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Simplified correlations of global, direct and diffuse luminous efficacy on horizontal and vertical surfaces
Energy and Buildings 40 (2008) 1991–2001
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Simplified correlations of global, direct and diffuse luminous efficacy on horizontal and vertical surfaces A. De Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli * Department of Mechanical Engineering, University of Calabria, Via P. Bucci, Cubo 44C, 87036 Arcavacata di Rende (CS), Italy
A R T I C L E I N F O
A B S T R A C T
Article history: Received 10 January 2008 Received in revised form 11 April 2008 Accepted 20 April 2008
A simple calculation method to calculate the mean hourly global, direct and diffuse illuminance on horizontal and vertical surfaces for all sky, clear sky, intermediate and overcast sky conditions, initially developed for Arcavacata di Rende (Italy), was compared with experimental data obtained at Geneva (Switzerland), Vaulx-en-Velin (France), Bratislava (Slovakia) and Osaka (Japan). The method is based on the use of constant luminous efficacies, adopted also for the vertical surfaces. In spite of its simplicity, the method furnishes reasonably good predictions, in comparison with a more complex reference calculation method and can be proposed as a simplified tool for design purposes. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Global Direct and diffuse illuminance Luminous efficacy Horizontal and vertical surfaces
1. Introduction The quantitative knowledge of solar illuminance inside rooms is very useful when aiming to save electrical energy in buildings. The starting datum for this calculation is, obviously, the natural incident illuminance on the outside surfaces of windows and this paper deals with this topic. For many years a network of instruments for measuring solar illuminance and irradiance has been in operation at the Mechanical Engineering Department of the University of Calabria, located in Arcavacata di Rende (CS), Italy (Lat. 398210 N, Long. 168130 E). This network is composed of five photometers to measure global illuminance on the horizontal plane and on four vertical planes exposed to the north, south, east and west and of a photometer mounted on a solar tracker to measure normal direct illuminance. The photometers for measuring global light are type FET-GV, and the photometer for measuring normal direct light is type FET L03 0U DX, supplied by PRC Krochmann of Berlin, while the solar tracker, type 2AP (two-axis positioner), was supplied by Kipp & Zonen of Delft (Holland). Five Kipp & Zonen CM 11-type pyranometers were also set up at the same site to measure global radiation on the horizontal plane and on the four vertical planes, and a Kipp & Zonen CH-1 NIP-type pyrheliometer to measure normal direct radiation was mounted on the solar tracker.
* Corresponding author. Tel.: +39 0984 494609; fax: +39 0984 494673. E-mail address: [email protected] (V. Marinelli). 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.04.018
The instantaneous experimental data are measured with a frequency of about 5 min, and the mean hourly values of illuminance and irradiance are then calculated. All data are subjected to the quality control recommended by CIE [1], applying some tests which eliminate irradiance and illuminance data that is too large in comparison with extraterrestrial values and the data which produce too low or too high luminous efficacies (ratios between illuminance and irradiance). Recently, an EKO sky scanner, model MS-321LR, able to measure the luminance and the radiance of the sky in the Tregenza 145 points, according to the indications of the standard CIE 108-1994 [1], was installed in the same Test Station. Computer codes [2,3] which evaluate the illuminance inside the rooms, can use, as input data, either the sky luminance of the piece of the sky viewed through the windows from the inside points, or the external natural illuminance of the windows, and this paper refers to this latter methods. In the literature it is possible to find many publications and models concerned with the calculation of global, direct and diffuse illuminance on the horizontal surface, and, to this purpose, the concept of luminous efficacy of the radiation is often used [4–11]. Instead, less papers on the subject of illuminance on vertical surfaces have been published, although the latter is of greater interest since the windows of buildings are placed vertically [12– 16] and particularly the knowledge of diffuse skylight entering the windows is very important, since the building rooms are mostly lit by diffuse light. To calculate the global and diffuse illuminance of a surface however oriented and inclined, the most widely used calculation
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
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method is the well-known Perez et al. model [6], and this model can be considered as the reference one with which to compare other new models. In this paper, an attempt is made to calculate the global, diffuse and direct illuminance, by using very simple correlations, based on the use of constant luminous efficacy of the radiation, extending the concept of luminous efficacy also to the vertical surfaces, for which usually it is not applied. This work was done within the Italian National Research Program PRIN 2005, entitled ‘‘Climate parameters, evaluation tools and technologies for natural and artificial luminous environment for visual comfort and energy saving’’. 2. Calculation methods of global, direct and diffuse illuminance on horizontal surfaces As is well known, the luminous efficacy of solar radiation is defined as the ratio of the illuminance produced by radiation to the radiation itself. Reference can be made to three luminous efficacies: those of global, beam and diffuse radiation [17]. The luminous efficacy of the global radiation Kg is defined as the ratio of the global illuminance on the horizontal surface Eo to the global irradiance Go on the same surface. Kg ¼
Eo Go
(1)
The luminous efficacy of the direct radiation Kb is defined as the ratio of the normal direct illuminance Ebn to the normal direct irradiance Gbn: Kb ¼
Ebn Gbn
(2)
The luminous efficacy of the diffuse radiation Kd is defined as the ratio of the diffuse illuminance on the horizontal surface Edo to the diffuse irradiance Gdo on the same surface.
Fig. 2. Normal direct illuminance Ebn as a function of the normal direct irradiance Gbn at Arcavacata di Rende.
diffuse irradiance gathered at Arcavacata di Rende in the same year. Diffuse illuminance on the horizontal plane was calculated by the relation: Edo ¼ Eo Ebn sin a
(4)
where a is the solar altitude angle, while diffuse irradiance on the horizontal plane was calculated by the relation: Gdo ¼ Go Gbn sin a
(5)
Fig. 1 shows the trend of the experimental mean hourly global illuminance as a function of the experimental mean hourly global irradiance gathered at Arcavacata di Rende in 2006. Fig. 2 shows the trend of the experimental mean hourly direct illuminance as a function of the experimental mean hourly direct irradiance gathered at Arcavacata di Rende also in 2006. Fig. 3 shows the trend of the experimental mean hourly diffuse illuminance as a function of the experimental mean hourly
Therefore, the directly obtained experimental data were Eo, Ebn, Go, and Gbn, while the quantities Edo and Gdo were calculated by relations (4) and (5). In the data analysis the values of illuminance and irradiance for solar altitudes lower than 68 were eliminated, owing to the presence of some obstacles around the Test Station, like hills, buildings, etc. The experimental apparatus used in Arcavacata, which include a sun-tracker with a pyreliometer and a photometer mounted on it, permits to obtain measurements of direct and diffuse irradiance and illuminance more accurate than the measurements obtained by instruments with shadow rings.
Fig. 1. Global illuminance as a function of global irradiance at Arcavacata di Rende.
Fig. 3. Diffuse illuminance as a function of diffuse irradiance at Arcavacata di Rende.
Kd ¼
Edo Gdo
(3)
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
where ai, bi, ci, di, are other 32 constants depending on the sky clearness index.
