Neural network for the estimation of UV erythemal irradiance using solar broadband irradiance

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 27: (7) Published online 22 March 7 in Wiley InterScience ( Neural network for the estimation of UV erythemal irradiance using solar broadband irradiance I. Alados, a, * M. A. Gomera, a I. Foyo-Moreno b and L. Alados-Arboledas b a Dpto de Física Aplicada II, Universidad de Málaga, Málaga, Spain b Dpto de Física Aplicada, Universidad de Granada, Granada, Spain Abstract: In recent years there has been a substantial increase in attempts to model radiative flux of ultraviolet radiation, UV. In this paper we present the development of an artificial neural network (ANN) model that can be used to estimate solar UV erythemal irradiance, UVER, based on optical air mass, ozone columnar content and broadband solar irradiance. The study was developed at seven stations in the Iberian Peninsula using data recorded at A Coruña, Málaga, Murcia and Santander, during 3; at Madrid in the period 2; at Valencia in, 1 and 3; and at Zaragoza, from 1 to 3. The UVER observations are recorded as half-hour average values. The measurements were performed in the framework of the Spanish UV-B radiometric network operated and maintained by the Spanish Meteorological Institute. In order to train and validate the Multi-layer Perceptron neural networks, independent subsets of data were extracted from the complete database at each station. The networks developed at each place when applied to an independent data set recorded at the same location provide estimates with mean bias deviation less than 1% and root mean square deviation below 17% for all the sites. The generalization network developed using data registered at A Coruña, Madrid, Murcia and Zaragoza provides estimates at all the locations with RMSD below 19%. According to these results, the use of solar broadband irradiances for the estimation of ultraviolet erythemal irradiance provides a tool that can solve the difficulties associated to the retrieval of appropriate information on the cloud field by human observers. In this sense, the proposed method seems appropriate to use the widespread networks of solar broadband irradiance to obtain ultraviolet erythemal irradiance data sets in places where this radiative flux is not measured or to extend back in time the existing data sets. Copyright 7 Royal Meteorological Society KEY WORDS ultraviolet irradiance; UVI index; ozone depletion; multi-layer perceptron network; artificial neural network Received 11 October 5; Revised 5 December 6; Accepted 14 December 6 INTRODUCTION During the past years there has been an increased concern on the increate in UV irradiance that reaches the surface as a result of the ozone layer depletion (World Meteorological Organization (WMO) 1998). The solar UV irradiance includes (CIE, 1987) wavelength bands from to 28 nm (UV-C), which is completely absorbed in the Earth s atmosphere, nm (UV-B), partially absorbed by stratospheric ozone and nm (UV- A), which makes up most of the UV irradiance at the surface. Ozone is an effective absorber of UV radiation, with a reduced effect in the UV-A region. Although in outer space UV-B and UV-A account for about 7.5% of the solar total irradiance, at the surface they typically make up between 3% and 5% of the solar total irradiance (Foyo-Moreno et al., 1998). Owing to its harmful effects on biological systems great attention has been paid to UV-B irradiance (Diffey, 1991; Van der Leun et al., * Correspondence to: I. Alados, Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, 1871, Granada, Spain. alados@ugr.es 1991, 1994, 1998). For human beings, the UV effect that has received most attention is the erythema, or sunburn. The contribution of the different wavelengths to this effect is described by an action spectrum (Diffey, 1982) standardized in 1987 by the Comission Internationale de l Eclarage (McKinlay and Diffey, 1987). This action spectrum is the weighting factor used for the computation of the UV erythemal irradiance (UVER). The attenuation of UVER reaching the Earth s surface is a result of the combined effects of solar zenith angle, surface elevation, cloud cover, aerosol loading and optical properties, surface albedo and vertical profile of ozone. The high temporal and spatial variability of cloud cover and especially aerosols is responsible for much of the variability in UVER. In recent years, there has been a substantial increase in attempts to model the UV irradiance. Unfortunately the cloud and aerosol characteristics determining radiation transfer are seldom known because of a general lack of observations, especially for the aerosols. Modelling the effect of cloud requires knowledge of cloud optical thickness and drop size distributions with high temporal and spatial resolution, information that is Copyright 7 Royal Meteorological Society

