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Solar Energy 86 (2012) 307–318

UV solar radiation on a tilted and horizontal plane: Analysisand comparison of 4 years of measurements

L.C. Navntoft a,b,⇑, P. Fernandez-Ibanez c, F. Garreta a

a Universidad Tecnologica Nacional – Facultad Regional Buenos Aires – Departamento de Ingenierıa Civil – Laboratorio de Estudios sobre

Energıa Solar, (UTN-FRBA-LESES), Mozart 2300, 1407 Ciudad Autonoma de Buenos Aires, Argentinab Instituto de Investigacion e Ingenierıa Ambiental (3iA), Universidad Nacional de San Martın, Peatonal Belgrano 3563, B1650ANQ San Martın, Argentina

c Plataforma Solar de Almerıa, Carretera Senes km 4, 04002 Tabernas, Spain

Received 9 February 2011; received in revised form 19 September 2011; accepted 5 October 2011Available online 28 October 2011

Communicated by: Associate Editor Frank Vignola

Abstract

In the global wavelength range (300–3000 nm), it is known that a plane with a slope equal to the latitude of the location, receives moreannual energy than the horizontal plane, mainly due to the increase in direct irradiation on the interest plane. The UV (280–400 nm)spectra at the earth surface, has a larger component of diffuse and a minor component of direct solar radiation compared to the globalwavelength range, therefore the increase in annual energy due to plane inclination should also be different. This work, analyzes 4 years ofsolar UV radiation measurements performed on tilted and horizontal planes located at the Plataforma Solar de Almerıa, Spain. Themonthly mean ratio of tilted/horizontal solar UV irradiation varies with the time of the year, reaching values of 1.25 and 0.95 for winterand summer, respectively. The same ratio in the solar global spectra rises up to 1.70 and 0.85 for the same months. The annual UV solarenergy increase on a plane tilted 37� and oriented towards the equator is around 3–4%, whereas is around 10% in the global spectra. Inthis way UV annual energy increase due to inclination and orientation of the plane is much lower than that for global radiation. Deter-mination of a unique method to assess all possible inclinations and orientations, require simultaneous measurement of diffuse and directUV radiation performed with radiometers of identical spectral response. Given the worldwide scarcity of these type of data, an empiricalcorrelation that relates horizontal UV irradiation to that on a 37� inclined plane was determined. Monthly and annual tendencies of solarUV irradiation have been analyzed and compared with the solar global irradiation.� 2011 Elsevier Ltd. All rights reserved.

Keywords: UV; Global; Tilted plane; Measurements; Comparison

1. Introduction

In recent decades, much attention has been given theamount of ultraviolet (UV) radiation reaching the earth’s

0038-092X/$ - see front matter � 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2011.10.004

⇑ Corresponding author at: Universidad Tecnologica Nacional – Fac-ultad Regional Buenos Aires – Departamento de Ingenierıa Civil –Laboratorio de Estudios sobre Energıa Solar, (UTN-FRBA-LESES),Mozart 2300, 1407 Ciudad Autonoma de Buenos Aires, Argentina. Fax:+54 11 4601 8112x7139.

E-mail address: christian.navntoft@solarmate.com.ar (L.C. Navntoft).

surface because of the thinning stratospheric ozone layerand the rapid advance of wastewater treatment mediatedby the solar UV spectrum. Knowledge of the amount ofUV radiation received by plants and animals near theearth’s surface is important in a wide range of fields suchas cancer research, forestry, tropospheric chemistry, agri-culture, oceanography and solar chemistry (Madronichand Flocke, 1995).

Such information is also important in the design of thesolar photocatalytic systems used for water detoxificationtechnologies (Blesa and Blanco, 2005). The efficiency of

308 L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318

these systems depend on the availability of UV radiation atthe selected location. With the development of this technol-ogy and several pilot plants (Vidal et al., 1999; Curco et al.,1996; Blanco et al., 1999), the need for an adequate evalu-ation of the ultraviolet solar resource has emerged. World-wide scarcity of information on the distribution of the UVresource makes it necessary to find this information indi-rectly through correlations of global (300–3000 nm) andUV (280–400 nm) radiation, estimation from satellite dat-abases, mathematical models, etc. (Al-aruri et al., 1988;Feister and Grasnick, 1992; Dilmac et al., 1996; Koronakiset al., 2002; Canada et al., 2003; Ogunjobi and Kim, 2004;Robaa, 2004; Kudish et al., 2005; Bo et al., 2007; Jacovideset al., 2009). There is however some difference amongst theresults of different works due to the different spectralresponse of the instruments used for measuring the UVsolar range and determining the correlations. The spectralresponse is the range of wavelengths in which the measur-ing instrument gives a signal as a function of incident radi-ation (Webb, 2003). In most cases, global solar radiationmeasuring instruments have the same response for allwavelengths (also known as flat response) (Thekaekara,1976). UV measuring instruments have a spectral responsewhich is a function of the amount of incident radiation butalso of the wavelength. Furthermore, the calibration of UVinstruments is still a matter of controversy and in mostcases, they are calibrated against a xenon lamp (Webb,2003; Roy et al., 1995). In this way, the instruments withdifferent spectral responses, yield different UV/Global cor-relations for the same nominal spectral ranges. Despite thisdifferences, in all of the cited work, the ratio of solar UV toglobal irradiation reaching the earth’s surface, is neverabove 8%.

