accuracy analysis of computational algorithms for prediction of … · 2017-07-11 · accuracy...

Solar Energy 153 (2017) 700–717

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Solar Energy

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Accuracy analysis of computational algorithms for prediction of daylightilluminance in space with shading devices

http://dx.doi.org/10.1016/j.solener.2017.05.0480038-092X/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: [email protected] (Y. Yoon), [email protected]

(J.W. Moon), [email protected] (H.H. Alzoubi), [email protected] (S. Kim).

Younju Yoon a, Jin Woo Moon b, Hussain H. Alzoubi c, Sooyoung Kimd,⇑a Samsung C&T Corporation, Construction Technology Center, Seoul, South Koreab School of Architecture and Building Science, Chung-Ang University, Seoul, South KoreacDepartment of Architecture, Jordan University of Science & Technology, Irbid, JordandDepartment of Interior Architecture & Built Environment, Yonsei University, Seoul, South Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 June 2016Received in revised form 5 May 2017Accepted 15 May 2017

Keywords:Annual daylight simulation methodDaylight illuminanceSky conditionsRadianceDaylight coefficient approachSun-matching method

This study examines the accuracy of annual daylight simulation method (ADSM) in predicting illumi-nance for spaces with shading device conditions. ADSM algorithms were developed separately for thesun and sky to predict their effect on indoor daylight illuminance. Sun-matching and daylight coefficientmethods were developed for the sun, while sky-matching and daylight coefficient methods with one andfour sky patches were developed for the sky. The daylight illuminance computed from ADSM under var-ious daylight conditions was compared with those calculated from Radiance and field measurements.Results imply strong linear correlations existed between the predicted daylight illuminance levels by

the ADSM and Radiance under diverse sky conditions based on weather data. The predicted illuminancefrom ADSM was lower than field measurements for all sky conditions. ADSM computations mostly agreewith field measurements. For clear and partly cloudy sky conditions, the daylight coefficient approach forsky of ADSM generated a stronger correlation to measured data, but the sky-matching algorithm showeda stronger correlation to field data. The daylight coefficient approach for sky, combined with ADSM com-putation algorithms for sun, effectively reduced the difference between the predicted and measured illu-minance under clear or partly cloudy sky conditions. Under overcast conditions, there was no significantreduction in difference between simulated and measured illuminance.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Energy is consumed in buildings to maintain the indoor envi-ronment comfortable for the occupants. Buildings take up 41% ofthe total energy consumed in a country (D&R International Ltd.,2012). In particular, residential and commercial buildings accountfor 54% and 46%, respectively. In addition, electric lighting energyconstitutes 9% of the energy consumption in buildings.

The introduction of daylight to building interiors has the poten-tial to enhance the quality of the environment while providingopportunities to save energy and reduce greenhouse gases by dis-placing or supplementing electric lighting. The use of daylighthelps to reduce heating and cooling loads, which offers additionalenergy saving opportunities as well as reductions in heating, ven-tilation, and air conditioning equipment sizing and initial cost(Papamichael et al., 1998).

However, improper selection or design of window systems maynegate the benefits of electric lighting energy reduction by increas-ing requirements for air conditioning and degrading the quality ofvisual environment. Accordingly, appropriate designs and selec-tions of window systems with shading devices should be applied.

To compare the effectiveness of different window systems, sim-ulations based on hourly local weather data need to be performedto estimate the annual daylight availability and total buildingenergy consumption. Accurate simulation of annual daylightavailability, coupled with the building thermal simulations,provides the most reliable estimation of electric lighting energyconsumption and results in more accurate calculations of coolingand heating energy demands (Guglielmetti et al., 2010).

Thus, successful designs or selections of energy-efficientdaylight systems considering all factors that influence energyperformance of buildings can be achieved. Accurate estimation ofannual daylight availability is achieved by performing a series ofdaylight simulations for hourly or subhourly annual daylight con-ditions (Winkelmann, 2002). Hourly daylight simulation for a yearis computationally very expensive, thus selective simulations for

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Nomenclature

xsun solid angle of the sun [sr]xsky;patch solid angle of a sky patch [sr]Eref ;sun inter-reflected illuminance contribution from the

sun [lx]DCref ;sky i inter-reflected component of daylight coefficient

from sky patch iLsun luminance of the sun [cd/m2]

Wsky; i weighting factor for sky patch iWsun;i weighting factor for sun iEsun;test date illuminance from the sun on a test date [lx]Erep: sun;i illuminance from the representative sun i [lx]SolarRadiancei solar radiance for the representative sun i

[W/m2/sr]SolarRadiancetest date solar radiance for test date [W/m2/sr]

Y. Yoon et al. / Solar Energy 153 (2017) 700–717 701

representative hours of the year are usually performed for annualdaylight availability simulation (Architectural EnergyCorporation, 2006). Fast, yet accurate annual daylight simulationmethod considering all hourly daylight conditions needs to bedeveloped.

