A study of zenith luminance on Madrid cloudless skies

Solar Energy Vol. 69, No. 5, pp. 403–411, 20002000 Elsevier Science Ltd

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A STUDY OF ZENITH LUMINANCE ON MADRID CLOUDLESS SKIES

, , ,1†A. SOLER* ** and K. K. GOPINATHAN*´ ´*Departamento de Fısica, Escuela Tecnica Superior de Arquitectura, UPM, Avda. Juan de Herrera 4,

28040 Madrid, Spain´**Facultad de Ciencias Ambientales, UPM, Avda. de Martın Fierro s /n, 28040 Madrid, Spain

Received 9 March 1999; revised version accepted 28 April 2000

Communicated by RICHARD PEREZ

Abstract—The zenith luminance (L ) has been measured for cloudless skies at the IDMP station in Madrid.z

Mean values obtained at every 15 min have been fitted vs. solar elevation (a). A 5th degree polynomialconnecting log (L ) against (a) gives the best correlation in terms of the correlation coefficient (r 5 0.9358). Az

possible explanation of the dependence of the zenith luminance on solar elevation at low values is given.Án exponential model obtained by other authors (Vazquez and Bernabeu, 1997) for a nearby temporary

station in the same city does not account for the qualitative dependence of L vs. a for a , ¯ 158, and alsoz

overestimates experimental values for high solar elevations.The effect of turbidity on L is studied categorizing available data in three specified groups of T , the visualz v

or luminous / illuminance turbidity. Best fits with 5th degree polynomials connecting log (L ) against (a) arez

given for: T , 3, 3 , T , 5, and T . 5. 2000 Elsevier Science Ltd. All rights reserved.v v v

1. INTRODUCTION from hourly values usually found in the solarradiation literature.

Characterization of the luminous climate availableThe Spanish station in the IDMP is located at

at different sites is of interest for a variety of´the flat roof of the Escuela Tecnica Superior de

purposes such as to quantify energy savings fromArquitectura de Madrid (408 259N, 38 419W). As

the adequate use of photoelectric controls (Lit-a part of ongoing research at the station (Soler

tlefair, 1984), to evaluate daylighting systemsand Oteiza, 1997; Oteiza and Soler, 1995, 1997;

(Soler and Oteiza, 1997), to estimate illuminanceRobledo and Soler, 1996, 1997, 1998a,b,

levels in rooms for design purposes (Oteiza and2000a,b,c; Soler and Robledo, 2000) a brief and

Soler, 1997), or to evaluate daylighting softwaresimplified study of the dependence of the zenith

(Ubbelholde and Humann, 1998).luminance L on solar elevation a for cloudlesszSince 1991 continuous measurements of at leastskies is given in the present work. The present

global and diffuse illuminance on horizontal andpaper is partly motivated by the publication of

global illuminance on vertical surfaces have beenanother study on the same subject based on data

underway in more than 40 stations distributedobtained for the same city at the Universidad

worldwide, within the International Daylight Mea-Ćomplutense, close to our measuring site (Vazq-

surement Programme (IDMP), (Dumortier et al.,uez and Bernabeu, 1997). A comparison between

1994). This international effort was promoted byour model, and the model proposed by these

a CIE Technical Committee because it was feltauthors is performed.

that the daylighting characterization data wasZenith luminance under cloudless sky condi-

inadequate for the purposes of daylighting design.tions is influenced not only by solar altitude but

In some of the stations the direct normal or beamalso by turbidity. Recent research on zenith

illuminance, the zenith luminance or even the skyluminance has made extensive use of the visual or

luminance distribution are also measured. The skyluminous / illuminance turbidity factor T (Kittlervluminance distribution is measured with currentlyet al., 1998). In the present work the effect of

available sky scanners in a time scale (min) farturbidity on L is studied categorizing availablez

data in three specified groups of T .v†Author to whom correspondence should be addressed. Tel.:

134-91-33-66-569; fax: 134-91-33-66-554; e-mail:[email protected] 2. EXPERIMENTAL DATA

1Permanent adress: Department of Physics, National Universi-ty of Lesotho, Roma, Lesotho, South Africa. The experimental data used are mean 15-min