In global solar radiation applications, such as solar ther-mal collectors or photovoltaic panels, the annual energyreceived by a plane can be enhanced by giving a fixed slopeand orientation to the plane of interest. For a surface witha slope equal to the latitude, the annual energy increase isroughly 10% (Iqbal, 1983; Duffie and Beckman, 2005).

Such information relating surface slope with annual UVenergy increase has not been the subject of large research.Very few works have dealt with this subject: Grant(1998), studied the UV-B solar radiation reaching tiltedplanes for agricultural applications, he proposed a modelto determine the amount of UV radiation reaching cano-pies; Hess and Koepke (2008), developed a model to

Table 1Characteristics of UV radiometers used for measurements.

Number Model Company Nominal wavelength(nm)

Spectral re(nm)

1 CUV3 KippZonen

280–400 315–378

2 CUV3 KippZonen

280–400 315–378

3 CUV4 KippZonen

280–400 305–385

calculate UV irradiance on arbitrarily oriented surfaces,yet the model has not been thoroughly tested; Grant andGao (2003), proposed a model to estimate the diffuseUV-A (315–400 nm) fraction at several locations. Noneof them have been checked against long term measureddata, mainly due to the scarcity of long term inclined andhorizontal UV measurements.

With the aim to explore this subject, this article presentsthe analysis of 4 years of measurements of solar UV radia-tion performed on inclined and horizontal surfaces at thePlataforma Solar de Almerıa, Spain. Comparison with asolar radiation model and global solar radiation measure-ments is also performed. Finally, an empirical correlationfor monthly mean solar UV irradiation reaching a tiltedplane is determined.

2. Materials and methods

2.1. UV Measurements

For March 2007–July 2010, uninterrupted measure-ments of solar UV irradiance were performed every 1 minwith three different radiometers. The characteristics andmounting slope of each radiometer during the mentionedperiod are described in Table 1. All the radiometers werelocated at the Plataforma Solar de Almerıa (PSA),37�840N and 2�340W and mounted on a white painted sur-face free of surrounding obstacles and reflections.

2.2. Data quality assurance

Before processing all the measured data and in order toassess possible instrument drifts, radiometers 1, 2 and 3were placed on a horizontal plane during the month ofAugust 2010, and their measurements compared againsteach other and a radiative transfer model.

The chosen model to perform the comparison was theTUV 4.1. According to the work of Bais et al. (2003), thismodel has an accuracy of 95% at solar noon on clear days.One big advantage is that it can model the whole UV spec-trum as well as discrete wavelengths or ranges such as UV-A or UV-B. This model uses a discrete ordinate method tosolve the radiative transfer equation, and considers absorp-tion and scattering as two independent phenomena (two-stream approximation). It divides the atmosphere in layersand then solves the equations for each layer. The model is

sponse Sensitivity (lV/W/m2)

Year ofcalibration

Inclination(Deg)

264 November 1995 0�

234 July 2005 37�

335 November 2007 37�

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widely used (Madronich and Flocke, 1995; Palancar andToselli, 2004) for estimation of solar UV radiation reachingthe earth’s surface. In general, every constituent (gas orparticle) can both scatter and absorb radiation, but in prac-tice at UV wavelengths, scattering by gases is so weak thatonly air (N2 + O2) contributes, while only a few gases (O3,SO2 and NO2) have strong enough absorption to requireconsideration. On the other hand, SO2 and NO2 occur inthe order of parts per billion (PPB) and are generally aproduct of photochemical smog. Such gases are consideredonly in locations with a high degree of pollution or highlypopulated cities (Madronich and Flocke, 1995). Ozoneabsorption is negligible at wavelengths larger than320 nm (UV-A) and affects mainly the UV-B (Madronichand Flocke, 1995).

According to the model, the attenuation of the directsolar radiation by any gas or particle is given by thebeer-lambert law, described by Eq. (A.1), where Idir is thesolar UV irradiance at a horizontal surface at altitude z,I0 is the solar extraterrestrial irradiance in the same wave-length range, h is the solar zenith angle and s is the opticaldepth (Madronich and Flocke, 1995).

For atmospheric gases, such as air or ozone, the opticaldepth is given by Eq. (A.2), where nj is the altitude depen-dent concentration (molecules per cm3) of the various (j)gases that attenuate radiation, each with effective absorp-tion or scattering cross section rj (cm2 per molecule).Absorption cross sections for various atmospheric gasesare usually measured in the laboratory and tabulationsare available (Madronich and Flocke, 1995).

For aerosols, the optical depth is a function of wave-length and is expressed by the Angstrom expression givenby Eq. (A.3), where b is the Angstrom turbidity coefficient,which represents the aerosol concentration in the atmo-sphere with usual values between 0 and 0,5 (Iqbal, 1983),k is the wavelength of interest and a is a measure of the sizeof the aerosols, having values of 0 for large particles and 4for small particles, usually around 1.3 ± 0.5 (Iqbal, 1983).Typical values of s for aerosols are usually between 0.1and 1 (Madronich and Flocke, 1995) for the UV range.

In larger particles such as aerosols, scattering andabsorption can be simultaneously important dependingon specific size distributions and the presence of absorbingimpurities, and it is possible to define separate crosssections for absorption rabs and scattering rsc, so that r =

rabs + rsc. The relative importance of scattering an absorp-tion is given by the single scattering albedo x0, defined byEq. (A.4). In the UV range, values of x0 are in the range of0.90–0.99 for clouds and 0.80–0.99 for boundary layeraerosols (Madronich and Flocke, 1995).

