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Development of a meteorological illuminance model for daylight computations
Applied Energy, Vol. 59, No. 4, pp. 235±260, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S0306-2619(98)00008-7 0306-2619/98 $19.00+0.00
Development of a Meteorological Illuminance Model for Daylight Computations T. Muneer,* M. Gul and D. Kinghorn Napier University, Edinburgh, UK, EH10 5DT
ABSTRACT Building simulation programmes need detailed hour-by-hour weather data. In the absence of measured irradiation and illuminance data, validated meteorological radiation and illuminance models may be used. These models are primarily based on the estimation of solar-beam attenuation through the terrestrial atmosphere. Broadly speaking, there are two strands of such computations. One of these strands is based on sunshine, temperature and humidity data and takes into consideration the attenuation due to mixed gases (such as oxygen, nitrogen and carbon dioxide), water vapour, ozone and aerosols. The other procedure requires cloud-cover data to obtain the degree of attenuation of clear-sky beam irradiance due to clouds. The authors have extended the application of the above models to obtain hourly and sub-hourly values of solar illuminance, via an interface with a luminous ecacy model. An account of the physical basis of the presently-proposed models and their validation is presented herein. # 1998 Elsevier Science Ltd. All rights reserved
NOTATION ai ; bi ; ci ; di Cbeam DPT Eeb Eed Eeg Eeg;c Ees
Perez model coecients (dimensionless) (eqn (8)) Beam clearness index (dimensionless) ( Eeb =Ee ) Dew point temperature ( C) Beam normal irradiance (W mÿ2) Diuse horizontal irradiance (W mÿ2) Global horizontal irradiance (W mÿ2) Global horizontal irradiance under clear-sky conditions (W mÿ2) Beam normal irradiance (W mÿ2)
*Author for correspondence; e-mail:[email protected] 235
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Ee Evb Evd Evg KD KG Kt m N NI SF W z s g o r w s
Normal incidence extraterrestrial irradiance (W mÿ2) Beam normal illuminance (lx) Diuse horizontal illuminance (lx) Global horizontal illuminance (lx) Diuse luminous ecacy (lm Wÿ1) Global luminous ecacy (lm Wÿ1) Global clearness index (dimensionless) ( Eeg =Ee ) Air mass (dimensionless) Eighths of sky covered by cloud (octas) Nebulosity index (dimensionless) Hourly sunshine fraction (dimensionless) Atmospheric precipitable water content (cm H2O) Solar zenith angle (radians) Solar altitude angle ( ) Atmospheric brightness parameter (dimensionless) Transmittance due to mixed gases (dimensionless) Transmittance due to ozone (dimensionless) Transmittance due to Rayleigh scattering (dimensionless) Transmittance due to water vapour (dimensionless) Transmittance due to Mie scattering (dimensionless) Transmittance due to aerosol absorption (dimensionless) Transmittance due to aerosol scattering (dimensionless) INTRODUCTION
In today's energy-conscious world, research is being actively undertaken on improving the weather data sets for use in the building-services engineering sector. Indeed, design professionals continually face the challenge of meeting the ever tightening environmental constraints. Because lighting demand can account for up to 50% of a building's energy consumption, increased focus has been placed on this area of research with particular emphasis on the usage of natural daylight to supplement the lighting load supplied by arti®cial means. However, until recent developments, there has been a world-wide dearth of information regarding daylight data. In particular, in the United Kingdom, only seven sites were recording global horizontal illuminance until 1970 and, until as recently as 1992, no records of vertical illuminance were available for any location in the UK north of London. As a result, the Commission International de' Eclairage declared 1991 as the International Daylight Measurement Year (IDMY). This led to world-wide activity in this ®eld, known as the International Daylight Measurement Program (IDMP).
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Consequently, horizontal and vertical illuminance values have since been recorded on a continuous, sub-hourly, basis at ®ve sites in the UK ; namely Garston (North London), Sheeld, Manchester, Napier University (Edinburgh urban) and Heriot-Watt University (Edinburgh suburban) sites. This information was used as the foundation of a solar irradiance and illuminance database, compiled by the Energy in Buildings research group at Napier University.1 The database has been produced on a CD-ROM and is freely available from the authors. Using the information recorded for the UK, individual site-speci®c luminous ecacy models were derived. These were later compiled to form an average, nation-wide, luminous ecacy model for the UK.2 In the past, this methodology has been applied successfully to Japanese data.3 Luminous Ecacy Models (LEMs) require measured or computed horizontal global or diuse irradiance data to provide the corresponding illuminances. However, measured irradiance values are recorded at only 25 sites in the UK with a preponderance of these sites in Southern England.4 Cowley5 has shown that irradiance, and thus illuminance information, may be seriously impaired by interpolating data from neighbouring sites which are at a distance of 20 km or more. On the other hand, over 200 stations in the UK currently record simpler meteorological data such as dry- and wetbulb temperatures, sunshine fraction and cloud-cover. Therefore, using these data as the basis for solar irradiation prediction, two models have been developed by the present team. Firstly, the Meteorological Radiation Model (MRM) requires hourly synoptic information, and dry- and wet-bulb temperature and sunshine fraction. Such information is routinely reported by newspapers. Long-term validation of the MRM has been undertaken by the authors.6,7 A Cloud-cover Radiation Model (CRM) has been presently developed. This model is based on the data related to fractional area of the sky obscured by clouds. Validation of the procedures to determine global and diuse illuminance are reported herein. The procedure involved is shown schematically in Fig. 1. Solar irradiance values are determined via the MRM or CRM (depending on the hourly, or indeed sub-hourly, availability of input data) and are combined with luminous ecacy models2 to predict illuminance. Results are analysed graphically as well as statistically. This article will provide the lighting design engineer with a simple, yet comprehensive, method for predicting illuminance values at all locations in the UK where synoptic data are recorded and will therefore enable the production of a long-term dataset. Synthetic generation of solar irradiance and illuminance will become increasingly more important as evident by the call for such actions by professional bodies such as CIBSE and ASHRAE, who are seeking to provide such information for hundreds of locations across the globe.
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Fig. 1. Computation of illuminance from synoptic data
METEOROLOGICAL RADIATION MODEL MRM6,7 estimates the horizontal beam and diuse components from ground-based meteorological data, that is dry- and wet-bulb temperatures or relative humidity and hourly sunshine fraction. Such data are readily available world-wide. MRM is therefore an extremely useful tool for obtaining irradiation estimates where no such records are kept and also for ®lling-in data for those periods when the irradiation logging was inoperational. The model estimates the horizontal solar irradiance components (diuse, beam and global irradiance) on an hourly, daily or monthly averaged basis.
