. In Radiation Measure- ment in Photobiology (Edited by B. L. Diffey). Aca- demic Press, London.

Blumthaler, M. and W. Ambach (1985) Neuere Mes- sungen der Albedo verschiedener Oberflachen fur ery- themwirksame Strahlung. Ann. Meteorol. 22, 114-1 15.

Blumthaler, M. and W. Ambach (1988) Solar UVB- Albedo of various surfaces. Photochem. Photobiol. 48,

Diffey, B. L., 0. Larko and G. Swanbeck (1982) UV-B doses received during different outdoor activities and UV-B treatment of psoriasis. Br. J. Dermatol. 106, 33-41.

Diffey, B. L., E. F. Meanwell and M. J. Loftus (1988) Ambient ultraviolet radiation and skin cancer incidence. Photodermatology 5 , 174-178.

Diffey, B. L., T . J. Tate and A. Davis (1979) Solar dosimetry of the face: the relationship of natural ultra- violet radiation exposure to basal cell carcinoma localis- ation. Phys. Med. Biol. 24, 931-939.

Holmes, M. G. (1989) Action spectroscopy. In Radiation Measurement in Photobiology (Edited by B. L. Diffey). Academic Press, London.

Parrish, J. A., K. F. Jaenick and R. R. Anderson (1982) Erythema and melanogensis action spectra of normal human skin. Photochem. Photobiol. 36, 187-191.

Slaper, H. and J. C. van der Leun (1987) Human exposure to ultra-violet radiation: quantitative modelling of skin cancer incidence. In Human Exposure to Ultraviolet Radiation-Risk and Regulations (Edited by W. F. Passchier and B. F. M. Bosnjakovic). Excerpta Medica, Internal Congress Series 744, Amsterdam.

Steven, M. D. and M. H. Unsworth (1979) The diffuse solar irradiance of slopes under cloudless skies. Q. J. Roy. Meteorol. SOC. 105, 593-602.

Steven, M. D. and M. H. Unsworth (1980) The angular distribution of diffuse solar radiation below overcast skies. Q. J. Roy. Meteorol. SOC. 106, 57-61.

Valko, P. (1980) Some Empirical Properties of Solar Radi- ation and Related Parameters. Swiss Meteorological Institut Zurich.

Valko, P. (1988) Joint analysis of simultaneous sky radi- ance and slope irradiance measurements from different sites in Europe. Euroforum New Energies Congress, Saarbrucken, W. Germany.

85-88.