neural network for the estimation of uv erythemal irradiance using solar broadband irradiance

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. 27: 1791–1799 (2007)Published online 22 March 2007 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/joc.1496

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

I. Alados,a,* M. A. Gomera,a I. Foyo-Morenob and L. Alados-Arboledasb

a Dpto de Fısica Aplicada II, Universidad de Malaga, Malaga, Spainb Dpto de Fısica 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. Inthis paper we present the development of an artificial neural network (ANN) model that can be used to estimate solar UVerythemal irradiance, UVER, based on optical air mass, ozone columnar content and broadband solar irradiance. The studywas developed at seven stations in the Iberian Peninsula using data recorded at A Coruna, Malaga, Murcia and Santander,during 2000–2003; at Madrid in the period 2000–2002; at Valencia in 2000, 2001 and 2003; and at Zaragoza, from 2001to 2003. The UVER observations are recorded as half-hour average values. The measurements were performed in theframework of the Spanish UV-B radiometric network operated and maintained by the Spanish Meteorological Institute. Inorder to train and validate the Multi-layer Perceptron neural networks, independent subsets of data were extracted from thecomplete database at each station. The networks developed at each place when applied to an independent data set recordedat 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 Coruna, Madrid, Murcia and Zaragozaprovides estimates at all the locations with RMSD below 19%. According to these results, the use of solar broadbandirradiances for the estimation of ultraviolet erythemal irradiance provides a tool that can solve the difficulties associated tothe retrieval of appropriate information on the cloud field by human observers. In this sense, the proposed method seemsappropriate to use the widespread networks of solar broadband irradiance to obtain ultraviolet erythemal irradiance datasets in places where this radiative flux is not measured or to extend back in time the existing data sets. Copyright 2007Royal Meteorological Society

KEY WORDS ultraviolet irradiance; UVI index; ozone depletion; multi-layer perceptron network; artificial neural network

Received 11 October 2005; Revised 5 December 2006; Accepted 14 December 2006

INTRODUCTION

During the past years there has been an increased concernon the increate in UV irradiance that reaches the surfaceas a result of the ozone layer depletion (World Mete-orological Organization (WMO) 1998). The solar UVirradiance includes (CIE, 1987) wavelength bands from100 to 280 nm (UV-C), which is completely absorbed inthe Earth’s atmosphere, 280–315 nm (UV-B), partiallyabsorbed by stratospheric ozone and 315–400 nm (UV-A), which makes up most of the UV irradiance at thesurface. Ozone is an effective absorber of UV radiation,with a reduced effect in the UV-A region. Although inouter space UV-B and UV-A account for about 7.5% ofthe solar total irradiance, at the surface they typicallymake up between 3% and 5% of the solar total irradi-ance (Foyo-Moreno et al., 1998). Owing to its harmfuleffects on biological systems great attention has been paidto UV-B irradiance (Diffey, 1991; Van der Leun et al.,

* Correspondence to: I. Alados, Departamento de Fısica Aplicada,Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain.E-mail: [email protected]

1991, 1994, 1998). For human beings, the UV effectthat has received most attention is the erythema, or sun-burn. The contribution of the different wavelengths tothis effect is described by an action spectrum (Diffey,1982) standardized in 1987 by the Comission Interna-tionale de l’Eclarage (McKinlay and Diffey, 1987). Thisaction spectrum is the weighting factor used for the com-putation of the UV erythemal irradiance (UVER). Theattenuation of UVER reaching the Earth‘s surface is aresult of the combined effects of solar zenith angle, sur-face elevation, cloud cover, aerosol loading and opticalproperties, surface albedo and vertical profile of ozone.The high temporal and spatial variability of cloud coverand especially aerosols is responsible for much of thevariability in UVER. In recent years, there has been a sub-stantial increase in attempts to model the UV irradiance.

Unfortunately the cloud and aerosol characteristicsdetermining radiation transfer are seldom known becauseof a general lack of observations, especially for theaerosols. Modelling the effect of cloud requires knowledgeof cloud optical thickness and drop size distributions withhigh temporal and spatial resolution, information that is

