Empirical models of UV total radiation and cloud effect study

Transcription

1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 30: (2010) Published online 28 July 2009 in Wiley InterScience ( DOI: /joc.1983 Empirical models of UV total radiation and cloud effect study David Mateos Villán,* Argimiro de Miguel Castrillo and Julia Bilbao Santos Applied Physics Department, Valladolid University, Prado de la Magdalena Street s/n, 47005, Valladolid, Spain ABSTRACT: Several empirical models of hourly ultraviolet total radiation (UVT) have been proposed in this study. Measurements of UVT radiation, nm, have been recorded at ground level from February 2001 to June 2008 in Valladolid, Spain (latitude N, longitude 4 50 W and 840 m a.s.l.). The empirical models have emerged due to the lack of some radiometric variables in measuring stations. Hence, good forecasts of them can be obtained from usual measures in these stations. Therefore, some advantages of the empirical models are that they allow the estimation of past missing data in the database and the forecast of future ultraviolet solar availability. In this study, reported models in the bibliography have been assessed and recalibrated. New expressions have been proposed that allow obtaining hourly values of ultraviolet radiation from global radiation measures and parameters as clearness index and relative optical air mass. The accuracy of these models has been assessed through the following statistical indices: mean bias, mean-absolute bias and root-mean-square errors whose values are close to zero, below 7% and below 10%, respectively. Two new clear sky models have been used to evaluate two new parameters: ultraviolet and global cloud modification factors, which can help to understand the role of the clouds on solar radiation. The ultraviolet cloud modification factor depends on cloudiness in such a way that its value under overcast skies is half of the cloudless skies one. Exponential and potential fits are the best relationships between both cloud factors. Finally, these parameters have been used to build new UV empirical models which show low values of the statistical indices mentioned above. Copyright 2009 Royal Meteorological Society KEY WORDS ultraviolet solar radiation; global solar radiation; UV empirical models; cloudiness; cloud modification factor; clearness index Received 25 March 2009; Revised 3 June 2009; Accepted 23 June Introduction Solar ultraviolet radiation (UV) has received considerable attention in the past few years because it is involved in chemical and biological processes and it is responsible for the stratospheric ozone creation controlling its variation (Bilbao et al., 2008). Hence, the amount of UV radiation recorded on the surface has increased considerably owing mainly to the decrease in the amount of ozone (WMO, 2007). This fact, together with the increase in the number of cases of diseases related to UV radiation, has increased the interest in accurately quantifying the UV radiation that reaches the surface. Hence, the number of studies that try to model this radiation has significantly grown. The use of surface measures allows making a detailed study of the intensity levels and of the climate variability of the UV radiation that reaches the surface. Despite the recommendations of World Meteorological Organization (WMO), one of the great difficulties in working with UV radiation is the poor spatial coverage that presents on the surface (Josefsson, * Correspondence to: David Mateos Villán, Applied Physics Department, Valladolid University, Prado de la Magdalena Street s/n, 47005, Valladolid, Spain. dmateos@fa1.uva.es 2006). This is due to the high cost and great difficulty in maintaining the sensors that record these wavelengths. In Spain, the Meteorological National Agency (AEMet) manages 25 stations where UV radiation is measured, which is not enough to cover the whole Spanish geography. Therefore, other forms of assessing the dose of this radiation are required. One of the most widely used is the estimation by models either radiative transfer or empirical type. The first one explains the processes of interaction between the UV radiation and the atmospheric components by physical laws. Its accuracy depends on the input parameters, because it needs to receive good information about different atmospheric variables. On the other hand, the empirical models are based on fitted mathematical relationships between the responses of UV radiation under variations of main factors that have effects on this radiation. Although more simplified relationships are obtained compared with the radiative transfer models, good results are achieved when the levels of UV radiation on the surface are predicted. Their great advantage is that they link the UV radiation, rarely available at measuring stations, with radiometric and meteorological variables which are easily found in them, such as the global solar radiation (Ogunjobi and Kim, 2004) and, therefore, the usefulness of Copyright 2009 Royal Meteorological Society

