Influence of cloudiness over the values of erythemal radiation in Valencia, Spain

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 30: (010) Published online 3 March 009 in Wiley InterScience ( Influence of cloudiness over the values of erythemal radiation in Valencia, Spain A. R. Esteve, a M. J. Marín, b F. Tena, a M. P. Utrillas a and J. A. Martínez-Lozano a, * a Solar Radiation Group, Departament de FísicadelaTerraiTermodinàmica, Universitat de València, Burjassot, Valencia, Spain b Fundación Centro de Estudios Ambientales del Mediterráneo (CEAM), Paterna, Valencia, Spain ABSTRACT: The influence of cloudiness over experimental UV erythemal radiation (UVER) has been studied. This influence has been analysed considering total cloudiness and low clouds. The measurements of cloudiness correspond to the daily values registered at 13 : 00 GMT at the Meteorological Centre of Valencia, which is part of the State Agency of Meteorology of Spain (AEMET). The UVER measurements were made using a YES UVB-1 radiometer located on the roof terrace of the Physics Faculty at the Burjassot Campus, Valencia (latitude , longitude 18, 60 m above sea level). First, a statistical analysis of cloudiness at 13 : 00 GMT in Valencia was carried out, confirming that the situation is mainly clear skies or very few clouds. Next, the influence of cloudiness on experimental UVER values was analysed, for both total cloudiness and low clouds. The experimental UVER values decrease as cloudiness increases for all solar zenith angles (SZA), and this reduction increases with the zenith angle. Next, the cloud modification factor () has been defined to reduce the influence of the zenith angle and ozone over the UVER. In order to quantify the relationship between and the degree of cloudiness in oktas, linear, quadratic and potential regressions for both total cloudiness and low clouds have been calculated. Transmissivity due to total cloudiness and for overcast skies reaches 40%. On the other hand, the analysis of the influence over the zenith angle shows that reduces as the zenith angle increases in the case of both total cloudiness and low clouds. With regard to the low cloud, the results are comparable to those proposed by the COST-713 Action UV-B Forecasting for partially cloudy or cloudy skies (70% and 50%, respectively). Finally, the relationship between the and the clearness index (k T ) has been analysed, as both parameters are simple indicators of cloudiness. It has been proved that such relationship is close to unity for zenith angles in the mid-range, while the is greater than k T for lower SZA and is less than k T for high SZA, which indicates a certain dependence of these two parameters on the zenith angle. Copyright 009 Royal Meteorological Society KEY WORDS UV erythemal radiation (UVER); cloudiness (oktas); cloud modification factor () Received 8 July 008; Revised 0 January 009; Accepted 8 January Introduction The effects of UV radiation on human beings have received considerable attention over the past 0 years (Frederick and Lubin, 1988; Scotto et al., 1988), leading to guidelines and recommendations about UV radiation exposure in order to avoid specific or chronic damage to the skin (WMO, 1998a; ICNIRP, 004). The most common effect of UV radiation on humans is erythema or sunburn. The Comission Internationale de l Eclariage (CIE) adopted a standard erythema curve in 1987 (McKinlay and Diffey, 1987; CIE, 1999) which is currently recommended for determining the UV erythemal radiation (UVER). The erythemal action spectrum has been defined by humans to describe the dependence of skin reaction (sunburn) on the spectral irradiance. The UVER is calculated by weighting the spectral curve of the incident solar radiation at ground level with the spectral action curve proposed by the CIE. * Correspondence to: J. A. Martínez-Lozano, Solar Radiation Group, University of Valencia, Dr. Moliner 50, Burjassot (Valencia), Spain. jmartine@uv.es The erythemal irradiance reaching the surface of the earth is the result of a combination of factors, most notably the zenith angle, the cloud cover, the height above sea level, the aerosol load, the surface albedo and the total ozone column (WMO, 1998b). In a previous paper, we studied the influence of the stratospheric ozone and the aerosol amount on experimental UVER values (Esteve et al., 009). The present paper is focused on the role that clouds play on the UVER