Ž .Energy and Buildings 31 2000 25–28www.elsevier.comrlocaterenbuild

Estimation of global illuminance for clear skies at Madrid

Luis Robledo a,), Alfonso Soler b,c

a Departamento de Sistemas Inteligentes Aplicados, E.U. Informatica, UniÕersidad Politecnica de Madrid, Ctra. de Valencia km 7, 28031 Madrid, Spain´ ´b Departamento de Fısica e Instalaciones, ETSAM, AÕda Juan de Herrera 4, 28040 Madrid, Spain´

c Facultad de Ciencias Ambientales, UPM, Madrid, Spain

Received 22 May 1998; accepted 21 October 1998

Abstract

Two elementary empirical models for the dependence of global illuminance on solar elevation for clear skies are provided. The modelsŽ .are developed from hourly data obtained from 1 year data collected at the International Daylight Measurement Programme IDMP

Ž .general class station at the Escuela Tecnica Superior de Arquitectura in Madrid ETSAM , and are statistically assessed with data´Ž . Ž .obtained during another period of 6 months. Values of the mean bias deviation MBD and root mean square deviation RMSD of

respectively less than 5% and 7% of the average illuminance measured were obtained. The qualitative dependence of global illuminanceon solar elevation, common to that found by other researchers for other locations is justified, and found to be different to that given by

w Ž .Vazquez and Bernabeu D. Vazquez, E. Bernabeu, Quantitative estimation of clear sky light in Madrid, Energy and Buildings, 26 1997´ ´x331 using data obtained at a site which is in close proximity to our station. q 2000 Elsevier Science S.A. All rights reserved.

Keywords: Daylight; Natural lighting; Global illuminance modelling; Madrid

1. Introduction

Knowledge of the luminous flux incident on inclined orhorizontal surfaces is needed for a variety of purposes,such us: computing values of illuminance in rooms from

w xcorresponding values at windows 1 , obtaining cumulativedistributions of illuminances to quantify energy savings for

w xphotoelectric controls 2 , or evaluating daylighting sys-w xtems 3 . For many years, continuous reliable long term

measurements of illuminances on horizontal surfaces havew xbeen rarely available 4,5 , but since 1991 continuous

measurements have been underway at many locationsw xworldwide 6 , under the aegis of the International Day-

Ž .light Measurement Programme IDMP . The only Spanishstation in the IDMP is located at the Escuela Tecnica´

Ž .Superior de Arquitectura at Madrid ETSAM . As a part ofw xongoing research at this station 7–12 , a brief and simpli-

fied study of the global illuminance incident for clear skieson a horizontal surface is reported in this work.

The present paper is partly motivated by another studyw xfor the same city by Vazquez and Bernabeu 13 . The´

) Corresponding author. Tel.: q34-1-336-7854; Fax: q34-1-336-7522;E-mail: asoler@corbu.aq.upm.es

model for global illuminance on a horizontal surface pre-sented by these authors, developed from clear sky dataobtained for a period of measurement of 6 months, showsa dependence of global illuminance on solar altitude quali-tatively different from that usually found in the literature.In the present study, mean hourly global illuminance ob-tained for a period of 18 months at our IDMP station isused for modelling global illuminance. To support ourmodels for global illuminance, we compare the depen-dence on solar elevation of direct and global illuminancesfor clear skies. The dependence on solar elevation for clearskies of direct and global solar irradiances measured onhorizontal surfaces at our station are also given, to showsimilar trends to those obtained for illuminances.

The qualitative dependence of global illuminance onsolar elevation obtained in the present work is shown to besimilar to that usually provided in the literature.

Finally, the proposed models will be statistically as-sessed with data not used to develop them.

2. Experimental data

Before we proceed any further, it is important to deter-mine what we understand by clear skies in relation to the

0378-7788r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved.Ž .PII: S0378-7788 98 00071-1

( )L. Robledo, A. SolerrEnergy and Buildings 31 2000 25–2826

present work. To establish the sky types we use theclearness index ´

X and the brightness index D as definedw x Xby Perez et al. 14 . We consider clear skies when ´ )5.0

and D-0.12 as evaluated from solar radiation data. Theexperimental data used are mean hourly values of globaland diffuse illuminances and global and diffuse irradi-ances, measured on horizontal surfaces during the periodJune 1994–November 1995, for the values of ´

X and D

considered. Of these, the data corresponding to the periodJune 1995–November 1995, have been used to evaluatethe models obtained with data for the period June 1994–May 1995. Measurements have been performed at the flat

Ž .roof of the ETSAM at Madrid 40.48N, 4.48W . TheLICOR illuminance sensors used were recalibrated each 6months by the manufacturers representatives following themanufacturers approved procedure. The Kipp–ZonnenCM6B pyranometers used were recalibrated after 1 year ofuse, by the Instituto Nacional de Meteorologıa. The cali-´bration of the illuminance sensors was tested against areference standard circulated by the Commission Interna-

Ž .tionale de l’Eclairage CIE through European IDMP sta-tions. Corrections for the shadow bands were performed asspecified by the manufacturers.