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The MRM for non-overcast conditions consists of a regression between hourly diuse to beam irradiance ratio (Eed =Eeb ) and beam clearness index (Cbeam Eeb =Ee ), Eed =Eeb 0:285211Cÿ1:00648 beam
1
where the beam irradiance is obtained from horizontal extraterrestrial radiation, Ee , attenuated with the hourly sunshine fraction (SF) for nonovercast conditions. Thus, Eeb SF:Ee r g o w
2
where w and are the respective transmittances for the Rayleigh and Mie scattering and g , o , and w the mixed-gases, ozone and water-vapour transmittances. The respective equations for these transmittances are described in Refs 6 and 7. Under an overcast sky, the direct radiation reaching the earth is nil. Therefore, based on the studies of Dave8 and Bird and Hulstrom,9 the corresponding diuse component has been modelled as Eeg Eed Ee g o w
0:5 1 ÿ r 0:84 1 ÿ s 1 ÿ m m1:02 1 ÿ m m1:02
3
Cloud-cover radiation model Cloud-cover observations are taken at many stations across the globe. It is desirable to investigate the relationship between cloudiness and the incoming solar-radiation. The term cloud-cover is de®ned as the fractional representation of the sky being obscured by clouds. The conventional unit of measure is the octa with a value of N 0 indicating clear-sky and N 8 an overcast condition. The dependence of radiation ¯ux on cloud amount has been previously investigated. In this respect, Kasten and Czeplak10 have derived a relationship between global irradiation, Eeg;c , under a cloudless sky and the solar elevation angle Eeg;c 910 sin s ÿ 30
4
The global irradiation, Eeg , attenuated with the cloud amount N is then obtained as " Eeg Eeg;c
3:4 # N 1 ÿ 0:75 8
5
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T. Muneer, M. Gul, D. Kinghorn
The global clearness index, a parameter often required for diuse irradiation estimation, is de®ned as the ratio of global to extraterrestrial irradiation. Thus Kt
Eeg Ee
6
Once Kt is known, the horizontal diuse irradiation may then calculated by using the relationship presented by Muneer and Saluja11 Evd A0 A1 Kt A2 K2t A3 K3t ; Kt > 0:2 Evg
7
otherwise Kt 0:98 for overcast conditions. LUMINOUS-EFFICACY MODELS There are an increasing number of luminous-ecacy models available to the lighting engineer. A selection of such models is summarised below. Reference 2 provides detailed evaluation of the models presently being discussed. Average value models Derived as a result of simultaneously recorded illuminance and irradiance data, average value models have been proposed by research teams throughout the world. Amongst the earliest are the works of Pleijel12 in Scandanavia, Blackwell13 at Kew, England, Dogniaux14 at Uccle, Belgium and Drummond15 at Pretoria, South Africa. Blackwell concluded that global ecacy varied between 105 and 128 lm Wÿ1 for average sky conditions. Although no diuse ecacy values were available at the time, combination of Blackwell's irradiance measurements with corresponding illuminance values for Kew outlined by McDermott and Gordon-Smith for nearby Teddington,16 led Hopkinson17 to propose a constant value of 125 lm Wÿ1 for KD . More recent research in this ®eld by Muneer and Angus18,19 has suggested all-sky, average global and diuse luminous ecacy values of 110 and 120 lm Wÿ1, respectively. Perez model The Perez model20 is an internationally tried and tested method of determining luminous ecacy. The governing equation for the Perez model is
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241
KG or KD ai bi W ci cos z di ln
8
Coecients ai , bi , ci and di are step-functions of global clearness index. The term in the Perez model represents sky brightness and may be found from eqn (9): Eed m= Ees
9
Atmospheric precipitable water-content, W, is found from eqn (10) W exp 0:07DPT ÿ 0:075
10
JOULE model This model has been used in the development of the European Solar Radiation Atlas.21 The sequential estimation of the three luminance ecacy components, KD , KB and KG is given in eqns (11)±(14). KD 144 ÿ 29 1 ÿ 055NI 1:22NI2 ÿ 1:68NI3 for s > 5
11
otherwise KD 120 lm Wÿ1. The nebulosity index, NI, required in eqn (11), is obtained via a step-wise computation, details of which are provided in Ref. 2. Beam luminous ecacy is obtained as follows. For 50 < s 60 : KB 103 0:2 s ÿ 50 For s 50 : KB 62:134 ÿ 0:75885 s 0:27749 2s ÿ 0:012108 3s 0:0002052 4s ÿ 1:2278E ÿ 06 5s
12 13
otherwise KB 105 lm Wÿ1. Global luminous ecacy is then found as the weighted average of the beam and diuse ecacies, viz., KG KB :Ees sin h KD :Eed =Eeg
14
Muneer±Kinghorn model Based on the earlier work of Delaunay22 and Muneer,3 Muneer and Kinghorn2 have proposed luminous ecacy models based solely on the variation of KG and KD against the global clearness index, Kt . Thus,
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T. Muneer, M. Gul, D. Kinghorn
KG 136:6 ÿ 74:541Kt 57:3421K2t
15
KD 130:2 ÿ 39:828Kt 49:9797K2t
16
It has been shown2 that the models presented in eqns (15) and (16) may be used to precisely compute values of global and diuse illuminances for all sites in the UK. These models (eqns (15) and (16)) are statistically proven to perform with a degree of accuracy on a par with JOULE and Perez luminous ecacy models and yet they are far less complex in structure. As such, eqns (15) and (16) have been used throughout this work. However, users may substitute the above equations with any of the previously mentioned LEMs, once the irradiance has been computed using the MRM or CRM procedures. RESULTS AND DISCUSSION As mentioned earlier in the introduction, the aim of this work is to present a coherent scheme for predicting global and diuse illuminances. The routine requires synoptic information such as hourly dry- and wet-bulb temperatures and sunshine fraction or cloud-cover data to obtain horizontal global and diuse irradiances. The computed irradiances are then used in conjunction with the respective luminous ecacy models to compute the respective illuminances. The current validation has been performed using data from three sites in the UK, i.e. Heriot-Watt University, Edinburgh (55.93 N, 3.30 W), Napier University, Edinburgh (55.95 N, 3.20 W) and Manchester (53.50 N, 2.25 W), and two sites in Japan, i.e. Chofu (35.65 N, 139.55 E) and Fukuoka (33.55 N, 130.48 E). In an ideal situation, illuminance and irradiance would be concurrently recorded at the same site. However, this was not the case with Edinburgh and Manchester data. For the UK sites, synoptic and cloud-cover information was obtained from the local Meteorological Oce sites, which were situated at the respective airports. Turnhouse, the location of Edinburgh airport is situated approximately 12 km from the Napier and 5 km from the Heriot-Watt sites. Likewise, Manchester's Ringway airport is situated 12 km from the city centre, where the irradiance and illuminance sensors were placed on the roof of a Manchester University building. To enable a study of microclimatological eects, synoptic data from Ringway have been used to compute irradiance. These values were also compared with concurrent measurements undertaken at Aughton, a Meteorological Oce site, which is 40 km from Ringway. Figure 2(a) and (b) respectively, show the plots of measured irradiance for Aughton and MRM based computations (using the Ringway data) against
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243
Fig. 2. Comparative plots for (a) Manchester-Aughton and (b) Manchester-Ringway data, 1992±94.
244
T. Muneer, M. Gul, D. Kinghorn
global irradiance recorded at Manchester University. Lower scatter is noticable in Fig. 2(b) which con®rms the ®ndings of Cowley,5 i.e. that the Ringway derived irradiances are much closer to the measured city centre data-set than those that were recorded at Aughton. MRM derived irradiance values have further been used in conjunction with the luminous ecacy model to obtain illuminances. An evaluation of this procedure may be seen in Fig. 3(a) and (b). There is a de®nite linear trend in both plots, though the scatter associated with global illuminance is much lower. Likewise, Fig. 4 shows the performance of the MRM-LEM computation procedure for Edinburgh sites. Once again a linear trend between calculated and measured illuminances is evident. At any given location, clear-sky radiation is associated with maximum sunshine and minimal cloud-cover and diuse irradiation. The extreme clearsky irradiation and illuminance may form the basis of simulations and is therefore an important factor in the design of buildings and plant sizing. An evaluation of the MRM-LEM link for clear-sky conditions is shown in Fig. 5 for a Japanese and a UK location. It has been shown previously that the MRM has the capability of computing clear-sky irradiation with an average error of under 9%.5 Figure 5 provides a qualitative assessment of the MRM and MRM-LEM, and reinforces the previous evaluation.5 Similar plots for other UK and Japanese locations were produced, each of which showed a similar performance. They were not reproduced for the sake of brevity. Computed values of global irradiation and illuminance, derived via the CRM for Manchester using cloud-cover data are depicted in Fig. 6(a) and(b), respectively. Figure 6(a) and(b) may, respectively, be compared with Figs 2(b) and 3(a) which show the scatter diagrams for the MRM for Manchester. A lower scatter seems to be associated with the MRM based procedure. Scatter plots for diuse illuminance are shown in Fig. 7. The degree of scatter in this case, when compared with the global illuminance plot, is signi®cantly greater. This is due to the fact that CRM-LEM diuse illuminance is a three-step algorithm, i.e. the sequential estimation of global and diuse irradiance (respectively using eqns (4), (5) and (7)) followed by diuse luminous ecacy using eqn (16). Figure 7 may also be viewed in contrast with Fig. 3(b) which shows a reduced scatter particularly for the lower illuminance band which is associated with thin-to-heavy overcast conditions. In this case, the MRM-LEM oers a two-step estimate for diuse illuminance (eqns (3) and (16)) rather than the three-step routine for CRM-LEM discussed above. Thus, the latter procedure may only be improved if further re®nements are made to the diuse irradiance model (eqn (17)). In this respect, some work has been undertaken for USA locations.23,24 However, no such validations have yet been undertaken for the data from UK sites.
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245
Fig. 3. Calculated and measured global (a) and diuse (b) illuminance for Manchester-Ringway data, 1992±94.
246
T. Muneer, M. Gul, D. Kinghorn
Fig. 4. MRM-LEM performance for Edinburgh, 1992±94.
A meteorological illuminance model for daylight computations
Fig. 5. LEM performance for clear-sky irradiance and illuminance.
247
248
T. Muneer, M. Gul, D. Kinghorn
Fig. 6. CRM-LEM performance for Manchester, 1992±94 data.
A meteorological illuminance model for daylight computations
Fig. 7. CRM-LEM performances for Edinburgh sites.