values that reach the ground level. For this, the information routinely registered in most meteorological stations is used: cloud type and amount, expressed in terms of fractional cloud coverage in oktas, which are usually recorded in a 3- hourly database. This kind of approach has been followed in previous studies (Ilyas, 1987; Frederick and Snell, 1990; Frederick et al., 1993; Blumthaler et al., 1994, 1996; Thiel et al., 1997; Kuchinke and Núñez, 1999; Grant and Heisler, 000; Josefsson and Landelius, 000; Alados-Arboledas et al., 003). As clouds are formed by small water droplets or ice crystals, radiation is scattered when passing through them, resulting in complete extinction or diminished Copyright 009 Royal Meteorological Society

2 18 A. R. ESTEVE ET AL. transmissivity of the atmosphere. Clouds are highly variable in time and space, so there is great difficulty in their specification, and their usual effect is attenuation of surface UV irradiance. Attenuation depends on different cloud properties such as cloud amount, cloud optical thickness, relative position between the sun and clouds, cloud type, number of cloud layers, etc. (Calbó et al., 005). These factors are usually grouped under the term cloud modification factor (), which is the incident irradiance divided by the modelled clear-sky estimation (Schafer et al., 1996; Kuchinke and Núñez, 1999; Renaud et al., 000; Foyo-Moreno et al., 001; Krzyscin et al., 003; Adam and El Shazly, 007). It provides a first distinction of cloud radiative effects using the available data base (Foyo-Moreno et al., 001). Different studies have followed similar procedures in their analysis of the cloud radiative effect over the whole solar spectrum, over UV and over photosynthetically active radiation (Kasten and Czeplak, 1980; Blumthaler et al., 1994; Davies, 1995; Alados et al., 000).. Materials and Methods The erythemal radiation measurements were obtained using a YES (Yankee Environment Systems) UVB-1 radiometer which has a spectral range between 80 and 400 nm, and a spectral sensitivity close to the erythemal action spectrum. The UVB-1 is designed to be stable over long periods of time and to operate continuously and autonomously in the field. The cosine response is less than 4% for solar zenith angles below 55 (Dichter et al., 1993) according to the manufacturer. This instrument was subjected to a standard calibration in the National Institute for Aerospace Technology (INTA) in Spain. It consists of a measurement of the spectral response of the radiometer indoors and a comparison with a Brewer MKIII spectroradiometer outdoors (Vilaplana et al., 006). The clearness index, k T, has also been determined experimentally using the measurements of total irradiance registered with a CM6 pyranometer from Kipp & Zonen. The spectral range of this instrument includes wavelengths between 300 and 800 nm. Its stability and precision have been described previously (Martínez-Lozano et al., 1996, 1999). Measurements are taken every 10 s (instantaneous irradiance) and averages are calculated for 5-min intervals. Thus, the values considered as instantaneous here are actually 5-min interval average values. Calibration is regularly performed by comparison with an Eppley PSP (Precision Spectral Pyranometer), which has been referenced as a world-standard, first-class radiometer. These instruments were installed on the roof of the Faculty of Physics in Burjassot, Valencia, Spain (latitude , longitude 18, 60 m above sea level). Burjassot is a town of some inhabitants located 5 km from Valencia and 10 km from the Mediterranean coast. Valencia is located in the central eastern area of Spain and has a moderate climate because it is near the Mediterranean Sea. The mean climate characteristics from a typical year for Valencia are the following: (1) average relative humidity: 65%; () mean daily temperature: 17.8 C (State Agency of Meteorology of Spain (AEMET), The complete period of measurements is from June 003 to December 006. There was no data during calibration periods. Three-hourly cloud amounts, measured in oktas, C T, were obtained from the Valencia-Viveros meteorological station. They correspond with the observations carried out in the Meteorological Centre of Valencia, part of the AEMET, at 07 : 00, 13 : 00 and 18 : 00 GMT during the period of UVER measurements. For this study we have included only the cloudiness measured at 13 : 00 GMT, which