2 1408 D. MATEOS VILLÁN ET AL. empirical models is not only focused on the prediction, because they offer the possibility of estimating past missing data in databases. But, the main drawback is that they present local kind, because they have been generated by a data series from a particular place. For example, in places with different climatic conditions would not be very reliable to apply these models. The main factors involved in the modulation of UV radiation are solar elevation, cloud cover and stratospheric ozone column. The attenuation by aerosols also has an effect on the UV radiation which can be quite significant in polluted areas. Several authors studied the trends of UV radiation levels and measurements of these variables. For example, the analysis of ozone influence on UV radiation was reported by the authors Casale et al. (2000); Guarnieri et al. (2004); Palancar and Toselli (2004); Bilbao et al. (2005); the influence of aerosols was studied, e.g. by Meloni et al. (2005). The combined evolution of ozone and aerosols was showed that contributes significantly to the modulation of the UV radiation at surface by di Sarra et al. (2002). The relationship between UV and global solar radiation and its dependence on total ozone column, cloudiness or aerosol was analysed, e.g. by Antón et al. (2008) and Borkowski (2008). Previous studies show that the UV radiation can be estimated from the solar elevation angle, the solar global radiation, the cloudiness, the total ozone column and other meteorological variables. The following authors evaluated the relationships between UV and global solar radiation: Ilyas et al. (1999); Kudish et al. (2000); Ogunjobi and Kim (2004); Sabziparvar (2009). Several empirical models among UV radiation, relative optical air mass and cloudiness (through the clearness index) was proposed by Foyo-Moreno et al. (1999); Murillo et al. (2003); Barbero et al. (2006). The aim of this paper is to investigate empirical models that link the hourly ultraviolet total radiation, nm (UVT), with the most important factors that may control the variability of ultraviolet radiation, such as solar elevation and clearness index, and with other radiometric variables like global solar radiation. Two new models for UVT and global solar radiation under cloudless skies and five models for all sky conditions are proposed, two of them use the cloud modification factor which is studied in this paper. In the following sections, a description of the measurement station, the data series characteristics, methodologies, the proposed parameterization and the assessing in central Spain can be seen. 2. Site, instrumentation and methodology The Research Centre of the Low Atmosphere (CIBA, latitude N, longitude 4 50 W and 840 m a.s.l.) is located in a wide-open area (free of obstructions) close to Valladolid, Spain. The climate at CIBA station is continental, with dry and warm summers and cold and wet winters. CIBA solar monitoring station contains a large number of radiometric and meteorological sensors, a more detailed description of each one can be found at (Bilbao et al., 2002). An Eppley total ultraviolet radiometer (TUVR) records horizontal ultraviolet total radiation (UVT, nm). According to the manufacturer, this radiometer has an expected error of about ±5%. Measurements of UVT solar radiation were analysed during the period from February 2001 to June Global solar radiation on a horizontal surface was measured by a Kipp & Zonen radiometer model CM-11 ( nm). Measurements of global solar radiation were analysed between November 2000 and June These radiometric sensors are connected to a two CR23X Campbell Dataloggers which are programmed for registering measurements every 10-min integration time. The data quality control followed in this work was explained in detail in a previous paper (Bilbao et al., 2008), taking to account the detection limits of the sensor and comparison