249
250
T. Muneer, M. Gul, D. Kinghorn
Earlier in this article, the proposed models' performances have been presented diagramatically by means of Figs 2±7. The level of data scatter provides the reader with a visual aid in evaluating the models. Determination of a model's validity, however, is more rigorously achieved through the use of performance indicators, such as mean bias error (mbe) and root mean square error (rmse). However, in view of the large amount of data involved, it was envisaged that these indicators may not provide a complete picture of the model performance. Therefore, additional methods for error analysis were used. In accordance with the techniques outlined,25±28 the dierence between computed and measured values (errors), were regressed against the corresponding computed irradiance or illuminance. As a result of this analysis, the slope and intercept of each regressed line were obtained. The more accurate a model, the closer the slope and intercept are to zero. Positive values of mbe and slope are indicative that the model will tend to over-predict. A higher value of rmse suggests a large scatter. Model inadequacies may also be brought to light if the intercept is seen to be large, which suggests a signi®cant deviation of the regressed line from the origin. The above statistical properties for each of the three UK and two Japanese sites are shown in Table 1, which provides an assessment of the validity of the MRM and CRM to compute global and diuse irradiances and illuminance. In the case of Japanese sites, the cloud data were unavailable and hence no comparison between MRM and CRM could be undertaken. Several interesting points may be picked up from Table 1 and these are listed below. . The MRM outperforms the CRM for global irradiance and illuminance estimations. . In the case of diuse irradiance and illuminance estimations, the MRM outperforms the CRM in three out of four cases. . There is a considerable improvement in accuracy of the above predictions if local synoptic data are used. This is evident by a two to three fold performance gain when the Manchester±Aughton and Manchester± Ringway error statistics are examined. This result therefore con®rms the ®ndings of Cowley.5 Table 2 provides a banded error analysis for three clearness-index bandwidths. These bandwidths, 0 < Kt 40:2, 0:2 < Kt 40:6 and 0:6 < Kt 41:0, respectively represent the overcast, intermediate- and clear-sky conditions. Comparison of model performances has been made easier with the depiction of the average of the absolute values of mbe and rmse. The following observations may be made. . The MRM outperforms the CRM for all cases of global illuminance computation.
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251
. For diuse illuminance computation, the MRM is on a par with the CRM for the overcast-sky, outperforms the CRM for the intermediatesky and is less eective under clear-skies. . The average errors are kept low by either of the two models. With the use of the MRM, the relative errors, associated with global illuminance errors, are around 15% for the overcast- and 5% for the intermediateand clear-sky regimes. The corresponding ®gures for the CRM are 19% for the overcast-, 10% for the intermediate- and 7% for clear-sky conditions. TABLE 1 Statistical error-analysis (a) UK data
MRM Irradiance (W mÿ2)
Global Napier Heriot-Watt Manchester± Aughton Manchester± Ringway Average of absolute values Diuse Napier Heriot-Watt Manchester± Aughton Manchester± Ringway Average of absolute values a
Illuminance (klux)
Illuminance (klux)
ÿ10
0.1
ÿ8
0.2
76
ÿ0.3
ÿ8
0.3
38
0.1
7
0.2
89
0.4
10
0.4
Intercept Slope Intercept Slope Intercept Slope Intercept Slope 81 ÿ0.4 10 ÿ0.4 78 ÿ0.3 ÿ10 0.3 ÿ95 0.0 ÿ11 0.5 ÿ115 0.6 ÿ13 0.5 ÿ43 0.3 n/a n/a ÿ64 0.3 n/a n/a ÿ24
0.0
ÿ7
0.3
61
ÿ0.2
ÿ6
0.3
61
0.2
9
0.4
79
0.4
10
0.4
Denotes dimensionless property. MRM Irradiance (W mÿ2)
Global Chofu Fukuoka Diuse Chofu Fukuoka
Irradiance (W mÿ2)
Intercept Slopea Intercept Slope Intercept Slope Intercept Slope 60 ÿ0.2 7 ÿ0.2 97 ÿ0.4 ÿ11 0.4 ÿ42 0.0 ÿ5 0.1 ÿ103 0.4 ÿ12 0.4 ÿ39 0.2 n/a n/a ÿ80 0.3 n/a n/a
(b) Japanese data
a
CRM
Illuminance (klux)
Intercept Slopea Intercept Slope ÿ57 0.0 ÿ7 0.1 ÿ74 ÿ0.1 ÿ4 0.2 Intercept Slope Intercept Slope ÿ93 0.0 ÿ13 0.3 ÿ153 0.1 ÿ9 0.5
Denotes dimensionless property.
252
T. Muneer, M. Gul, D. Kinghorn TABLE 2 Banded global and diuse illuminance error analysis
(a) UK data
Global (klux)
Kt 0±0.2
MRM Napier Heriot-Watt Manchester
mbe ÿ0.6 ÿ1.7 ÿ2.2
Diffuse (klux)
CRM
rmse 3.7 4.5 3.6
mbe ÿ3.3 ÿ1.8 ÿ0.7
MRM
rmse 10.6 10.2 7.4
mbe rmse mbe rmse 0.1 3.3 ÿ1.7 ÿ1.2 ÿ1.2 4.3 ÿ0.5 8.6 ÿ1.8 3.1 ÿ0.1 6.4
Average of absolute values
1.5
3.9
1.9
9.4
1.0
0.2±0.6
1.3 1.1 1.6
10.2 9.5 9.2
ÿ9.2 0.3 0.8
20.6 13.4 11.4
2.3 ÿ0.4 1.8
Napier Heriot-Watt Manchester
Average of absolute values
1.3
9.6
3.4
15.1
0.6±1.0
4.3 5.0 2.0
11.9 13.3 1.1
ÿ13.0 ÿ0.8 ÿ2.3
24.5 12.2 12.6
3.8
8.8
5.4
16.4
Napier Heriot-Watt Manchester
Average of absolute values (b) Japanese data Kt 0±0.2 0.2±0.6 0.6±1.0
1.5
3.6
0.8
5.4
8.4 ÿ3.5 11.9 9.1 1.5 10.8 7.0 2.6 7.5 8.2
2.5 10.1
3.0 8.2 ÿ1.1 7.6 ÿ6.3 17.0 ÿ6.9 18.1 12.0 6.2 0.4 6.5 7.1 10.5
2.8 10.7
MRM Global (klux)
Chofu Fukuoka Chofu Fukuoka Chofu Fukuoka
CRM
mbe ÿ1.6 0.8 2.6 2.6 5.2 5.6
rmse 12.0 2.6 12.2 10.2 10.9 11.6
Diffuse (klux) mbe ÿ0.9 0.4 4.6 3.4 13.0 12.6
rmse 11.0 2.6 10.8 9.8 16.0 18.5
It has been shown that the MRM and CRM are good estimators of hourly irradiation. There are merits and demerits associated with either of the two models. Collection of cloud-cover data requires no instrumentation and, hence, is easy to record for a large number of locations. On the other hand, a single spot-reading of the cloud amount is observed and this datum is obviously of inferior quality to that of a continuous trace registered by a sunshine recorder. Many weather stations have now switched from paperbased to electronic sunshine loggers and this practice has therefore removed the ambiguities associated with lower irradiation and moisture deposition on the card of the formerly mentioned instrument. Thus, quality sunshine data are increasingly being made available for many world-wide sites. Figures 2±7 enabled evaluation of the MRM and CRM based procedures using scatter diagrams. Quite often time-series plots are additionally used for model evaluation and these are shown in Figs 8±10. These plots show a continuous trace of measured and computed global and diuse illuminances
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Fig. 8. Variations in global (a) and diuse (b) illuminance derived from measured irradiances, Edinburgh-Napier April 1993 data.
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for a one-week period in April 1993. This particular time period was chosen as it is usually associated with temperate weather conditions and hence allows a test of the durability of MRM and CRM under varying conditions of sunshine and cloud. Computed global and diuse illuminances, shown in Fig. 8, have been derived via LEM using ®ve-minute averaged measured values of irradiance data from a post-sunrise to a pre-sunset period. There is a remarkable concordance between the computed and measured values. Figures 9 and 10 show plots similar to those in Fig. 8, although computed values of illuminance in this case are respectively obtained through MRMLEM and CRM-LEM interface. Either of the two ®gures display illuminances which were obtained from hourly records of sunshine, temperature and cloud-cover. As such, the plots do not reveal the sub-hourly dynamics of the illuminance trace. However, the ®gures do show an acceptable degree of concordance between the computed and measured values. Variations between the latter may partly be attributed to the fact that the synoptic input TABLE 3 Synoptic data and computed global irradiances, the 4 and the 8 April 1993 MRM derived Day
Measured
CRM derived
Hour
Global irradiance
SF
Global irradiance
Global irradiance
N
4 4 4 4 4 4 4 4 4 4 4 4
6 7 8 9 10 11 12 13 14 15 16 17
35.2 205.0 326.8 405.1 549.7 606.2 583.7 594.3 457.3 345.2 259.2 143.9
0 0.9 0.9 0.8 1 1 0.9 1 0.8 0.7 0.8 0.8
50.1 153.2 328.3 332.8 432.4 472.2 447.0 380.4 415.5 362.2 255.2 128.9
53.9 107.4 232.9 222.3 261.1 283.7 395.7 377.7 397.1 354.3 252.5 136.4
6 7 6 7 7 7 6 6 5 4 4 4
8 8 8 8 8 8 8 8 8 8 8 8
6 7 8 9 10 11 12 13 14 15 16 17
40.2 85.0 129.6 168.3 195.9 212.7 216.5 202.6 177.7 144.8 104.0 59.8
0 0 0 0 0 0 0 0 0 0 0 0
24.7 32.2 42.5 53.8 41.2 96.9 121.5 122.9 75.8 51.5 18.8 13.8
50.9 118.8 180.9 232.9 271.3 293.6 298.1 135.9 121.3 99.6 72.1 40.9
7 7 7 7 7 7 7 8 8 8 8 8
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255
Fig. 9. Variations in (a) global and (b) diuse illuminances derived from MRM irradiances, Edinburgh-Napier April 1993 data.