is the time nearest to midday and when most irradiance is registered. A total of 854 combined measurements of cloudiness, UVER and ozone values have been considered as valid. The estimation of irradiance in cloudless skies for the days under consideration has been carried out using the radiative transfer model SBDART.4 (Ricchiazzi et al., 1998) using current values of total ozone column given by the TOMS (Total Ozone Mapping Spectrometer, overhead.html) and, more recently (since January 006), by its successor OMI (Ozone Monitoring Instrument, nasa.gov/teacher/ozone overhead v8.html). We obtain, moreover, monthly average climatic values of aerosol optical depth for Valencia by means of a CIMEL CE318 photometer (Estellés et al., 007). 3. Results First, a statistical analysis of cloudiness at 13 : 00 GMT in Valencia was carried out to analyse its influence on UVER, considering the total cloudiness and choosing only the low clouds. Its influence over erythemal radiation was analysed according to the solar zenith angle (SZA). Furthermore, in order to define the, UVER values were normalized by the corresponding cloud-free sky value, I UVERc : = I UVER (1) I UVERC This factor has been analysed in relation to both total cloudiness and low clouds. Finally, the relationship between the and the clearness index k T (Liu and Jordan, 1960) was analysed, as both of these parameters are simple indicators of the amount of clouds Total Cloudiness Using the available measurements of total cloudiness at 13 : 00 GMT in Valencia, a statistical analysis was carried out dividing the data according to the following

3 INFLUENCE OF CLOUDINESS OVER THE VALUES OF ERYTHEMAL RADIATION θ < < θ < < θ < 65 % 30 0 UVER (W/m ) C T (oktas) 0 C T (oktas) Figure 1. Total cloudiness at 13 : 00 GMT for clear skies (0 oktas), partially cloudy skies (3 5 oktas), cloudy skies (6 7 oktas) and overcast skies (8 oktas). categories: clear skies (0 oktas), partially cloudy skies (3 5 oktas), cloudy skies (6 7 oktas) and overcast skies (8 oktas), in line with the World Meteorological Organization classification (WMO) ( int/oktas.htm). The results are shown in Figure 1. It can be observed that approximately 45% of the cases correspond to a situation of completely clear skies or with very few clouds; in 9% of the cases the sky is partially cloudy; in 18% it is cloudy; while only 8% of the cases correspond to completely overcast skies. Therefore, it could be confirmed that the situation in Valencia is predominately clear skies or skies with very few clouds. These results agree with previous studies based on the analysis of the clearness index (Tena et al., 009). In order to study the influence of total cloudiness over experimental UVER, the average value of the erythemal irradiance between 1 : 30 and 13 : 30 GMT was taken as representative of 13 : 00 GMT. Next, these values of UVER were classified according to the number of oktas and to the solar zenith angle, using three intervals: (1) θ<30, () 30 θ<50 and (3) 50 θ<65. The influence of total cloudiness over UVER for these solar zenith angle intervals is shown in Figure. It can be seen that UVER decreases as total cloudiness increases. The values of UVER were also divided into the three categories of clouds: clear skies, partially cloudy skies and cloudy skies, for the three SZA intervals. Table I shows the percentages of UVER decrease with total cloudiness passing from one cloudiness category to another according to the SZA. From these results, it can be deduced that the attenuation of UVER on passing from clear skies to cloudy skies is much greater for high zenith angles, changing from a decrease of 9% when the SZA is less than 30, to a decrease of half the value, 50%, when the SZA is between 50 and 65. This result was expected since the lower the sun is, the greater is the optical path the solar radiation has to travel and therefore the greater is the atmospheric attenuation. However, the result is different considering the change Figure. Average value of UVER, according to the solar zenith angle, in relation to total cloudiness oktas for θ<30, 30 θ 50, and 50 θ<65. Table I. UVER decrease over total cloudiness between the categories of clear skies (0 oktas), partially cloudy skies (3 5 oktas) and cloudy skies (6 7 oktas), according to the solar zenith angle (SZA) for θ<30, 30 <θ<50 and 50 <θ<65. Total cloudiness (oktas) SZA ( ) Decrease (%) Clear cloudy θ< <θ< <θ<65 50 