An additional consideration is the change in direction ofphoton propagation upon a scattering event. This dependsto a large extent on the size of the scatterer. The generalmathematical representation of this change in direction iscontained in the phase function P(h,/,h0,/0), which givesthe probability that a photon incident with angular coordi-nates (h,/) is scattered into the direction (h0,/0). The scat-

tering phase function for scattering of unpolarized photonsby air molecules is given by Eq. (A.5) (Madronich andFlocke, 1995).

Scattering by larger particles is more complex and tendsto be biased towards the forward direction. The asymmetryfactor g gives a simple measure of the directionality of scat-tering, with g = +1 implying complete forward scattering,g = �1 complete back scattering and g = 0 for isotropicRayleigh (air) scattering. Typical values of g for aerosolparticles are between 0.5 and 0.7 (Madronich and Flocke,1995). The asymmetry factor is described by Eq. (A.6).

It should be noted that absorption and scattering crosssections and quantities derived from them such as s, x0

and g are dependant on wavelength (Madronich andFlocke, 1995).

The atmosphere is not vertically homogeneous, due tostratification of constituents such as ozone, clouds, aero-sols and local pollutants. This complication is overcomedby subdividing the vertical extent of the atmosphere intolayers sufficiently thin that each can individually be consid-ered homogeneous. Analytic solutions of adjacent layersare then coupled and the resulting numerical system issolved using standard techniques to yield the radiation fieldat all altitudes.

Further model description is out of the scope of thiswork. For more information regarding the characteristicsand methods of the model, the reader is referred to theTUV 4.1 website (http://acd.ucar.edu/models/open/TUV4.1/) or the work by Madronich and Flocke, 1995.

To calculate the solar UV irradiance at a given horizon-tal surface on a clear day (no clouds), the model requiresthe following inputs:

� Geographical parameters: Latitude, longitude and heightabove sea level� Time parameters: Year, month, day, hour (alternatively,

time can also be expressed by means of the solar zenithangle, h)� Atmospheric parameters: Aerosol optical depth at

550 nm(s), ozone concentration (in Dobson Units),alpha wavelength coefficient (a) and single scatteringalbedo (x0). Other parameters such as scattering by airmolecules or g factor are automatically calculated bythe model and use reference data tabulated therein.

The model yields the solar UV irradiance (W/m2) at anydesired wavelength range in the UV spectrum and solarzenith angle. Single values of irradiance must then be inte-grated upon all zenith angles to obtain daily irradiation(Wh/m2) or energy on the horizontal surface of interest.

Previous work (Navntoft et al., 2009) have dealt with thesensitivity of the model for different atmospheric condi-tions given by ozone concentration, s and a. In the citedwork, ozone concentration was a minor influence in theUV-A range (315–400 nm) but necessary to obtain accuratedata in the whole UV (280–400 nm) range. The mostimportant parameter input of the model is the aerosol opti-

310 L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318

cal depth, s. Other aerosol parameters, such as a, have asecondary effect, even for large variations. Air scatteringfollows an automatic calculation procedure. To determinethe most appropriate aerosol optical depth value for themodel, the AERONET database was consulted. AERON-ET is an optical ground based aerosol monitoring network.Data from this network provide near real time observa-tions of aerosol optical depth, aerosol size distributionsand precipitable water in diverse aerosol regimes (Holbenet al., 1998). This data base is not available for all loca-tions. Particularly, there was no data available for thePSA. There are two near by locations which had aerosoloptical depth measurements available. The first wasMalaga (36�N, 4�W) and the second was Granada station(37�N, 3�W). Even though they are located in different con-texts than the PSA, the atmosphere at both sites is mostlyclean and their data was used as a starting point to assessthe aerosol parameters for the radiative transfer model.The model TUV 4.1, can only assess solar radiation in ahorizontal surface, hence the need to position all three radi-ometers horizontal during the month of August to obtain agood comparison. Three clear days of August were selectedto perform the comparison. The selection criteria was thatthe sky was completely clear throughout the entire day.The AERONET network measures the aerosol opticaldepth at 500 nm and 675 nm. Data at 550 nm (the modelinput) was interpolated. The average daily data fromAERONET (500 nm, 675 nm) was retrieved from theAERONET website (http://aeronet.gsfc.nasa.gov) for bothstations. The retrieved data and the interpolation at550 nm for the selected days of August 2010 are shownin Table 2. The comparison model and measurements,allowed to identify the quality of the data obtained bythe different radiometers. Based on this information, oneradiometer was taken as reference and the entire data set(March 2007–July 2010) was corrected against it by meansof a correlation.

2.3. Data analysis

Once the measurements were corrected according to theprocedure described in the previous section, daily UV irra-diation on the horizontal (HUV) and tilted plane (HUVT)was calculated by integrating irradiance measurementsavailable from March 2007 to July 2010. Monthly (HUV ,HUVT ) and annual (HUVANNUAL ,H UVTANNUAL) averages werealso determined.

Table 2Aerosol optical depth (AOD) obtained from AERONET at 500 and 657 nm.