Windows introduce daylight into a space and admit solar radi-ation, which increases cooling energy demands and risk of thermaldiscomfort. Daylight systems, which simultaneously control thethermal and visual environment, should be installed to preventexcessive solar heat gain and direct sunlight. Most daylight simu-lation programs are used to identify suitable shading and redirec-tion devices and control strategies (Reinhart and Friz, 2005).Shading devices, especially blinds, have variable light and solarheat transmission characteristics depending on the incoming andoutgoing direction of light. Moreover, blinds significantly influencethe performance of a photosensor-based daylight dimming system.The tilt angle of the blind slats changes the ratio of a photosensorsignal to workplane illuminance and affects the ability of the sys-tem to maintain the target illuminance level (Lee et al., 1999;Rubinstein et al., 1998).

Most annual daylight simulation tools did not accurately modelthe blinds geometry and assumed a constant transmittance valuefor the inclusion of blinds until the daylight coefficient approachwas adopted as an efficient algorithm for annual daylight simula-tion (Reinhart, 2005). In this approach, the daylight coefficient isdefined as the contribution of a sky patch to the total illuminanceat a point in a building, assuming that the hemispherical sky isdivided into disjoint sky patches (Tregenza and Waters, 1983).The introduction of the daylight coefficient approach enabledannual daylight simulation at hourly or subhourly time steps withreasonable computation time and accuracy for windows with orwithout a daylight system (Janak and Macdonald, 1999;Mardaljevic, 1999; Reinhart and Herkel, 2000). DAYSIM is anexample of a tool that implements the daylight coefficientapproach to estimate the annual daylight level and the lightingenergy savings using window systems with blinds (Reinhart,2005).

To effectively compute the annual daylight availability for acomplex fenestration system, Radiance incorporated a three-phase model, which computes the daylight contribution in threesteps: (1) sky to exterior fenestration, (2) fenestration transmis-sion, and (3) fenestration to the simulation space. Measured orcomputed bidirectional scattering distribution functions (BSDFs)of complex window systems such as blinds are considered insteadof modeling the geometry of system (McNeil, 2014).

The three-phase model, which follows the standard daylightcoefficient model for dynamic daylight simulations, enhanced theaccuracy by separately computing direct solar components fromthe inter-reflected solar component (Bourgeois et al., 2008;McNeil, 2013). This model provided a mean bias error below 13%and a root mean square error below 23%, compared to the mea-sured illuminance levels for a test office equipped with an innova-tive daylight system (McNeil and Lee, 2012).

The accurate simulation of the annual performance of complexfenestration systems can be achieved if BSDF data for daylighting,shading, and fenestration systems are available. With the Window5 software, BSDF data are much easier to obtain than before, butstill, in many cases, such data are not easily available for glazing,which is mostly used for buildings. Additionally, a simple and easymethod is necessary for the estimation of annual daylight avail-ability (Mitchwell et al., 2001).

Therefore, this study develops annual daylight simulationsmethods (ADSM) and examines the accuracy of ADSM in predictingilluminance with shading devices. The ADSM was developed theo-retically and the illuminance calculations using the ADSM wereconducted separately for the sun and sky. The prediction accuracyof the ADSM was tested through comparison of an hourly illumi-nance output from Radiance simulations and field measurementdata under actual diverse daylight conditions.

2. Development of prediction method

In this study, annual daylight simulation algorithms weredeveloped separately for the sun and the sky in order to predictthe effect of sun and sky to indoor daylight illuminance. For thesun, the sun-matching method and daylight coefficient methodswith one and four sky patches were developed theoretically. And,the sky-matching and daylight coefficient method were developedfor the sky. The five computation algorithms were used to computethe total daylight illuminance at calculation points in space.

For the computation algorithm, the one or four sky patches wasused to derive the reflected solar illuminance from the reflectedilluminance contribution from the sky. Single sky patch was usedbecause it contains the sun. However, the sun may not be at thecenter of the sky patch but at one corner where a neighboringsky patch can be closer to the sun. Therefore, neighboring foursky patches was also used.

Among the ADSMs, the daylight coefficient approach developedin this study uses daylight coefficients computed using Radiance.The daylight coefficient method computes daylight coefficientsseparately for the sky and the sun. The method differs from thethree-phase and five phase method used for Radiance. The three-phase method computes sky and solar contributions concurrentlyand the five phase method conducts separate addition of directsolar contribution for better accuracy.

Compared to the five-phase method of Radiance, the daylightcoefficient approach developed in this study uses a different num-ber of direct sun positions in the simulation. The five-phase uses5,185 sun positions located at the center of 5,185 subdivided skypatches, whereas the approach used in this study uses actual sunpositions that can vary in number depending on the time simu-lated. For example, if the direct solar illuminance is computed onan hourly basis from 8:00 to 17:00 for a year, the total simulationcase is 3,650 (10 sun positions per day multiplied by 365 days).Also, the three-phase and five-phase methods compute the

702 Y. Yoon et al. / Solar Energy 153 (2017) 700–717

reflected contributions from 145 sun positions, but the daylightcoefficient method developed in this study uses the coefficientsof reflected daylight from 145 sky patches to derive the reflectedsun illuminances.