Clear partly cloudy θ< <θ< <θ<65 5 Partly cloudy cloudy θ< <θ< <θ<65 8 from clear skies to partially cloudy skies, or from partially cloudy skies to overcast skies. In the former case, the UVER decreases as the zenith angle increases, and in the latter case it increases along with the SZA. However, UVER attenuates in the same percentage on passing from a situation of clear skies to one of partially cloudy skies, and from partially cloudy skies to overcast conditions when the sun is virtually overhead, with zenith angles less than 30. The following linear regressions show the decreasing tendency of UVER with total cloudiness: θ<30 UVER = (0.176 ± 0) (07 ± 004)C T () 30 <θ<50 UVER = (0.15 ± 0) (053 ± 005)C T (3)

4 130 A. R. ESTEVE ET AL. 50 <θ<65 UVER = (51 ± 04) (03 ± 01)C T (4) all of them having a correlation factor of Again, the average values of UVER for all the available SZA values were calculated for each category of total cloud conditions (Figure 3). The linear regression shows the tendency for the UVER to decrease with total cloudiness: UVER = (0.146 ± 05) (11 ± 01)C T (5) with a correlation factor of Later, the UVER values were divided as a function of cloudiness: clear skies (0 oktas), partially cloudy skies (3 5 oktas) and cloudy skies (6 7 oktas). Table II shows the percentage of UVER decrease considering the change from one category of total cloudiness to another. The highest decrease, 40%, occurs on passing from completely clear skies (0 oktas) to cloudy skies (6 7 oktas). On passage from partially cloudy skies to cloudy skies a slightly higher attenuation, 4%, is produced compared to the evolution from clear skies to partially cloudy skies. 3.. Low clouds By means of the available measurements of low clouds at 13 : 00 GMT in Valencia, a statistical analysis was carried out by dividing the cloudiness data according to UVER (W/m ) the categories: clear skies (0 oktas), partially cloudy skies (3 5 oktas), cloudy skies (6 7 oktas) and overcast skies (8 oktas). In a similar way as the total cloudiness, a statistical analysis of low clouds at 13 : 00 GMT in Valencia was carried out, dividing the data into the same categories as for total cloudiness, as can be seen in Figure 4. It can be seen that approximately 76% of the data reflect a situation of completely clear skies or with very few clouds, in 18% of the cases the sky is partially cloudy and it is cloudy in 4%, while completely overcast skies is only % of the cases. The percentage of totally overcast skies with low clouds is much smaller than with total cloudiness (% vs 8%). However, skies with very few clouds are more frequent for low cloud conditions (76% vs 45%). Once more, the average values of UVER for each category of cloud cover due to low clouds were calculated. The zenith angle intervals were defined as in the previous section. These values were correlated to the low cloud values (Figure 5), from which it can be seen that UVER decreases considerably as low clouds increase. The UVER values have been divided into the three categories: clear skies, partially cloudy skies and cloudy skies, and considering also the previous SZA intervals. Table III shows the UVER decrease percentages with low clouds changing from one category to another according to the SZA. From these results, it can be deduced that the attenuation of UVER with low clouds is greater for high zenith angles, varying between a decrease of 30% when the SZA is less than 30 and 40% when the SZA is between 50 and 65 changing from clear skies to cloudy skies. This behaviour also occurs on passing from partially cloudy skies to overcast skies, changing between a decrease of 1% when the SZA is less than 30 and an extinction of 7% when the SZA is between 50 and 65. However, the behaviour is different in the case of a change from clear skies to partially cloudy skies, where the attenuated percentage of UVER remains approximately constant (around 0%) C T (oktas) % Figure 3. Average value of UVER in relation to total cloudiness oktas. Table II. UVER decrease over total cloudiness between the categories of clear skies (0 oktas), partially cloudy skies (3 5 oktas) and cloudy skies (6 7 oktas). Total cloudiness (oktas) Decrease (%) Clear cloudy 40 Clear partly cloudy 0 Partly cloudy cloudy C L (oktas) Figure 4. Low clouds at 13 : 00 GMT for clear skies (0 oktas), partially cloudy skies (3 5 oktas), cloudy skies (6 7 oktas) and overcast skies (8 oktas).