3. Global illuminance for clear skies

Global illuminance E has two components: directG

illuminance E , and diffuse illuminance E . In Fig. 1, weB D

can see the dependence on solar elevation a of E ,B

obtained as the difference between global and diffuseilluminances. As the optical air mass decreases with in-creasing values of a , it can be shown that the increase ofE with solar elevation is in qualitative agreement withB

theoretical prediction. The diffuse fraction of global illumi-

Fig. 1. Dependence of direct illuminance for a horizontal surface on solarelevation for clear skies.

Fig. 2. Dependence of the diffuse fraction of global illuminance for ahorizontal surface on solar elevation for clear skies.

nance is plotted vs. solar elevation in Fig. 2. It can be seenthat, as expected for clear skies, the contribution of E toD

E is relatively small when compared with that of E . AsG B

a consequence we expect a dependence of E on a of theG

type shown in Fig. 3, where the experimental data obtainedfor E in the period June 1994–May 1995 have beenG

plotted.On the other hand, the qualitative dependence of EG

and the global irradiance I on a should be similar forG

clear skies. This is indeed the case as we can see from thedependence of I on a shown in Fig. 4 for the periodG

considered.w xSeveral authors 15–18 have obtained empirical algo-

rithms for the dependence of E on a for clear skies. InG

the present work, we have developed two empirical models

Fig. 3. Dependence of global illuminance for a horizontal surface on solarelevation for clear skies.

( )L. Robledo, A. SolerrEnergy and Buildings 31 2000 25–28 27

Fig. 4. Dependence of global irradiance for a horizontal surface on solarelevation for clear skies.

Ž .Bfor E in klux. The first one being E sA sina with AG G

and B local constants, and a second one expressing apolynomial dependence of E on a . The best possible fitsG

give the following equations for clear skies:

1.076E s109.19 sina , rs0.977 1Ž . Ž .G

E sy8.29q2.173ay1.07P10y3a 2 y1.19P10y4a 3 ,G

rs0.975 2Ž .

Following a stepwise procedure, the polynomial fittingobtained is:

E sy7.72q2.128ay0.00013a 3 , rs0.975 3Ž .G

These models show a dependence of E on a that weG

have already justified, qualitatively similar to that usuallyfound in the available literature. As an example, we have

Ž . Ž .plotted in Fig. 5 the models in Eqs. 1 and 2 , togetherwith the results obtained with the model by Chroscickiw x16 . Although Chroscicki’s model, obtained for high tur-bidity conditions, performs badly for Madrid, the qualita-tive dependence of E on a is as expected. Other models,G

w xas reported in Ref. 13 , show a similar qualitative depen-dence. However, as shown in Fig. 5, the model by Vazquez´

w xand Bernabeu 13 obtained also for Madrid using datameasured for the period June 1993–January 1994 at theflat roof of the Physics Building at the Universidad Com-plutense, a site located about 2 km away from our IDMPstation, provides a rather different qualitative dependenceof E on a . In fact, not only a different qualitativeG

w xdependence is given in Ref. 13 , but also the estimatedvalues of E are lower than those estimated with ourG

Fig. 5. Global horizontal illuminance for clear skies for the models givenŽ . Ž .by Eqs. 1 and 2 , which are close one to each other, for the model by

Ž . Ž .Chroscicki 3 , and for the model by Vazquez and Bernabeu 4 .´

model obtained using data for the period June 1994–May1995.

4. Statistical assessment of the global illuminance mod-els

Table 1 shows the values of the mean bias deviationŽ . Ž .MBD and the root mean square deviation RMSD , bothin klx, obtained when estimating E for the period JuneG

Ž .1995–November 1995 with the models given by Eqs. 1Ž .and 2 . The MBD and RMSD are also given in Table 1

for the model by Chroscicki and for the model by Vazquez´and Bernabeu. It can be seen from Table 1 that the models

Ž . Ž .corresponding to Eqs. 1 and 2 give very similar devia-tions, with RMSD and MBD values respectively about 7%and 5% of the average global illuminance measured. Themodel by Chroscicki gives MBD and RMSD values of upto 20% of the average global illuminance measured. Fi-nally, the model by Vazquez and Bernabeu gives values of´the MBD and RMSD higher than 35%, perhaps due intheir case to loss of calibration, a not large enough dataset, etc.