2.1. Computational algorithm of ADSM for sun

2.1.1. Sun-matching methodAmong the ADSMs for sun, the sun-matching method is based

on representative sun positions. The sun positions are from 8:00to 18:00 on the 21st of February, March, April, June, and December.These sun positions cover the highest and lowest attitude angles ata given time throughout the year and are almost equidistant fromeach neighboring month. The time range from 8:00 to 18:00 is thetypical operation time for commercial buildings, and these hourscan be altered depending on simulation purposes.

For the annual daylight simulation, illuminances at computa-tion points under the representative sun positions are computed.The illuminance due to the actual sun is derived by interpolatingilluminances from two neighboring sun positions with the samesolar time. The weighting factors for interpolation are the inversesof their relative linear distances to the actual position of sun.

Fig. 1 shows the concept applied for interpolation regarding theactual sun position. For example, the illuminance from the sun onMay 17, 11:00 is computed using two neighboring representativesun positions, those of April 21 and June 21, 11:00. The distancesfrom the actual sun position to the two representative sunpositions are of the ratio 1:1.72, and the weighting factors of0.633:0.367 are applied for the illuminance of these two sun

36.7%

63.3%

June/2110:00

June/2111:00

June/2112:00

Apr/2112:00

Apr/2111:00

Apr/2110:00

May/1711:00

Fig. 1. Example of interpolation for actual position of sun.

Table 1Altitude and azimuth angle for representative sun position (Site: Boulder, Colorado, USA,

Time Feb/21, Oct/21 Mar/21, Sept/21 Apr/21,

Azimuth Altitude Azimuth Altitude Azimuth

8:00 �59.54 14.57 �65.44 22.24 �78.829:00 �47.25 24.03 �55.23 32.49 �66.6610:00 �32.65 31.78 �39.60 41.22 �50.6811:00 �15.55 37.00 �19.93 47.34 �28.2512:00 3.13 38.86 2.74 49.60 0.9913:00 21.47 37.00 24.93 47.34 29.9314:00 37.78 31.78 43.66 41.22 51.8715:00 51.55 24.03 58.55 32.49 67.5316:00 63.21 14.57 70.65 22.24 79.5217:00 73.45 4.03 81.10 11.17 89.68

positions. Table 1 summarizes the angular information on the rep-resentative sun positions for a certain site at a given time. The illu-minance is computed using Eq. (1) by the sun-matching method.The representative sun files were generated using Radiance basedon TMY weather file and their resulting illuminances werecomputed.

Esun;test date ¼ Erep: sun;i � Solar RadianceiSolar Radiancetest date

�Wsun;i

þ Erep: sun;j � Solar RadiancejSolarRadiancetest date �Wsun;j

ð1Þ

2.1.2. Daylight coefficient methodThe daylight coefficient method for the sun separately com-

putes direct and inter-reflected illuminance. The direct solar illu-minance is computed for all sun positions. The reflected sunilluminance for a specific sun position is calculated using theinter-reflected component of the daylight coefficient for either asingle sky patch or four sky patches among 145 Tregenza skypatches shown in Fig. 2. The solar daylight coefficient approachwith a single sky patch (DCA-1 sky) uses the reflected componentof daylight coefficients for the sky patch with the sun. The reflectedcomponent of sky daylight coefficient is multiplied by the

Unit: degree).

Aug/21 June/21 Dec/21

Altitude Azimuth Altitude Azimuth Altitude

30.23 �87.91 37.38 �51.65 5.5041.22 �81.93 48.83 �40.45 13.9651.10 �68.32 59.81 �27.65 20.6758.56 �46.36 69.17 �13.31 25.0461.49 �7.02 73.45 1.95 26.5658.56 36.98 69.17 17.06 25.0451.10 63.14 59.81 31.05 20.6741.22 78.42 48.83 43.43 13.9630.23 89.31 37.38 54.26 5.5018.81 98.47 25.96 63.87 �4.23

Fig. 2. Layout of sky patch for calculation of daylight illuminance [8].


irradiance of the actual sun and scaled by the ratio of the solidangle of the sun and the single sky patch.

The daylight coefficient approach with four sky patches (DCA-4sky) interpolates the inter-reflected daylight coefficients from fourneighboring sky patches to the actual sun according to the relativedistances from each sky patch to the actual sun. Similar to theDCA-1 sky, the irradiance of the actual sun is incorporated intothe illuminance calculation as a scaling factor (actual sun irradi-ance to uniform sky irradiance).

Eq. (2) explains the daylight coefficient approach for a single skypatch and four sky patches. For example, the sun position at 11:00on September 21 is within sky patch 95 and its neighboring foursky patches include sky patch 95, which contains the actual skypatches 94, 116, and 117, as shown in Fig. 3.