5 INFLUENCE OF CLOUDINESS OVER THE VALUES OF ERYTHEMAL RADIATION θ < < θ < < θ < UVER (W/m ) UVER (W/m ) C L (oktas) 0 C L (oktas) Figure 5. Average value of UVER, according to the solar zenith angle, in relation to low clouds oktas for θ<30, 30 <θ<50 and 50 <θ<65. Table III. UVER decrease over low clouds between the categories of clear skies (0 oktas), partially cloudy skies (3 5 oktas) and cloudy skies (6 7 oktas), according to the solar zenith angle (SZA) for θ<30, 30 <θ<50 and 50 <θ<65. Low clouds (oktas) SZA ( ) Decrease (%) Clear cloudy θ< <θ< <θ<65 40 Clear partly cloudy θ< <θ<50 50 <θ<65 19 Partly cloudy cloudy θ< <θ< <θ<65 7 This UVER tendency of decreasing with low clouds can be quantified through the following linear regressions: θ<30 UVER = (0.165 ± 07) (08 ± 0)C L (6) 30 <θ<50 UVER = (0.116 ± 04) (070 ± 009)C L (7) 50 <θ<65 UVER = (47 ± 01) (031 ± 001)C L (8) all of them having a correlation coefficient of This calculation was repeated for the available SZA values. The average value of UVER was calculated for each category of low clouds (Figure 6). The linear regression shows the tendency for the UVER to decrease Figure 6. Average value of UVER in relation to low clouds oktas. Table IV. UVER decrease over low clouds between the categories of clear skies (0 oktas), partially cloudy skies (3 5 oktas) and cloudy skies (6 7 oktas). Low clouds (oktas) Decrease (%) Clear cloudy 38 Clear partly cloudy 31 Partly cloudy cloudy 10 with low clouds: UVER = (0.1 ± 1) (08 ± 0)C L (9) with the correlation factor of 4. The UVER values were again divided into the three categories of cloudiness: clear skies (0 oktas), partially cloudy skies (3 5 oktas) and cloudy skies (6 7 oktas). Table IV summarizes the percentages of the UVER decrease with low clouds on passing from one category to another. The highest reduction, 38%, occurs on going from completely clear skies (0 oktas) to cloudy skies (6 7 oktas). On changing from clear skies to partially cloudy skies, a much greater attenuation, 31%, occurs than on going from partially cloudy skies to cloudy skies Cloud modification factor in relation to total cloudiness is defined by the expression (1). In order to determine the I UVERc, which represents the irradiance received during the same period as I UVER but for skies completely free of clouds, the SBDART.4 multiple scatter model (Ricchiazzi et al., 1998) was used for simulating the 13 : 00 GMT values. The inputs for the SBDART were the ozone data provided by the TOMS and OMI satellites, along with the monthly average climatic values of aerosol optical thickness measuredwith a CIMEL CE318 photometer in Valencia (Estellés et al., 007).

6 13 A. R. ESTEVE ET AL. θ < < θ < < θ < 65 C T (oktas) C T (oktas) Figure 7. Cloud modification factor () in relation to total cloudiness (C T ). Figure 8. Cloud modification factor () in relation to total cloudiness (C T ), for θ<30, 30 <θ<50 and 50 <θ<65. The was calculated by employing the simulated UVER values for cloud-free skies and UVER measurements. In order to quantify the relationship between and the number of oktas, linear and quadratic regressions were calculated. Figure 7 represents in relation to total cloudiness in oktas. The values were fitted using both a linear regression and a quadratic one, whose correlation coefficient improves the linear regression. A more general method consists of finding the degree of the polynomial closest to the experimental data by means of a potential regression. This method has been used by other authors (Thiel et al., 1997; Alados-Arboledas et al., 003). = C T r = 0.93 (10) Quadratic : = C T 093C T r = 0.98 (11).54 Potential : = 6 04C T r = 0.99 (1) These results suppose an overcast sky transmissivity (C T of 8) of 50% according to the linear regression and of 40% according to the quadratic and the potential ones. This value is of the same