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T. Muneer, M. Gul, D. Kinghorn
Fig. 10. Variations in (a) global and (b) diuse illuminances derived from CRM irradiances, Edinburgh-Napier April 1993 data.
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data for both the MRM and CRM were recorded at a site 12 km from Napier University, where the illuminances were recorded. A closer examination of Figs 9 and 10 reveals that in certain instances, e.g. 8 April, either of the MRM and CRM based procedures fail badly. Further, the MRM seems to generate unacceptably high illuminances around noon for 4 April. Table 3 shows the relevant synoptic information for the two days under discussion. Measured irradiance and cloud data for 4 April suggest an almost complete and thin overcast sky, although an unbroken spell of sunshine was recorded for hours 10 and 11. There is a strong possibility of an ambiguity among the irradiation, cloud and sunshine data. As mentioned above, better equipment for sunshine records are increasingly being used and this action may alleviate the kind of problem presently under discussion. Data for 8 April quite clearly indicates an overcast day. The cloud and sunshine log, however, cannot dierentiate between a thin-cloud and a heavy overcast sky . When the sunshine-and-cloud record suggest an overcast sky, MRM and CRM provide irradiance estimates for an ``average'' overcast sky. Further improvements to this part of the model were attempted using visibility and cloud-type data without any signi®cant accuracy gains. CONCLUSIONS Solar irradiance and illuminance models which use commonly observed weather data were presented. Irradiance may be obtained from the Meteorological Radiation Model (MRM), which is based on sunshine and temperature data, or Cloud-cover Radiation Model (CRM) which uses visual observations of the sky cover. Further, it was shown that the above models may be linked with previously developed Luminous Ecacy Models (LEM) to provide the daylight illuminance. Graphical and statistical evaluations of the above procedures were undertaken using data from three UK and two Japanese locations. The statistical evaluation was based on regressions being respectively performed between the errors and the dependent variables. Further, the banded mbe and rmse were obtained for the overcast-, intermediate- and clear-sky regimes. It was noted that in all cases the global irradiance and illuminance were better estimated with the MRM. For diuse illuminance computation, the MRM is on a par with the CRM for the overcast-sky, out performs the CRM for the intermediate-sky and is less eective under clear-skies. The average errors are kept low by either of the two models. With the use of the MRM, the relative errors, associated with global illuminance errors, are around 15% for the overcast- and 5% for the intermediate- and clear-sky regimes. The corresponding ®gures for the CRM are 19% for the overcast-,
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10% for the intermediate- and 7% for clear-sky conditions. Both the MRM and CRM have therefore demonstrated their capabilities to model the solar irradiance and illuminance climate for UK and Japan with almost equal eectiveness. The foregoing comparison of the two models has revealed that the MRM is the better of the two models. This may be due to the fact that the input parameters for the MRM are more rigorously recorded, whereas cloud-cover information is often based on visual estimates. The continuous sunshine trace through the hour, obviously provides much more detailed information than a spot reading of the cloud-cover. Haurwitz29 has shown that a much stronger correlation exists between irradiation and sunshine than between sunshine and cloudiness. According to Bennet,30 sunshine explains 70 to 85% of the irradiation variance. Cloud-cover, on the other hand, seldom explains more than 70% and frequently less than 50% of the irradiation variance. This study con®rms the above cited performance and recommends the use of sunshine-based irradiation models if the required data are available. It was also pointed out that the quality of sunshine records may be further improved with the use of electronic loggers. Replacement of the existing Campbell±Stokes recorders with the latterly mentioned device has been recommended to improve the quality of the sunshine data and also, thus, the performance of the MRM. ACKNOWLEDGEMENTS The authors wish to extend their thanks to the project's funding body, the UK Engineering and Physical Science Research Council. REFERENCES 1. Muneer, T. and Kinghorn, D., Solar Irradiation and Daylight Data for the United Kingdom and Japan (with Compact Disk). Napier University, Edinburgh, 1996. 2. Muneer, T. and Kinghorn, D., Improved methods for the luminous ecacy of solar irradiance. LR&T, 1997, 29(4), 185±191. 3. Muneer, T., Solar irradiance and illuminance models for Japan II: luminous ecacies. LR&T, 1995, 27(4), 223±230. 4. Muneer, T., Availability of solar irradiation for the United Kingdom. BSER&T, 1989, 10(2), 75±80. 5. Cowley, J. P., The distribution in Great Britain of global solar radiation on a horizontal surface. Meteorological Magazine, 1978, 107, 357±373. 6. Muneer, T., Gul, I., Kambezidis, H. and Allwinkle, S., A simple meteorological radiation model. Proc. Joint CIBSE/ASHRAE Conference Harrogate, 1996, 271±279.
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7. Muneer, T., Gul, M. and Kambezedis, H., Long-term evaluation of a meteorological solar radiation model against UK data. Energy Conversion and Management, 1998, 38(3/4), 303±317. 8. Dave, J. V., Extensive data sets of the diuse radiation in realistic atmospheric models with aerosols and common absorbing gases. Solar Energy, 1979, 21, 361±369. 9. Bird, R. E and Hulstrom, R. L., A simpli®ed clear-sky model for the direct and diuse insolation on horizontal surfaces. US-SERI Technical Report TR-642761, Golden, CO, 1981. 10. Kasten, F. and Czeplak, G., Solar and terrestrial radiation dependent on the amount and type of cloud cover. Solar Energy, 1979, 24, 177±189. 11. Muneer, T. and Saluja, G. S., Correlation between hourly diuse and global radiation for the United Kingdom. Building Services Engineering Research Technology, 1986, 7, 37±43. 12. Pleijel, G., The computation of natural radiation in architecture and town planning. Meddelande Bull., Statens Namnd for Byggnadsforskning, Stockholm, 1954, 25, 30. 13. Blackwell, M. J., Five-years continuous recordings of total and diuse solar radiation at Kew Observatory. Met. Res. Publication 895, Met. Oce, London, 1954. 14. Dogniaux, R., Donnees Meteorologiques concernant l'Ensoleillement et l'Eclairage Naturel. Cah. Cent. Sci. Batim., 1960, 44, 24. 15. Drummond, A. J., Notes on the measurement of natural illumination II. Daylight and skylight at Pretoria: The luminous ecacy of daylight. Architectural Meteorology Vienna, Series B, 1958, 9, 149. 16. McDermott, L. H. and Gordon-Smith, G. W., Daylight illumination recorded at Teddington. Proc. Build. Res. Congr., Division 3, Part III, vol. 156, 1940, 1951. 17. Hopkinson, R. G., Petherbridge, P. and Longmore, J., Daylighting. Heinemann, London, 1966. 18. Muneer, T. and Angus, R. C., Daylight illuminance models for the United Kingdom. LR&T, 1993, 25(3), 113±123. 19. Muneer, T. and Angus R. C., , Luminous ecacy: evaluation of models for the United Kingdom. LR&T, 1995, 27(2), 71±77. 20. Perez, R., Ineichen, P. and Seals, R., Modelling daylight availability and irradiance components from direct and global irradiance. Solar Energy, 1990, 44, 271Ð289. 21. Palz, W. and Grief, J., (eds). CEC European Solar Radiation Atlas. Springer± Verlag, Berlin, 1996. 22. Delaunay, J. J., Development and performance assessment of luminous ecacy models. Internal Report. Fraunhofer Institute for Solar Energy Systems, Freiburg, Germany, 1995. 23. Maxwell, E. L., A quasi-physical model for converting hourly global horizontal to direct normal insolations. Report SERI/TR-215-3087, Solar Energy Research Institute, Golden, CO, 1987. 24. Reindl, D. T., Beckman, W. A. and Due, J. A., Diuse fraction correlations. Solar Energy, 1990, 45(1), 1±7. 25. A®®, A. A. and Azen, S. P., Statistical AnalysisÐA Computer Oriented Approach. Academic Press, London, 1979. 26. Draper, N. R. and Smith, H., Applied Regression Analysis. John Wiley & Sons, New York, 1981.
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27. Montgomery, D. C. and Peck, E. A., Introduction to Linear Regression Analysis. John Wiley & Sons, New York, 1982. 28. Hamilton, L. C., Regression with Graphics. Duxbury Press, Belmont, CA, 1992. 29. Haurwitz, B., Insolation in relation to cloud type. Journal of Meteorology, 1948, 5, 110±113. 30. Bennet, I., Correlation of daily insolation with daily total sky-cover, opaque sky-cover and percentage of possible sunshine. Solar Energy, 1969, 12, 391±393.