with the extraterrestrial values. Owing to differences in the cosine response and in the temporal response of the radiometers, the analysis has been limited to solar elevation angles higher than 10. Moreover, only hours without data gaps have been considered and hourly values are expressed in irradiation units (kj m 2 ). Once the quality control of data has been passed, from the 10- min data, hourly values of UVT irradiation and hourly values of global irradiation were obtained, resulting pairs of UV-global hourly values. To simplify notation, onwards, UVT radiation is going to be cited as UV. Cloud cover observed by the trained staff of Villanubla Airport (Valladolid) has been obtained from the Spanish Meteorological Agency (AEMet). The distance between this observatory and CIBA station is 10 km. Cloudiness was recorded three times per day (7 : 00, 13 : 00 and 18 : 00 GMT) in octas, and these measurements were extrapolated to three ranges. The first one is applied to the data until 10 : 00, the second one is assigned to the data up to 16 : 00 and the last one is linked to the data from 16 : 00 GMT. Once obtained hourly irradiation values, several parameters have been calculated. The first of all is the relative optical air mass (m), evaluated using the expression suggested by Kasten and Young (1989): m = 1/(cos θ z ( θ z ) ) (1) where θ z is the zenith angle of the Sun (complementary angle of the solar elevation). Another evaluated parameter is the hourly global clearness index, which is defined as: k t = G/G 0 (2) where G is the hourly measured global solar radiation on a horizontal surface and G 0 is the hourly extraterrestrial

3 EMPIRICAL MODELS OF UV TOTAL RADIATION 1409 solar radiation. In total analogy, UV clearness index is defined as: k tuv = UV/UV 0 (3) where UV is the hourly measured ultraviolet solar radiation on a horizontal surface and UV 0 is the hourly ultraviolet extraterrestrial solar radiation. The extraterrestrial radiation values are evaluated following (Iqbal, 1983): X 0 = I SC (X) E 0 [sin sin δ + (24/π) sin(π/24) cos cos δ cos ω i ] (4) where I SC (X) is the integrated value of the solar radiation in the selected band (X = global: I SC (G) = kj m 2 ; or X = ultraviolet: I SC (UV ) = kj m 2 ) (Gueymard, 2004), E 0 is the correction to the sun earth distance, ω i is the hourly angle in the middle of the hour, is the latitude and δ is the solar declination. In this study, several empirical models of UV radiation are proposed. First, it is necessary to establish the appropriate relationships to build these models. To this end, lots of attempts have been done as polynomial, logarithmic, rational, exponential and potential fits, among others. So, the fit with the best correlation coefficient has been chosen as our proposal. For the construction of each model, a different set of data to the next validation are used. The data set for the construction of the model contains hourly data of the years 2001, 2003, 2004, 2005 and the first 6 months of 2008, resulting in a total of hourly values. In the validation process hourly data of the years 2002, 2006 and 2007 are selected for that purpose, resulting in a total of 2549 hourly values. The model accuracy is assessed by scatter-plots of the dependence of the estimated values as a function of the measured ones and by means of widely used statistical estimators: mean bias error (mbe), mean-absolute bias error (mabe) and root-mean-square error (rmse). To this end, the following expressions have been used (Miguel et al., 2001): mbe(%) = 100 X mea mabe(%) = 100 X mea rmse(%) = 100 X mea n (X est X mea ) 1 n n X est X mea 1 n n (X est X mea ) 2 1 n (5) (6) (7) where X est is the predicted values, X mea means the measured ones, X mea is the database average value of this variable and n is the data number. Figure 1. Dependence of hourly UV irradiation values (kj m 2 )on optical air mass for cloudless sky (black points) and all (grey points) conditions in Valladolid, Spain. 