Malaga AERONET station

Day AOD (500 nm) AOD (675 nm) AOD (550

04/08/2010 0.25 0.17 0.2306/08/2010 0.19 0.15 0.1807/08/2010 0.26 0.24 0.26

The relationship between horizontal and inclined planeUV irradiation was analyzed on a daily, monthly andannual basis for the entire data set. The correspondingratios RUV ; RUV i and RUVANNUAL, are given respectively byEqs. (A.7), (A.8), and (A.9). The subscript i refers to themonth in question, being 1 for January and 12 forDecember. The monthly UV ratio was compared with theanalogous ratio for solar global radiation defined byEq. (A.10). The monthly global ratio (RGLOBAL i) was calcu-lated using the algorithm developed by Liu and Jordan(1962), and described in Duffie and Beckman, 2005. Themethod considers the three components of solar radiationreaching a plane: direct, diffuse and ground reflected. If dif-fuse and ground reflected radiation are each assumed to beisotropic (one of the assumptions of the theoretical modelof Liu and Jordan, 1962), then RGLOBAL i can be expressedby Eq. (A.11), where u is the plane tilt, slope or inclination,q is the surface albedo and stands for the hemisphericalreflection of the ground in front of the tilted surface(typical values for global radiation are around 0.20–0.30for grass, 0.70–0.80 for snow, 0.20–0.30 for cement and0.50–0.60 for clear painted surfaces (Chasseriaux, 1990)),Hdi is the monthly mean diffuse irradiation, H i is themonthly mean global irradiation on the horizontal planeand H T i is the monthly mean global irradiation on the tiltedplane. Rbi is a dimensional parameter the accounts for theratio of average beam irradiation on the tilted surface tothat on a horizontal surface and is given by Eq. (A.12),where / is the latitude of the location (North(+),(South(�)), di is the mean monthly declination (the angularposition of the sun at solar noon with respect to the planeof the equator). The value of the mean monthly declinationcorresponds to a specific nth julian or astronomical day ofeach month. For calculation purposes, (Duffie andBeckman, 2005; Klein, 1977 ), recommend the use ofTable 3, which shows the nth day of the month that corre-sponds to mean monthly declination values. The parameterxsi is the sunset hour angle for the horizontal surface forthe day of the month that corresponds to the monthlymean declination of Table 3, and is given by Eq. (A.13),x0si is the sunset hour angle for the tilted surface for themean day of the month described in Table 3 and is givenby Eq. (A.14), where “min” means the smaller of the twoitems in the brackets. The sunrise hour angle is the negativeof the sunset hour angle.

Due to the characteristics of Almeria, where there is nosnow and no major climate changes during the year, a fixed

Values at 550 nm were interpolated.

Granada AERONET station

nm) AOD 500 nm) AOD (675 nm) AOD (550 nm)

0.19 0.13 0.170.15 0.11 0.140.24 0.20 0.22

Table 3Julian day for monthly mean declinationvalues obtained from Klein (1977) andDuffie and Beckman (2005).

Month N d (�)

January 17 �20.90February 47 �13.00March 75 �2.40April 105 9.40May 135 18.80June 162 23.10July 198 21.20August 228 13.50September 258 2.20October 288 �9.60November 318 �18.90December 344 �23.00

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value of 0.2 was considered representative for thecalculations.

Another widely used model for these calculations is thatdeveloped by Klein and Theilacker (1981). It is a bit morecumbersome but the obtained results can be obtained forany surface orientation or azimuth other than south. Bothmethods, either that of Liu and Jordan (1962) or Klein andTheilacker (1981) yield similar values for tilted surfaces ori-ented towards equator. The first one was selected for prac-tical calculation reasons.

The resolution of Eq. (A.11) requires knowledge of themonthly mean of all mentioned parameters. The parame-ters such as H di can be obtained by direct measurementof data or can be estimated by other methods such as theone described by Collares-Pereira and Rabl (1979), pro-vided that H i is known from measurements. In this work,measured data (H i and H di ) from the report of Barberoet al. (1998) was used for the calculation of RGLOBAL. Thereport contains monthly means of needed parameters thatwere obtained in Almerıa, with measurements performedduring the period 1990–1996. The obtained values can beseen in Table 4. The applied calculation method is widelyused in solar thermal and photovoltaics applications for

Table 4Values of monthly mean global and diffuse irradiation used for calculatingEq. (A.11) and obtained from Barbero et al. (1998).

Month Hi (Wh/m2) Hdi (Wh/m2)

January 2513.91 790.31February 3526.63 1016.69March 4487.71 1405.89April 6068.34 1791.11May 7053.26 1993.66June 7629.11 2172.37July 7402.74 2176.34August 6600.51 1878.49September 5345.54 1536.94October 3868.17 1123.91November 2911.06 778.40December 2231.94 770.46

calculating monthly global irradiation on tilted planes fac-ing equator (Duffie and Beckman, 2005).

Such calculation cannot be applied to the UV spectrasince there is no availability of long term measurementsof monthly mean diffuse UV irradiation.

There is also the matter of the UV radiometers spectralresponse. The radiometers used for measuring solar globalradiation have a flat response, independent of the wave-length within the range of interest. This means that theinstrument has the same response for the different wave-lengths in the global spectra that reaches the earth surface.In other words, it does not matter which is the spectralcomposition of the light of interest as long as it lies inthe mentioned range, what matters is the total intensity.

UV radiometers do not have a flat response, all of theUV sensors in the market and research field are made withphotodiodes that respond only to a specific range of wave-lengths, being this range different for each instrument. Fur-thermore, they do not have a flat or single response in theUV spectra but rather different spectral responses for dif-ferent wavelengths. This means that spectral compositionof UV light does matter when performing measurementsand calibrations.