2.1. Authors’ calculation method Figs. 1–3 show an almost linear relation between illuminance and irradiance, and, consequently, by means of the minima square method, the following simplified correlations of global, beam and diffuse luminous efficacy for Arcavacata di Rende were obtained [18,19]: Eo Kg ¼ ¼ 110 lumen W Go
MBD ¼ 0:58%
RMSD ¼ 7:62%
(6)
Kb ¼
Ebn ¼ 102 lumen W G
MBD ¼ 0:68%
RMSD ¼ 17:84%
(7)
Kd ¼
Edo ¼ 123 lumen W Gdo
MBD ¼ 0:02%
RMSD ¼ 18:09%
(8)
In Eqs. (6)–(8) MBD is the percentage mean bias deviation, and RMSD is the root percentage mean square deviation between the calculated data and the experimental data, defined as: P ðV calc;i V meas;i Þ=V meas;i 100 (9) MBD ¼ N sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ½ðV calc;i V meas;i Þ=V meas;i 1002 RMSD ¼ N
(10)
where Vcalc is the calculated datum, Vmeas the measured datum and N the number of data. 2.2. The reference calculation method: Perez et al. model The method proposed by the authors was compared with the best method available at present, the Perez et al. method [6]. These authors correlate global luminous efficacy to a sky clearness index (e), to the atmospheric precipitable water content (w), to the solar zenith angle (z), and to the sky brightness index (D), by the correlation: K g ¼ ai þ bi w þ ci cos z þ di lnðDÞ
(11)
where ai, bi, ci, di, are constants depending on the sky clearness index, and are provided by the authors for eight types of sky, variable from very clear sky to overcast sky. In total in this model 32 constants are used, and, moreover, for the estimation of the parameter w the knowledge of air temperature and of air relative humidity is needed. The sky clearness index e is defined as:
e¼
Gdo þ ððGbo =sin aÞ=Gdo Þ þ 5:535 106 z3 1 þ 5:535 106 z3
The sky brightness index (D) is defined as G D ¼ m do Io
(12)
(13)
where m is the relative air mass, Gbo the direct irradiance on the horizontal plane and Io is the normal direct extraterrestrial irradiance). Usually m is calculated by the Kasten correlation [20]. Perez et al. correlate diffuse luminous efficacy [6] to the same parameters as above, by the correlation: K d ¼ ai þ bi w þ ci cos z þ di lnðDÞ
(14)
where ai, bi, ci, di, are other 32 constants depending on the sky clearness index. The Perez’s direct luminous efficacy [6] has instead the form K b ¼ ai þ bi w þ ci eð5:73z5Þ þ di D
1993
(15)
3. Comparisons with other experimental data on horizontal surfaces The predictions of simplified correlations (6)–(8), developed for Arcavacata di Rende and the reference Perez correlations, were compared not only with the experimental data measured in Arcavacata di Rende, but also with the mean hourly experimental data measured in other four localities, for a period of 1 year. The localities considered are: Geneva, Switzerland (Lat: 468200 N, Long: 68010 E), data of 1993 Vaulx-en-Velin, France (Lat: 458470 N, Long: 48560 E), data of 2005 Bratislavia, Slovakia (Lat: 488100 N, Long: 178050 E), data of 2005 Osaka, Japan (Lat: 348360 N, Long: 1358300 E), data of 2006 Before comparing the experimental data with the predictions of calculation models, the expected uncertainty of the luminous efficacy, due to the measurement errors of photometers and radiometers was estimated. The main error affecting the photometers is the deviation of the spectral responsivity of the instruments from the standard human eye photopic curve V(lambda): this mismatch is characterized by means of the parameter f10 , equal to the percentage average deviation in absolute value [21]. The photometers installed in Arcavacata di Rende present values of f10 close to 2%. A similar precision is furnished by all the photometers installed in the other localities. The photometers average cosine error f2 [21], for all photometers used, is about 1%. All broadband solar pyranometers used are secondary standard instruments and have 2% average total uncertainties. The pyrheliometers used at Arcavacata, Geneva and Osaka, are first class instruments and present 1% errors. In the other two localities, Vaulx-en-Velin and Bratislava, the direct irradiance is evaluated as difference between global and diffuse irradiance, the latter measured by a pyranometer provided with a shadow ring. For these localities, the average error is close to 2%. Since the luminous efficacy of solar radiation K is defined as the ratio of illuminance E to irradiance G, naming these variables x and y, whose absolute (not percentage) uncertainty are ux and uy, the combined uncertainty uF of the function K = F(x,y) can be obtained applying the formula [22]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @F @F uF ¼ ðux Þ2 þ ðuy Þ2 @x @y
(16)
From Eq. (16) it emerges that the percentage uncertainty (uF/ F) 100 of the function K = x/y is: u F 100 ¼ F
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u 2 u y x 100 þ 100 x y
(17)
Inserting in Eq. (17) a total uncertainty in the illuminance measurement of 3% and a total uncertainty in the irradiance measurements of 2%, the expected uncertainty of the luminous efficacy is of 3.6%. It was considered interesting to evaluate the constant experimental global, direct and diffuse luminous efficacy not only in all sky conditions, but also under other three sky conditions: clear sky,
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Table 1 Experimental values of global luminous efficacy in different sky conditions
Arcavacata Geneva Vaulx-en-Velin Bratislava Osaka
Table 2 Experimental values of direct luminous efficacy in different sky conditions
All Sky
Clear sky
Intermediate sky
Overcast sky
110 111 107 108 115
110 110 106 105 110
110 110 106 106 113
122 122 118 116 136
Arcavacata Geneva Vaulx-en-Velin Bratislava Osaka
kt 0:65 0:2 kt < 0:65 kt < 0:2
Clear sky
Intermediate sky
102 93 97 105 99
104 100 100 101 107
102 88 94 108 95
Table 3 Experimental values of diffuse luminous efficacy in different sky conditions
intermediate sky and overcast sky, defined as [7]: clear sky intermediate sky overcast sky
All sky
(18)
being kt the clearness index, defined as the ratio of the global irradiance on the horizontal plane to the extraterrestrial irradiance on the horizontal plane. In Table 1 the values of the experimental global efficacy in all localities are reported. In Table 2 the values of the direct efficacy in all localities are reported. In Table 3 the values of the diffuse efficacy in all localities are reported. In Fig. 4, for the four types of sky, and for all localities, the ranges of percentage mean bias deviations MBD and the ranges of percentage root mean square deviations RMSD between the values of global and direct luminous efficacy calculated by the two methods and the experimental data are reported. In Model 1G the global efficacies obtained for Arcavacata are used, while in Model
Arcavacata Geneva Vaulx-en-Velin Bratislava Osaka
All sky
Clear sky
Intermediate sky
Overcast sky
123 128 125 114 120
125 140 132 116 111
123 122 124 112 120
122 122 118 114 136
1G-loc the local efficacies are used; in Model 1B the direct efficacies obtained for Arcavacata are used, whereas in Model 1Bloc the local efficacies are used. Fig. 4 indicates that, for all types of sky, all the models give acceptable predictions of global efficacy, the best models being Model 1G-loc and Model 1G; for the direct efficacy, the errors are larger than those for global efficacy, and the best models appears to be the 1B-loc, Perez and Model 1B being almost equivalent. In Fig. 5 the ranges of the percentage mean bias deviations MBD and the ranges of the percentage root mean square deviations
Fig. 4. Ranges of MBD and RMSD values between calculated and experimental global and direct luminous efficacy in different sky conditions for horizontal surfaces.
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
Fig. 5. Ranges of MBD and RMSD values between calculated and experimental diffuse luminous efficacy in different sky conditions for horizontal surfaces.
Fig. 6. Diffuse illuminance versus diffuse irradiance on vertical surfaces at Arcavacata di Rende.