Copyright 2007 Royal Meteorological Society

1792 I. ALADOS ET AL.

limited to specific sites and campaigns. Thus, a differ-ent approach, based on commonly accessible data, mustbe used to model UVER to obtain long time series orextended spatial distributions. In previous works (Alados-Arboledas et al., 2003; Alados et al., 2004), we havecharacterised the cloud effects on UVER using informa-tion routinely registered in most meteorological stations:cloud type and amount, expressed in terms of fractionalcloud coverage in octas (eighths). This kind of approachhas been followed in different studies (Ilyas, 1987; Fred-erick and Snell, 1990; Frederick et al., 1993; Blumthaleret al., 1994, 1996; Thiel et al., 1997; Kuchinke andNunez, 1999; Grant and Heisler, 2000; Josefsson andLandelius, 2000). The approach followed in these studiesincluded modelling cloud effects using non-linear func-tions in combination with more or less complex modelsfor cloudless skies. In this work, we use the dimensionlessratios of total solar irradiance (integrated over the entiresolar spectrum): k, ratio of diffuse to global horizontalsolar irradiance, kb, ratio of direct irradiance to extrater-restrial horizontal irradiance and kt, ratio of global hor-izontal irradiance to extraterrestrial horizontal irradianceto characterise the sky conditions. These dimensionlessratios of solar total irradiance are influenced markedly bythe cloud amount. In this sense, we characterize the cloudeffect on a particular range of the solar spectrum troughthe effect they produce on the total solar spectrum. Thus,in this work these dimensionless ratios have been usedas input data for the estimation of UVER.

Artificial neural network (ANN) models may be usedas an alternative method in engineering, analysis andprediction. These models mimic somewhat the learningprocesses of a human brain. They operate as a ‘blackbox’ model, requiring no detailed information about

the system. Instead, they learn relationship betweeninput parameters and the controlled and uncontrolledvariables by studying previously recorded data, similarto the manner a non-linear regression might perform(Kalogirou, 2001). Another advantage of using ANNis their ability to handle large and complex systemswith many interrelated parameters. They seem to simplyignore excess data that are of minimal significanceand concentrate instead on the more important inputs.They have been used in diverse applications in control,robotics, pattern recognition, forecasting, medicine andpower systems, as well as manufacturing, optimisation,signal processing and social–psychological sciences.

Neural networks are used to learn the behaviour of thesystem and are subsequently used to simulate and predictthe behaviour of the system.

The aim of the present study is to develop ANNmodels that can be used to estimate UVER on thebasis of optical air mass, ozone columnar content, thedimensionless ratios, kt, k and kb. In this sense, thiswork represents a new step in the UVER modelling byANNs. In fact, in a previous work (Alados et al., 2004)we have approached this technique using a different setof input parameters. This can be viewed as a multi-variable interpolation problem in which it is requiredto estimate the function relating the input to the output.In our study, we apply this analysis to seven stationswith rather different environments. Madrid and Zaragozaare inland locations more than 200 km from the coast;Murcia is an inland location about 50 km away fromthe Mediterranean Sea; whereas Valencia and Malaga arecoastal locations situated in the western Mediterranean. ACoruna and Santander are located in the Atlantic Oceancoast 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.

Copyright 2007 Royal Meteorological Society Int. J. Climatol. 27: 1791–1799 (2007)DOI: 10.1002/joc

NEURAL NETWORK FOR THE ESTIMATION OF UV ERYTHEMAL IRRADIANCE 1793

Table I. Climatic data for the stations analysed.

Station (1971–2000) T TM Tm R H DD I

A Coruna (43°21′N, 8°25′W, 67 m a.s.l.) 14.4 17.4 11.4 1008 77 48 1966Madrid (40°27′N, 3°44′W, 580 m a.s.l.) 14.1 20.6 7.6 386 59 94 2658Malaga (36°43′N, 4°29′W, 61 m a.s.l.) 18.0 22.9 13.1 524 66 107 2815Murcia (38°00′N, 1°10′W, 69 m a.s.l.) 17.8 24.4 11.2 301 59 94 2797Santander (43°29′N, 3°48′W, 63 m a.s.l.) 14.1 18.1 10.2 1246 75 38 1638Valencia (39°29′N, 0°22′W, 11 m a.s.l.) 17.8 22.3 13.4 454 65 91 2660Zaragoza (41°38′N, 0°55′W, 250 m a.s.l) 15.0 20.4 9.5 318 62 80 2614

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, Yearlyaverage of sunshine duration.