2 1792 I. ALADOS ET AL. limited to specific sites and campaigns. Thus, a different approach, based on commonly accessible data, must be used to model UVER to obtain long time series or extended spatial distributions. In previous works (Alados- Arboledas et al., 3; Alados et al., 4), we have characterised the cloud effects on UVER using information routinely registered in most meteorological stations: cloud type and amount, expressed in terms of fractional cloud coverage in octas (eighths). This kind of approach has been followed in different studies (Ilyas, 1987; Frederick and Snell, 199; Frederick et al., 1993; Blumthaler et al., 1994, 1996; Thiel et al., 1997; Kuchinke and Nunez, 1999; Grant and Heisler, ; Josefsson and Landelius, ). The approach followed in these studies included modelling cloud effects using non-linear functions in combination with more or less complex models for cloudless skies. In this work, we use the dimensionless ratios of total solar irradiance (integrated over the entire solar spectrum): k, ratio of diffuse to global horizontal solar irradiance, k b, ratio of direct irradiance to extraterrestrial horizontal irradiance and k t, ratio of global horizontal irradiance to extraterrestrial horizontal irradiance to characterise the sky conditions. These dimensionless ratios of solar total irradiance are influenced markedly by the cloud amount. In this sense, we characterize the cloud effect on a particular range of the solar spectrum trough the effect they produce on the total solar spectrum. Thus, in this work these dimensionless ratios have been used as input data for the estimation of UVER. Artificial neural network (ANN) models may be used as an alternative method in engineering, analysis and prediction. These models mimic somewhat the learning processes of a human brain. They operate as a black box model, requiring no detailed information about the system. Instead, they learn relationship between input parameters and the controlled and uncontrolled variables by studying previously recorded data, similar to the manner a non-linear regression might perform (Kalogirou, 1). Another advantage of using ANN is their ability to handle large and complex systems with many interrelated parameters. They seem to simply ignore excess data that are of minimal significance and concentrate instead on the more important inputs. They have been used in diverse applications in control, robotics, pattern recognition, forecasting, medicine and power systems, as well as manufacturing, optimisation, signal processing and social psychological sciences. Neural networks are used to learn the behaviour of the system and are subsequently used to simulate and predict the behaviour of the system. The aim of the present study is to develop ANN models that can be used to estimate UVER on the basis of optical air mass, ozone columnar content, the dimensionless ratios, k t, k and k b. In this sense, this work represents a new step in the UVER modelling by ANNs. In fact, in a previous work (Alados et al., 4) we have approached this technique using a different set of input parameters. This can be viewed as a multivariable interpolation problem in which it is required to estimate the function relating the input to the output. In our study, we apply this analysis to seven stations with rather different environments. Madrid and Zaragoza are inland locations more than km from the coast; Murcia is an inland location about km away from the Mediterranean Sea; whereas Valencia and Málaga are coastal locations situated in the western Mediterranean. A Coruña and Santander are located in the Atlantic Ocean coast of the Iberian Peninsula (Figure 1). Figure 1. Map Iberian Peninsula and situation of different stations, the asterisk shows stations with measurements of ozone columnar contents.