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RMSD between calculated and experimental values of diffuse luminous efficacy are reported. Model 1D uses the Arcavacata efficacy for all localities, while Model 1D uses the local efficacies. Again for the prediction of diffuse luminous efficacy all the models give acceptable results, Model 1D-loc being the best one. 4. Calculation of diffuse and global illuminance on vertical surfaces To calculate the diffuse and global illuminance of a surface however oriented and inclined, the most widely used calculation method is the Perez et al. model [6], and this model can be again considered as the reference one with which to compare other new models. The luminous efficacy of the diffuse radiation Kdv on a vertical surface is defined as the ratio of the diffuse illuminance on the vertical surface Edv to the diffuse irradiance Gdv on the same surface: K dv ¼
Edv Gdv
(19)
The experimental diffuse illuminance on each vertical plane, can be obtained by the relation: Edv ¼ Ev Ebn cos #
(20)
where Ev is the experimental global illuminance of the vertical surface, Ebn is the experimental beam normal illuminance and W is the angle between the direction of the sun’s rays and the normal direction to the surface. Similarly, the experimental diffuse irradiance on each vertical plane, can be calculated by the relation: Gdv ¼ Gv Gbn cos #
(21)
where Gv is the experimental global irradiance of the vertical surface and Gbn is the experimental beam normal irradiance. The diffuse illuminance values Edv calculated by Eq. (20) in Arcavacata di Rende do not contain any ground reflection components since the measurement instrument of global illuminance Ev on the four vertical surfaces is provided with a cylindrical shield which intercepts the light reflected from the ground. So the measured values of Ev refer only to the direct and diffuse sky illuminance. Instead, the global irradiance Gv in Eq. (21) was purged of the ground reflection component using a ground reflection coefficient r = 0.15 suitable for Arcavacata di Rende. The luminous efficacy of the global radiation Kgv on a vertical surface is defined as the ratio of the global illuminance on the vertical surface Ev to the global irradiance Gv on the same surface: K gv ¼
Ev Gv
Fig. 7. Global Illuminance as a function of global irradiance for vertical surfaces at Arcavacata di Rende.
(22)
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001 Table 4 Experimental values of diffuse luminous efficacy on vertical surfaces in different sky conditions Arcavacata
Osaka
All days
North East South West
107 114 112 108
121 112 109 112
Clear days
North East South West
113 118 112 111
127 108 100 115
Intermediate days
North East South West
103 112 110 101
117 111 110 110
Overcast days
North East South West
109 114 114 112
123 119 115 121
4.1. Authors’ method As already stated above, the authors of the present paper propose the use of a constant value of the diffuse and global luminous efficacy for each vertical surface to calculate the illuminance of the surface. This method was developed for Arcavacata di Rende, by analysing the experimental data measured in a complete year [23]. Fig. 6 shows the trend of the experimental mean hourly diffuse illuminance as a function of the experimental mean hourly diffuse irradiance gathered at Arcavacata di Rende in 2006 for the four surfaces exposed to the north, east, south and east. The figure shows an almost linear relation between illuminance and irradiance, and, consequently, by means of the square minima
1997
method, simplified correlations of constant diffuse luminous efficacy on vertical surfaces for Arcavacata di Rende were obtained. These values, having being revised, prove to be a little different from those reported in the reference [23]. Fig. 7 shows the trend of the experimental mean hourly global illuminance as a function of the experimental mean hourly global irradiance gathered at Arcavacata di Rende in the same year. The figure shows again an almost linear relation between illuminance and irradiance, and, consequently, simplified correlations of constant global luminous efficacy on vertical surfaces for Arcavacata di Rende were obtained. Since the authors were able to access to the experimental data of illuminance and irradiance on vertical surfaces measured simultaneously in the course of 2006 in Osaka, also the data for this locality were analysed, obtaining the Osaka’s values of diffuse and global efficacy on vertical surfaces. Both the photometers and the pyranometers for the measurement of global illuminance and irradiance on the vertical surfaces used in the Osaka Test Station were provided with shields to eliminate the radiation reflected from the ground. According to Eqs. (19) and (22), the diffuse and global illuminances of a vertical surface can be obtained multiplying the surface irradiances by the values of the efficacies. If the diffuse and global irradiances on the surfaces are not experimentally known, they must be in some way calculated, for example, by a method again developed by Perez [6]. 4.2. Perez et al. model Perez et al. [6] proposed the use of a general calculation method of the global illuminance on a surface however orientated and inclined. In the method account is taken of the anisotropy of the diffuse light, interpreted as the sum of three parts, the circumsolar part, deriving from a region around the sun and striking the inclined surface with an angle of incidence equal to that of the
Fig. 8. Ranges of MBD and RMSD values between calculated and experimental data of diffuse illuminance on vertical surfaces in all sky and clear sky conditions.
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Fig. 9. Ranges of MBD and RMSD values between calculated and experimental data of diffuse illuminance on vertical surfaces in intermediate sky and overcast sky conditions.
direct light, an isotropic part evenly received from the rest of the sky, and a third part called brightness of the horizon, coming from a thin strip of sky adjacent to the horizon. 1 þ cos b a E ¼ K d Gdo ð1 F 1 Þ þ K d Gdo F 1 b 2 a (23) þ K d Gdo F 2 sin b þ K b Gbn sin a b where a ¼ maxð0; cos #Þ; b ¼ maxð0:087; cos zÞ The first term of Eq. (23) is the isotropic diffuse component, the second the circumsolar diffuse component, the third the component owing to the brightness of the horizon and the fourth the direct component. In Eq. (23), Kd is the Perez luminous efficacy of diffuse radiation on the horizontal plane, b is the inclination angle of the surface, the ratio a/b the tilt factor of the direct radiation, F1 the circumsolar brightening coefficient, F2 the horizon brightening coefficient and Kb is the Perez luminous efficacy of direct radiation. The diffuse luminous efficacy according to Perez, as well as the coefficients F1 and F2, are a function of four parameters [6]: the sky clearness index e, the atmospheric precipitable water content w, the solar zenith angle z, and the sky brightness index D, by means of several constants provided by the authors in a tabular form for the eight different types of sky. In Eq. (23), the parameters F1 and F2 have the form: F 1 ¼ f 11 þ f 12 D þ f 13 z
(24)
F 2 ¼ f 21 þ f 22 D þ f 23 z
(25)
The coefficients f11, f12, f13, f21, f22, f23 are furnished by Perez for each e bin [6]. If in Eq. (23) last term is cancelled, the diffuse illuminance on the surface is obtained.
For the application of Eq. (23), 112 constants for the calculation of global illuminance and 80 constants for the calculation of diffuse illuminance are needed. 5. Comparison with experimental data on vertical surfaces The method developed by the authors and the reference Perez method were compared with the experimental data of mean hourly diffuse illuminance on vertical surfaces exposed to the north, east, south and west, measured in Arcavacata, Osaka, Vaulxen-Velin and Geneva. In Table 4 the experimental values of diffuse luminous efficacy on vertical surfaces is reported, for Arcavacata and Osaka, in different sky conditions. Table 5 Experimental values of global luminous efficacy on vertical surfaces in different sky conditions Arcavacata
Osaka
All days
North East South West
110 115 112 113
120 113 110 112
Clear days
North East South West
117 115 113 122
125 112 108 117
Intermediate days
North East South West
103 113 109 105
117 111 109 107
Overcast days
North East South West
107 113 113 110
124 122 115 122
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
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Fig. 10. Ranges of MBD and RMSD values between calculated and experimental data of global illuminance on vertical surfaces in all sky and clear sky conditions.
By comparing the values obtained in the two localities, it is possible to notice a maximum difference of about 13% between the luminous efficacies for all orientations. In Figs. 8 and 9 the ranges of MBD and RMSD values, for all sky conditions and all localities, among the predictions of five
calculation methods and the experimental data of diffuse illuminance are reported. The author’s calculation methods were called KA-1, KO-1, KA-2 and KO-2. In the KA-1 method Arcavacata’s diffuse efficacies and the experimental diffuse irradiances are used, in the KO-1 method Osaka’s efficacies and the experimental
Fig. 11. Ranges of MBD and RMSD values between calculated and experimental data of global illuminance on vertical surfaces in intermediate sky and overcast sky conditions.