403

404 A. Soler and K. K. Gopinathan

values of L obtained using a sampling time of 5 s were always in agreement with the airport reports.z

in the period July 1997–June 1998. The sensor Also the fraction of possible sunshine was mea-used is a LICOR illuminance sensor fitted in a sured each h at the measuring site and found to beblack collimator tube, designed for a view angle 1 for the selected data when the four hourlyof 10.58 following a standard procedure (Rommel measurements corresponded to cloudless skies. Aet al., 1994). The luminance sensor was calibrated total of 3013 mean 15-min values of L werez

at the Instituto de Optica of the Consejo Superior obtained in this way.´de Investigaciones Cientıficas a few days before Simultaneous measurements of global (G ) andv

starting the experiment. The whole unit was fixed diffuse (D ) illuminances from which T valuesv v

on top of a semi-spherical dome. The L sensor can be determined, were also performed. Prob-z

was one of the 15 used in a larger experiment that lems related with the electricity supply to the dataintended to help in the characterization of the logger used for these measurements reduced toluminous climate at Madrid. The other sensors 1704 the number of data sets with simultaneouswere placed on the dome in 14 of the 145 possible values of L and T . The LICOR sensors usedz v

positions according to the pattern suggested by were calibrated at the manufacturer representa-the CIE and described elsewhere (e.g. Enarun and tives a few days before starting the experiment.Littlefair, 1995).

In the present work, only L values for cloud-z

less sky conditions are used. Cloudless skies are 3. ZENITH LUMINANCE DATA ANALYSISdefined as those without clouds, corresponding to

3.1. Dependence of zenith luminance on solarvisual observers reporting a cloud cover of 0elevationoktas. To make sure that this is the case for the

present data, visual observations routinely per- The experimental values of L are plottedz

formed by trained observers of the Instituto against a in Fig. 1 a logarithmic scale. AttemptsŃacional de Meteorologıa at the airport of Madrid were made to fit the experimental data against a

were used. Observations of the sky cloudiness using various forms of functional equations. Sim-were also undertaken at the measuring site and ple models based on exponential, polynomial,

Fig. 1. Experimental values of zenith luminance L (15-min means) against solar elevation a for cloudless skies and 5th degreez

polynomial fit (Eq. (1)).

A study of zenith luminance on Madrid cloudless skies 405

power, logarithmic and linear equations were tried dependence of log (L ) on the 5th degree polyno-z

by considering various combinations of L , mial of a, mean experimental values of L werez z

log (L ), a, tan (a), sin (a), etc. to obtain the best calculated at every 58 interval of a and the valuesz

fit for the experimentally measured data. By are plotted in Fig. 2 on a logarithmic scale.carrying out such an analysis it was observed that Fifteen mean values of L are plotted at every 58z

a 5th degree polynomial connecting log (L ) interval of a and the data points are fitted with az

against a gives the best correlation in terms of the 5th degree polynomial. The following equation iscorrelation coefficient. The polynomial obtained obtained from the analysis of the data:is:

2log (L ) 5 2 0.60647 1 0.08594a 2 0.00444az2log (L ) 5 2 0.6826 1 0.09922a 2 0.005160az 3 41 (1.2961E 2 4) a 2 (1.7942E 2 6)a

3 41 (1.4430 E 2 4) a 2 (1.8918 E 2 6)a 5

1 (9.4016E 2 9)a (2)5

1 (9.3644 E 2 9) a

with r 5 0.9358 (1) The correlation coefficient obtained for thefitting is found to be 0.9987, clearly supportingthe validity of earlier observations on scatter data.The second best representation of the measured

Ín Vazquez and Bernabeu (1997) an exponen-data is given by a power equation of the formb tial model has been developed for L against aL 5b [tan a] . The values of the constants zz o

with values of L obtained in 1993–1994 at aobtained are b 52.6774, and b50.6542, with zo

temporary station at the nearby Faculty of Physicsr50.9241. For a 5th degree polynomial connect-at the Universidad Complutense apparently usinging L against a a value r50.8848 was obtained.z

25-day data. However the authors have not indi-The best fit with the 5th degree polynomial givencated the number of experimental values used, orby Eq. (1) is shown in Fig. 1. As seen in Fig. 1,the way used to check the state of the sky, and theluminance values gradually increase with a, fol-time interval of each measurement. In Robledolowing the pattern reported by, among others,and Soler (2000a), it was shown that the quali-Nakamura et al. (1986). To fully establish the

Fig. 2. Mean experimental values of the zenith luminance L for cloudless skies calculated at every 58 interval of a, and 5thz

degree polynomial fit (Eq. (2)).