In this way, the adaptation of the described method forcalculating UV on a tilted, south oriented plane, requirestotal and diffuse UV irradiation obtained from a measuringnetwork of UV radiometers with the same spectralresponse. With the worldwide scarcity of UV measure-ments and the different instruments used in each research,this option is not possible to achieve. Hence, an empiricalapproach is better justified. Therefore, a correlation thatyields UV irradiation on a 37� inclined plane as a functionof horizontal plane irradiation was determined.

3. Results

3.1. Data quality assurance

During August 2010, all radiometers were positionedhorizontal in order to compare the measurements undersimilar conditions and identify possible instrument drifts.Measurements from three clear days during August 2010were compared against the TUV 4.1 radiative transfermodel. The comparison between the measurements andthe model for one of the clear days of august 2010 can beseen in Fig. 1.

The TUV 4.1 model can yield the same results for differ-ent atmospheric conditions. Several atmospheric condi-tions for the model were tested. Based on the previouswork by Navntoft et al. (2009), atmospheric parametersdata of nearby AERONET stations, radiative transfermodel characteristics (Bais et al., 2003) and other refer-ences (Iqbal, 1983; Madronich and Flocke, 1995; Oteroet al., 2003) the following parameters were chosen as repre-sentative of the atmospheric situation at the PSA on a clearday of August:

Fig. 1. Comparison of measurements of radiometers 1, 2, 3 and the TUV4.1 model for a clear day in August.

Fig. 2. Correlation between data measured by radiometers 1 and 2.

312 L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318

� Aerosol optical depth (s) = 0.2� Alpha wavelength coefficient (a) = 1.3� Single scattering albedo (x) = 0.99

The ozone concentration for each of the modeled dayswas obtained from the TOMS satellite measurements data-base (http://toms.gsfc.nasa.gov/teacher/ozone_overhead.html).

A detailed analysis of Fig. 1 provides valuableinformation on the real spectral range measured by theradiometers.

The measurements of radiometers 2 and 3 are in closeagreement with the TUV modeled irradiance in the rangeof 315–378 nm and 300–385 nm, respectively. On the otherhand, radiometer 2 does not coincide with the modeledirradiance. The agreement found between model and mea-surements in radiometers 2 and 3, confirm several facts.The first is that the atmospheric chosen parameters are cor-rect. The second is that, each radiometer is measuring inthe range specified by the instrument spectral response.The third is that there is a possibility that radiometer 1has a drift.

The precise methodology for the assessment is either bycomparison against a spectroradiometer or against a cali-brated radiometer of the same spectral response. Since nosuch instruments are available, an intercomparison of dif-ferent instruments by means of a radiative transfer modelcan give also accurate information on the status of eachinstrument, provided that at least one of the instrumentsis measuring correctly.

If the chosen parameters would have been incorrect, nonof the radiometer data would fit with the TUV model. Inthis case, two radiometers (2 and 3), with different spectralresponses, fitted within a difference of 5% with the model.This fact confirms that the chosen atmospheric parametersare correct and representative of a clear day in the monthof August at the PSA.

This information in addition to that obtained fromFig. 1, can be used to justify the following statements:

(1) Radiometers 2 and 3 are assumed to be measuringcorrectly in the region defined by their spectralresponse. This is confirmed by an almost perfect fitwith the model.

(2) Radiometer 1 is measuring below expected and datamust be therefore corrected against radiometer 2,which has a similar spectral response.

(3) Radiometers 1, 2 and 3 cannot be used simulta-neously because they are measuring the UV spectrain different wavelengths. In this way, the data analysiscan only be established by the measurements per-formed by radiometers 1 and 2, which have the samespectral response. Analysis of measurements fromradiometer 3 must be discarded.

(4) Radiometers 1 and 2, actually measure a fraction ofthe solar UV-A spectrum in the wavelength rangeof their spectral response (315–378 nm), and not theentire UV spectrum. This can be observed by the fitof the spectral response of the instrument with thatof the TUV model in that wavelength range and alsobecause both radiometers yield measurements belowthe UV-A output of the model.

Based on the quality assurance analysis, radiometer 1data was corrected using radiometer 2 as a reference. Thiswas done by correlating the data obtained during themonth of August 2010, and applying the correlation tothe entire data set. The data correlation between bothequipments can be seen in Fig. 2.

An observation at Fig. 2 shows a linear correlationbetween both radiometers, which confirms that radiometer1 has a drift, and that they are both measuring in the samewavelength range. If such correlation had been quadraticor cubic, then that information would be showing that bothinstruments are measuring in different wavelengths, given

Fig. 4. Daily irradiation 315–378 nm on the tilted plane in Wh/m2,calculated from irradiance measurements performed with radiometer 2.

L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318 313

that the difference would vary with the solar angle of inci-dence due to the wavelength dependance of different atmo-spheric phenomena.

The correlation is given by Eq. (A.15), where IRAD2 isthe irradiance measured by radiometer 2 and IRAD1 is theirradiance measured by radiometer 1.