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irradiances are used, in the KA-2 method the Arcavacata efficacies and the irradiances calculated by the Perez method are used, in the KO-2 method the Osaka efficacies and the irradiances calculated by the Perez method are used, and in the Perez method the illuminance is calculated according to Eq. (23). Fig. 8 refers to all sky and clear sky conditions, while Fig. 9 refers to intermediate and overcast conditions. From these figures it is evident that generally, for all oriented surfaces, the best models are KA-1 and KO-1, with KA-1 superior. Since, generally, in most localities, the experimental diffuse irradiances on the vertical surfaces are not known, only methods KA-2 or KO-2 can be applied: from the figures appear that these methods furnish MBD and RMSD values better than those obtained by the Perez method. From these observations, it emerges that the calculation methods (KA-1, KO-2, KA-2 and KO-2) proposed by the authors, in spite of their simplicity, allow good predictions of diffuse illuminance on the vertical surfaces. In order to evaluate how much the errors of methods KA-2 and KO-2 depend on the error in the calculations of the diffuse irradiance on each surface by the Perez model, for Arcavacata and Osaka, the only localities of this work where the irradiances on the vertical surface were measured, the MBD and RMSD deviations between the calculated and the experimental data of diffuse irradiance were also calculated. From the results, not reported in this paper, it was evident that the errors in the diffuse irradiance were very close to the errors in the diffuse illuminance, their differences being within 3–4%. This means that most of the errors in calculating the illuminance by the methods KA-2 and KO-2 arise from the error in calculating the irradiance on the vertical planes, rather than from the error in the luminous efficacy. If a more accurate method than the Perez method is available in the future, also the illuminance values will be more accurate. In Table 5 the experimental values of global luminous efficacy for Arcavacata and Osaka are reported. In Figs. 10 and 11 the ranges of the percentage mean bias deviations MBD and the ranges of the percentage root mean square deviations RMSD between the calculation methods and the experimental data are reported. From the study of the two figures, it emerges that, generally, methods KA-1 and KO-1 are the best, while KA-2, KO-2 and Perez are almost equivalent. 6. Conclusions A simple calculation method to evaluate natural global, direct and diffuse illuminance on horizontal and vertical surfaces, consisting in multiplying a constant value of luminous efficacy for each surface by the experimental or calculated diffuse irradiance on the same surface, originally developed for Arcavacata di Rende (Italy), was compared with experimental data obtained in the course of a year in four localities of Japan, France, Slovakia and Switzerland. The method behaves well, furnishing good results, in spite of its simplicity, in all sky, clear, intermediate and overcast sky conditions, often better than the results obtained by a more complex method. More exactly, for the horizontal plane, the use of the constant global luminous efficacy obtained for Arcavacata in all sky conditions, predicts the luminous efficacy of the other four localities with MBD deviations between 4% and 4% and RMSD deviation between 5% and 9%. For clear days, the method furnishes MBD values in the range 0– 5% and RMSD values in the range 4–7%; for intermediate days, MBD values in the range 1% to 4% and RMSD values in the range 4–9%; for overcast days, MBD values in the range 10% to 5% and RMSD values in the range 8–12%.
The use of the constant direct luminous efficacy on the horizontal plane obtained for Arcavavata in all sky conditions, predicts the luminous efficacy of the other four localities with MBD deviations between 2% and 12% and RMSD deviation between 18% and 27%. For clear days, the method gives MBD values in the range 3% to 5% and RMSD values in the range 8–13%; for intermediate days, shows MBD values in the range 5% to 18% and RMSD values in the range 23–32%. The use of the constant diffuse luminous efficacy on the horizontal plane obtained for Arcavavata in all sky conditions, predicts the luminous efficacy of the other four localities with MBD deviations between 3% and 9% and RMSD deviation between 12% and 18%. For clear days, the model furnishes MBD values in the range 13% to 14% and RMSD values in the range 11–20%; for intermediate days, MBD values in the range 0–11% and RMSD values in the range 8–19%; for overcast days, MBD values in the range 10% to 5% and RMSD values in the range 8–13%. For the vertical surfaces, the global and diffuse irradiance on the surfaces are not generally measured, and their values are almost always calculated: the method proposed by the authors, for the estimation of the diffuse irradiance on the vertical surfaces, using the efficacies obtained for Arcavacata, furnishes, for all sky conditions, MBD values between 13% and +13% and RMSD between 15% and 37%, while the more complex reference method furnishes MBD between 33% and +22% and RMSD between 20% and 47%; for clear sky, the method gives MBD between 18% and +13% and RMSD between 5% and 37%, while the reference method furnishes MBD between 20% and +14% and RMSD between 9% and 35%; for overcast sky, the simplified method gives MBD between 10% and +23% and RMSD between 13% and 33%, while the reference method furnishes MBD between 3% and +30% and RMSD between 17% and 36%. The global illuminance on the vertical surfaces is predicted, by the constant efficacies of Arcavacata, for all sky conditions, with MBD between 6% and +14% and RMSD between 14% and 33%, while the reference method furnishes MBD between 1% and +14% and RMSD between 14% and 31%; in clear sky conditions, the authors method furnishes MBD between 18% and +13% and RMSD between 5% and 37%, while the reference method furnishes MBD between 20% and +14% and RMSD between 9% and 35%; for intermediate sky conditions MBD between 11% and +13% and RMSD between 14% and 34%, while the reference method, furnishes MBD between 1% and +14% and RMSD between 12% and 32%; for overcast sky conditions MBD between 14% and +18% and RMSD between 15% and 31%, while the reference method furnishes MBD between 2% and +26% and RMSD between 11% and 37%. Acknowledgements For having provided their experimental data, the authors wish to warmly thank the following: Dr. Prof. Dominique Dumortier, Ecole Nationale des Travaux Publics del’Etat (ENTPE), Vaulx-en-Velin, France, Dr. Prof. Pierre Ineichen, Centre Universitaire d’Etude des Proble`mes dell’Energie (CUEPE) University of Geneve, Switzerland, Dr. Prof. Stanislav Darula, Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia, Dr. Prof. Norio Igawa, Graduate School of Human Life Science, Osaka City University, Osaka, Japan. References [1] CIE 108-1994, Technical Report Guide to Recommended Practice of Daylight Measurement, Wien, 1994. [2] G. Ward, R. Shakespeare, Rendering with RADIANCE, the Art and Science of Lighting Visualization, Space and Light, California, 2003.
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001 [3] M. Szerman, H. Erhorn, Tageslichttechinische Bewertung Gebaudemodellen unter kunstlichem Himmel und Kunstilicher Sonne, IBP Mitteillung 237, FraunhoferInstitut fur Bauphysik, 1993. [4] P.J. Littlefair, The luminous efficacy of daylight: a review, Lighting Research Technology 17 (4) (1985) 162–182. [5] P.E. Gillette, S.J. Treado, Correlations of solar irradiance and daylight illuminance for building energy analysis, ASHRAE Transactions 91 (1A) (1985) 180– 192. [6] R. Perez, P. Ineichen, R. Seals, J. Michalsky, R. Stewart, Modelling daylight availability and irradiance components from direct ad global irradiance, Solar Energy 44 (5) (1990) 271–289. [7] T. Muneer, M.S. Gul, J. Kubie, Models for estimating solar radiation and illuminance from meteorological parameters, Journal of Solar Energy Engineering, Transactions of the ASME 122 (2000) 146–153. [8] E. Ruiz, A. Soler, L. Robledo, Assessments of Muneer’s Luminous Efficacy Models in Madrid and a proposal for new models based on his approach, Journal of Solar Energy Engineering, Transactions of the ASME 123 (2001) 220–224. [9] L. Robledo, A. Soler, On the luminous efficacy of diffuse solar radiation, Energy Conversion and Management 42 (2001) 1181–1190. [10] L. Robledo, A. Soler, Luminous efficacy of direct solar radiation for all sky types, Energy 26 (2001) 669–677. [11] R.G. De Souza, L. Robledo, A. Soler, F.O.R. Pereira, Clear sky and all sky direct luminous efficacies for Florianopolis, Brazil, Energy Conversion and Management 46 (2005) 361–371. [12] L. Robledo, A. Soler, Dependence on surface orientation of coefficients in the circumsolar simplified Perez illuminance model for vertical planes at Madrid, Energy Conversion and Management 39 (15) (1998) 1585–1595.