´tative dependence of global illuminance on solar the experimental equation recommended in Vaz-elevation for a horizontal surface as given in quez and Bernabeu (1997), in the form L 5z

2´Vazquez and Bernabeu (1997), was neither phys- exp (6.3610.042 a) cd /m . The large variationically sound nor in agreement with the one found between the plots for Eq. (1) and for the exponen-

át our station, similar to those obtained by several tial equation given in Vazquez and Bernabeuinvestigators for other stations. Relating L , the (1997) indicate that their equation is not accuratez

best fit of our experimental data for L with an enough to calculate L for Madrid. A possiblez z

éxponential model, as proposed in Vazquez and reason for the discrepancy is that the model in´Bernabeu (1997), does not account for the quali- Vazquez and Bernabeu (1997) was developed

tative dependence of L against a for a ,¯158, using a small amount of data.z

as shown in Fig. 3 on an enlarged scale. Indeed, It is a well established fact that for a .¯158 Lz

observation of the data suggests that up to a(158 increases with a in a similar way to that showna convex curve will fit the data in Fig. 3, while for for our data in Fig. 3 (Nakamura et al., 1986;higher values of a, a concave curve will give the Kittler, 1970; Dogniaux, 1979; Krochman, 1970;best fit. Krochman and Seidel, 1974; Karayel et al.,

To emphasize some aspects of dependence of 1984). Perhaps due to the scarcity of data forthe zenith luminance on solar elevation for clear a ,¯158 the corresponding part of these plots

´skies, the graph for L vs. a has been again has not received much attention. Even in Vazquezz ]plotted in Fig. 4 using a logarithmic scale for L . and Bernabeu (1997) for the same site not manyz

The best fits obtained with the exponential equa- data are available for the range 08,a ,158. Our´tion given in Vazquez and Bernabeu (1997) and results clearly show that the polynomial giving

with a 5th degree polynomial (Eq. 1) have also the best fit for our data does account for thebeen plotted in Fig. 4 for comparison. The linear regions of convex and concave curvatures ob-fit for the exponential equation obtained as a best served in Fig. 3, corresponding respectively tofit for our data does not account well for the a ,¯158, and a .¯158.experimental values, and specifically does not fit the An explanation for the experimental results forobserved dependence of L with a for a ,¯158. low values of a, is that for low solar elevationsz

Fig. 4 also shows L values calculated using the anisotropic effect known as horizon brighten-z

Fig. 3. Experimental values of zenith luminance L against solar elevation a for cloudless skies with an exponential fit.z


Fig. 4. Experimental values of zenith luminance L against solar elevation a for cloudless skies, with exponential and 5th degreez

´polynomial fits. The plot for the exponential model given in Vazquez and Bernabeu (1997) is also shown.

ing is superimposed to the isotropic sky zenith both, the broadband turbidity and the solar al-luminance. This effect is usually admitted as titude have been used in computer programs forbeing restricted to a band of solar elevations from illuminance calculations. In Scartezzini et al.a 508 to about a 5108 and is taken into account (1994) a relative difference of 15% was givenin illuminance modeling (Perez et al., 1990). Our between the illuminances calculated with Super-experimental data would show that the effect lite and Radiance using the equations for L ,z

could be observed for clear skies in the zenith given in Karayel et al. (1984) and Liebelt (1978).luminance measurements. If global and diffuse illuminances are recorded,

If the explanation given above is correct, the the luminous turbidity T should be used. Thev

horizon brightening should be detectable with luminous turbidity T can be calculated (Kittler etv

other sensors. The luminance values for clear al., 1998; Karayel et al., 1984) as:skies measured during the same period with a