Eq. (A.15) was obtained with data from 3 clear days and8 cloudy days from August 2010. Prediction error wasassessed with the rest of the measurements of August2010, yielding an overall mean square error (RMS) of1.36%. Eq. (A.15) was systematically applied to correctthe rest of the data from March 2007 to July 2010. Strictlyspeaking, in a summer clear day, a radiometer faces theworse operating conditions: high ambient and instrumenttemperature. It is under these conditions when the largererror deviations are expected. Hence, the RMS of the cor-relation is expected to be minor in more favorableconditions.

3.2. Daily analysis

After data correction with correlation (A.15), the mea-surements corresponding to the period March 2007–July2010, and the operating conditions described in Table 1were processed. Daily irradiation for the horizontal(HUV) and inclined plane (HUVT) was calculated integratingirradiance measurements from radiometers 1 and 2, respec-tively, over the entire day.

According to the results obtained in Section 3.1, themeasured irradiance corresponds to the 315–378 nm UVregion. Strictly speaking, the UV-B region (280–315 nm)is out of the measurements range, so it seems correct tosay that the measurements correspond to the UV-A spec-trum (315–400 nm) and not the entire UV spectrum (280–400 nm). Daily irradiation for both planes (horizontaland inclined, radiometer 1 and 2, respectively) are plottedas a function of the Julian day of the year in

Fig. 3. Daily irradiation 315–378 nm on the horizontal plane in Wh/m2,calculated from irradiance measurements performed with radiometer 1.

Figs. 3 and 4. An inspection of both figures, shows thatthe tilted plane (radiometer 2) receives more energy thanthe horizontal plane (radiometer 1) in the winter seasonand less energy in the summer season. The increase in win-ter is larger than the decrease in summer.

The daily ratio, RUV, for each day of all the availabledata is shown in Fig. 5. The value of the ratio has a max-imum of approximately 1.35 in the winter days and a min-imum of 0.9 in the summer days. The value for the otherdays of the year fall somewhere in between the extremementioned values. A great dispersion of points is observedin days 1–151 and 241–365, which coincides with the win-ter, beginning of spring and autumn. The combination ofthe high share of diffuse solar UV irradiation, lower solarzenith angles and presence of clouds, are responsible forthe phenomena. Less dispersion is observed in summerdays between 151 and 241, when the sun is higher, thesky is clear and there is less diffuse UV irradiation.

Fig. 5. Daily ratio of UV irradiation on the tilted plane with respect to thehorizontal plane (RUV).

Fig. 6. Monthly means irradiation for the horizontal plane (HP) and 37�inclined plane (IP) for each month and year.

314 L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318

3.3. Monthly analysis

Monthly mean daily UV irradiation was calculated foreach month and each year of the data set. The values for

Table 5Monthly mean UV irradiation at horizontal plane (315–378 nm) for eachmonth and year. ND: No data available for the period.

Month 2007 2008 2009 2010

January N/D 115 ± 20 97 ± 32 N/DFebruary N/D 120 ± 37 143 ± 35 147 ± 45March 197 ± 45 208 ± 50 190 ± 54 167 ± 63April 198 ± 72 253 ± 67 240 ± 52 228 ± 50May 280 ± 56 263 ± 67 293 ± 44 307 ± 38June 306 ± 67 315 ± 41 320 ± 32 301 ± 48July 318 ± 15 306 ± 40 312 ± 33 300 ± 45August 263 ± 33 303 ± 13 284 ± 26 N/DSeptember 205 ± 45 197 ± 48 190 ± 56 N/DOctober 146 ± 49 139 ± 50 169 ± 28 N/DNovember 115 ± 28 115 ± 24 168 ± 28 N/DDecember 86 ± 25 87 ± 22 100 ± 31 N/DAnnual 211 ± 91 204 ± 92 204 ± 90 251 ± 78

Table 6Monthly mean UV Irradiation at a plane inclined 37� oriented towardsequator (315–378 nm) for each month and year. ND: No data availablefor the period.

Month 2007 2008 2009 2010

January N/D 147 ± 37 119 ± 50 N/DFebruary N/D 141 ± 55 171 ± 50 168 ± 63March 221 ± 59 234 ± 59 210 ± 67 178 ± 76April 197 ± 76 257 ± 70 245 ± 56 223 ± 55May 266 ± 55 247 ± 65 276 ± 44 284 ± 36June 283 ± 62 289 ± 37 292 ± 30 278 ± 43July 300 ± 13 286 ± 39 290 ± 30 281 ± 42August 260 ± 34 296 ± 12 282 ± 27 N/DSeptember 223 ± 54 209 ± 57 201 ± 66 N/DOctober 168 ± 65 157 ± 63 200 ± 38 N/DNovember 145 ± 44 145 ± 40 201 ± 38 N/DDecember 112 ± 41 110 ± 38 126 ± 46 N/DAnnual 216 ± 80 209 ± 81 212 ± 79 242 ± 70

each month, year and inclination are plotted in Fig. 6and are shown together with the standard deviation inTables 5 and 6, respectively.

From the information in Tables 5 and 6, the lower val-ues of mean daily irradiation occur between the months ofdecember and january and the higher values occur betweenjune and august for both planes, corresponding to winterand summer months, respectively. The horizontal planesvalues are higher than the inclined plane values for summerand the opposite occurs in the winter season.

The lowest standard deviation is given for the summermonths, were cloudy days are very few. The oppositeoccurs for the winter months.

Table 7, shows the monthly mean ratio (RUV ). As ex-pected, the ratio is higher in winter months and lower insummer months.