DATA AND MEASUREMENTS

The UVER observations, performed within the SpanishUV-B radiometric network, were recorded as half-houraverage values. Martinez-Lozano et al. (2002) reporteda detailed description of this network. Yankee UV-B-1radiometers are operated and maintained by the Span-ish Meteorological Institute (INM). In some of the sta-tions selected for this study, simultaneous observationsof ozone columnar content were performed using theBrewer instrument operated within the same network atthe selected locations (see Figure 1). After analysing theavailable measurements and considering the marked lati-tudinal pattern of this variable, different criteria has beenused for the assignment of ozone columnar content atthose stations where measurements were not available.Thus for Malaga we have used the measurements per-formed at El Arenosillo, the closest station that alsopresents similar latitude. A similar procedure has beenfollowed at Santander that uses data set registered at ACoruna. Finally, for Valencia we have used the averagebetween Madrid and Murcia.

Solar global irradiance has been registered on an hourlybase using a Kipp & Zonen model CM-11, while anotherKipp&Zonen model C-11 with a polar axis shadowband was used to measure solar diffuse irradiance.Measurements of solar, global and diffuse irradiance havean estimated experimental error of about 2–3%.

The Yankee UV-B-1 radiometer is a broadband(280–315 nm) Robertson–Berger type radiometer. Thespectral response of the instrument is designed to approx-imate the spectral response of the human skin to UV(McKinlay and Diffey, 1987). The maintenance of thecalibration constant of the instruments included in theSpanish UV-B radiometric network is described in thestudy of Martinez-Lozano et al. (2002). The experimentaluncertainty of this instrument is about 8–9% (Leszczyn-ski et al., 1998; Pearson et al., 2000).

Data were registered at Madrid (40°27′N, 3°44′W,580 m above sea level [a.s.l.]) during the period2000–2002; A Coruna (43°21′N, 8°25′W, 67 m a.s.l.),Malaga (36°43′N, 4°29′W, 61 m a.s.l.) Murcia (38°00′N,1°10′W, 69 m a.s.l.), Santander (43°29′N, 3°48′W, 63 ma.s.l.) during the period 2000–2003; Valencia (39°29′N,0°22′W, 11m a.s.l.) during the years 2000, 2001 and

2003; and Zaragoza (41°38′N, 0°55′W, 250 m a.s.l.),during 2001–2003. To avoid problems associated to theinstrument deviations from the ideal cosine law, welimited our study to solar elevation angles greater than10°; in any case, the UVER values measured for largerzenith angles are relatively small.

Table I presents some climatic data for stations anal-ysed in this study. The different mean yearly valuesshown have been computed using data registered in theperiod 1971–2000 (www.inm.es). Especially relevant arethe differences in yearly precipitation and sunshine dura-tion. In some sense, it can be assessed that the stationsused are representative of the variety of climatic condi-tions representatives of the Iberian Peninsula.

NEURAL NETWORK MODELS

The human brain is composed of neurons that provideus with the ability to apply our previous experiences toour actions (Fausett, 1994; Haykin, 1994). ANNs, arecomputing algorithms that mimic the four basic functionsof these biological neurons. These functions are to receiveinputs from other neurons or sources, combine them,perform operations on the result and output the finalresult. Alados et al. (2004) presents a discussion of themain features of the kind of algorisms when used for theUVER estimation.

ANN design

There are various studies addressing the estimationof cloud effects on solar UV irradiance as a func-tion of either the observed cloud amount (Ilyas, 1987;Lubin and Frederick, 1991; Bais et al., 1993; Blumthaleret al., 1996; Nemeth et al., 1996; Schafer et al., 1996;Thiel et al., 1997; Kuchinke and Nunez, 1999; Alados-Arboledas et al., 2003; Alados et al., 2004), the cloudeffect on other spectral ranges of solar irradiance (Ala-dos et al., 2000; Foyo-Moreno et al., 2001, 2003) or acombination of the two (Schwander et al., 2002). A dif-ferent approach has been followed by Sabburg and Wong(2000) that used additional information on the cloud fieldobtained by sky cameras.



In our study, we approach the estimation by training amulti-layer perceptron (MLP) ANN that consists of threelayers. The variables considered for these models werethe optical air mass, ma, total columnar content of ozone,lo, and a set of additional input parameters describingclouds. Three different approaches have been consideredby including various input data: (MLP) Model 1 usesas input variable kt, ratio of global horizontal irradianceto extraterrestrial horizontal irradiance; MLP Model 2uses input variables kt, and k, ratio of diffuse to globalhorizontal solar irradiance. Finally, MLP Model 3 usesthe same input variables used in Model 2 but includingkb, ratio of direct irradiance to extraterrestrial horizontalirradiance.