Development of a Meteorological Illuminance Model for Daylight Computations T. Muneer,* M. Gul and D. Kinghorn Napier University, Edinburgh, UK, EH10 5DT
ABSTRACT Building simulation programmes need detailed hour-by-hour weather data. In the absence of measured irradiation and illuminance data, validated meteorological radiation and illuminance models may be used. These models are primarily based on the estimation of solar-beam attenuation through the terrestrial atmosphere. Broadly speaking, there are two strands of such computations. One of these strands is based on sunshine, temperature and humidity data and takes into consideration the attenuation due to mixed gases (such as oxygen, nitrogen and carbon dioxide), water vapour, ozone and aerosols. The other procedure requires cloud-cover data to obtain the degree of attenuation of clear-sky beam irradiance due to clouds. The authors have extended the application of the above models to obtain hourly and sub-hourly values of solar illuminance, via an interface with a luminous ecacy model. An account of the physical basis of the presently-proposed models and their validation is presented herein. # 1998 Elsevier Science Ltd. All rights reserved
NOTATION ai ; bi ; ci ; di Cbeam DPT Eeb Eed Eeg Eeg;c Ees
Perez model coecients (dimensionless) (eqn (8)) Beam clearness index (dimensionless) ( Eeb =Ee ) Dew point temperature ( C) Beam normal irradiance (W mÿ2) Diuse horizontal irradiance (W mÿ2) Global horizontal irradiance (W mÿ2) Global horizontal irradiance under clear-sky conditions (W mÿ2) Beam normal irradiance (W mÿ2)
*Author for correspondence; e-mail:[email protected] 235
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T. Muneer, M. Gul, D. Kinghorn
Ee Evb Evd Evg KD KG Kt m N NI SF W z s g o r w s
Normal incidence extraterrestrial irradiance (W mÿ2) Beam normal illuminance (lx) Diuse horizontal illuminance (lx) Global horizontal illuminance (lx) Diuse luminous ecacy (lm Wÿ1) Global luminous ecacy (lm Wÿ1) Global clearness index (dimensionless) ( Eeg =Ee ) Air mass (dimensionless) Eighths of sky covered by cloud (octas) Nebulosity index (dimensionless) Hourly sunshine fraction (dimensionless) Atmospheric precipitable water content (cm H2O) Solar zenith angle (radians) Solar altitude angle ( ) Atmospheric brightness parameter (dimensionless) Transmittance due to mixed gases (dimensionless) Transmittance due to ozone (dimensionless) Transmittance due to Rayleigh scattering (dimensionless) Transmittance due to water vapour (dimensionless) Transmittance due to Mie scattering (dimensionless) Transmittance due to aerosol absorption (dimensionless) Transmittance due to aerosol scattering (dimensionless) INTRODUCTION
In today's energy-conscious world, research is being actively undertaken on improving the weather data sets for use in the building-services engineering sector. Indeed, design professionals continually face the challenge of meeting the ever tightening environmental constraints. Because lighting demand can account for up to 50% of a building's energy consumption, increased focus has been placed on this area of research with particular emphasis on the usage of natural daylight to supplement the lighting load supplied by arti®cial means. However, until recent developments, there has been a world-wide dearth of information regarding daylight data. In particular, in the United Kingdom, only seven sites were recording global horizontal illuminance until 1970 and, until as recently as 1992, no records of vertical illuminance were available for any location in the UK north of London. As a result, the Commission International de' Eclairage declared 1991 as the International Daylight Measurement Year (IDMY). This led to world-wide activity in this ®eld, known as the International Daylight Measurement Program (IDMP).
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Consequently, horizontal and vertical illuminance values have since been recorded on a continuous, sub-hourly, basis at ®ve sites in the UK ; namely Garston (North London), Sheeld, Manchester, Napier University (Edinburgh urban) and Heriot-Watt University (Edinburgh suburban) sites. This information was used as the foundation of a solar irradiance and illuminance database, compiled by the Energy in Buildings research group at Napier University.1 The database has been produced on a CD-ROM and is freely available from the authors. Using the information recorded for the UK, individual site-speci®c luminous ecacy models were derived. These were later compiled to form an average, nation-wide, luminous ecacy model for the UK.2 In the past, this methodology has been applied successfully to Japanese data.3 Luminous Ecacy Models (LEMs) require measured or computed horizontal global or diuse irradiance data to provide the corresponding illuminances. However, measured irradiance values are recorded at only 25 sites in the UK with a preponderance of these sites in Southern England.4 Cowley5 has shown that irradiance, and thus illuminance information, may be seriously impaired by interpolating data from neighbouring sites which are at a distance of 20 km or more. On the other hand, over 200 stations in the UK currently record simpler meteorological data such as dry- and wetbulb temperatures, sunshine fraction and cloud-cover. Therefore, using these data as the basis for solar irradiation prediction, two models have been developed by the present team. Firstly, the Meteorological Radiation Model (MRM) requires hourly synoptic information, and dry- and wet-bulb temperature and sunshine fraction. Such information is routinely reported by newspapers. Long-term validation of the MRM has been undertaken by the authors.6,7 A Cloud-cover Radiation Model (CRM) has been presently developed. This model is based on the data related to fractional area of the sky obscured by clouds. Validation of the procedures to determine global and diuse illuminance are reported herein. The procedure involved is shown schematically in Fig. 1. Solar irradiance values are determined via the MRM or CRM (depending on the hourly, or indeed sub-hourly, availability of input data) and are combined with luminous ecacy models2 to predict illuminance. Results are analysed graphically as well as statistically. This article will provide the lighting design engineer with a simple, yet comprehensive, method for predicting illuminance values at all locations in the UK where synoptic data are recorded and will therefore enable the production of a long-term dataset. Synthetic generation of solar irradiance and illuminance will become increasingly more important as evident by the call for such actions by professional bodies such as CIBSE and ASHRAE, who are seeking to provide such information for hundreds of locations across the globe.
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Fig. 1. Computation of illuminance from synoptic data
METEOROLOGICAL RADIATION MODEL MRM6,7 estimates the horizontal beam and diuse components from ground-based meteorological data, that is dry- and wet-bulb temperatures or relative humidity and hourly sunshine fraction. Such data are readily available world-wide. MRM is therefore an extremely useful tool for obtaining irradiation estimates where no such records are kept and also for ®lling-in data for those periods when the irradiation logging was inoperational. The model estimates the horizontal solar irradiance components (diuse, beam and global irradiance) on an hourly, daily or monthly averaged basis.