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[13] A. Soler, L. Robledo, Global luminous efficacies on vertical surfaces for all sky types, Renewable Energy 19 (2000) 61–64. [14] D.H.W. Li, J.C. Lam, Evaluation of slope irradiance and illuminance models against measured Hong Kong data, Building and Environment 35 (2000) 501–509. [15] S. Chirarattanon, P. Rukkwansuk, P. Chaiwiwatworakul, P. Pakdeepol, Evaluation of vertical illuminance and irradiance models against data from North Bangkok, Building and Environment 42 (11) (2007) 3894–3904. [16] L. Robledo, A. Soler, Estimation of global illuminance on inclined surfaces for clear sky, Energy Conversion and Management 44 (2003) 2455–2469. [17] M.A. Cucumo, V. Marinelli, G. Oliveti, Ingegneria Solare Principi ed Applicazioni, Pitagora Editrice Bologna, 1994. [18] M.A. Cucumo, A. De Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli, Correlations of global and diffuse solar luminous efficacy for all sky conditions and comparisons with experimental data of five localities, Renewable Energy 33 (09) (2008) 2036– 2047. [19] M.A. Cucumo, A. De Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli, Correlations of direct solar luminous efficacy for all sky, clear sky and intermediate sky conditions and comparisons with experimental data of five localities. Renewable Energy, (2008), doi:10.1016/ j.renene.2008.01.013. [20] A. Kasten, A new table and approximate formula for relative optical air mass, Archive Meteorological Geophysics Bioclimatology Ser. B 14 (1966) 206–223. [21] CIE 69-1987, Technical Report, Methods of Characterizing Illuminance Meters and Luminance Meters, 1987. [22] R.H. Dieck, Measurement uncertainty, in: Methods and Applications, ISA, 1997. [23] M.A. Cucumo, A. De Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli, Predicting diffuse illuminance on vertical surfaces at Arcavacata di Rende (Italy) for various types of sky, Building and Environment 43 (2008) 1678–1686.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Simplified correlations of global, direct and diffuse luminous efficacy on horizontal and vertical surfaces A. De Rosa, V. Ferraro, D. Kaliakatsos, V. Marinelli * Department of Mechanical Engineering, University of Calabria, Via P. Bucci, Cubo 44C, 87036 Arcavacata di Rende (CS), Italy
A R T I C L E I N F O
A B S T R A C T
Article history: Received 10 January 2008 Received in revised form 11 April 2008 Accepted 20 April 2008
A simple calculation method to calculate the mean hourly global, direct and diffuse illuminance on horizontal and vertical surfaces for all sky, clear sky, intermediate and overcast sky conditions, initially developed for Arcavacata di Rende (Italy), was compared with experimental data obtained at Geneva (Switzerland), Vaulx-en-Velin (France), Bratislava (Slovakia) and Osaka (Japan). The method is based on the use of constant luminous efficacies, adopted also for the vertical surfaces. In spite of its simplicity, the method furnishes reasonably good predictions, in comparison with a more complex reference calculation method and can be proposed as a simplified tool for design purposes. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Global Direct and diffuse illuminance Luminous efficacy Horizontal and vertical surfaces
1. Introduction The quantitative knowledge of solar illuminance inside rooms is very useful when aiming to save electrical energy in buildings. The starting datum for this calculation is, obviously, the natural incident illuminance on the outside surfaces of windows and this paper deals with this topic. For many years a network of instruments for measuring solar illuminance and irradiance has been in operation at the Mechanical Engineering Department of the University of Calabria, located in Arcavacata di Rende (CS), Italy (Lat. 398210 N, Long. 168130 E). This network is composed of five photometers to measure global illuminance on the horizontal plane and on four vertical planes exposed to the north, south, east and west and of a photometer mounted on a solar tracker to measure normal direct illuminance. The photometers for measuring global light are type FET-GV, and the photometer for measuring normal direct light is type FET L03 0U DX, supplied by PRC Krochmann of Berlin, while the solar tracker, type 2AP (two-axis positioner), was supplied by Kipp & Zonen of Delft (Holland). Five Kipp & Zonen CM 11-type pyranometers were also set up at the same site to measure global radiation on the horizontal plane and on the four vertical planes, and a Kipp & Zonen CH-1 NIP-type pyrheliometer to measure normal direct radiation was mounted on the solar tracker.
* Corresponding author. Tel.: +39 0984 494609; fax: +39 0984 494673. E-mail address: [email protected] (V. Marinelli). 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.04.018
The instantaneous experimental data are measured with a frequency of about 5 min, and the mean hourly values of illuminance and irradiance are then calculated. All data are subjected to the quality control recommended by CIE [1], applying some tests which eliminate irradiance and illuminance data that is too large in comparison with extraterrestrial values and the data which produce too low or too high luminous efficacies (ratios between illuminance and irradiance). Recently, an EKO sky scanner, model MS-321LR, able to measure the luminance and the radiance of the sky in the Tregenza 145 points, according to the indications of the standard CIE 108-1994 [1], was installed in the same Test Station. Computer codes [2,3] which evaluate the illuminance inside the rooms, can use, as input data, either the sky luminance of the piece of the sky viewed through the windows from the inside points, or the external natural illuminance of the windows, and this paper refers to this latter methods. In the literature it is possible to find many publications and models concerned with the calculation of global, direct and diffuse illuminance on the horizontal surface, and, to this purpose, the concept of luminous efficacy of the radiation is often used [4–11]. Instead, less papers on the subject of illuminance on vertical surfaces have been published, although the latter is of greater interest since the windows of buildings are placed vertically [12– 16] and particularly the knowledge of diffuse skylight entering the windows is very important, since the building rooms are mostly lit by diffuse light. To calculate the global and diffuse illuminance of a surface however oriented and inclined, the most widely used calculation
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
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method is the well-known Perez et al. model [6], and this model can be considered as the reference one with which to compare other new models. In this paper, an attempt is made to calculate the global, diffuse and direct illuminance, by using very simple correlations, based on the use of constant luminous efficacy of the radiation, extending the concept of luminous efficacy also to the vertical surfaces, for which usually it is not applied. This work was done within the Italian National Research Program PRIN 2005, entitled ‘‘Climate parameters, evaluation tools and technologies for natural and artificial luminous environment for visual comfort and energy saving’’. 2. Calculation methods of global, direct and diffuse illuminance on horizontal surfaces As is well known, the luminous efficacy of solar radiation is defined as the ratio of the illuminance produced by radiation to the radiation itself. Reference can be made to three luminous efficacies: those of global, beam and diffuse radiation [17]. The luminous efficacy of the global radiation Kg is defined as the ratio of the global illuminance on the horizontal surface Eo to the global irradiance Go on the same surface. Kg ¼
Eo Go
(1)
The luminous efficacy of the direct radiation Kb is defined as the ratio of the normal direct illuminance Ebn to the normal direct irradiance Gbn: Kb ¼
Ebn Gbn
(2)
The luminous efficacy of the diffuse radiation Kd is defined as the ratio of the diffuse illuminance on the horizontal surface Edo to the diffuse irradiance Gdo on the same surface.
Fig. 2. Normal direct illuminance Ebn as a function of the normal direct irradiance Gbn at Arcavacata di Rende.
diffuse irradiance gathered at Arcavacata di Rende in the same year. Diffuse illuminance on the horizontal plane was calculated by the relation: Edo ¼ Eo Ebn sin a
(4)
where a is the solar altitude angle, while diffuse irradiance on the horizontal plane was calculated by the relation: Gdo ¼ Go Gbn sin a
(5)
Fig. 1 shows the trend of the experimental mean hourly global illuminance as a function of the experimental mean hourly global irradiance gathered at Arcavacata di Rende in 2006. Fig. 2 shows the trend of the experimental mean hourly direct illuminance as a function of the experimental mean hourly direct irradiance gathered at Arcavacata di Rende also in 2006. Fig. 3 shows the trend of the experimental mean hourly diffuse illuminance as a function of the experimental mean hourly
Therefore, the directly obtained experimental data were Eo, Ebn, Go, and Gbn, while the quantities Edo and Gdo were calculated by relations (4) and (5). In the data analysis the values of illuminance and irradiance for solar altitudes lower than 68 were eliminated, owing to the presence of some obstacles around the Test Station, like hills, buildings, etc. The experimental apparatus used in Arcavacata, which include a sun-tracker with a pyreliometer and a photometer mounted on it, permits to obtain measurements of direct and diffuse irradiance and illuminance more accurate than the measurements obtained by instruments with shadow rings.