Therefore, with a single sky patch, the reflected daylightcoefficient from sky patch 95 is used to compute the reflectedsun illuminance at 11:00 on September 21. With four sky patches,the reflected illuminance contribution from sky patches 94, 95,116, and 117 is 19.37%, 31.57%, 28.08%, and 20.98%, respectively,because the distance from the center of the sun to the centers ofthese four sky patches has a ratio of 1:0.61:0.69:0.92.

(1) Single sky patch condition

Eref ;sun ¼ DCref ;sky � Lsun � xsun

xsky patch

116

117

31.57%

19.37%

28.08%

20.98%

95

94

11:00Sep/21

Fig. 3. Conceptual explanation for sky patch (Lef

1.2m 3.6m 3.6m 1.2m

2.4m

3.6m

3.0m

2.4m 2.4m 2.4m 2.4m

: Calculation Point

0.13

3m

1.2m

Louver type Overhang

N

W2

W1

C2 E2

C1 E1

Fig. 4. Layout of space and calculation points for lou

(2) Four sky patch condition

Eref ;sun ¼ ðDCref ;sky1 �Wsky; 1 � xsun

xsky;1þ DCref ;sky2 �Wsky; 2 � xsun

xsky ;2

þ DCref ;sky3 �Wsky; 3 � xsun

xsky ;3

þ DCref ;sky4 �Wsky; 4 � xsun

xsky;3Þ � Lsun ð2Þ

2.2. ADSM algorithm for sky

2.2.1. Sky-matching methodIn the sky-matching method, the hourly vertical and horizontal

illuminances and their ratios were computed at 0.25 m below thewindow top. In Figs. 4 and 5, the orientation of vertical illuminanceis south. The computed values for the sun position of the four rep-resentative days in a year are summarized in Table 2. A group ofrepresentative sky conditions was selected on the basis of the ratioof the exterior vertical illuminance to horizontal illuminance (VHratio) and the solar azimuth angles of the skies. Solar azimuthangles were used considering that the sky in the circumsolar areahas a brighter luminance distribution compared to the remainingsky area.

The selection process was as follows. First, hourly or subhourlyvertical to horizontal illuminance ratios for annually occurringskies were computed. Second, solar azimuth angles for each time

Sep/2111:00

94

95

100%

117

116

t: four sky patches, Right: single sky patch).

N

Louver type overhang

1.2m

o54.3

3.0m 2.4m3.6m

Calculation point

1.1m0.75m

2.2m

Detail of overhang0.133m0.133m

o54.3

ver-typed overhang (Left: plan, Right: section).

1.2m 3.6m 3.6m 1.2m

2.4m

3.6m

3.0m

2.4m 2.4m 2.4m 2.4m

: Calculation Point

Window and Venetian Blind

N

W2

W1

C2 E2

C1 E1

N

Blind

3.0m 2.4m3.6m

Calculation point

1.1m0.75m

2.2m

Detail of blind

o452.54cm

2.54cm 45o

Fig. 5. Layout of space and calculation points for Venetian blind (Left: plan, Right: section).

Table 2Ratio of outdoor vertical illuminance to outdoor horizontal illuminance.

Day Property Time

8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Mar/21 Azimuth angle [o] �67.98 �55.33 �39.60 -19.93 2.74 24.93 43.66 58.55 70.65 81.10Vertical illuminance [lx] 5692.3 5919.1 7727.8 6334.2 9657 11536 11344 10870 7439.2 5244.3Horizontal illuminance [lx] 5005.1 4323.3 5459.8 4257.1 7225.2 9615.4 10088 11068 7333.3 6442.7VH ratio 1.137 1.369 1.415 1.488 1.337 1.200 1.124 0.982 1.014 0.814

June/21 Azimuth angle [o] �87.91 �81.89 -68.32 -46.36 -7.02 36.98 63.14 78.42 89.31 98.47Vertical illuminance [lx] 3731.8 4105.4 4274.9 5881.7 6652.2 6721.5 6337.2 8402.6 7578.3 5086Horizontal illuminance [lx] 3959.5 3943.7 3851.8 5181.9 5729.8 5911.2 5792.8 10913 11175 8147.8VH ratio 0.943 1.041 1.110 1.135 1.161 1.137 1.094 0.770 0.678 0.624

Sep/21 Azimuth angle [o] -71.46 -59.39 -44.50 -25.67 -3.18 19.88 39.83 55.70 68.41 79.17Vertical illuminance [lx] 6362.6 9077.1 9185.1 10117 9786.1 10259 9514.3 8532.9 6653.5 2649.9Horizontal illuminance [lx] 5310.5 7875.5 7131.1 8051.2 7634.2 8305.2 8101.6 7814.3 7413.2 3897VH ratio 1.198 1.153 1.288 1.257 1.282 1.235 1.174 1.092 0.898 0.680