In order to establish a comparison with the global spec-tra, the monthly inclined/horizontal ratio (RGLOBAL) for glo-bal radiation was calculated according to the methoddescribed in Section 2.3. The comparison both ratios areshown in Fig. 7 and Table 8.

Fig. 7 shows that there is an important difference in theinclined/horizontal ratio for the different spectral ranges.

Table 7Monthly ratio of inclined/horizontal solar UV irradiation (315–378 nm)for each year.

Month 2007 2008 2009 2010 RUV

January ND 1.27 1.19 ND 1.23(±0.06)February ND 1.14 1.18 1.04 1.12(±0.07)March 1.11 1.12 1.09 1.03 1.09(±0.04)April 0.98 1.01 1.02 0.97 0.99(±0.02)May 0.95 0.93 0.94 0.93 0.94(±0.01)June 0.92 0.92 0.91 0.93 0.92(±0.01)July 0.95 0.93 0.93 0.94 0.94(±0.01)August 0.99 0.98 0.99 ND 0.99(±0.01)September 1.08 1.05 1.04 ND 1.06(±0.02)October 1.12 1.11 1.18 ND 1.14(±0.04)November 1.23 1.23 1.19 ND 1.22(±0.03)December 1.26 1.22 1.19 ND 1.22(±0.03)

Fig. 7. Ratios of monthly mean inclined/horizontal solar irradiation forthe UV and global spectra.

Table 8Average monthly ratio of inclined/hori-zontal UV and global irradiation.

Month RUV RGLOBAL

January 1.23 1.69February 1.12 1.47March 1.09 1.20April 0.99 1.02May 0.94 0.90June 0.92 0.85July 0.94 0.87August 0.99 0.97September 1.06 1.13October 1.14 1.37November 1.22 1.67December 1.22 1.74

Fig. 8. Empirical correlation of UV (315–378 m) reaching a plane inclined37� oriented towards equator.

L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318 315

The increment in the winter, spring and autumn months inglobal solar radiation due to the inclination, is larger thanthat for the UV range. This is directly related to the largerdirect component of the global wavelength range.

3.4. Annual analysis

Annual UV irradiation on both planes (horizontal andtilted) was calculated by summarizing all the daily integralsof each year. The results are shown in Table 9.

Measurements from a few months of 2010 are missing,so in this case, the annual integral should not be taken intoconsideration. The same case occurs with the data from2007, where the data from the winter months is missing.

Only years 2008 and 2009, should be considered toassess annual implicancies of UV energy on a tilted plane.Based on these years data, it can be seen that the inclinedplane receives approximately between 3% and 4% moreannual energy than the horizontal plane. The annualincrease in global radiation rises up to 10–12% per year.

3.5. Correlation

The empirical correlation of average monthly values ofUV irradiation on the inclined plane as a function of thehorizontal plane can be seen in Fig. 8.

The determined empirical correlation is shown in Eq.(A.16). A quadratic relation fitted best than a lineal, givingsupport to the evidence of the influence of the solar zenith

Table 9Annual ratio of inclined/horizontal solar UV irradiation (315–378 nm).

Year Horizontal annualenergy (Wh/m2)

37� Inclined annualenergy (Wh/m2)

Month PI/PH

2010 40,464.80 38,987.07 February–July

0.96

2009 73,816.74 76,830.75 January–December

1.04

2008 64,856.98 67,134.97 January–December

1.04

2007 57,910.95 59,482.83 March–December

1.03

angles and the weight of the diffuse solar irradiance in theUV range.

The second order polynomial regression was the best fitfor the data. The data was forced to be fitted through (0,0)since there is no physical sense for an empirical equationthat gives a non null value of H UVT for null values of HUV .

4. Discussion

The analysis of the presented data show that in theassessed UV range (315–378 nm), the annual UV energyincrease for a plane located at 37�N and tilted the samedegrees as the latitude, lies between 3% and 4%. In the glo-bal wavelength range (300–3000 nm), this percentage risesup to 10–12% for the same conditions. The main reasonsfor this difference is that the UV range has a much largerdiffuse component than global radiation.

The plane inclination rises the UV irradiation inter-cepted by the plane in 30–40% in the last days of autumn,winter, and the first days of spring. On the contrary, theinclined plane receives about a 10–15% less irradiation onthe summer months. It is important to mention that sum-mer irradiation losses are about the same values for bothwavelength ranges, UV and global, yet the increase in win-ter is much larger for global. Again, mainly due to theinfluence of direct solar radiation.

On the overall annual analysis, the inclined planereceives more solar UV irradiation than the horizontalplane. In this way, the annual gainings in direct UV irradi-ation are larger than the losses in diffuse UV irradiation,even though both components are present in approxi-mately the same proportion in the UV range.

Regarding solar water treatment applications, it wouldbe more convenient to regulate the inclination of the reac-tor or the plane of interest each month, in order to capturemore useful photons for photoreactions. In this way, 30–40% more UV energy per month could be obtained. Theoptimum monthly inclination values for the PSA are given

Table 10Optimum monthlyinclination (b) valuesfor solar reactorslocated at the PSA.