3. Results and discussion 3.1. Empirical models of UV and global radiation under cloudless skies The solar elevation alone cannot give an exact determination of UV radiation. Figure 1 shows a wide dispersion when UV radiation is plotted versus the optical air mass (grey points), however, the radiation decreases as the optical air mass increases. Moreover, the maxima are achieved when conditions are cloudless skies. If the global clearness index is greater than 0.75 (k t > 0.75) in 1 h, this is considered cloudless sky. This classification is chosen to ensure that the data correspond to cloudless sky conditions (Antón et al., 2008). Figure 1 also shows the dependence of UV irradiation values under cloudless skies (black points) on optical air mass and it can be seen that the obtained dispersion is now smaller than when all conditions are considered (grey points). Hence, the next aim of this section is to get a model that gives a good estimation of UV radiation under cloudless skies. After the evaluation of the global clearness index, 2560 h show an index higher than Thus, the use of different construction and assessing databases is necessary (the databases described in Section 2 are not suitable here): 1977 UV irradiation values corresponding to the period from February 2001 to December 2006 and 583 irradiation values from January 2007 to June 2008 have been used respectively. The relationship that best shows the dependence of UV radiation under cloudless skies (UV clea ) on optical air mass (m), after a complete analysis of the data, is given in the following equation and it constitutes the UVT-CIBA-CLEA model: UV clea = m m 2 (8) When this new model is applied to validation database, the followings values of mbe, mabe and rmse are obtained

4 1410 D. MATEOS VILLÁN ET AL. Figure 2. Comparison of hourly measured (UV mea ) and estimated (UV est ) ultraviolet irradiation values in Valladolid, Spain. Each equation is the linear fit (solid line). The dotted line is the unit slope line. as 6.93, 6.98 and 7.82%, respectively. The comparison between the estimation and measured values and the linear fit between them are shown in Figure 2a. The low values of statistical indices and the excellent correlation coefficient (0.99) mean the model assessing has provided very good results. The global radiation model under cloudless sky has been elaborated with a procedure similar to the followed in the UVT-CIBA-CLEA model. The same databases explained above have been used for this model. The following relationship has been obtained as the G-CIBA- CLEA model: G clea = m m 2 (9) The assessing of this model provides excellent results (mbe = 4.85%, mabe = 5.24% and rmse = 5.98%) Previous models for any atmospheric condition Some authors have proposed different empirical models for hourly UV irradiation values based on the UV clearness index (k tuv, Equation (3)). Foyo-Moreno et al. (1999) proposed the following relationship between k tuv and global clearness index (k t ): For the coefficients a and b, these authors evaluated the following dependence on the relative optical air mass (m) in Granada (Spain): a = e (m 0.97)/ e (m 0.97)/1.86 (11) b = e (m 1.05)/1.62 (12) Murillo et al. (2003) reported the same type of model. They worked in two towns (Córdoba and Valencia, Spain), but only the obtained results for Córdoba have been used in this study, due to different climate between Valladolid and Valencia. Córdoba has many similarities with Valladolid, for example, both are not coastal cities and there are mountains around these areas. Therefore, coefficients a and b for Córdoba are: a = Ln(m) (13) b = Ln(m) (14) Barbero et al. (2006) proposed a new potential relationship among k tuv,k t and m, which can be used in Equation (3), resulting a new type of model for UV radiation: k tuv = e a+b Ln(k t) (10) UV = UV k t m (15)

5 EMPIRICAL MODELS OF UV TOTAL RADIATION 1411 Table I. Comparison of statistical estimators of three original UV models in Valladolid, Spain. Model mbe (%) mabe (%) rmse (%) Foyo-Moreno Murillo Barbero The three previous models are assessed with the validation database (2549 data) explained in Section 2; Table I shows the results. It can be seen that Foyo-Moreno and Barbero s models give the lowest mbe, mabe and rmse values. Murillo s model overestimates the UV radiation in Valladolid and the other ones underestimate this radiation Recalibration of previous models for any atmospheric condition In this study, the models based on the definition of UV clearness index have been recalibrated with Valladolid database. Hence, one aim of this section is to find the best relationship among k tuv, k t and optical air mass. First, the coefficients a and b of Equation (10) have been evaluated from k t and k tuv values following Foyo- Moreno and Murillo s models. Table II shows the dependence of these coefficients on optical air mass (evaluated as a mean value) for each range of solar elevation. It can be seen that both coefficients