Figure 2 shows the MLP used for estimating UVER.The number of input neurons depends on the type ofcloud information used as input. For the hidden layer,we have selected the optimal number of hidden neuronsequal to the number of input variable neurons. For thispurpose we have used an empirical procedure. Thus, wehave tested different combinations selecting the one thatprovides the best results, in terms of convergence androot mean square deviation. The output layer consists ofa unique neuron corresponding to the estimated UVER,UVERm.

The training of the ANNs has been done using 10%of the data measured at each station. The remaining90% of the data corresponding to the data sets has beenused as testing data set. These two subsets have beenselected using a random process. In fact these testingdata sets are used in order to select among ten possibleANNs obtained after the corresponding trainings at eachlocation. The idea is to select at each location the ANNthat provides the lowest RMSD between the estimatedand measured values corresponding to the testing data

set. We must follow this procedure because the initialweights used in the ANN training are randomly selected.This circumstance could lead in some cases to a low levelof convergence. In this way, the use of the testing dataallow the selection of the best trained ANN among theten obtained.

Validation of the models

As mentioned above, the design of an ANN requires theuse of the training and the testing data sets, used in train-ing and selecting the best ANN, and the validation dataset that is an independent data set used to characterizethe estimating capability of the ANN. In our case, for thelast purpose we have used the whole data sets at eachlocation.

Figure 3 shows the scatter plot of estimated versusmeasured UVER for the seven data sets and Model 3.The performance of the models was evaluated usingthe RMSD and the means bias deviation (MBD). Thesestatistics allow for the detection of both the differencesbetween experimental data and model estimates and theexistence of systematic data over or underestimationtendencies, respectively. Linear regression between esti-mated and measured values was also computed. Thelinear fitting was forced through zero, thus the slope,b, provides information about the relative underestima-tion or overestimation associated with the model. Finally,the determination coefficient, R2, gives an evaluation ofthe experimental data variance explained by the model.Table II presents results of these analyses, including thestatistics previously described together with the numberof data included in each data set and the average valuefor UVER, UVERave.

The slope of the linear regression between estimatedand measured values is close to unity in all the cases, thus

Figure 2. Scheme of the MLP Artificial Neural Network used for UVER models.



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b = 0.980; R2=0.96MBD = -0.5%; RMSD = 16.4%

b = 0.988; R2=0.97MBD = 0.03%; RMSD = 14.0%

b = 0.994; R2=0.97MBD = 0.5%; RMSD = 15.3%

b = 1.000; R2=0.98MBD = 0.08%; RMSD = 11.9%

b = 0.991; R2=0.97MBD = 0.5%; RMSD = 15.5%

b = 0.985; R2=0.97MBD = -0.005%; RMSD = 14.3%

b = 0.990; R2=0.98MBD = -0.08%; RMSD = 13.9%

Figure 3. Scatter plot of UVER estimated versus UVER measured for the seven stations. The model used in each case is the local Model 3tested at the same location where it is developed.

indicating the goodness of the fit. On the other hand, thevariance explained for the models is better than 96%.It is evident that the local models provide estimates atthe different places with MBD that are smaller than theexpected experimental errors over the average value. It isinteresting to note that the RMSD obtained are lower than17% for the three types of neural network. The overall

performance is better than that associated to the use ofANN based on cloud observations registered routinelyin meteorological stations, in this sense Alados et al.(2004) obtained RMSD values of 18% at Madrid, 19.6%at Murcia and 14.6% at Zaragoza, using cloud amountand type. On the other hand, using empirical modelsdeveloped with the same data sets, Alados-Arboledas



Table II. Results for local models at the different locations. Themodels were developed and tested at the same station.

Stations UVERmWm−2

b R2 MBD%

RMSD%

Model 1A Coruna 68 0.986 0.96 −0.07 16.4Madrid 72 0.987 0.98 −0.6 14.0Malaga 77 0.981 0.97 −0.8 14.3Murcia 76 0.989 0.97 −0.4 14.4Santander 60 0.984 0.97 −0.4 15.2Valencia 67 0.978 0.97 −0.4 15.6Zaragoza 79 0.995 0.98 0.4 12.3

Model 2A Coruna 68 0.984 0.96 −0.004 16.4Madrid 72 0.993 0.98 0.1 13.9Malaga 77 0.982 0.97 −0.9 14.2Murcia 76 0.986 0.97 −0.05 14.2Santander 60 0.991 0.97 0.2 14.9Valencia 67 0.988 0.97 0.2 15.3Zaragoza 79 0.990 0.98 −0.8 12.0