Fig. 1. Global illuminance as a function of global irradiance at Arcavacata di Rende.
Fig. 3. Diffuse illuminance as a function of diffuse irradiance at Arcavacata di Rende.
Kd ¼
Edo Gdo
(3)
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
where ai, bi, ci, di, are other 32 constants depending on the sky clearness index.
2.1. Authors’ calculation method Figs. 1–3 show an almost linear relation between illuminance and irradiance, and, consequently, by means of the minima square method, the following simplified correlations of global, beam and diffuse luminous efficacy for Arcavacata di Rende were obtained [18,19]: Eo Kg ¼ ¼ 110 lumen W Go
MBD ¼ 0:58%
RMSD ¼ 7:62%
(6)
Kb ¼
Ebn ¼ 102 lumen W G
MBD ¼ 0:68%
RMSD ¼ 17:84%
(7)
Kd ¼
Edo ¼ 123 lumen W Gdo
MBD ¼ 0:02%
RMSD ¼ 18:09%
(8)
In Eqs. (6)–(8) MBD is the percentage mean bias deviation, and RMSD is the root percentage mean square deviation between the calculated data and the experimental data, defined as: P ðV calc;i V meas;i Þ=V meas;i 100 (9) MBD ¼ N sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ½ðV calc;i V meas;i Þ=V meas;i 1002 RMSD ¼ N
(10)
where Vcalc is the calculated datum, Vmeas the measured datum and N the number of data. 2.2. The reference calculation method: Perez et al. model The method proposed by the authors was compared with the best method available at present, the Perez et al. method [6]. These authors correlate global luminous efficacy to a sky clearness index (e), to the atmospheric precipitable water content (w), to the solar zenith angle (z), and to the sky brightness index (D), by the correlation: K g ¼ ai þ bi w þ ci cos z þ di lnðDÞ
(11)
where ai, bi, ci, di, are constants depending on the sky clearness index, and are provided by the authors for eight types of sky, variable from very clear sky to overcast sky. In total in this model 32 constants are used, and, moreover, for the estimation of the parameter w the knowledge of air temperature and of air relative humidity is needed. The sky clearness index e is defined as:
e¼
Gdo þ ððGbo =sin aÞ=Gdo Þ þ 5:535 106 z3 1 þ 5:535 106 z3
The sky brightness index (D) is defined as G D ¼ m do Io
(12)
(13)
where m is the relative air mass, Gbo the direct irradiance on the horizontal plane and Io is the normal direct extraterrestrial irradiance). Usually m is calculated by the Kasten correlation [20]. Perez et al. correlate diffuse luminous efficacy [6] to the same parameters as above, by the correlation: K d ¼ ai þ bi w þ ci cos z þ di lnðDÞ
(14)
where ai, bi, ci, di, are other 32 constants depending on the sky clearness index. The Perez’s direct luminous efficacy [6] has instead the form K b ¼ ai þ bi w þ ci eð5:73z5Þ þ di D
1993
(15)
3. Comparisons with other experimental data on horizontal surfaces The predictions of simplified correlations (6)–(8), developed for Arcavacata di Rende and the reference Perez correlations, were compared not only with the experimental data measured in Arcavacata di Rende, but also with the mean hourly experimental data measured in other four localities, for a period of 1 year. The localities considered are: Geneva, Switzerland (Lat: 468200 N, Long: 68010 E), data of 1993 Vaulx-en-Velin, France (Lat: 458470 N, Long: 48560 E), data of 2005 Bratislavia, Slovakia (Lat: 488100 N, Long: 178050 E), data of 2005 Osaka, Japan (Lat: 348360 N, Long: 1358300 E), data of 2006 Before comparing the experimental data with the predictions of calculation models, the expected uncertainty of the luminous efficacy, due to the measurement errors of photometers and radiometers was estimated. The main error affecting the photometers is the deviation of the spectral responsivity of the instruments from the standard human eye photopic curve V(lambda): this mismatch is characterized by means of the parameter f10 , equal to the percentage average deviation in absolute value [21]. The photometers installed in Arcavacata di Rende present values of f10 close to 2%. A similar precision is furnished by all the photometers installed in the other localities. The photometers average cosine error f2 [21], for all photometers used, is about 1%. All broadband solar pyranometers used are secondary standard instruments and have 2% average total uncertainties. The pyrheliometers used at Arcavacata, Geneva and Osaka, are first class instruments and present 1% errors. In the other two localities, Vaulx-en-Velin and Bratislava, the direct irradiance is evaluated as difference between global and diffuse irradiance, the latter measured by a pyranometer provided with a shadow ring. For these localities, the average error is close to 2%. Since the luminous efficacy of solar radiation K is defined as the ratio of illuminance E to irradiance G, naming these variables x and y, whose absolute (not percentage) uncertainty are ux and uy, the combined uncertainty uF of the function K = F(x,y) can be obtained applying the formula [22]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 @F @F uF ¼ ðux Þ2 þ ðuy Þ2 @x @y
(16)
From Eq. (16) it emerges that the percentage uncertainty (uF/ F) 100 of the function K = x/y is: u F 100 ¼ F
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u 2 u y x 100 þ 100 x y
(17)
Inserting in Eq. (17) a total uncertainty in the illuminance measurement of 3% and a total uncertainty in the irradiance measurements of 2%, the expected uncertainty of the luminous efficacy is of 3.6%. It was considered interesting to evaluate the constant experimental global, direct and diffuse luminous efficacy not only in all sky conditions, but also under other three sky conditions: clear sky,
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
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Table 1 Experimental values of global luminous efficacy in different sky conditions
Arcavacata Geneva Vaulx-en-Velin Bratislava Osaka
Table 2 Experimental values of direct luminous efficacy in different sky conditions
All Sky
Clear sky
Intermediate sky
Overcast sky
110 111 107 108 115
110 110 106 105 110
110 110 106 106 113
122 122 118 116 136
Arcavacata Geneva Vaulx-en-Velin Bratislava Osaka
kt 0:65 0:2 kt < 0:65 kt < 0:2
Clear sky
Intermediate sky
102 93 97 105 99
104 100 100 101 107
102 88 94 108 95
Table 3 Experimental values of diffuse luminous efficacy in different sky conditions
intermediate sky and overcast sky, defined as [7]: clear sky intermediate sky overcast sky
All sky
(18)
being kt the clearness index, defined as the ratio of the global irradiance on the horizontal plane to the extraterrestrial irradiance on the horizontal plane. In Table 1 the values of the experimental global efficacy in all localities are reported. In Table 2 the values of the direct efficacy in all localities are reported. In Table 3 the values of the diffuse efficacy in all localities are reported. In Fig. 4, for the four types of sky, and for all localities, the ranges of percentage mean bias deviations MBD and the ranges of percentage root mean square deviations RMSD between the values of global and direct luminous efficacy calculated by the two methods and the experimental data are reported. In Model 1G the global efficacies obtained for Arcavacata are used, while in Model
Arcavacata Geneva Vaulx-en-Velin Bratislava Osaka
All sky
Clear sky
Intermediate sky
Overcast sky
123 128 125 114 120
125 140 132 116 111
123 122 124 112 120
122 122 118 114 136
1G-loc the local efficacies are used; in Model 1B the direct efficacies obtained for Arcavacata are used, whereas in Model 1Bloc the local efficacies are used. Fig. 4 indicates that, for all types of sky, all the models give acceptable predictions of global efficacy, the best models being Model 1G-loc and Model 1G; for the direct efficacy, the errors are larger than those for global efficacy, and the best models appears to be the 1B-loc, Perez and Model 1B being almost equivalent. In Fig. 5 the ranges of the percentage mean bias deviations MBD and the ranges of the percentage root mean square deviations
Fig. 4. Ranges of MBD and RMSD values between calculated and experimental global and direct luminous efficacy in different sky conditions for horizontal surfaces.