Dec/21 Azimuth angle [o] -51.65 -40.45 -27.65 -13.31 1.95 17.06 31.05 43.43 54.26 63.87Vertical illuminance [lx] 2171.7 4344.1 9382.4 7974.4 4988.5 6196.3 8168.3 7118 3455.2 *Horizontal illuminance [lx] 1229.1 2460.1 5181.2 4108.8 2798.9 3432 4480.2 3981.4 2886.5 *VH ratio 1.767 1.766 1.811 1.941 1.782 1.805 1.823 1.788 1.197 *


step in the year were computed, and the minimum and maximumsolar angles were determined. The range of azimuth angles wasdetermined depending on the required number of solar azimuthangle zones. Thus, a single azimuth angle zone corresponds tothe difference from the maximum to minimum azimuth angledivided by the number of azimuth angle zones.

Third, after a set of azimuth angle zones was fixed, the skieswere grouped according to the solar azimuth angle zones. Amongthe skies belonging to the same solar azimuth angle zone, repre-sentative skies were considered as those with the minimum andmaximum VH ratios and VH ratios obtained by cumulatively add-ing a VH ratio increment to the minimum VH ratio till it reachesthe maximum VH ratio. The VH ratio increment is the ratio ofthe difference between the maximum and minimum VH ratios tothe number of representative skies per solar azimuth angle zone.

Finally, skies with VH ratios closest to the representative VHratios were selected as representatives. This selection of represen-tative skies was repeated for other azimuth angle zones. After a setof representative skies was determined, daylight simulations were

performed only for those representative sky conditions. The illumi-nances from the actual sky were replaced with those from one ofthe representative skies and scaled according to the incident verti-cal illuminance on the glazing.

For the sky-matching method, 12 different azimuth angle zonesand 12 different VH ratios per azimuth zone were used to formu-late a group of representative skies, because 144 representativeskies provided the smallest percent errors among the combinationsof azimuth angle zones and the number of representative skies wastested in a previous research (Yoon, 2006).

For example, if the range of the solar azimuth angles for allannually occurring sun positions was from �87.91� to 98.47�, asshown in Table 2, the azimuth angle zone increment would be15.68� ((98.47� + 87.91�)/12), assuming 12 azimuth angle zones.Thus, the first azimuth angle zone was from �89.71� to �72.37�and the second azimuth angle zone was from �72.37� to�56.85�. The representative VH ratios of skies, whose azimuthangles were assigned to from the 12 azimuth zones, were com-puted. The skies at 8:00 and 9:00 on June 21 in Table 2 belong to


the first azimuth zone. If the minimum and maximum VH ratioswere 0.756 and 1.082 in the first azimuth angle zone and 12 repre-sentative skies per azimuth angle zone were used, the VH ratioincrement step would be (1.082–0.756)/11 or 0.029.

Therefore, the first representative VH ratio would be 0.756; thesecond, third, and fourth representative VH ratios would 0.786,0.816, and 0.845, respectively. Skies with their VH ratios closestto the representative VH ratios became the representative skiesin a specific azimuth angle zone.

2.2.2. Sky daylight coefficient approachA daylight coefficient is a ratio of the luminance of a sky patch

to the resulting illuminance at an illuminance point (Ward andShakespeare, 1998). As the sky is subdivided into 145 sky patchesaccording to the Tregenza sky patches, 145 daylight coefficientswere calculated on the basis of a uniformly luminous sky. The illu-minance contribution from the sky at a given time of the year iscomputed by summing the individual products of the luminancesof the 145 sky patches with the respective daylight coefficients.

Once a set of sky luminances of 145 sky patches was computedfor all sky conditions occurring annually, at a given time step, illu-minances from the sky could be easily computed by multiplyingthe luminance of each sky patch to the daylight coefficient. In thisstudy, the rtcontrib program in Radiance was used to compute day-light coefficients (Perez et al., 1990).

0

2

4

6

8

10

12

8:00 9:00 10:00 11:00 12;00 13:00 14:00 15:00 16:00 17:00Time

Sky

Cov

er

Mar/21 June/21Sep/21 Dec/21

Fig. 6. Opaque sky cover value for selected day and time from TMY2 weather data(Boulder, Colorado, USA).

3. Methods for validation of ADSM

3.1. Computer simulations of ADSM and Radiance

Indoor daylight illuminance levels computed from the ADSMand Radiance were compared to examine the consistency betweencomputational agreements of the two software applications. Aclassroom with south-facing windows was used for the simula-tions to predict the illumination levels under various daylight con-ditions. The space used for the simulations was assumed to belocated in Boulder, Colorado, USA (latitude: 40�N; longitude:105.2�W).