3 NEURAL NETWORK FOR THE ESTIMATION OF UV ERYTHEMAL IRRADIANCE 1793 Table I. Climatic data for the stations analysed. Station (1971 ) T TM Tm R H DD I ACoruña (43 21 N, 8 25 W, 67 m a.s.l.) Madrid (4 27 N, 3 44 W, 58 m a.s.l.) Málaga (36 43 N, 4 29 W, 61 m a.s.l.) Murcia (38 N, 1 1 W, 69 m a.s.l.) Santander (43 29 N, 3 48 W, 63 m a.s.l.) Valencia (39 29 N, 22 W, 11 m a.s.l.) Zaragoza (41 38 N, 55 W, m a.s.l) T, Yearly average temperature ( C); TM, Yearly average of the maximum temperature ( C); Tm, Yearly average of the minimum temperature ( C); R, Yearly average of precipitation (mm); H, Yearly average of relative humidily ; DD, Yearly average of cloudless days; I, Yearly average of sunshine duration. DATA AND MEASUREMENTS The UVER observations, performed within the Spanish UV-B radiometric network, were recorded as half-hour average values. Martinez-Lozano et al. (2) reported a detailed description of this network. Yankee UV-B-1 radiometers are operated and maintained by the Spanish Meteorological Institute (INM). In some of the stations selected for this study, simultaneous observations of ozone columnar content were performed using the Brewer instrument operated within the same network at the selected locations (see Figure 1). After analysing the available measurements and considering the marked latitudinal pattern of this variable, different criteria has been used for the assignment of ozone columnar content at those stations where measurements were not available. Thus for Málaga we have used the measurements performed at El Arenosillo, the closest station that also presents similar latitude. A similar procedure has been followed at Santander that uses data set registered at A Coruña. Finally, for Valencia we have used the average between Madrid and Murcia. Solar global irradiance has been registered on an hourly base using a Kipp & Zonen model CM-11, while another Kipp&Zonen model C-11 with a polar axis shadow band was used to measure solar diffuse irradiance. Measurements of solar, global and diffuse irradiance have an estimated experimental error of about 2 3%. The Yankee UV-B-1 radiometer is a broadband ( nm) Robertson Berger type radiometer. The spectral response of the instrument is designed to approximate the spectral response of the human skin to UV (McKinlay and Diffey, 1987). The maintenance of the calibration constant of the instruments included in the Spanish UV-B radiometric network is described in the study of Martinez-Lozano et al. (2). The experimental uncertainty of this instrument is about 8 9% (Leszczynski et al., 1998; Pearson et al., ). Data were registered at Madrid (4 27 N, 3 44 W, 58 m above sea level [a.s.l.]) during the period 2; A Coruña (43 21 N, 8 25 W, 67 m a.s.l.), Málaga (36 43 N, 4 29 W, 61 m a.s.l.) Murcia (38 N, 1 1 W, 69 m a.s.l.), Santander (43 29 N, 3 48 W, 63 m a.s.l.) during the period 3; Valencia (39 29 N, 22 W, 11m a.s.l.) during the years, 1 and 3; and Zaragoza (41 38 N, 55 W, m a.s.l.), during 1 3. To avoid problems associated to the instrument deviations from the ideal cosine law, we limited our study to solar elevation angles greater than 1 ; in any case, the UVER values measured for larger zenith angles are relatively small. Table I presents some climatic data for stations analysed in this study. The different mean yearly values shown have been computed using data registered in the period 1971 ( Especially relevant are the differences in yearly precipitation and sunshine duration. In some sense, it can be assessed that the stations used are representative of the variety of climatic conditions representatives of the Iberian Peninsula. NEURAL NETWORK MODELS The human brain is composed of neurons that provide us with the ability to apply our previous experiences to our actions (Fausett, 1994; Haykin, 1994). ANNs, are computing algorithms that mimic the four basic functions of these biological neurons. These functions are to receive inputs from other neurons or sources, combine them, perform operations on the result and output the final result. Alados et al. (4) presents a discussion of the main features of the kind of algorisms when used for the UVER estimation. ANN design There are various studies addressing the estimation of cloud effects on solar UV irradiance as a function of either the observed cloud amount (Ilyas, 1987; Lubin and Frederick, 1991; Bais et al., 1993; Blumthaler et al., 1996; Nemeth et al., 1996; Schafer et al., 1996; Thiel et al., 1997; Kuchinke and Nunez, 1999; Alados- Arboledas et al., 3; Alados et al., 4), the cloud effect on other spectral ranges of solar irradiance (Alados et al., ; Foyo-Moreno et al., 1, 3) or a combination of the two (Schwander et al., 2). A different approach has been followed by Sabburg and Wong () that used additional information on the cloud field obtained by sky cameras.