A meteorological illuminance model for daylight computations
239
The MRM for non-overcast conditions consists of a regression between hourly diuse to beam irradiance ratio (Eed =Eeb ) and beam clearness index (Cbeam Eeb =Ee ), Eed =Eeb 0:285211Cÿ1:00648 beam
1
where the beam irradiance is obtained from horizontal extraterrestrial radiation, Ee , attenuated with the hourly sunshine fraction (SF) for nonovercast conditions. Thus, Eeb SF:Ee r g o w
2
where w and are the respective transmittances for the Rayleigh and Mie scattering and g , o , and w the mixed-gases, ozone and water-vapour transmittances. The respective equations for these transmittances are described in Refs 6 and 7. Under an overcast sky, the direct radiation reaching the earth is nil. Therefore, based on the studies of Dave8 and Bird and Hulstrom,9 the corresponding diuse component has been modelled as Eeg Eed Ee g o w
0:5 1 ÿ r 0:84 1 ÿ s 1 ÿ m m1:02 1 ÿ m m1:02
3
Cloud-cover radiation model Cloud-cover observations are taken at many stations across the globe. It is desirable to investigate the relationship between cloudiness and the incoming solar-radiation. The term cloud-cover is de®ned as the fractional representation of the sky being obscured by clouds. The conventional unit of measure is the octa with a value of N 0 indicating clear-sky and N 8 an overcast condition. The dependence of radiation ¯ux on cloud amount has been previously investigated. In this respect, Kasten and Czeplak10 have derived a relationship between global irradiation, Eeg;c , under a cloudless sky and the solar elevation angle Eeg;c 910 sin s ÿ 30
4
The global irradiation, Eeg , attenuated with the cloud amount N is then obtained as " Eeg Eeg;c
3:4 # N 1 ÿ 0:75 8
5
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T. Muneer, M. Gul, D. Kinghorn
The global clearness index, a parameter often required for diuse irradiation estimation, is de®ned as the ratio of global to extraterrestrial irradiation. Thus Kt
Eeg Ee
6
Once Kt is known, the horizontal diuse irradiation may then calculated by using the relationship presented by Muneer and Saluja11 Evd A0 A1 Kt A2 K2t A3 K3t ; Kt > 0:2 Evg
7
otherwise Kt 0:98 for overcast conditions. LUMINOUS-EFFICACY MODELS There are an increasing number of luminous-ecacy models available to the lighting engineer. A selection of such models is summarised below. Reference 2 provides detailed evaluation of the models presently being discussed. Average value models Derived as a result of simultaneously recorded illuminance and irradiance data, average value models have been proposed by research teams throughout the world. Amongst the earliest are the works of Pleijel12 in Scandanavia, Blackwell13 at Kew, England, Dogniaux14 at Uccle, Belgium and Drummond15 at Pretoria, South Africa. Blackwell concluded that global ecacy varied between 105 and 128 lm Wÿ1 for average sky conditions. Although no diuse ecacy values were available at the time, combination of Blackwell's irradiance measurements with corresponding illuminance values for Kew outlined by McDermott and Gordon-Smith for nearby Teddington,16 led Hopkinson17 to propose a constant value of 125 lm Wÿ1 for KD . More recent research in this ®eld by Muneer and Angus18,19 has suggested all-sky, average global and diuse luminous ecacy values of 110 and 120 lm Wÿ1, respectively. Perez model The Perez model20 is an internationally tried and tested method of determining luminous ecacy. The governing equation for the Perez model is
A meteorological illuminance model for daylight computations
241
KG or KD ai bi W ci cos z di ln
8
Coecients ai , bi , ci and di are step-functions of global clearness index. The term in the Perez model represents sky brightness and may be found from eqn (9): Eed m= Ees
9
Atmospheric precipitable water-content, W, is found from eqn (10) W exp 0:07DPT ÿ 0:075
10
JOULE model This model has been used in the development of the European Solar Radiation Atlas.21 The sequential estimation of the three luminance ecacy components, KD , KB and KG is given in eqns (11)±(14). KD 144 ÿ 29 1 ÿ 055NI 1:22NI2 ÿ 1:68NI3 for s > 5
11
otherwise KD 120 lm Wÿ1. The nebulosity index, NI, required in eqn (11), is obtained via a step-wise computation, details of which are provided in Ref. 2. Beam luminous ecacy is obtained as follows. For 50 < s 60 : KB 103 0:2 s ÿ 50 For s 50 : KB 62:134 ÿ 0:75885 s 0:27749 2s ÿ 0:012108 3s 0:0002052 4s ÿ 1:2278E ÿ 06 5s
12 13
otherwise KB 105 lm Wÿ1. Global luminous ecacy is then found as the weighted average of the beam and diuse ecacies, viz., KG KB :Ees sin h KD :Eed =Eeg
14
Muneer±Kinghorn model Based on the earlier work of Delaunay22 and Muneer,3 Muneer and Kinghorn2 have proposed luminous ecacy models based solely on the variation of KG and KD against the global clearness index, Kt . Thus,
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T. Muneer, M. Gul, D. Kinghorn
KG 136:6 ÿ 74:541Kt 57:3421K2t
15
KD 130:2 ÿ 39:828Kt 49:9797K2t
16
It has been shown2 that the models presented in eqns (15) and (16) may be used to precisely compute values of global and diuse illuminances for all sites in the UK. These models (eqns (15) and (16)) are statistically proven to perform with a degree of accuracy on a par with JOULE and Perez luminous ecacy models and yet they are far less complex in structure. As such, eqns (15) and (16) have been used throughout this work. However, users may substitute the above equations with any of the previously mentioned LEMs, once the irradiance has been computed using the MRM or CRM procedures. RESULTS AND DISCUSSION As mentioned earlier in the introduction, the aim of this work is to present a coherent scheme for predicting global and diuse illuminances. The routine requires synoptic information such as hourly dry- and wet-bulb temperatures and sunshine fraction or cloud-cover data to obtain horizontal global and diuse irradiances. The computed irradiances are then used in conjunction with the respective luminous ecacy models to compute the respective illuminances. The current validation has been performed using data from three sites in the UK, i.e. Heriot-Watt University, Edinburgh (55.93 N, 3.30 W), Napier University, Edinburgh (55.95 N, 3.20 W) and Manchester (53.50 N, 2.25 W), and two sites in Japan, i.e. Chofu (35.65 N, 139.55 E) and Fukuoka (33.55 N, 130.48 E). In an ideal situation, illuminance and irradiance would be concurrently recorded at the same site. However, this was not the case with Edinburgh and Manchester data. For the UK sites, synoptic and cloud-cover information was obtained from the local Meteorological Oce sites, which were situated at the respective airports. Turnhouse, the location of Edinburgh airport is situated approximately 12 km from the Napier and 5 km from the Heriot-Watt sites. Likewise, Manchester's Ringway airport is situated 12 km from the city centre, where the irradiance and illuminance sensors were placed on the roof of a Manchester University building. To enable a study of microclimatological eects, synoptic data from Ringway have been used to compute irradiance. These values were also compared with concurrent measurements undertaken at Aughton, a Meteorological Oce site, which is 40 km from Ringway. Figure 2(a) and (b) respectively, show the plots of measured irradiance for Aughton and MRM based computations (using the Ringway data) against
A meteorological illuminance model for daylight computations
243
Fig. 2. Comparative plots for (a) Manchester-Aughton and (b) Manchester-Ringway data, 1992±94.
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global irradiance recorded at Manchester University. Lower scatter is noticable in Fig. 2(b) which con®rms the ®ndings of Cowley,5 i.e. that the Ringway derived irradiances are much closer to the measured city centre data-set than those that were recorded at Aughton. MRM derived irradiance values have further been used in conjunction with the luminous ecacy model to obtain illuminances. An evaluation of this procedure may be seen in Fig. 3(a) and (b). There is a de®nite linear trend in both plots, though the scatter associated with global illuminance is much lower. Likewise, Fig. 4 shows the performance of the MRM-LEM computation procedure for Edinburgh sites. Once again a linear trend between calculated and measured illuminances is evident. At any given location, clear-sky radiation is associated with maximum sunshine and minimal cloud-cover and diuse irradiation. The extreme clearsky irradiation and illuminance may form the basis of simulations and is therefore an important factor in the design of buildings and plant sizing. An evaluation of the MRM-LEM link for clear-sky conditions is shown in Fig. 5 for a Japanese and a UK location. It has been shown previously that the MRM has the capability of computing clear-sky irradiation with an average error of under 9%.5 Figure 5 provides a qualitative assessment of the MRM and MRM-LEM, and reinforces the previous evaluation.5 Similar plots for other UK and Japanese locations were produced, each of which showed a similar performance. They were not reproduced for the sake of brevity. Computed values of global irradiation and illuminance, derived via the CRM for Manchester using cloud-cover data are depicted in Fig. 6(a) and(b), respectively. Figure 6(a) and(b) may, respectively, be compared with Figs 2(b) and 3(a) which show the scatter diagrams for the MRM for Manchester. A lower scatter seems to be associated with the MRM based procedure. Scatter plots for diuse illuminance are shown in Fig. 7. The degree of scatter in this case, when compared with the global illuminance plot, is signi®cantly greater. This is due to the fact that CRM-LEM diuse illuminance is a three-step algorithm, i.e. the sequential estimation of global and diuse irradiance (respectively using eqns (4), (5) and (7)) followed by diuse luminous ecacy using eqn (16). Figure 7 may also be viewed in contrast with Fig. 3(b) which shows a reduced scatter particularly for the lower illuminance band which is associated with thin-to-heavy overcast conditions. In this case, the MRM-LEM oers a two-step estimate for diuse illuminance (eqns (3) and (16)) rather than the three-step routine for CRM-LEM discussed above. Thus, the latter procedure may only be improved if further re®nements are made to the diuse irradiance model (eqn (17)). In this respect, some work has been undertaken for USA locations.23,24 However, no such validations have yet been undertaken for the data from UK sites.
A meteorological illuminance model for daylight computations
245
Fig. 3. Calculated and measured global (a) and diuse (b) illuminance for Manchester-Ringway data, 1992±94.
246
T. Muneer, M. Gul, D. Kinghorn
Fig. 4. MRM-LEM performance for Edinburgh, 1992±94.
A meteorological illuminance model for daylight computations
Fig. 5. LEM performance for clear-sky irradiance and illuminance.
247
248
T. Muneer, M. Gul, D. Kinghorn
Fig. 6. CRM-LEM performance for Manchester, 1992±94 data.
A meteorological illuminance model for daylight computations
Fig. 7. CRM-LEM performances for Edinburgh sites.