Model 3A Coruna 68 0.980 0.96 −0.5 16.4Madrid 72 0.990 0.98 −0.08 13.9Malaga 77 0.988 0.97 0.03 14.0Murcia 76 0.985 0.97 −0.005 14.3Santander 60 0.994 0.97 0.5 15.3Valencia 67 0.991 0.97 0.5 15.5Zaragoza 79 1.000 0.98 0.08 11.9

The numbers of data included each stations are: 8890 (A Coruna),10375 (Madrid), 5550 (Malaga), 11920 (Murcia), 9910 (Santander),74400 (Valencia) and 7216 (Zaragoza).

et al. (2003) have obtained larger MBD and RMSD thanthat obtained in the present study for some of the stationsanalysed (Madrid, −2.2% and 17.6%; Murcia, 2.1% and16.4%; Zaragoza, −0.3% and 16.4%).

A test, not shown here, reveals that the use of the modeldeveloped at a given place to estimate the UVER at otherlocations provide slightly larger MBD and RMSD. In thissense, we have approached the design of a generalizedmodel using data registered at four stations, A Coruna,Madrid, Murcia and Zaragoza. Thus, we have used asubset that includes 10% of the data registered at eachone of these four stations to train a new neural network.The choice of these four stations is justified by tworeasons, first at theses stations we have both UVERand ozone columnar content measurements, second thesestations covered different climatic conditions in theIberian Peninsula, including Atlantic, Mediterranean andContinental influences.

Table III shows the results obtained when using thisgeneralized model at different locations. It is evidentthat the RMSD presents only slightly larger values thanthose obtained with the local models. On the otherhand, the MBD presents appreciable deviations fromthe ideal values, 0, at A Coruna, Madrid and Valen-cia. It is interesting to note that all the stations theMBD values are smaller than the experimental error

Table III. Results for the generalized models at the differentlocations.

Stations UVERmWm−2

b R2 MBD%

RMSD%

Model 1A Coruna 68 0.928 0.96 −5.7 18.0Madrid 72 1.051 0.97 7.0 16.6Malaga 77 0.988 0.97 0.5 14.8Murcia 76 0.988 0.97 0.03 14.4Santander 60 0.948 0.97 −4.0 16.2Valencia 67 1.050 0.96 7.4 18.0Zaragoza 79 0.960 0.98 −3.4 12.8



The numbers of data included each stations are: 8890 (A Coruna),10375 (Madrid), 5550 (Malaga), 11920 (Murcia), 9910 (Santander),74400 (Valencia) and 7216 (Zaragoza).

associated to the UV-B radiometer used in this study.In any case, both the slope and correlation coefficientof the linear regression between measured and esti-mated values reveals the goodness of the estimationmodel.

Estimation of the UV-index

In order to offer to the population information onthe potentially harmfull effects of the UV-B irradi-ance, an index called UVI has been introduced duringthe past years. The UV-Index itself is an irradiancescale computed by multiplying the UVER irradiance inWm−2 by 40. Thus, the clear sky value at sea levelin the tropics would normally be in the range 10–12(250–300 mWm−2) and 10 is an exceptionally high valuefor northern mid-latitudes. This scale has been adoptedby the WMO and WHO and is in use in a number ofother countries. UV intensity is also described in termsof ranges running from low values (less than 2), mod-erate(3–5), high (6–7), very high (8–10) and extreme(11–).

Table IV presents the performance of the differentmodels 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



Table IV. Results of the different models, local (Model 1, Model 2 and Model 3) or generalized (Model 1G, Model 2G andModel 3G) at each location in terms of the percentage of cases with differences of 0 UVI unit and with differences less or equal

to one UVI unit.

UVIm − UVIe A Coruna(%)

Madrid(%)

Malaga(%)

Murcia(%)

Santander(%)

Valencia(%)

Zaragoza(%)

Model 10 67.5 64.8 65.5 65.7 74.1 65.7 68.2[−1, 1] 98.3 96.6 99.0 99.2 99.3 97.8 99.5

Model 1G0 64.5 62.2 64.0 65.4 72.6 64.2 67.5[−1, 1] 97.9 96.1 98.9 99.1 99.2 97.1 99.5

Model 20 67.6 65.1 66.3 66.1 74.2 67.7 68.8[−1, 1] 98.3 96.9 99.2 99.1 99.4 97.8 99.6

Model 2 G0 64.4 62.2 63.9 65.5 72.6 64.2 67.4[−1, 1] 98.0 95.9 98.8 98.8 99.2 97.0 99.5

Model 30 67.6 65.4 66.5 66.4 74.4 68.8 69.1[−1, 1] 98.4 96.8 99.0 99.1 99.3 97.8 99.6