4 1794 I. ALADOS ET AL. In our study, we approach the estimation by training a multi-layer perceptron (MLP) ANN that consists of three layers. The variables considered for these models were the optical air mass, m a, total columnar content of ozone, l o, and a set of additional input parameters describing clouds. Three different approaches have been considered by including various input data: (MLP) Model 1 uses as input variable k t, ratio of global horizontal irradiance to extraterrestrial horizontal irradiance; MLP Model 2 uses input variables k t,andk, ratio of diffuse to global horizontal solar irradiance. Finally, MLP Model 3 uses the same input variables used in Model 2 but including k b, ratio of direct irradiance to extraterrestrial horizontal irradiance. Figure 2 shows the MLP used for estimating UVER. The number of input neurons depends on the type of cloud information used as input. For the hidden layer, we have selected the optimal number of hidden neurons equal to the number of input variable neurons. For this purpose we have used an empirical procedure. Thus, we have tested different combinations selecting the one that provides the best results, in terms of convergence and root mean square deviation. The output layer consists of a unique neuron corresponding to the estimated UVER, UVER m. The training of the ANNs has been done using 1% of the data measured at each station. The remaining 9% of the data corresponding to the data sets has been used as testing data set. These two subsets have been selected using a random process. In fact these testing data sets are used in order to select among ten possible ANNs obtained after the corresponding trainings at each location. The idea is to select at each location the ANN that provides the lowest RMSD between the estimated and measured values corresponding to the testing data set. We must follow this procedure because the initial weights used in the ANN training are randomly selected. This circumstance could lead in some cases to a low level of convergence. In this way, the use of the testing data allow the selection of the best trained ANN among the ten obtained. Validation of the models As mentioned above, the design of an ANN requires the use of the training and the testing data sets, used in training and selecting the best ANN, and the validation data set that is an independent data set used to characterize the estimating capability of the ANN. In our case, for the last purpose we have used the whole data sets at each location. Figure 3 shows the scatter plot of estimated versus measured UVER for the seven data sets and Model 3. The performance of the models was evaluated using the RMSD and the means bias deviation (MBD). These statistics allow for the detection of both the differences between experimental data and model estimates and the existence of systematic data over or underestimation tendencies, respectively. Linear regression between estimated and measured values was also computed. The linear fitting was forced through zero, thus the slope, b, provides information about the relative underestimation or overestimation associated with the model. Finally, the determination coefficient, R 2, gives an evaluation of the experimental data variance explained by the model. Table II presents results of these analyses, including the statistics previously described together with the number of data included in each data set and the average value for UVER, UVER ave. The slope of the linear regression between estimated and measured values is close to unity in all the cases, thus Figure 2. Scheme of the MLP Artificial Neural Network used for UVER models.

5 NEURAL NETWORK FOR THE ESTIMATION OF UV ERYTHEMAL IRRADIANCE 1795 b =.98; R 2 =.96 MBD = -.5%; RMSD = 16.4% UVER Measured Values b =.988; R 2 =.97 MBD =.3%; RMSD = 14.% UVER Measured Values (e) (a) (c) A Coruña Málaga Santander b =.994; R 2 =.97 MBD =.5%; RMSD = 15.3% UVER Measured Values b =.99; R 2 =.98 MBD = -.8%; RMSD = 13.9% UVER Measured Values b =.985; R 2 =.97 MBD = -.5%; RMSD = 14.3% UVER Measured Values (f) (b) (d) Madrid Murcia Valencia b =.991; R 2 =.97 MBD =.5%; RMSD = 15.5% UVER Measured Values (g) Zaragoza b = 1.; R 2 =.98 MBD =.8%; RMSD = 11.9% Figure 3. Scatter plot of UVER estimated versus UVER measured for the seven stations. The model used in each case is the local Model 3 tested at the same location where it is developed. indicating the goodness of the fit. On the other hand, the variance explained for the models is better than 96%. It is evident that the local models provide estimates at the different places with MBD that are smaller than the expected experimental errors over the average value. It is interesting to note that the RMSD obtained are lower than 17% for the three types of neural network. The overall performance is better than that associated to the use of ANN based on cloud observations registered routinely in meteorological stations, in this sense Alados et al. (4) obtained RMSD values of 18% at Madrid, 19.6% at Murcia and 14.6% at Zaragoza, using cloud amount and type. On the other hand, using empirical models developed with the same data sets, Alados-Arboledas