249
250
T. Muneer, M. Gul, D. Kinghorn
Earlier in this article, the proposed models' performances have been presented diagramatically by means of Figs 2±7. The level of data scatter provides the reader with a visual aid in evaluating the models. Determination of a model's validity, however, is more rigorously achieved through the use of performance indicators, such as mean bias error (mbe) and root mean square error (rmse). However, in view of the large amount of data involved, it was envisaged that these indicators may not provide a complete picture of the model performance. Therefore, additional methods for error analysis were used. In accordance with the techniques outlined,25±28 the dierence between computed and measured values (errors), were regressed against the corresponding computed irradiance or illuminance. As a result of this analysis, the slope and intercept of each regressed line were obtained. The more accurate a model, the closer the slope and intercept are to zero. Positive values of mbe and slope are indicative that the model will tend to over-predict. A higher value of rmse suggests a large scatter. Model inadequacies may also be brought to light if the intercept is seen to be large, which suggests a signi®cant deviation of the regressed line from the origin. The above statistical properties for each of the three UK and two Japanese sites are shown in Table 1, which provides an assessment of the validity of the MRM and CRM to compute global and diuse irradiances and illuminance. In the case of Japanese sites, the cloud data were unavailable and hence no comparison between MRM and CRM could be undertaken. Several interesting points may be picked up from Table 1 and these are listed below. . The MRM outperforms the CRM for global irradiance and illuminance estimations. . In the case of diuse irradiance and illuminance estimations, the MRM outperforms the CRM in three out of four cases. . There is a considerable improvement in accuracy of the above predictions if local synoptic data are used. This is evident by a two to three fold performance gain when the Manchester±Aughton and Manchester± Ringway error statistics are examined. This result therefore con®rms the ®ndings of Cowley.5 Table 2 provides a banded error analysis for three clearness-index bandwidths. These bandwidths, 0 < Kt 40:2, 0:2 < Kt 40:6 and 0:6 < Kt 41:0, respectively represent the overcast, intermediate- and clear-sky conditions. Comparison of model performances has been made easier with the depiction of the average of the absolute values of mbe and rmse. The following observations may be made. . The MRM outperforms the CRM for all cases of global illuminance computation.
A meteorological illuminance model for daylight computations
251
. For diuse illuminance computation, the MRM is on a par with the CRM for the overcast-sky, outperforms the CRM for the intermediatesky and is less eective under clear-skies. . The average errors are kept low by either of the two models. With the use of the MRM, the relative errors, associated with global illuminance errors, are around 15% for the overcast- and 5% for the intermediateand clear-sky regimes. The corresponding ®gures for the CRM are 19% for the overcast-, 10% for the intermediate- and 7% for clear-sky conditions. TABLE 1 Statistical error-analysis (a) UK data
MRM Irradiance (W mÿ2)
Global Napier Heriot-Watt Manchester± Aughton Manchester± Ringway Average of absolute values Diuse Napier Heriot-Watt Manchester± Aughton Manchester± Ringway Average of absolute values a
Illuminance (klux)
Illuminance (klux)
ÿ10
0.1
ÿ8
0.2
76
ÿ0.3
ÿ8
0.3
38
0.1
7
0.2
89
0.4
10
0.4
Intercept Slope Intercept Slope Intercept Slope Intercept Slope 81 ÿ0.4 10 ÿ0.4 78 ÿ0.3 ÿ10 0.3 ÿ95 0.0 ÿ11 0.5 ÿ115 0.6 ÿ13 0.5 ÿ43 0.3 n/a n/a ÿ64 0.3 n/a n/a ÿ24
0.0
ÿ7
0.3
61
ÿ0.2
ÿ6
0.3
61
0.2
9
0.4
79
0.4
10
0.4
Denotes dimensionless property. MRM Irradiance (W mÿ2)
Global Chofu Fukuoka Diuse Chofu Fukuoka
Irradiance (W mÿ2)
Intercept Slopea Intercept Slope Intercept Slope Intercept Slope 60 ÿ0.2 7 ÿ0.2 97 ÿ0.4 ÿ11 0.4 ÿ42 0.0 ÿ5 0.1 ÿ103 0.4 ÿ12 0.4 ÿ39 0.2 n/a n/a ÿ80 0.3 n/a n/a
(b) Japanese data
a
CRM
Illuminance (klux)
Intercept Slopea Intercept Slope ÿ57 0.0 ÿ7 0.1 ÿ74 ÿ0.1 ÿ4 0.2 Intercept Slope Intercept Slope ÿ93 0.0 ÿ13 0.3 ÿ153 0.1 ÿ9 0.5
Denotes dimensionless property.
252
T. Muneer, M. Gul, D. Kinghorn TABLE 2 Banded global and diuse illuminance error analysis
(a) UK data
Global (klux)
Kt 0±0.2
MRM Napier Heriot-Watt Manchester
mbe ÿ0.6 ÿ1.7 ÿ2.2
Diffuse (klux)
CRM
rmse 3.7 4.5 3.6
mbe ÿ3.3 ÿ1.8 ÿ0.7
MRM
rmse 10.6 10.2 7.4
mbe rmse mbe rmse 0.1 3.3 ÿ1.7 ÿ1.2 ÿ1.2 4.3 ÿ0.5 8.6 ÿ1.8 3.1 ÿ0.1 6.4
Average of absolute values
1.5
3.9
1.9
9.4
1.0
0.2±0.6
1.3 1.1 1.6
10.2 9.5 9.2
ÿ9.2 0.3 0.8
20.6 13.4 11.4
2.3 ÿ0.4 1.8
Napier Heriot-Watt Manchester
Average of absolute values
1.3
9.6
3.4
15.1
0.6±1.0
4.3 5.0 2.0
11.9 13.3 1.1
ÿ13.0 ÿ0.8 ÿ2.3
24.5 12.2 12.6
3.8
8.8
5.4
16.4
Napier Heriot-Watt Manchester
Average of absolute values (b) Japanese data Kt 0±0.2 0.2±0.6 0.6±1.0
1.5
3.6
0.8
5.4
8.4 ÿ3.5 11.9 9.1 1.5 10.8 7.0 2.6 7.5 8.2
2.5 10.1
3.0 8.2 ÿ1.1 7.6 ÿ6.3 17.0 ÿ6.9 18.1 12.0 6.2 0.4 6.5 7.1 10.5
2.8 10.7
MRM Global (klux)
Chofu Fukuoka Chofu Fukuoka Chofu Fukuoka
CRM
mbe ÿ1.6 0.8 2.6 2.6 5.2 5.6
rmse 12.0 2.6 12.2 10.2 10.9 11.6
Diffuse (klux) mbe ÿ0.9 0.4 4.6 3.4 13.0 12.6
rmse 11.0 2.6 10.8 9.8 16.0 18.5
It has been shown that the MRM and CRM are good estimators of hourly irradiation. There are merits and demerits associated with either of the two models. Collection of cloud-cover data requires no instrumentation and, hence, is easy to record for a large number of locations. On the other hand, a single spot-reading of the cloud amount is observed and this datum is obviously of inferior quality to that of a continuous trace registered by a sunshine recorder. Many weather stations have now switched from paperbased to electronic sunshine loggers and this practice has therefore removed the ambiguities associated with lower irradiation and moisture deposition on the card of the formerly mentioned instrument. Thus, quality sunshine data are increasingly being made available for many world-wide sites. Figures 2±7 enabled evaluation of the MRM and CRM based procedures using scatter diagrams. Quite often time-series plots are additionally used for model evaluation and these are shown in Figs 8±10. These plots show a continuous trace of measured and computed global and diuse illuminances
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253
Fig. 8. Variations in global (a) and diuse (b) illuminance derived from measured irradiances, Edinburgh-Napier April 1993 data.
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T. Muneer, M. Gul, D. Kinghorn
for a one-week period in April 1993. This particular time period was chosen as it is usually associated with temperate weather conditions and hence allows a test of the durability of MRM and CRM under varying conditions of sunshine and cloud. Computed global and diuse illuminances, shown in Fig. 8, have been derived via LEM using ®ve-minute averaged measured values of irradiance data from a post-sunrise to a pre-sunset period. There is a remarkable concordance between the computed and measured values. Figures 9 and 10 show plots similar to those in Fig. 8, although computed values of illuminance in this case are respectively obtained through MRMLEM and CRM-LEM interface. Either of the two ®gures display illuminances which were obtained from hourly records of sunshine, temperature and cloud-cover. As such, the plots do not reveal the sub-hourly dynamics of the illuminance trace. However, the ®gures do show an acceptable degree of concordance between the computed and measured values. Variations between the latter may partly be attributed to the fact that the synoptic input TABLE 3 Synoptic data and computed global irradiances, the 4 and the 8 April 1993 MRM derived Day
Measured
CRM derived
Hour
Global irradiance
SF
Global irradiance
Global irradiance
N
4 4 4 4 4 4 4 4 4 4 4 4
6 7 8 9 10 11 12 13 14 15 16 17
35.2 205.0 326.8 405.1 549.7 606.2 583.7 594.3 457.3 345.2 259.2 143.9
0 0.9 0.9 0.8 1 1 0.9 1 0.8 0.7 0.8 0.8
50.1 153.2 328.3 332.8 432.4 472.2 447.0 380.4 415.5 362.2 255.2 128.9
53.9 107.4 232.9 222.3 261.1 283.7 395.7 377.7 397.1 354.3 252.5 136.4
6 7 6 7 7 7 6 6 5 4 4 4
8 8 8 8 8 8 8 8 8 8 8 8
6 7 8 9 10 11 12 13 14 15 16 17
40.2 85.0 129.6 168.3 195.9 212.7 216.5 202.6 177.7 144.8 104.0 59.8
0 0 0 0 0 0 0 0 0 0 0 0
24.7 32.2 42.5 53.8 41.2 96.9 121.5 122.9 75.8 51.5 18.8 13.8
50.9 118.8 180.9 232.9 271.3 293.6 298.1 135.9 121.3 99.6 72.1 40.9
7 7 7 7 7 7 7 8 8 8 8 8
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255
Fig. 9. Variations in (a) global and (b) diuse illuminances derived from MRM irradiances, Edinburgh-Napier April 1993 data.