order of magnitude as that obtained by Cutchis (1980) for the whole USA, given as 50%, and is considerably higher than the 30% obtained for Sweden (Josefsson and Landelius, 000) and the 0% obtained for Greece (Bais et al., 1993). A cubic regression, as proposed by some authors (Schafer et al., 1996; Adam and El Shazly, 007), does not seem to be justified since it does not introduce any additional improvement. aims to eliminate the influence of the zenith angle and other highly influential parameters such as ozone over-radiation attenuated by clouds. However, the different behaviour of diffused radiation on clear days and overcast days has to be taken into account. To analyse whether the position of the sun has an influence, the data were divided according to the zenith angle, considering three intervals as in the previous sections: (1) θ<30, () 30 <θ<50 and (3) 50 <θ<65. Figure 8 shows the in relation to C T for each of these intervals. The qualitative regressions of these curves are shown below: θ<30 = C T r = 0.94 (13) Quadratic : = C T 065C T r = 0.98 (14) 1.94 Potential : = C T r = 0.98 (15) 30 <θ<50 = C T r = 3 (16) Quadratic : = C T 165C T r = 0.95 (17) 5.80 Potential : = C T r = 0.98 (18) 50 <θ<65 = 8 54C T r = 0.91 (19) Quadratic : = C T 093 C T r = 0.98 (0).43 Potential : = 09 08C T r = 0.98 (1)

7 INFLUENCE OF CLOUDINESS OVER THE VALUES OF ERYTHEMAL RADIATION 133 The transmissivity for low zenith angles (<30 ) is equal to or greater than that obtained taking into account all the data. However, considering greater angles, the transmissivity is of the same order or lower than the one for all zenith angles. This is due to the attenuation for low zenith angles being less because the irradiance travels through a shorter optical path in relation to low clouds The previous analysis was repeated taking into account only low clouds. The, in relation to low clouds, C L, is shown in Figure 9. Similar to the total cloudiness case, three types of regressions were used: linear, quadratic and potential. The results are as follows: = 61 59C L r = 0.93 () Quadratic : = 6 60C L C L r = 0.93 (3) 6 Potential : = 53 5C L r = 0.95 (4) The potential regression improves the correlation coefficient, and the value of the exponent is very near unity, which means that the linear regression is a better option than the quadratic one, contrary to the total cloudiness case. These results suppose a transmissivity of 60% in the case of partially cloudy skies, 50% in the case of cloudy skies and 40% in the case of overcast skies for all of the previous expressions. If the cloud cover values are now divided as proposed by COST-713 Action UV-B Forecasting (Vanicek et al., 000) (3 4 oktas partially cloudy, 5 6 oktas cloudy and 7 8 overcast), the values obtained are 70%, 50% and 40%, respectively. The results for partially cloudy and cloudy skies are comparable with the proposed by COST-713 Action UV-B Forecasting (80% and 50%, respectively). However, for totally overcast skies a much higher transmissivity value is obtained (40% instead of 0%). This result agrees with those of other authors. For example, Krzyscin et al. (003) obtain a value of 50% for Belsk in Poland. In this section, the data were also divided according to the zenith angle, as shown in Figure 10. The corresponding regressions are: θ<30 = 7 45C L r = 0.97 (5) Quadratic : = 89 59C L C L r = 0.98 (6) 0.90 Potential : = 8 55C L r = 0.97 (7) 30 <θ<50 = 99 68C L r = 0.96 (8) Quadratic : = 50 19C L 069C L r = 0.98 (9) 1.64 Potential : = 47 19C L r = 0.98 (30) 50 <θ<65 = 3 76C L r = 0.97 (31) Quadratic : = C L 045C L r = 0.98 (3) 1.40 Potential : = C L r = 0.98 (33) θ < < θ < < θ < 65 C L (oktas) C L (oktas) Figure 9. Cloud modification factor () in relation to low clouds (C L ). Figure 10. Cloud modification factor () in relation to low clouds (C L ) for different zenith angles.