T 5 2 [ln ((G 2 D ) /E )] /a m (3)v v v v vsensor collimated as the one used to measure Lz,

but positioned in the dome with the elevation of where E is the extraterrestrial illuminance com-v668 and the azimuth of 08, have been plotted puted using a luminous solar constant of 133.8against a in Fig. 5, and similar features to those klux, a 51/(9.910.043 m), and m is the opticalvobserved in Fig. 1 are obtained. air mass from Kasten and Young (1989) as given

by:3.2. Effect of turbidity on zenith luminance

21.6364m 5 1/ [sin a 1 0.50572 (a 1 6.079958) ]Generally speaking zenith luminance under(4)cloudless sky conditions in its absolute level is

influenced not only by solar altitude but also byturbidity. Some scientists have proposed equa- In the present work the air mass given by Eq.tions relating zenith luminance, solar altitude and (4) has been corrected for the station elevationthe broadband or energetic turbidity, among them, above see level (Iqbal, 1983), 0.678 km, and theDogniaux (1971, 1979), Liebelt (1978), Karayel values of a are taken at the middle of eachet al. (1984). Relations giving L as a function of measuring interval of 15 min.z,


Fig. 5. Experimental values of zenith luminance L against solar elevation a (15-min means) for cloudless skies, obtained for thez

elevation of 668 and the azimuth of 08.

The actual value of T represents the number of For T , 3v v

absolutely clean atmospheric filter substituting a 2log (L ) 5 2 0.61538 1 0.08580a 2 0.00448 azreal, e.g. polluted atmosphere having the same3 4

1 (1.2619E 2 4) a 2 (1.6824E 2 6) afiltering effect on the (G 2 D ) /E ratio underv v v

5the actual solar altitude and directional air mass1 (8.54789E 2 9) a

(Kittler et al., 1998).with r 5 0.9326 (5)The effect of turbidity on L is studiedz

categorizing available data in three specifiedFor 3 , T , 5vgroups: T ,3, 3,T ,5, and T .5. By carryingv v v

2out the same analysis as for the study performed log (L ) 5 2 0.60897 1 0.09129a 2 0.00452 azin Section 3.1 it was observed that a 5th degree 3 4

1 (1.2235E 2 4) a 2 (1.5829E 2 6) apolynomial connecting log (L ) against a givesz5the best correlation in terms of the correlation 1 (7.8464E 2 9) a

coefficient for each of the T groups. The datav with r 5 0.9555 (6)available and the curves for the best fits of log(L ) vs. a with 5th degree polynomials are givenz For T . 5vin Fig. 6 for: T ,3, 3,T ,5, and T .5. It isv v v 2log (L ) 5 2 0.58487 1 0.09023 a 2 0.00388 aobserved that there is considerable overlapping z

3 4between data for the three groups. The best fits for 1 (9.9654E 2 5) a 2 (1.2851E 2 6) aT .5 and T ,3 lie respectively above and belowv v 5

1 (6.5557E 2 9) athe best fit for 3,T ,5. This is in generalv

agreement with the results in Kittler et al. (1998), with r 5 0.9879 (7)given for solar elevations up to 508, for differentT values and each of the cloudless sky standards Although the data consists of 3013 sets ofv

they propose. values for Eq. (1), and of respectively 915, 632,The following 5th degree polynomials are and 157 sets of values for Eqs. (5)–(7), co-

obtained from the analysis of the data: efficients of correlation are high in all cases. On


Fig. 6. Experimental values of zenith luminance L against solar elevation a for cloudless skies and three ranges of luminousz

turbidity T , and best fits with 5th degree polynomials.v

Fig. 7. Fifth degree polynomial fits of zenith luminance L against solar elevation a for cloudless skies: for the three T rangesz v

(Eqs. (5) to (7)); the 1705 data sets including all the available T values (Eq. (8)), and the 3013 data sets (Eq. (1)).v


network of daylight measuring stations. In Report IEA-the other hand and as observed in Fig. 7, there is aSHCP-17E-2, vol. 2, See also http: / / idmp.entpe.fr.

similarity between the 5th degree polynomial fits Enarun D. and Littlefair P. J. (1995) Luminance models forfor the 3013 data sets (Fig. 1), the 1704 data sets overcast skies: assessment using measured data. The Inter-

national Journal of Lighting Research and Technology 27,used to study the dependence on T , and thev 53–57.3,T ,5 data sets (Fig. 6).v Karayel M., Navvab M., Ne’eman E. and Selkowitz S. (1984)

For the 1704 data sets the following 5th degree Zenith luminance and sky luminance distributions fordaylighting calculations. Energy and Buildings 6, 283–291.polynomial fit is obtained:

Kasten F. and Young A. T. (1989) Revised optical air masstables and approximation formula. Appl. Optics 28, 4735–

log (L ) 5 2 0.57942 1 0.07896 a 4738.zKittler R. (1970). Some considerations concerning the zenith

2 3 luminance of the cloudless sky, Attached document of2 0.00361 a 1 (9.1811E 2 5) acircular letter No 11 of CIE Committee E23.2.