Month b

January 58.30February 50.30March 39.40April 27.80May 18.70June 14.40July 16.20August 23.60September 34.50October 46.10November 55.80December 60.40

316 L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318

in Table 10. The values are numerically equal to the meanmonthly sun zenith angle at noon. Hence, each month theplane will have normal sun incidence in the moments wheremore energy is available. If monthly inclination regulationis restricted due to functioning systems conditions, thefixed inclination has the advantages and disadvantagesalready described. Weather conditions at the PSA are veryfavorable for solar applications. Nevertheless, much atten-tion must be paid to the interpretation of the presenteddata, since the increase in monthly and annual energycan vary with the location and local climate conditions.For example, at particular locations, the rain season is dur-ing winter and is characterized by strong rain and cloudedsky most of the days. Under these circumstances, all of UVis diffuse and no increase in the overall irradiation would bedetected, mainly, due to the lack of direct UV. The opti-mum plane inclination will be different for different loca-tions, different climates and use regimes.

The main factor affecting the quantity of diffuse radia-tion in the UV-A wavelength range is Rayleigh scatteringand aerosol scattering and absorption. The UV range, suf-fers the phenomena in larger quantities than the rest of thespectrum reaching the earth surface.

5. Conclusions

A 4 year data analysis of UV measurements on the hor-izontal an inclined plane has been presented. Daily,monthly and annual values of UV irradiation on bothplanes have been analyzed in detail. Before analysis, dataquality was assessed by comparison with other radiometersand with modeled irradiance, and possible drifts were iden-tified and corrected.

The overall results is that at the PSA, a photoreactor orplane inclined 37� facing equator will annually receive about3–4% more UV energy than the horizontal plane. Monthlymean inclined/horizontal UV solar radiation ratio rangefrom 1.25 in the winter months to 0.95 in the summer

months. Daily inclined/horizontal ratio range from 1.35 inwinter to 0.85 in summer days. For the global wavelengthrange, the mean annual gainings due to plane inclinationrange from 10% to 12%, and monthly mean ratios rangefrom 1.70 in the winter months to 0.80 in the summermonths. The difference in the gainings is attributed to thelarge diffuse component in the UV range, a product of largeRayleigh scattering and aerosol absorption.

An empirical correlation to obtain UV irradiation on a37� inclined plane, from horizontal plane measurementshas been obtained. Horizontal UV radiation can be esti-mated from other wavelengths such as global or PARand subsequently extrapolated to an inclined plane usingthe proposed correlation. In principle, the equation appliesto places located near the same latitude (south or north)and similar weather characteristics (clear atmosphere).Regarding reactors for solar UV water treatment, the bestchoice is to give different inclinations for each month,always trying to have normal sun incidence onto the planeof interest. If this option is unavailable due to technical,economical or other type of constraints, an analysis ofthe location climate must be performed before determiningthe fixed inclination value. If a heavy rain season coincideswith winter, then the gainings due to inclination will besmaller than those explained above, since there will be littledirect UV component available.

Different plane inclinations have to be studied sepa-rately. The derivation of a generalized method, such asthe ones for global energy, requires simultaneous measure-ment of total, diffuse and direct UV irradiation at differentinclination angles. This is the subject of future studies.

Acknowledgements

This work was performed with the help of the “Access tothe PSA Program” (Plan de Acceso Nacional a la Platafor-ma Solar de Almerıa) and travel grants from the UTN-FRBA (National Technological University-Buenos AiresRegional Faculty) and 3iA-UNSAM (Institute for Envi-ronmental Engineering-National Unversity of San Martın).

We would also like to thank Francisco Jose OlmosReyes and Lucas Alados Arboledas and their staff forestablishing and maintaining the (Malaga and GranadaAERONET sites) used in this work and Inmaculada Polofor helpful suggestions.

Appendix A. Equations

IdirðzÞ ¼ I0 � e�s

cos hð Þ ðA:1Þ

s ¼Z 1

znjðzÞ � rj � dz ðA:2Þ

s ¼ bðkÞ�a ðA:3Þ

xo ¼rsc

ðrsc þ rabsÞðA:4Þ

L.C. Navntoft et al. / Solar Energy 86 (2012) 307–318 317

P ðh� h0Þ ¼ 3

4� ð1þ cos2ðh� h0ÞÞ ðA:5Þ

g � 1

2

Z þ1

�1

P ðh� h0Þ � cosðh� h0Þ � dðcosðh� h0ÞÞ ðA:6Þ

RUV ¼HUVT

HUVðA:7Þ

RUVi ¼H UVT i

H UV i

ðA:8Þ

RUVANNUAL ¼P1

365H UVTP1365H UV

ðA:9Þ

RGLOBALi ¼HT i

H iðA:10Þ

RGLOBALi ¼H T i

Hi

¼ 1� Hdi

Hi

� �� Rbi þ

H di

Hi� 1þ cos u

2

� �

þ q � 1� cos u2

� �ðA:11Þ

Rbi ¼cosð/� uÞ � cos di � sin x0si þ x0si � sinð/� uÞ � sin di

cos / � cos di � sin xsi þ xsi � sin / � sin di

ðA:12Þxsi ¼ cos�1ð� tan / � tan diÞ ðA:13Þ

x0s ¼ mincos�1ð� tan / � tan diÞ

cos�1ð� tanð/� uÞ � tan diÞ

" #ðA:14Þ

IRAD2 ¼ IRAD1 � 1:0733ð�3:3212� 10�4Þ with

R2 ¼ 0998 and N ¼ 2455 ðA:15Þ

H UVT ¼� 0:0014ð�2442� 10�4Þ � ðHUV Þ2

þ 1:3688ð�0:1033Þ � H UV R2 ¼ 0:9856 N ¼ 40

ðA:16Þ

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