The detailed layout of the classroom is shown in Figs. 4 and 5.The classroom was 9.6 m wide, 9.0 m deep, and 3.3 m high, andthe floor area was 89.2 m2. A window with double clear glazingwas installed on the south façade. The transmittance of glazingfor light was 67%. The window area was 9.6 mwide and 2.2 m high.This resulted in a window area of 14.52 m2 and 66.77% of window-to-wall ratio. It was assumed that the reflectance of the ceiling,wall, and floor was 70%, 50%, and 25%, respectively. The reflectanceof the outdoor ground was assumed to be 20%. The furniture wasnot assumed to be installed in the classroom to avoid internalreflection between furniture and indoor surfaces, and electric light-ing was not used in the indoor daylight illuminance prediction.

To realistically model the environment, shading devices wereselected for the window because most classrooms had windowsequipped with shading devices. It was assumed that two differentshading devices were used for the classroom space either: (1) a1.2-m louver-type overhang at the window top, or (2) Venetianblinds with a 45� tilt angle at inside of the window.

Figs. 4 and 5 show detailed configurations of the exteriorlouver-type overhang and the Venetian blinds. The louver slatwas tilted by 54.3� toward the sky, counting from the vertical lineto the ground. The distance between each slat was 13.3 cm, and thereflectance of slat was 60%. The blind slat was tilted by 45� towardthe ground, counting from the horizontal line. The distancebetween each slat was 2.54 cm (1 in.), and the reflectance of slatwas 60%. Apart from the shading devices, no additional exterior

obstructions such as neighboring buildings were considered inthe simulations.

For computations of daylight illuminance in space, illuminancesensors were assumed to be positioned at the calculations pointsillustrated in Figs. 4 and 5. For the analysis of indoor daylight illu-minance, six representative positions at 0.75 m height wereselected as calculation points, since these points represent theworkplane near the window and at the back of the room. TheADSM and Radiance were used for the calculation of daylight illu-minance in the space with shading devices. The exterior verticaland horizontal illuminances were computed at a sensor position,which is 0.25 m below the window top to compute the amountof vertical and horizontal illuminances incoming through the glaz-ing and shading devices.

The luminous distribution from the sky was theoretically mod-eled for the computation of daylight illuminance. The sky wasmodeled using the Perez sky model based on the global and normalirradiance values according to a typical meteorological yearweather file (TMY2) for Colorado, USA. The TMY2 data sets hasknown to more closely match with actual weather solar radiationstatistics compared to other weather data sets such as WYEC2/WYEC (Crawley and Huang, 1997). The luminance distribution ofeach sky condition was described using the Perez all-weathermodel (Perez et al., 1993; Yoon et al., 2015; Marion, 1995).

According to the TMY weather data, opaque sky cover was usedto represent the amount of sky dome covered by clouds or variousconditions that block the observation of the sky from the calcula-tion point; lower opacity means a higher chance to observe thesky. For instance, the opaque sky cover ranges from 0, which corre-sponds to completely clear sky, to 10, which is overcast sky. Fig. 6shows the variation of opaque sky cover data of selected days andtimes used for the simulation site in this study.

Based on the Perez model with the various opaque sky coverthat represent all sky conditions, the ADSM and Radiance simula-tions were performed for four selected representative days on anhourly basis throughout the day to reflect the sun positions in ayear. The detailed daylight conditions used for the simulation aresummarized in Table 3.

The glazing areas were initially addressed using mkillum sur-faces for all simulation cases except for the daylight coefficientmethod. The following mkillum and rtrace simulation parameterswere applied for the reference Radiance calculation and sky-matching methods. The sky and solar daylight coefficients werecomputed using rtcontrib in Radiance (Ward and Shakespeare,1998).

Table 3Simulation conditions.

Case Orientation Shading Day Time

1 South Overhang Mar/21, June/21Sep/21, Dec/21

08:00–17:00(hourly base)2 South 45o blind


rtrace –ab 7 –ad 2048 –as 64 –ar 32 –aa 0.1 –lw 0.04mkillum –ab 5 –ad 2048 –as 32 –ar 32- -aa 0.1rtcontrib –ab 10 –ad 204,800 –lw 0.0001 –as 0 –aa 0

3.2. Field measurements for validation of ADSM

Field measurements were performed to compare the simulationresults of the ADSM to the actual daylight illuminance data moni-tored under real sky conditions. The measurements were con-ducted in a full-scale mock-up model located on the rooftop of abuilding in Seoul, South Korea (latitude: 37.54�N, longitude:126.98�E). Fig. 7 shows a detailed layout of the mock-up modelspace.

The space was 3.6 m wide, 4.2 m deep, and 2.65 m high. Itsmain façade consists of a double-skin envelope, which containsinternal and external envelopes with a cavity between the envel-opes. The cavity space was 3.6 m wide, 0.9 m deep, and 2.65 mhigh. The long axis of the space was rotated 22� toward the eastfrom the south.

All surfaces of the cavity space except the ceiling were coveredwith double glazing panels. The transmittance of the glazing was62.1% for light and 34.8% for solar irradiance. The ceiling of the cav-ity space was covered with a white acoustic panel board, and nodaylight penetrated through the surface. Light beige linoleumwas installed at the floor surface of the cavity space.