8 134 A. R. ESTEVE ET AL. Similar to the case of total cloudiness, the transmissivity, taking into consideration only low zenith angles (<30 ), is equal to or greater than that obtained considering all the data. However, for greater angles, the transmissivity is of the same order or less than for all zenith angles. For example, the transmissivity for overcast skies (C L = 8 oktas) for zenith angles greater than 50 is of the same order as that proposed by COST Action (0%); for low zenith angles it is twice The influence of the cloud modification factor on k T The clearness index, k T, gives the decrease of the incident global radiation as it passes through the atmosphere and, therefore, indicates the degree of availability of solar irradiance at the ground level. It is defined (Liu and Jordan, 1960) as: k T = I G (34) I 0 where I G is the global irradiance and I 0 the extraterrestrial irradiance, both on a horizontal plane. Furthermore, the clearness index is a parameter used to estimate whether a day is clear when additional measurements of cloudiness are not available. A value of k T above 0.7 can be considered as a clear day. Although the is related to erythemal irradiance and the k T to total radiation, they may be correlated, because both of them represent the attenuation due to cloudiness. In order to calculate the clearness index, the experimental measurements of total irradiance registered with a CM6 sensor were used. The relationship between the for total cloudiness (I UVER /I UVERc )andthe clearness index k T (I G /I 0 ) is represented in Figure 11. The corresponding linear regression is: = k T r = 0.94 (35) By dividing the values into the three zenith angles intervals considered before: (1) θ<30, () 30 <θ< θ < < θ < < θ < 65 k T Figure 1. Cloud modification factor for total cloudiness ( T )in relation to the clearness index k T for θ<30, 30 <θ<50 and 50 <θ< and (3) 50 <θ<65, Figure 1 is obtained. The qualitative regressions to these curves are: θ<30 : = k T r = 0.94 (36) 30 <θ<50 : = k T r = 0.94 (37) 50 <θ<65 : = k T r = 0.95 (38) The relationship between and k T is closer to unity for mid-range zenith angles, while the is greater than the clearness index for lower range zenith angles, and the is less than the k T for high SZA, which indicates a certain dependency of these two parameters with the zenith angle. k T Figure 11. Cloud modification factor () in relation to the clearness index k T. 4. Conclusions In this study the influence of cloudiness on the attenuation of UVER in Valencia has been analysed. By means of the available cloudiness measurements, a statistical analysis of cloudiness at 13 : 00 GMT in Valencia was carried out, dividing the cloudiness data according to the following categories: clear skies (0 oktas), partially cloudy skies (3 5 oktas), cloudy skies (6 7 oktas) and overcast skies (8 oktas). For both the cases of total cloudiness and low clouds, it was seen that the situation in Valencia is predominantly clear skies or skies with very few clouds (approximately 45% and 76%, respectively). Moreover, owing to the small sample of data, which can be considered to be non-representative, totally overcast skies have not been taken into account (8% and 4% of the cases, for total cloudiness and low clouds, respectively) in this study.

9 INFLUENCE OF CLOUDINESS OVER THE VALUES OF ERYTHEMAL RADIATION 135 Next, the influence of cloudiness over the experimental values of UVER with regard to the solar zenith angle for both total cloudiness and low clouds was analysed. In both cases it was seen that UVER decreases as cloudiness increases. Moreover, as the SZA increases, the percentage of UVER decrease is also greater. This increase is greater in the case of total cloudiness rather than of low clouds. The has also been defined as a quotient of the experimentally received radiance and the simulated radiance using the SBDART.4 model for cloudless days. This factor has been introduced to reduce the influence of the most influential parameters such as ozone or zenith angle over UVER attenuated by clouds. The variation in the has been studied for both total cloudiness (C T ) and for low clouds (C L ). In order to quantify the relationship between and the number of oktas, linear, quadratic and potential regressions were calculated. These results suppose a transmissivity for overcast skies (C T of 8) of 50% according to the linear regression and 40% according to the quadratic and the potential ones when considering total cloudiness. We have also found that transmissivity decreases as the zenith angle increases. For the low clouds, the results are comparable with those given by COST-713 Action UV-B Forecasting in the case of partially cloudy or cloudy skies. Nevertheless, for overcast skies much greater transmissivity values are obtained (40% vs 0% proposed). However, if the data is divided according to the zenith angle, the decreases as the SZA increases, and it reaches the value of 0% proposed by COST-713 Action when we consider zenith angles greater than 50. Finally, the relationship between the for total cloudiness and the clearness index k T was evaluated. 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