Model 3G0 64.4 62.2 64.0 65.5 72.4 64.3 67.2[−1, 1] 97.9 97.2 98.7 99.2 99.2 98.1 99.4

Figure 4. Histograms of the differences between measured and esti-mated UVI, UVIm − UVIe, local Model 3, developed at a given loca-

tion, when applied at each location.

cases with no difference between the measured and esti-mated UVI together with that associated to differencesless or equal to one UVI unit. This analysis providesan appropriate method to discriminate the goodness ofa given model in comparison with others. In general,the results for the local models are better than for thegeneralized models. Nevertheless, these differences arereduced in the case of Model 3, in that case the differ-ences between local and generalized models are negli-gible (Figures 4 and 5). In any case, the percentage ofcases with differences of 0 UVI units is in the range

Figure 5. Histograms of the differences between measured and esti-mated UVI, UVIm − UVIe, generalized Model 3, when applied at each

location.

62.2% to 67.5%. While the percentage of the cases withdifferences of ±1 UVI unit covers the range 95.9% to99.5%. This gives an idea of the goodness of the devel-oped model when applied to estimate the UVI index.This is especially relevant for the generalized model thataccording to these results could be applied with a highlevel of confidence to other locations in the Iberian Penin-sula, where measurements were not available, consideringthat the stations analysed in this study are represen-tative of a wide range of environment in the IberianPeninsula.



CONCLUSIONS

In this work, we have approached the estimation ofsolar ultraviolet irradiance incoming at surface level.For this purpose, we have developed an ANN modelthat estimates solar UVER irradiance based on opticalair mass, ozone columnar content and broadband solarirradiance. A MLP network, MLP, consisting in an inputlayer, an output layer and one hidden layer was used.The training of the neural network was done using theBayesian regulation back propagation algorithm.

The study was developed at seven stations in theIberian Peninsula using data recorded in the frameworkof the Spanish UV-B radiometric network.

The results suggest that a MLP neural network usingoptical air mass, ozone columnar content and the dimen-sionless ratios, k, ratio of diffuse to global horizontal solarirradiance, kb, ratio of direct irradiance to extraterrestrialhorizontal irradiance and kt, ratio of global horizontalirradiance to extraterrestrial horizontal irradiance, pro-vides better results than that obtained in a previouslypublished neural network model relying on cloud obser-vations as input variables. In fact, the networks developedat each place when applied to an independent data setrecorded at the same location provide estimates withmean bias deviation less than 1% and RMSD below 17%for all the sites. The proposed model exploits the widespreading of radiometric networks. A clear advantageof using radiometric variables as input over the use ofcloud observations is that radiometric observations aregathered in a continuous way while cloud observationsare performed in fixed schedules that in some cases arereduced to one observation every 3 h. On the other hand,the use of cloud observations present additional limita-tions associated to the subjective character of the humanobservations and the absence of relevant information onthe proximity of cloud fields to the solar disk.

A generalized network has been developed using dataregistered at A Coruna, Madrid, Murcia and Zaragoza.When tested against independent data sets this modelprovides estimates at all the locations with RMSDbelow 19%. According to these results, the use of solarbroadband irradiances for the estimation of ultravioleterythemal irradiance provides a tool that can solvethe difficulties associated to the retrieval of appropriateinformation on the cloud field by human observers. Inthis sense, the proposed method seems appropriate to usethe widespread networks of solar broadband irradianceto estimate ultraviolet erythemal irradiance data sets inplaces where this radiative flux is not measured or toextend back in time the existing data sets.

The models have been evaluated in reference totheir capability to estimate the UVI index. In thissense, the percentage of cases with differences of 0UVI unit is in the range 62.2% to 67.5%. While thepercentage of the cases with differences of ±1 UVIunit covers the range 95.9% to 99.5%. This resultconfirms the applicability of the developed models,specially the generalized versions, to estimate UVI index

at those locations in the Iberian Peninsula where thereare no UV radiation measurements, considering that thestations used in model development are representativeof the different conditions that characterize the IberianPeninsula.

ACKNOWLEDGEMENTS

This work was supported by CICYT from the Span-ish Ministry of Science and Technology through projectsNo: CGL2004-05984-C07-03 and REN2003-03175. TheInstituto Nacional de Meteorologıa kindly provided theradiometric, columnar ozone and meteorological infor-mation for the three stations used in this study.

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neural network for the estimation of uv erythemal irradiance using solar broadband irradiance

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