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
Fig. 5. Ranges of MBD and RMSD values between calculated and experimental diffuse luminous efficacy in different sky conditions for horizontal surfaces.
Fig. 6. Diffuse illuminance versus diffuse irradiance on vertical surfaces at Arcavacata di Rende.
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A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
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RMSD between calculated and experimental values of diffuse luminous efficacy are reported. Model 1D uses the Arcavacata efficacy for all localities, while Model 1D uses the local efficacies. Again for the prediction of diffuse luminous efficacy all the models give acceptable results, Model 1D-loc being the best one. 4. Calculation of diffuse and global illuminance on vertical surfaces To calculate the diffuse and global illuminance of a surface however oriented and inclined, the most widely used calculation method is the Perez et al. model [6], and this model can be again considered as the reference one with which to compare other new models. The luminous efficacy of the diffuse radiation Kdv on a vertical surface is defined as the ratio of the diffuse illuminance on the vertical surface Edv to the diffuse irradiance Gdv on the same surface: K dv ¼
Edv Gdv
(19)
The experimental diffuse illuminance on each vertical plane, can be obtained by the relation: Edv ¼ Ev Ebn cos #
(20)
where Ev is the experimental global illuminance of the vertical surface, Ebn is the experimental beam normal illuminance and W is the angle between the direction of the sun’s rays and the normal direction to the surface. Similarly, the experimental diffuse irradiance on each vertical plane, can be calculated by the relation: Gdv ¼ Gv Gbn cos #
(21)
where Gv is the experimental global irradiance of the vertical surface and Gbn is the experimental beam normal irradiance. The diffuse illuminance values Edv calculated by Eq. (20) in Arcavacata di Rende do not contain any ground reflection components since the measurement instrument of global illuminance Ev on the four vertical surfaces is provided with a cylindrical shield which intercepts the light reflected from the ground. So the measured values of Ev refer only to the direct and diffuse sky illuminance. Instead, the global irradiance Gv in Eq. (21) was purged of the ground reflection component using a ground reflection coefficient r = 0.15 suitable for Arcavacata di Rende. The luminous efficacy of the global radiation Kgv on a vertical surface is defined as the ratio of the global illuminance on the vertical surface Ev to the global irradiance Gv on the same surface: K gv ¼
Ev Gv
Fig. 7. Global Illuminance as a function of global irradiance for vertical surfaces at Arcavacata di Rende.
(22)
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001 Table 4 Experimental values of diffuse luminous efficacy on vertical surfaces in different sky conditions Arcavacata
Osaka
All days
North East South West
107 114 112 108
121 112 109 112
Clear days
North East South West
113 118 112 111
127 108 100 115
Intermediate days
North East South West
103 112 110 101
117 111 110 110
Overcast days
North East South West
109 114 114 112
123 119 115 121
4.1. Authors’ method As already stated above, the authors of the present paper propose the use of a constant value of the diffuse and global luminous efficacy for each vertical surface to calculate the illuminance of the surface. This method was developed for Arcavacata di Rende, by analysing the experimental data measured in a complete year [23]. Fig. 6 shows the trend of the experimental mean hourly diffuse illuminance as a function of the experimental mean hourly diffuse irradiance gathered at Arcavacata di Rende in 2006 for the four surfaces exposed to the north, east, south and east. The figure shows an almost linear relation between illuminance and irradiance, and, consequently, by means of the square minima
1997
method, simplified correlations of constant diffuse luminous efficacy on vertical surfaces for Arcavacata di Rende were obtained. These values, having being revised, prove to be a little different from those reported in the reference [23]. Fig. 7 shows the trend of the experimental mean hourly global illuminance as a function of the experimental mean hourly global irradiance gathered at Arcavacata di Rende in the same year. The figure shows again an almost linear relation between illuminance and irradiance, and, consequently, simplified correlations of constant global luminous efficacy on vertical surfaces for Arcavacata di Rende were obtained. Since the authors were able to access to the experimental data of illuminance and irradiance on vertical surfaces measured simultaneously in the course of 2006 in Osaka, also the data for this locality were analysed, obtaining the Osaka’s values of diffuse and global efficacy on vertical surfaces. Both the photometers and the pyranometers for the measurement of global illuminance and irradiance on the vertical surfaces used in the Osaka Test Station were provided with shields to eliminate the radiation reflected from the ground. According to Eqs. (19) and (22), the diffuse and global illuminances of a vertical surface can be obtained multiplying the surface irradiances by the values of the efficacies. If the diffuse and global irradiances on the surfaces are not experimentally known, they must be in some way calculated, for example, by a method again developed by Perez [6]. 4.2. Perez et al. model Perez et al. [6] proposed the use of a general calculation method of the global illuminance on a surface however orientated and inclined. In the method account is taken of the anisotropy of the diffuse light, interpreted as the sum of three parts, the circumsolar part, deriving from a region around the sun and striking the inclined surface with an angle of incidence equal to that of the
Fig. 8. Ranges of MBD and RMSD values between calculated and experimental data of diffuse illuminance on vertical surfaces in all sky and clear sky conditions.
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Fig. 9. Ranges of MBD and RMSD values between calculated and experimental data of diffuse illuminance on vertical surfaces in intermediate sky and overcast sky conditions.
direct light, an isotropic part evenly received from the rest of the sky, and a third part called brightness of the horizon, coming from a thin strip of sky adjacent to the horizon. 1 þ cos b a E ¼ K d Gdo ð1 F 1 Þ þ K d Gdo F 1 b 2 a (23) þ K d Gdo F 2 sin b þ K b Gbn sin a b where a ¼ maxð0; cos #Þ; b ¼ maxð0:087; cos zÞ The first term of Eq. (23) is the isotropic diffuse component, the second the circumsolar diffuse component, the third the component owing to the brightness of the horizon and the fourth the direct component. In Eq. (23), Kd is the Perez luminous efficacy of diffuse radiation on the horizontal plane, b is the inclination angle of the surface, the ratio a/b the tilt factor of the direct radiation, F1 the circumsolar brightening coefficient, F2 the horizon brightening coefficient and Kb is the Perez luminous efficacy of direct radiation. The diffuse luminous efficacy according to Perez, as well as the coefficients F1 and F2, are a function of four parameters [6]: the sky clearness index e, the atmospheric precipitable water content w, the solar zenith angle z, and the sky brightness index D, by means of several constants provided by the authors in a tabular form for the eight different types of sky. In Eq. (23), the parameters F1 and F2 have the form: F 1 ¼ f 11 þ f 12 D þ f 13 z
(24)
F 2 ¼ f 21 þ f 22 D þ f 23 z
(25)
The coefficients f11, f12, f13, f21, f22, f23 are furnished by Perez for each e bin [6]. If in Eq. (23) last term is cancelled, the diffuse illuminance on the surface is obtained.