increase when optical air mass decreases. The following relationships have been found as the best between each coefficient and optical air mass: a = Ln(m), with r 2 = 0.99 (16) b = Ln(m), with r 2 = 0.96 (17) Once obtained the expressions of coefficients, it can be proposed the UVT-CIBA-1 model by the Equations (3), Table II. Regression parameters of Equation (10), coefficient of determination (r 2 ) and number of data (n) for different ranges of solar elevation in Valladolid, Spain. Solar elevation a b r 2 n (10), (16), (17). After comparing the measured and estimated values, the following mbe, mabe and rmse indices are obtained as 2.71, 6.90 and 9.97%, respectively. Figure 2b shows the scatter-plot of UVT-CIBA-1 model versus the measures at Valladolid station and the linear fit between them. Satisfactory results can be observed due to the low values of the statistical indices and the correlation coefficient (0.97) is close to one. Next, the potential relationship among the UV and global clearness indices and the relative optical air mass is analysed following Barbero s model. The best relationship obtained that represents the UVT-CIBA-2 model is: UV = UV k t m (18) Assessing the UVT-CIBA-2 model, it can be seen that the mbe has been reduced to 0.49%, the mabe index has fallen two-tenths up to 6.77% and rmse has decreased one-tenth until 9.83%. Figure 2c shows the relationship between the model estimations and the measurements at CIBA station and the linear fit between them. So, the obtained results with the previous model have been improved with this model Proposal empirical model of UV radiation using cloudless sky model Once the radiation value under cloudless skies has been obtained from UVT-CIBA-CLEA model (Equation (8)), the real value will depend on a given atmospheric situation. To take into account the atmospheric transparency conditions, the parameter used is the global clearness index (k t ), which can be considered as a modulator of the value that would result under conditions of cloudless skies (Foyo-Moreno et al., 1999). Relationships that provide good estimations of UV radiation are required. The following functional relationship between the UV radiation under cloudless skies (UV clea ) and the clearness index (k t ) has been found as the most appropriate and it represents the UVT-CIBA-3 model: UV = k t UV clea (19) Applying this model to the validation database, the following values of mbe, mabe and rmse indices have been obtained: 1.86, 6.96 and 9.99%, respectively. Figure 2d shows the relationship between the estimations by the UVT-CIBA-3 model and the values measured at CIBA station, also shows the linear fit. The obtained results are similar to those with UVT-CIBA-2 model Cloud modification factor and UV modelling As solar radiation varies widely under different sky conditions, it is convenient to work with normalized parameters for minimizing the variability and maximizing the generality of the results. For this reason, the UVT-CIBA- CLEA model can be used for defining new parameters instead of clearness indices.

6 1412 D. MATEOS VILLÁN ET AL. Figure 3. Dependence of ultraviolet cloud modification factor (CMF UV ) on cloudiness for different ranges of solar elevation angle (h). Some authors Landelius and Josefsson (2000) and Calbó et al. (2005), among others, have defined the cloud modification factor as CMF UV = UV/UV clea, where UV is the measured ultraviolet radiation and UV clea means the radiation value under cloudless sky. This one can be estimated by any radiative transfer model or empirical model. In this study, the UVT-CIBA-CLEA model obtained before is used. Figure 3 shows the dependence of this cloud factor on cloud coverage for different sun elevation angle ranges. Points in the figure represent averages of all values in each class of cloudiness and solar height. It can be seen that the CMF UV presents a falling trend when the cloud cover increases. It takes a value around 1 under cloudless skies, but, under overcast skies conditions, its value decreases until to 0.5. Similar results were obtained by Foyo-Moreno et al. (2003), although the pattern of evolution is slightly different. Parisi et al. (2007) analysed the cloud modification factor for the cataract effective UV irradiances, and they obtained similar results too. Grant and Heisler (2000) reported this factor into the UV-B range and their cloud modification factor values were higher than in this study (UVT range). In analogy with CMF