To control the penetration of daylight through window, Vene-tian blinds were installed inside the internal envelope. Detailedconfigurations of blinds are shown in Fig. 7. The blind slat wastilted by 35� toward the ground, counting from the horizontal line.The distance between each slat was 2.54 cm (1 in.) and the color of

LuminaireFluorescent

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the slat surface was light white. Since the full-scale mock-upmodel space was located on the rooftop of a building, no neighbor-ing obstruction existed. The rooftop of the building was paintedgreen. The interior was used to furnish the mock-up space suchas a private small office. The walls and floor were covered withwhite wallpaper and light beige linoleum, respectively. Conse-quently, no specular reflection occurred from the surfaces of thewalls and floor.

A suspended grid of 0.6 m � 0.6 m unit cells was applied to theceiling with six recessed fluorescent lighting fixtures with T8lamps. The rest of the ceiling area was covered with white acousticpanels for interior finishing. Although the lighting fixtures wereinstalled in the space, they were not operated during the monitor-ing period. To investigate the variation of daylight illuminance inthe indoor space, two photometric sensors were positioned onthe desktop, and one photometric sensor was positioned at thecenter of the ceiling to facilitate the use a daylight dimming controlsystem. Fig. 7 shows the precise positions of the photometric sen-sors. The sensors at the ceiling and floor were aimed toward thefloor and ceiling, respectively. No shielding condition was appliedto the three photometric sensors.

For the full-scale mock-up space, illuminance data werecollected daily from January to December 2010. The datamonitoring interval for the collection points was 1 minute, andilluminance was collected from 7:00 to 18:00. Continuous datamonitoring was achieved using an automatic data logging systemwith a 2.5-mV accuracy range and a photometric sensor with adeviation range of 1% (Campbell Scientific Inc., 2000; LI-COR Inc.,1991).

To examine the difference between the measured and simu-lated data from the ADSM, the conditions applied to the full-scale mock-up model were also modeled by the ADSM. It wasassumed that the surface reflectance of the ceiling, wall, floorand rooftop was 80%, 60%, 40%, and 30%, respectively.

Since the Perez sky model requires the global horizontal irradi-ance and direct normal irradiance to generate sky models at hourlyintervals, the measured irradiance was used for the generation ofthe sky model (Perez et al., 1990). Based on the direct horizontal

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etric sensor positions (Left: plan, Right: section).

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irradiance, the direct normal irradiance was computed and dividedby the zenith angle of the sun at each time applied to the measure-ments for the full-scale mock-up model.

Finally, the daylight illuminance levels generated from the sim-ulations of the ADSM were compared to those from field measure-ments to validate the prediction accuracy of the ADSM. Linearregression analysis, analysis of variance (ANOVA), and frequencyanalysis were used to validate the prediction results of the ADSM.

4. Results

4.1. Computer simulation results of ADSM and Radiance

The prediction results from the ADSM and Radiance were com-pared to validate the computation results of the ADSM. UsingADSMs and Radiance, hourly contributions of the sun and sky toindoor daylight illuminance during the entire year were computedat all calculation points in Figs. 4 and 5 under the conditions inTable 3. Among the test results, some examples of daylight illumi-nance for these conditions are selected to discuss the differencebetween the prediction results.

Figs. 8 and 9 compare the daylight illuminance levels computedfrom the ADSM to those computed by the Radiance for simulationcases with a 1.2 m exterior louver-type overhang. Table 4 showsthe statistics of illuminance differences between the results ofthe ADSM and Radiance. Overall, the difference ranges betweenthe two results were not wide, although some cases with a notice-able difference occurred.

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(b) Illuminance from the sun on June 21

Fig. 8. Comparisons of daylight illuminance computed by ADSM and Radiance(Overhang, Point C1).

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(b) Illuminance from the sun on December 21

Fig. 9. Comparisons of daylight illuminance computed by ADSM and Radiance(Overhang, Point C2).

Fig. 8 shows the daylight illuminance difference between theADSM and Radiance at calculation point C1 on a day in June. Asshown in Fig. 8(a), the sky daylight coefficient approach predictedilluminance with a narrower range of difference than the sky-matching method when the illuminance contribution from thesky was considered. The maximum difference between Radianceand the sky-matching method occurred at 14:00 when the skycover was 3. The mean illuminance difference between them was337.7 lx.

As shown in Table 2, the sky at 14:00 on June 21 with an inci-dent illuminance of 6,337 lx and VH ratio of 1.094 was matchedto the representative sky at 16:00 on October 22 with 5,398 lx inci-dent glazing illuminance and 1.0723 VH ratio. The scaling factorapplied to the illuminances computed under the sky conditionwas 1.174.