For the application of Eq. (23), 112 constants for the calculation of global illuminance and 80 constants for the calculation of diffuse illuminance are needed. 5. Comparison with experimental data on vertical surfaces The method developed by the authors and the reference Perez method were compared with the experimental data of mean hourly diffuse illuminance on vertical surfaces exposed to the north, east, south and west, measured in Arcavacata, Osaka, Vaulxen-Velin and Geneva. In Table 4 the experimental values of diffuse luminous efficacy on vertical surfaces is reported, for Arcavacata and Osaka, in different sky conditions. Table 5 Experimental values of global luminous efficacy on vertical surfaces in different sky conditions Arcavacata
Osaka
All days
North East South West
110 115 112 113
120 113 110 112
Clear days
North East South West
117 115 113 122
125 112 108 117
Intermediate days
North East South West
103 113 109 105
117 111 109 107
Overcast days
North East South West
107 113 113 110
124 122 115 122
A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
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Fig. 10. Ranges of MBD and RMSD values between calculated and experimental data of global illuminance on vertical surfaces in all sky and clear sky conditions.
By comparing the values obtained in the two localities, it is possible to notice a maximum difference of about 13% between the luminous efficacies for all orientations. In Figs. 8 and 9 the ranges of MBD and RMSD values, for all sky conditions and all localities, among the predictions of five
calculation methods and the experimental data of diffuse illuminance are reported. The author’s calculation methods were called KA-1, KO-1, KA-2 and KO-2. In the KA-1 method Arcavacata’s diffuse efficacies and the experimental diffuse irradiances are used, in the KO-1 method Osaka’s efficacies and the experimental
Fig. 11. Ranges of MBD and RMSD values between calculated and experimental data of global illuminance on vertical surfaces in intermediate sky and overcast sky conditions.
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A. De Rosa et al. / Energy and Buildings 40 (2008) 1991–2001
irradiances are used, in the KA-2 method the Arcavacata efficacies and the irradiances calculated by the Perez method are used, in the KO-2 method the Osaka efficacies and the irradiances calculated by the Perez method are used, and in the Perez method the illuminance is calculated according to Eq. (23). Fig. 8 refers to all sky and clear sky conditions, while Fig. 9 refers to intermediate and overcast conditions. From these figures it is evident that generally, for all oriented surfaces, the best models are KA-1 and KO-1, with KA-1 superior. Since, generally, in most localities, the experimental diffuse irradiances on the vertical surfaces are not known, only methods KA-2 or KO-2 can be applied: from the figures appear that these methods furnish MBD and RMSD values better than those obtained by the Perez method. From these observations, it emerges that the calculation methods (KA-1, KO-2, KA-2 and KO-2) proposed by the authors, in spite of their simplicity, allow good predictions of diffuse illuminance on the vertical surfaces. In order to evaluate how much the errors of methods KA-2 and KO-2 depend on the error in the calculations of the diffuse irradiance on each surface by the Perez model, for Arcavacata and Osaka, the only localities of this work where the irradiances on the vertical surface were measured, the MBD and RMSD deviations between the calculated and the experimental data of diffuse irradiance were also calculated. From the results, not reported in this paper, it was evident that the errors in the diffuse irradiance were very close to the errors in the diffuse illuminance, their differences being within 3–4%. This means that most of the errors in calculating the illuminance by the methods KA-2 and KO-2 arise from the error in calculating the irradiance on the vertical planes, rather than from the error in the luminous efficacy. If a more accurate method than the Perez method is available in the future, also the illuminance values will be more accurate. In Table 5 the experimental values of global luminous efficacy for Arcavacata and Osaka are reported. In Figs. 10 and 11 the ranges of the percentage mean bias deviations MBD and the ranges of the percentage root mean square deviations RMSD between the calculation methods and the experimental data are reported. From the study of the two figures, it emerges that, generally, methods KA-1 and KO-1 are the best, while KA-2, KO-2 and Perez are almost equivalent. 6. Conclusions A simple calculation method to evaluate natural global, direct and diffuse illuminance on horizontal and vertical surfaces, consisting in multiplying a constant value of luminous efficacy for each surface by the experimental or calculated diffuse irradiance on the same surface, originally developed for Arcavacata di Rende (Italy), was compared with experimental data obtained in the course of a year in four localities of Japan, France, Slovakia and Switzerland. The method behaves well, furnishing good results, in spite of its simplicity, in all sky, clear, intermediate and overcast sky conditions, often better than the results obtained by a more complex method. More exactly, for the horizontal plane, the use of the constant global luminous efficacy obtained for Arcavacata in all sky conditions, predicts the luminous efficacy of the other four localities with MBD deviations between 4% and 4% and RMSD deviation between 5% and 9%. For clear days, the method furnishes MBD values in the range 0– 5% and RMSD values in the range 4–7%; for intermediate days, MBD values in the range 1% to 4% and RMSD values in the range 4–9%; for overcast days, MBD values in the range 10% to 5% and RMSD values in the range 8–12%.
The use of the constant direct luminous efficacy on the horizontal plane obtained for Arcavavata in all sky conditions, predicts the luminous efficacy of the other four localities with MBD deviations between 2% and 12% and RMSD deviation between 18% and 27%. For clear days, the method gives MBD values in the range 3% to 5% and RMSD values in the range 8–13%; for intermediate days, shows MBD values in the range 5% to 18% and RMSD values in the range 23–32%. The use of the constant diffuse luminous efficacy on the horizontal plane obtained for Arcavavata in all sky conditions, predicts the luminous efficacy of the other four localities with MBD deviations between 3% and 9% and RMSD deviation between 12% and 18%. For clear days, the model furnishes MBD values in the range 13% to 14% and RMSD values in the range 11–20%; for intermediate days, MBD values in the range 0–11% and RMSD values in the range 8–19%; for overcast days, MBD values in the range 10% to 5% and RMSD values in the range 8–13%. For the vertical surfaces, the global and diffuse irradiance on the surfaces are not generally measured, and their values are almost always calculated: the method proposed by the authors, for the estimation of the diffuse irradiance on the vertical surfaces, using the efficacies obtained for Arcavacata, furnishes, for all sky conditions, MBD values between 13% and +13% and RMSD between 15% and 37%, while the more complex reference method furnishes MBD between 33% and +22% and RMSD between 20% and 47%; for clear sky, the method gives MBD between 18% and +13% and RMSD between 5% and 37%, while the reference method furnishes MBD between 20% and +14% and RMSD between 9% and 35%; for overcast sky, the simplified method gives MBD between 10% and +23% and RMSD between 13% and 33%, while the reference method furnishes MBD between 3% and +30% and RMSD between 17% and 36%. The global illuminance on the vertical surfaces is predicted, by the constant efficacies of Arcavacata, for all sky conditions, with MBD between 6% and +14% and RMSD between 14% and 33%, while the reference method furnishes MBD between 1% and +14% and RMSD between 14% and 31%; in clear sky conditions, the authors method furnishes MBD between 18% and +13% and RMSD between 5% and 37%, while the reference method furnishes MBD between 20% and +14% and RMSD between 9% and 35%; for intermediate sky conditions MBD between 11% and +13% and RMSD between 14% and 34%, while the reference method, furnishes MBD between 1% and +14% and RMSD between 12% and 32%; for overcast sky conditions MBD between 14% and +18% and RMSD between 15% and 31%, while the reference method furnishes MBD between 2% and +26% and RMSD between 11% and 37%. Acknowledgements For having provided their experimental data, the authors wish to warmly thank the following: Dr. Prof. Dominique Dumortier, Ecole Nationale des Travaux Publics del’Etat (ENTPE), Vaulx-en-Velin, France, Dr. Prof. Pierre Ineichen, Centre Universitaire d’Etude des Proble`mes dell’Energie (CUEPE) University of Geneve, Switzerland, Dr. Prof. Stanislav Darula, Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia, Dr. Prof. Norio Igawa, Graduate School of Human Life Science, Osaka City University, Osaka, Japan. References [1] CIE 108-1994, Technical Report Guide to Recommended Practice of Daylight Measurement, Wien, 1994. [2] G. Ward, R. Shakespeare, Rendering with RADIANCE, the Art and Science of Lighting Visualization, Space and Light, California, 2003.
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