6 1796 I. ALADOS ET AL. Table II. Results for local models at the different locations. The models were developed and tested at the same station. Table III. Results for the generalized models at the different locations. Stations UVER b R 2 MBD mwm 2 % RMSD % Stations UVER b R 2 MBD mwm 2 % RMSD % Model 1 ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza Model 2 ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza Model 3 ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza The numbers of data included each stations are: 889 (A Coruna), 1375 (Madrid), 55 (Málaga), 1192 (Murcia), 991 (Santander), 744 (Valencia) and 7216 (Zaragoza). et al. (3) have obtained larger MBD and RMSD than that obtained in the present study for some of the stations analysed (Madrid, 2.2% and 17.6%; Murcia, 2.1% and 16.4%; Zaragoza,.3% and 16.4%). A test, not shown here, reveals that the use of the model developed at a given place to estimate the UVER at other locations provide slightly larger MBD and RMSD. In this sense, we have approached the design of a generalized model using data registered at four stations, A Coruña, Madrid, Murcia and Zaragoza. Thus, we have used a subset that includes 1% of the data registered at each one of these four stations to train a new neural network. The choice of these four stations is justified by two reasons, first at theses stations we have both UVER and ozone columnar content measurements, second these stations covered different climatic conditions in the Iberian Peninsula, including Atlantic, Mediterranean and Continental influences. Table III shows the results obtained when using this generalized model at different locations. It is evident that the RMSD presents only slightly larger values than those obtained with the local models. On the other hand, the MBD presents appreciable deviations from the ideal values,, at A Coruña, Madrid and Valencia. It is interesting to note that all the stations the MBD values are smaller than the experimental error Model 1 ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza Model 2 ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza Model 3 ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza The numbers of data included each stations are: 889 (A Coruna), 1375 (Madrid), 55 (Málaga), 1192 (Murcia), 991 (Santander), 744 (Valencia) and 7216 (Zaragoza). associated to the UV-B radiometer used in this study. In any case, both the slope and correlation coefficient of the linear regression between measured and estimated values reveals the goodness of the estimation model. Estimation of the UV-index In order to offer to the population information on the potentially harmfull effects of the UV-B irradiance, an index called UVI has been introduced during the past years. The UV-Index itself is an irradiance scale computed by multiplying the UVER irradiance in Wm 2 by 4. Thus, the clear sky value at sea level in the tropics would normally be in the range 1 12 ( 3 mwm 2 ) and 1 is an exceptionally high value for northern mid-latitudes. This scale has been adopted by the WMO and WHO and is in use in a number of other countries. UV intensity is also described in terms of ranges running from low values (less than 2), moderate(3 5), high (6 7), very high (8 1) and extreme (11 ). Table IV presents the performance of the different models when used for the estimation of the UVI index. For each model, local (Model 1, Model 2 and Model 3) or generalized (Model 1G, Model 2G and Model 3G), and for each location, we tabulated the percentage of the

7 NEURAL NETWORK FOR THE ESTIMATION OF UV ERYTHEMAL IRRADIANCE 1797 Table IV. Results of the different models, local (Model 1, Model 2 and Model 3) or generalized (Model 1G, Model 2G and Model 3G) at each location in terms of the percentage of cases with differences of UVI unit and with differences less or equal to one UVI unit. UVI m UVI e ACoruña Madrid Málaga Murcia Santander Valencia Zaragoza Model [ 1, 1] Model 1G [ 1, 1] Model [ 1, 1] Model 2 G [ 1, 1] Model [ 1, 1] Model 3G [ 1, 1] Figure 4. Histograms of the differences between measured and estimated UVI, UVI m UVI e, local Model 3, developed at a given location, when applied at each location. Figure 5. Histograms of the differences between measured and estimated UVI, UVI m UVI e, generalized Model 3, when applied at each location. cases with no difference between the measured and estimated UVI together with that associated to differences less or equal to one UVI unit. This analysis provides an appropriate method to discriminate the goodness of a given model in comparison with others. In general, the results for the local models are better than for the generalized models. Nevertheless, these differences are reduced in the case of Model 3, in that case the differences between local and generalized models are negligible (Figures 4 and 5). In any case, the percentage of cases with differences of UVI units is in the range 62.2% to 67.5%. While the percentage of the cases with differences of ±1 UVI unit covers the range 95.9% to 99.5%. This gives an idea of the goodness of the developed model when applied to estimate the UVI index. This is especially relevant for the generalized model that according to these results could be applied with a high level of confidence to other locations in the Iberian Peninsula, where measurements were not available, considering that the stations analysed in this study are representative of a wide range of environment in the Iberian Peninsula.