UV, it is possible to define a cloud modification factor for global solar radiation, CMF G = G/G clea,whereg means the measured global radiation and G clea is the estimation of the G-CIBA-CLEA model for global solar radiation under cloudless skies. In order to study the influence of cloudiness on both the factors (CMF UV and CMF G ), Figure 4 shows the relationship between them for the same database used in the construction of previous models. It can be seen that the points in the figure are separated from the unit slope line. Therefore, the clouds do not transmit the same way the UV and global solar radiation. For low values of the factors (CMF G and CMF UV lower than 0.4), it can be observed a linear behaviour between them and from these values the figure shows high dispersion. The Figure 4. Relationship between UV (CMF UV ) and global (CMF G ) cloud modification factors. values higher than the unit could be explained as an enhancement effect under partial cloud cover conditions when geometric conditions are the most favourable for the reflection of UV radiation at the edges of cumulus or very thin cirrus or between cloud base and the ground (Foyo-Moreno et al., 2003). Moreover, it can be seen that CMF UV presents higher values than CMF G. A similar shape was reported by several authors in a review of empirical studies of cloud effects on UV radiation (Calbó et al., 2005). The following relationships between CMF UV CMF G have been found: and CMF UV = CMF G (20) CMF UV = (1 e CMF G ) (21) Performing the validation of these two models, for Equation (20), the next values of mbe, mabe and rmse: 3.67, 9.21 and 12.57% have been obtained respectively. And for Equation (21): 3.04, 8.95 and 11.83%, respectively. Foyo-Moreno et al. (2003) reported a similar relationship to Equation (21) for their results of CMF UV. Recalling the CMF UV definition, a new type of empirical model of UV radiation has been proposed: UV = CMF UV UV clea,replacingcmf UV by Equation (20) and UV clea by Equation (8), the best relationship between CMF G and relative optical air mass (m) has been named UVT-CIBA-4 model: UV = (1.043 CMF G ) ( m (22) The evaluation of this model provides the following results: mbe = 0.86%, mabe = 7.82% and rmse = 10.46%. The comparison between hourly measured UV radiation and the UVT-CIBA-4 model estimation is shown in Figure 5a. This figure also shows the linear fit with a correlation coefficient of m 2 )

7 EMPIRICAL MODELS OF UV TOTAL RADIATION 1413 Figure 5. Comparison of hourly measured (UV mea ) and estimated (UV est ) ultraviolet irradiation values. Each equation is the linear fit (solid line). The dotted line is the unit slope line. Finally, UV radiation under cloudless skies, given by UVT-CIBA-CLEA model (Equation (8)), has been modulated with CMF G to obtain forecasts under any meteorological condition, so UVT-CIBA-5 model has been proposed as: UV = CMF G UV clea (23) The validation of this new model gives similar results to those obtained with the other models proposed in this study (mbe = 0.40%, mabe = 6.89% and rmse = 9.99%). In Figure 5b, the comparison between hourly measured and estimated UV irradiation values can be seen. The roles of the clearness index and the cloud modification factor on the proposed empirical UVT- CIBA-3 and UVT-CIBA-5 models, respectively, are similar; in fact, these parameters are elevated to a very similar exponent. In Table III, a summary with the equations and the values of calculated statistical indices can be found. The models for clear sky present low values of mbe, mabe and rmse indices. UVT-CIBA-CLEA underestimates UV radiation whereas G-CIBA-CLEA overestimates global radiation. With respect to the models for any atmospheric condition, the results are very similar but UVT-CIBA-2 Table III. Summary with the assessed results of the proposed models. Model Equation mbe (%) mabe (%) rmse (%) UVT-CIBA-CLEA G-CIBA-CLEA UVT-CIBA-1 3,10,16, UVT-CIBA UVT-CIBA UVT-CIBA UVT-CIBA Figure 6. Variability of daily measured and estimated UV irradiation values in Valladolid, Spain. presents values of mbe, mabe and rmse slightly better than the others Application to fill data gaps One of the advantages of obtaining empirical models, as mentioned above, is the ability to fill existing gaps in the database. This advantage is linked with obtaining relationships among variables that are difficult to find on terrestrial stations (such as UV radiation) and other more easily available (such as global radiation). At CIBA station, there were some periods without measurements of UV radiation due to breakdowns of the sensor or calibration campaigns. The UVT-CIBA-2 model (Equation (18)) has been selected among all the proposed ones, as it can be seen in the previous section. Figure 6 shows