Table 1Statistical results for models of global horizontal illuminance for clearskies

Ž . Ž .Model RMSD klx MBD klx

Ž .Eq. 1 4.91 y3.34Ž .Eq. 2 5.13 y3.35

Chroscicki 15.69 y14.82Vazquez and Bernabeu 27.98 y26.94´Average global horizontal 76.82 klxilluminance

( )L. Robledo, A. SolerrEnergy and Buildings 31 2000 25–2828

5. Conclusions

In the present paper, two elementary empirical modelsobtained with our IDMP station data have been givenwhich can be used to estimate global illuminance for clearskies at Madrid with values of the MBD and the RMSDabout 5% and 7%, respectively, of the average illuminancemeasured. The qualitative dependence of experimental andestimated values of E on a has been justified and foundG

in agreement with the observed dependence of I . TheG

observed qualitative dependence of E on a is in agree-G

ment with that measured by different authors for differentlocations.

From the arguments and results given in the presentpaper, it is clearly evident that the model presented for

w xMadrid by Vazquez and Bernabeu 13 developed with´data obtained at the Universidad Complutense, close to ourmeasuring site, shows a dependence of E on a qualita-G

tively different from that obtained with models availablefrom other researchers and with our models. Further on, asshown in Table 1, the model by Vazquez and Bernabeu´gives very high values of the MBD and RMSD when usedto estimate global illuminance with data obtained at ourstation for a period different to that used to develop theirmodel.

Acknowledgements

The present work has been financed by the DGICYTthrough the project PB95-0037.

References

w x1 C.L. Robbins, Daylighting, Van Nostrand Reinhold, New YorkŽ .1984 .

w x2 P.J. Littlefair, Daylight availability for lighting controls, Proc. CIBSEŽ .National Lighting Conf. 1984 215.

w x3 A. Soler, P. Oteiza, Light shelf performance in Madrid, Spain,Ž .Building and Environment 2 1997 87.

w x4 D.R.G. Hunt, Availability of daylight, Building Research Establish-Ž .ment, Garston, England 1979 .

w x5 A. Soler, Global and diffuse illuminance: estimation of monthlyaverage hourly values, The International Journal of Lighting Re-

Ž .search and Technology 22 1990 193.w x6 International Energy Agency, Report No. IEA-SHCP-17E-2, Vol. 2

Ž .1994 .w x7 L. Robledo, A. Soler, Point source Perez illuminance model. Depen-

dence of coefficients on surface orientation at Madrid, The Interna-Ž .tional Journal of Lighting Research and Technology 28 1996 141.

w x8 L. Robledo, A. Soler, Modelling daylight for applications to daylightconscious architecture, The International Journal of Renewable En-

Ž .ergy 11 1997 149.w x9 L. Robledo, A. Soler, Modelling irradiance on inclined planes with

Ž .an anisotropic model, Energy, The International Journal 23 1998193.

w x10 L. Robledo, A. Soler, Dependence on surface orientation of coeffi-cients in the circumsolar simplified Perez illuminance model forvertical planes at Madrid, Energy Conversion and ManagementŽ .1998 in press.

w x11 A. Soler, L. Robledo, Luminous efficacies on vertical surfaces, TheŽ .International Journal of Renewable Energy 1998 in press.

w x12 L. Robledo, A. Soler, Modelling direct illuminance on a horizontalsurface at Madrid for applications to low energy architecture, The

Ž .International Journal of Renewable Energy 1998 in press.w x13 D. Vazquez, E. Bernabeu, Quantitative estimation of clear sky light´

Ž .in Madrid, Energy and Buildings 26 1997 331.w x14 R. Perez, P. Ineichen, R. Seals, J. Michalsky, R. Stewart, Modelling

daylight availability and irradiance components from direct andŽ .global irradiance, Solar Energy 44 1990 271.

w x15 G. Gillet, W. Pierpoint, S. Treado, A general illuminance model fordaylight availability, Journal of the Illuminating Engineering SocietyŽ .1984 330.

w x16 W. Chroscicki, Calculation methods for determining the value ofdaylight intensity on the ground of photochemical and actinometricalmeasurements on an unobstructed plane, Proc. CIE, Barcelona,

Ž .Session 71 1971 24.w x17 R. Kittler, Standardization of the solar radiation with regard to the

prediction of insolation and shading of buildings, Teaching theŽ .Teachers on Building Climatology Conf., Vol. 2, Stockholm 1972

45.w x18 J. Krochman, K. Muller, V. Retzow, The horizontal illuminance¨

intensity and the zenith luminance of clear skies, Lichtteknik 22Ž .1970 551.