4 5 Kittler R., Darula S. and Perez R. (1998) A set of standard2 (1.1282E 2 6) a 1 (5.4292E 2 9) askies characterizing daylight conditions for computer andenergy conscious design. In Final Report, Institute ofwith r 5 0.9199 (8)Construction and Architecture, Slovak Academy of Sci-ences, Bratislava 842 20, Slovakia, and Atmospheric Sci-ences Research Center, State University of New York,Albany, NY 12205, USA.

4. CONCLUSIONS Krochman J. (1970) Uber die Horizontalbeleuchtungsstarkeund die Zenitleuchtdichte des klaren Himmels. In Lichttech-The zenith luminance has been measured for nik 22/II, pp. 551–554.

cloudless skies in Madrid and experimental mean Krochman J. and Seidel M. (1974) Quantitative data ondaylight for illuminating engineering. The International15-min values of L are obtained. A polynomialz Journal of Lighting Research and Technology 6, 165–171.of 5th degree for log (L ) vs. a has beenz Liebelt C. (1978). Leuchtdichte- und Strahldichteverteilung

accurately fitted to the whole data. ¨des Himmels, Universitat Karlsruhe, Dissertation; as cited inCIE Technical Report 110-1994 (1994) Spatial distributionThe fit of the experimental data for L with anz of daylight-luminance distributions of various referenceéxponential model given in Vazquez and Ber- skies.

nabeu (1997) obtained for a nearby temporary Littlefair P. J. (1984) Daylight availability for lighting con-trols. In Proceedings of the CIBSE National Lightingstation in the same city does not account for the qual-Conference, pp. 215–233.itative dependence of L against a for a ,¯158,z Nakamura H., Oki M., Hayashi Y. and Iwata T. (1986) The

and also over predicts experimental values for mean sky composed depending on the absolute luminancevalues of the sky elements and its application to thehigh solar elevations.daylighting prediction. In Proceedings of the InternationalThe effect of turbidity on L is studiedz Daylighting Conference, pp. 61–66, Long Beach.

categorizing available data in three specified Oteiza P. and Soler A. (1997) Experimental analysis forMadrid, Spain, of a simple graphic daylight calculationgroups of T , the visual or luminous / illuminancevmethod based on the CIE standard overcast sky. Buildingturbidity. The best fits for log (L ) vs. a with 5thz and Environment 32, 363–366.

degree polynomials for T .5 and T ,3, lie Oteiza P. and Soler A. (1995) A comparison of the daylightingv vperformance of different shading devices giving the samerespectively above and below the best fit forsolar protection. The Architectural Science Review 38, 171–3,T ,5, but there is considerable overlappingv 176.

between data for the three groups. Perez R., Stewart R., Arbogast C., Seals R. and Scott J. (1990)An anisotropic hourly diffuse radiation model for slopingsurfaces. Description, performance validation, site depen-dency evaluation. Solar Energy 36, 487–497.

Acknowledgements—The present work has been performed as Robledo L. and Soler A. (1996) Point source Perez illumi-the initial part of the project PB95-0037 financed by the nance model. Dependence of coefficients on surface orienta-Spanish Government through the DGICYT. A. Soler gratefully tion at Madrid. The International Journal of Lightingacknowledges the DGICYT for awarding the funds. Research and Technology 28, 141–148.K.K.Gopinathan has joined in data analysis during his sabbati- Robledo L. and Soler A. (1997) Modeling daylight forcal and gratefully acknowledges the DGICYT for financial applications to daylight conscious architecture. The Interna-support. We are grateful to the Instituto Nacional de tional Journal of Renewable Energy 11, 149–152.

´Meteorologıa for supplying the cloud data and to Mr. S.T. Robledo L. and Soler A. (1998a) Modeling irradiance onClaros for his assistance in running the computer programs. inclined planes with and anisotropic model. Energy, the

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A study of zenith luminance on Madrid cloudless skies