8 1414 D. MATEOS VILLÁN ET AL. that with this model, the number of UV radiation data increases. In fact, as it depends on measurements of global solar radiation, the temporal evolution starts in November 2000, instead of February The 1503 daily measured values of UV irradiation have increased up to 2568 evaluated from hourly estimations with the UVT-CIBA-2 model. 4. Conclusions Using the hourly measurements of UV and global solar irradiation values, five empirical models for any atmospheric condition and any zenith angle have been established between the main influence factors on UV radiation. Moreover, two new empirical models for clear sky conditions have been proposed. The performed statistical analysis has shown correlation coefficients higher than 0.97 between the hourly estimated and measured UV irradiation values; therefore, the hourly UV radiation can be accurately estimated from broadband global solar radiation values by the suggested relationships. The cloud modification factor has been evaluated to make a brief study of cloud effect on UV radiation. In general, this one has been proved as reducing effect; however, there are measured values in which the cloud effect is to increase the UV radiation on surface, this is called enhancement effect. When the conditions are under overcast skies, the UV cloud modification factor falls around 50% of the value under cloudless skies. The best relationships between UV and global cloud modification factors have been exponential and potential fits. Given a certain atmospheric condition, the CMF is, in general, higher for UV radiation than for global solar radiation. Despite the different relationships that have been proposed for hourly UV radiation models, the results of the evaluated statistical indices show high similarity among all them. Moreover, these small differences among the Foyo-Moreno and Barbero s models and the five proposed in this study suggest that empirical models do not have as pronounced local kind as expected, if the climate is not different. Finally, the UVT-CIBA-2 model has been selected as the best and has been used for filling the existing gaps in database. In fact, the daily values have increased from 1503 to With the proposed empirical models, UV radiation can be evaluated in places where measurements of global solar radiation are available. The results of this study are interesting for climatology, radiative transfer in the atmosphere and applications on biophysics and biological studies. Acknowledgements The authors gratefully acknowledge the financial support extended by the Spanish Innovation and Science Ministry and by the Autonomous Government of Castile and Leon region under the Projects: CGL and REF. GR , respectively. And also, the authors appreciate the help of Valladolid University to the research staff. Cloudiness observations were kindly provided by the Spanish Meteorological Agency (AEMet).. Nomenclature m relative optical air mass (dimensionless) θ z solar zenith angle (radians) h solar elevation (in degrees) UV hourly ultraviolet solar radiation (kj m 2 ) UVT hourly ultraviolet total solar radiation (kj m 2 ) G hourly global solar radiation (kj m 2 ) k t hourly global clearness index (dimensionless) k tuv hourly ultraviolet clearness index (dimensionless) UV 0 hourly UV extraterrestrial solar radiation on a horizontal surface (kj m 2 ) G 0 hourly global extraterrestrial solar radiation on a horizontal surface (kj m 2 ) UV clea hourly UV solar irradiation on a horizontal surface under cloudless skies (kj m 2 ) G clea hourly global irradiation on a horizontal surface under cloudless skies (kj m 2 ) CMF UV hourly ultraviolet cloud modification factor (dimensionless) CMF G hourly global cloud modification factor (dimensionless) UV est hourly ultraviolet solar irradiation estimation by a model (kj m 2 ) UV mea hourly ultraviolet solar irradiation measured in a measuring station (kj m 2 ) mbe mean bias error (%) mabe mean-absolute bias error (%) rmse root-mean-square error (%) References Antón M, Serrano A, Cancillo ML, García JA Relationship between erythemal irradiance and total solar irradiance in South- Western Spain. Journal of Geophysical Research 113: D14208, DOI: /2007JD Barbero FJ, López G, Batlles FJ Determination of daily solar ultraviolet radiation using statistical models and artificial neural networks. Annales Geophysicae 24: Bilbao J, de Miguel A, Ayuso A, Franco JA Sensores de medida de radiación solar: dispositivo experimental del laboratorio de radiación solar. ERA SOLAR 106: Bilbao J, de Miguel A, Salvador P. Hellenic Illumination Committee A study of the ultraviolet solar radiation at a rural area of Spain. Solaris nd Joint Conference May, Athens, Greece (Solar light advancements in the dawn of the 21st century). Bilbao J, Salvador González P, de Miguel Castrillo A UV-B climatology in Central Spain. International Journal of Climatology 28: , DOI: /joc Borkowski JL Modelling of UV radiation variations at different time scales. Annales Geophysicae 26: Calbó J, Pagès D, González JA Empirical studies of cloud effects on UV radiation: a review. Reviews of Geophysics 43: RG2002, DOI: /2004RG Casale GR, Meloni D, Miano S, Palmieri S, Siani AM, Cappellani F Solar UV-B irradiance and total ozone in Italy: fluctuations and trends. Journal of Geophysical Research 105(4):

9 EMPIRICAL MODELS OF UV TOTAL RADIATION 1415 Foyo-Moreno I, Alados I, Olmo FJ, Alados-Arboledas L The influence of cloudiness on UV global irradiance ( nm). Agricultural and Forest Meteorology 120: Foyo-Moreno I, Vida J, Alados-Arboledas L A simple all weather model to estimate ultraviolet solar radiation ( nm). Journal of Applied Meteorology 38(eq3): Grant RH, Heisler GM Estimation of ultraviolet-b irradiance under variable cloud conditions. Journal of Applied Meteorology 39: Guarnieri RA, Padilla LF, Guarnieri FL, Echer E, Makita K, Pinhero DK, Schuch AMP, Boeira LS, Schuch NJ A study of the anticorrelations between ozone and UV-B radiation using linear and exponential fits in southern Brazil. Advances in Space Research 34: , DOI: /j.asr Gueymard C The sun s total and spectral irradiance for solar energy applications and solar radiation models. Solar Energy 76: Ilyas M, Pandy A, Hassan SIS UV-B radiation at Penang. Atmospheric Research 51: Iqbal M An Introduction to Solar Radiation. Academic Press: London. Josefsson W UV-radiation measured at Norrköping, Sweden. Theoretical and Applied Climatology 83: 59 76, DOI: /s Kasten F, Young AT Revised optical air mass tables and approximation formula. Applied Optics 28: Kudish AI, Lyubansky V, Evseev EG, Ianetz A Intercomparison of the solar UVB, UVA and global radiation clearness and UV indices for Beer Sheva and Neve Zohar (Dead Sea), Israel. Energy 30: Landelius T, Josefsson W Methods for cosine correction of broadband UV data and their effect on the relation between UV irradiance and cloudiness. Journal of Geophysical Research 105(D4): Meloni D, di Sarra A, Herman JR, Monteleone F, Piacentino S Comparison of ground-based and total ozone mapping spectrometer erythemal UV doses at the island of Lampedusa in the period : role of tropospheric aerosols. Journal Of Geophysical Research 110: D01202, DOI: /2004JD Miguel A, Bilbao J, Aguilar R, Kambezidis H, Negro E Diffuse solar irradiation model evaluation in the north Mediterranean belt area. Solar Energy 70(2): Murillo W, Cañada J, Pedrós G Correlation between global ultraviolet ( nm) and global irradiation in Valencia and Cordoba (Spain). Renewable Energy 28: Ogunjobi K, Kim Y Ultraviolet ( ) and broadband solar hourly radiation at Kwangju, South Korea: analysis of their correlation with aerosol optical depth and clearness index. Atmospheric Research 71: Palancar GG, Toselli BM Effects of meteorology and tropospheric aerosols on UV-B radiation: a 4-year study. Atmospheric Environment 38: Parisi AV, Turnbull DJ, Turner J Calculation of cloud modifications factors for the horizontal plane eye damaging ultraviolet radiation. Atmospheric Research 86: , DOI: /j.atmosres Sabziparvar AA Estimation of clear-sky effective erythema radiation from broadband solar radiation ( nm) data in an arid climate. International Journal of Climatology. Published online, DOI: /joc di Sarra A, Cacciani M, Chamard P, Cornwall C, DeLuisi JJ, Di Iorio T, Disterhoft P, Fiocco G, Fuà D, Monteleone F Effects of desert dust on ozone on the ultraviolet irradiance at the Mediterranean island of Lampedusa during PAUR II. Journal of Geophysical Research 107(D18): 8135, DOI: /2000JD WMO (World Meteorological Organization) Scientific Assessment of Ozone Depletion: Global Ozone Research and Monitoring Project Report No. 50, Geneva, Switzerland, 572.