8 1798 I. ALADOS ET AL. CONCLUSIONS In this work, we have approached the estimation of solar ultraviolet irradiance incoming at surface level. For this purpose, we have developed an ANN model that estimates solar UVER irradiance based on optical air mass, ozone columnar content and broadband solar irradiance. A MLP network, MLP, consisting in an input layer, an output layer and one hidden layer was used. The training of the neural network was done using the Bayesian regulation back propagation algorithm. The study was developed at seven stations in the Iberian Peninsula using data recorded in the framework of the Spanish UV-B radiometric network. The results suggest that a MLP neural network using optical air mass, ozone columnar content and the dimensionless ratios, k, ratio of diffuse to global horizontal solar irradiance, k b, ratio of direct irradiance to extraterrestrial horizontal irradiance and k t, ratio of global horizontal irradiance to extraterrestrial horizontal irradiance, provides better results than that obtained in a previously published neural network model relying on cloud observations as input variables. In fact, the networks developed at each place when applied to an independent data set recorded at the same location provide estimates with mean bias deviation less than 1% and RMSD below 17% for all the sites. The proposed model exploits the wide spreading of radiometric networks. A clear advantage of using radiometric variables as input over the use of cloud observations is that radiometric observations are gathered in a continuous way while cloud observations are performed in fixed schedules that in some cases are reduced to one observation every 3 h. On the other hand, the use of cloud observations present additional limitations associated to the subjective character of the human observations and the absence of relevant information on the proximity of cloud fields to the solar disk. A generalized network has been developed using data registered at A Coruña, Madrid, Murcia and Zaragoza. When tested against independent data sets this model provides estimates at all the locations with RMSD below 19%. According to these results, the use of solar broadband irradiances for the estimation of ultraviolet erythemal irradiance provides a tool that can solve the difficulties associated to the retrieval of appropriate information on the cloud field by human observers. In this sense, the proposed method seems appropriate to use the widespread networks of solar broadband irradiance to estimate ultraviolet erythemal irradiance data sets in places where this radiative flux is not measured or to extend back in time the existing data sets. The models have been evaluated in reference to their capability to estimate the UVI index. In this sense, the percentage of cases with differences of UVI unit is in the range 62.2% to 67.5%. While the percentage of the cases with differences of ±1 UVI unit covers the range 95.9% to 99.5%. This result confirms the applicability of the developed models, specially the generalized versions, to estimate UVI index at those locations in the Iberian Peninsula where there are no UV radiation measurements, considering that the stations used in model development are representative of the different conditions that characterize the Iberian Peninsula. ACKNOWLEDGEMENTS This work was supported by CICYT from the Spanish Ministry of Science and Technology through projects No: CGL C7-3 and REN The Instituto Nacional de Meteorología kindly provided the radiometric, columnar ozone and meteorological information for the three stations used in this study. REFERENCES Alados I, Olmo JF, Foyo-Moreno I, Alados-Arboledas L.. Estimation of photosynthetically active radiation under cloudy conditions. Agricultural and Forest Meteorology 12: 39. Alados I, Mellado JA, Ramos F, Alados-Arboledas L. 4. Estimating UV erythemal irradiance by means of neural networks. Photochemistry and Photobiology 8(2): Alados-Arboledas L, Alados I, Foyo-Moreno I, Olmo FJ, Alcantara A. 3. The influence of clouds on surface UV erythemal irradiance. Atmospheric Research 112: Bais AF, Zerefos CS, Meleri C, Ziomas IC, Tourpali K Spectral measurements of solar UV-B radiation and its relations to total ozone, SO 2 and clouds. 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