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T. Muneer, M. Gul, D. Kinghorn
Fig. 10. Variations in (a) global and (b) diuse illuminances derived from CRM irradiances, Edinburgh-Napier April 1993 data.
A meteorological illuminance model for daylight computations
257
data for both the MRM and CRM were recorded at a site 12 km from Napier University, where the illuminances were recorded. A closer examination of Figs 9 and 10 reveals that in certain instances, e.g. 8 April, either of the MRM and CRM based procedures fail badly. Further, the MRM seems to generate unacceptably high illuminances around noon for 4 April. Table 3 shows the relevant synoptic information for the two days under discussion. Measured irradiance and cloud data for 4 April suggest an almost complete and thin overcast sky, although an unbroken spell of sunshine was recorded for hours 10 and 11. There is a strong possibility of an ambiguity among the irradiation, cloud and sunshine data. As mentioned above, better equipment for sunshine records are increasingly being used and this action may alleviate the kind of problem presently under discussion. Data for 8 April quite clearly indicates an overcast day. The cloud and sunshine log, however, cannot dierentiate between a thin-cloud and a heavy overcast sky . When the sunshine-and-cloud record suggest an overcast sky, MRM and CRM provide irradiance estimates for an ``average'' overcast sky. Further improvements to this part of the model were attempted using visibility and cloud-type data without any signi®cant accuracy gains. CONCLUSIONS Solar irradiance and illuminance models which use commonly observed weather data were presented. Irradiance may be obtained from the Meteorological Radiation Model (MRM), which is based on sunshine and temperature data, or Cloud-cover Radiation Model (CRM) which uses visual observations of the sky cover. Further, it was shown that the above models may be linked with previously developed Luminous Ecacy Models (LEM) to provide the daylight illuminance. Graphical and statistical evaluations of the above procedures were undertaken using data from three UK and two Japanese locations. The statistical evaluation was based on regressions being respectively performed between the errors and the dependent variables. Further, the banded mbe and rmse were obtained for the overcast-, intermediate- and clear-sky regimes. It was noted that in all cases the global irradiance and illuminance were better estimated with the MRM. For diuse illuminance computation, the MRM is on a par with the CRM for the overcast-sky, out performs the CRM for the intermediate-sky and is less eective under clear-skies. The average errors are kept low by either of the two models. With the use of the MRM, the relative errors, associated with global illuminance errors, are around 15% for the overcast- and 5% for the intermediate- and clear-sky regimes. The corresponding ®gures for the CRM are 19% for the overcast-,
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10% for the intermediate- and 7% for clear-sky conditions. Both the MRM and CRM have therefore demonstrated their capabilities to model the solar irradiance and illuminance climate for UK and Japan with almost equal eectiveness. The foregoing comparison of the two models has revealed that the MRM is the better of the two models. This may be due to the fact that the input parameters for the MRM are more rigorously recorded, whereas cloud-cover information is often based on visual estimates. The continuous sunshine trace through the hour, obviously provides much more detailed information than a spot reading of the cloud-cover. Haurwitz29 has shown that a much stronger correlation exists between irradiation and sunshine than between sunshine and cloudiness. According to Bennet,30 sunshine explains 70 to 85% of the irradiation variance. Cloud-cover, on the other hand, seldom explains more than 70% and frequently less than 50% of the irradiation variance. This study con®rms the above cited performance and recommends the use of sunshine-based irradiation models if the required data are available. It was also pointed out that the quality of sunshine records may be further improved with the use of electronic loggers. Replacement of the existing Campbell±Stokes recorders with the latterly mentioned device has been recommended to improve the quality of the sunshine data and also, thus, the performance of the MRM. ACKNOWLEDGEMENTS The authors wish to extend their thanks to the project's funding body, the UK Engineering and Physical Science Research Council. REFERENCES 1. Muneer, T. and Kinghorn, D., Solar Irradiation and Daylight Data for the United Kingdom and Japan (with Compact Disk). Napier University, Edinburgh, 1996. 2. Muneer, T. and Kinghorn, D., Improved methods for the luminous ecacy of solar irradiance. LR&T, 1997, 29(4), 185±191. 3. Muneer, T., Solar irradiance and illuminance models for Japan II: luminous ecacies. LR&T, 1995, 27(4), 223±230. 4. Muneer, T., Availability of solar irradiation for the United Kingdom. BSER&T, 1989, 10(2), 75±80. 5. Cowley, J. P., The distribution in Great Britain of global solar radiation on a horizontal surface. Meteorological Magazine, 1978, 107, 357±373. 6. Muneer, T., Gul, I., Kambezidis, H. and Allwinkle, S., A simple meteorological radiation model. Proc. Joint CIBSE/ASHRAE Conference Harrogate, 1996, 271±279.
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7. Muneer, T., Gul, M. and Kambezedis, H., Long-term evaluation of a meteorological solar radiation model against UK data. Energy Conversion and Management, 1998, 38(3/4), 303±317. 8. Dave, J. V., Extensive data sets of the diuse radiation in realistic atmospheric models with aerosols and common absorbing gases. Solar Energy, 1979, 21, 361±369. 9. Bird, R. E and Hulstrom, R. L., A simpli®ed clear-sky model for the direct and diuse insolation on horizontal surfaces. US-SERI Technical Report TR-642761, Golden, CO, 1981. 10. Kasten, F. and Czeplak, G., Solar and terrestrial radiation dependent on the amount and type of cloud cover. Solar Energy, 1979, 24, 177±189. 11. Muneer, T. and Saluja, G. S., Correlation between hourly diuse and global radiation for the United Kingdom. Building Services Engineering Research Technology, 1986, 7, 37±43. 12. Pleijel, G., The computation of natural radiation in architecture and town planning. Meddelande Bull., Statens Namnd for Byggnadsforskning, Stockholm, 1954, 25, 30. 13. Blackwell, M. J., Five-years continuous recordings of total and diuse solar radiation at Kew Observatory. Met. Res. Publication 895, Met. Oce, London, 1954. 14. Dogniaux, R., Donnees Meteorologiques concernant l'Ensoleillement et l'Eclairage Naturel. Cah. Cent. Sci. Batim., 1960, 44, 24. 15. Drummond, A. J., Notes on the measurement of natural illumination II. Daylight and skylight at Pretoria: The luminous ecacy of daylight. Architectural Meteorology Vienna, Series B, 1958, 9, 149. 16. McDermott, L. H. and Gordon-Smith, G. W., Daylight illumination recorded at Teddington. Proc. Build. Res. Congr., Division 3, Part III, vol. 156, 1940, 1951. 17. Hopkinson, R. G., Petherbridge, P. and Longmore, J., Daylighting. Heinemann, London, 1966. 18. Muneer, T. and Angus, R. C., Daylight illuminance models for the United Kingdom. LR&T, 1993, 25(3), 113±123. 19. Muneer, T. and Angus R. C., , Luminous ecacy: evaluation of models for the United Kingdom. LR&T, 1995, 27(2), 71±77. 20. Perez, R., Ineichen, P. and Seals, R., Modelling daylight availability and irradiance components from direct and global irradiance. Solar Energy, 1990, 44, 271Ð289. 21. Palz, W. and Grief, J., (eds). CEC European Solar Radiation Atlas. Springer± Verlag, Berlin, 1996. 22. Delaunay, J. J., Development and performance assessment of luminous ecacy models. Internal Report. Fraunhofer Institute for Solar Energy Systems, Freiburg, Germany, 1995. 23. Maxwell, E. L., A quasi-physical model for converting hourly global horizontal to direct normal insolations. Report SERI/TR-215-3087, Solar Energy Research Institute, Golden, CO, 1987. 24. Reindl, D. T., Beckman, W. A. and Due, J. A., Diuse fraction correlations. Solar Energy, 1990, 45(1), 1±7. 25. A®®, A. A. and Azen, S. P., Statistical AnalysisÐA Computer Oriented Approach. Academic Press, London, 1979. 26. Draper, N. R. and Smith, H., Applied Regression Analysis. John Wiley & Sons, New York, 1981.
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27. Montgomery, D. C. and Peck, E. A., Introduction to Linear Regression Analysis. John Wiley & Sons, New York, 1982. 28. Hamilton, L. C., Regression with Graphics. Duxbury Press, Belmont, CA, 1992. 29. Haurwitz, B., Insolation in relation to cloud type. Journal of Meteorology, 1948, 5, 110±113. 30. Bennet, I., Correlation of daily insolation with daily total sky-cover, opaque sky-cover and percentage of possible sunshine. Solar Energy, 1969, 12, 391±393.