The right-side wall of the classroom illuminated by the sky at14:00 on June 21 is brighter than when it was illuminated at16:00 on October 22 after being scaled by 0.851 to match the inci-dent vertical illuminance for both skies conditions. With the exte-rior overhang, only a small portion of the hemispherical sky isvisible from the illuminance measurement point, which canincrease the discrepancy in direct illuminance contribution fromthe actual sky as opposed to the matched sky.

As shown in Fig. 8(b), the daylight coefficient approach for thesun generated less illuminance difference from the calculationresults of Radiance compared to the sky-matching method. In addi-tion, as shown in Table 4, the mean of illuminance differencebetween the ADSM and Radiance did not exceed 35.61 lx for all

Table 4Statistics of difference between illuminance and ADSM and Radiance.

Case Statistics Computation method

#1 #2 #3 #4 #5

1 N 819 819 819 819 776Mean 48.03 �0.45 �8.18 �35.61 7.93Mode 31.63 �10.18 �0.13 �8.16 0.00Std. Deviation 200.78 52.16 91.21 106.22 66.38Minimum �537.06 �122.49 �491.27 �1156.73 �14.48Maximum 1163.51 310.06 889.02 264.10 1285.84

2 N 819 819 819 819 817Mean �3.35 1.74 �59.08 �75.74 3.43Mode �0.67 �6.32 0.01 �0.14 0.00Std. Deviation 15.64 25.15 71.20 82.66 33.40Minimum �81.15 �55.64 �453.94 �503.45 �10.43Maximum 39.67 116.73 214.88 25.88 702.37

Where #1: Radiance - Skymatching method of ADSM. #2: Radiance - Daylight coefficient approach of ADSM. #3: Radiance - Daylight coefficient approach with 1 sky patch ofADSM. #4: Radiance - Daylight coefficient approach with 4 sky patches of ADSM. #5: Radiance - Sunmatching method of ADSM.

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(b) Illuminance from sun on June 21

Fig. 10. Comparisons of daylight illuminance computed by ADSM and Radiance (45degree blind, Point C1).


cases. The sun-matching method showed the smallest deviation ofilluminance from the computation results of Radiance. Since, theexterior overhang blocked direct sunlight, the computed illumi-nances by the sun-matching method and solar daylight coefficientfor one sky patch or four sky patches were in good agreement withthose computed using Radiance for the illuminance calculationpoint C1.

Fig. 9(a, b) shows the illuminance difference between the ADSMand Radiance results at calculation point C2 on a day in December.The statistics of illuminance difference between the two simula-tions are summarized in Table 4. Similar to the case in June, theresults provided by the sky-matching method deviate more fromthe results of Radiance than the daylight coefficient approachwhen considering the contribution of the sky to illuminance. Themaximum deviation of 79.66 lx occurs at 10:00 when the sky coverwas 2. The mean difference was within 3.25 lx during the entireperiod of calculation.

The contribution of sun to daylight illuminance increases thedeviation range of illuminance compared to the contribution ofthe sky. The maximum illuminance difference (198.9 lx) betweenthe results of the ADSM and Radiance occurred at 14:00 whenthe sky cover is 6. The sun-matching method provided the smallestdeviation range than the other two methods. The mean illumi-nance difference between the sun-matching method and Radiancewas 7.93 lx.

As shown in Fig. 9(b), the solar daylighting coefficient approachfor four sky patches overestimated illuminances, whereas itunderestimated them for one sky patch. It seems that the skypatches located at the lowest points among the four sky patcheswere not blocked by the exterior overhang; thus, they were visiblefrom C2.

On the other hand, the actual sun was partially obstructed bythe overhang, and thus, sunlight passed through only the lowerpart of the window. For example, the nearest sky patch 50 shownin Fig. 3 from the actual sun at 15:00 on September 21 was locatedhigh enough so that the exterior overhang blocked sunlight, whilethe actual sun was partially exposed. Thus, sunlight passedthrough the lower part of the window. Accordingly, sky patch 95underestimates illuminance. Combining illuminance distributionsfrom sky patches 94, 95, 116, 117 in Fig. 3 results in higher illumi-nances than when using sky patch 95 alone, but still providedhigher illuminance than the actual sun.

Figs. 10 and 11 show the daylight difference between theresults of the ADSM and Radiance at calculation points C1 andC2, when 45� blind conditions were used in June and December.The statistics of illuminance difference are summarized inTable 4.

The deviation between the ADSM and Radiance results is nar-row when the contribution of sky to illuminance is consideredgreater than the contribution of sun for one sky patch and foursky patches. However, the sun-matching method of ADSM pro-vided the smallest deviation range from the illuminance calculatedfrom Radiance. The mean difference between the results of thesun-matching method and Radiance was 3.43 lx during the entireperiod of calculation as shown in Table 4.

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(b) Illuminance from the sun on December 21

Fig. 11. Comparisons of daylight illuminance computed by ADSM and Radiance (45degree blind, Point C2).


The sky-matching method performed very well for the spacewith interior blinds. Interior illuminance was mainly composedof reflected light from interior blinds. as shown in Figs. 10(a) and 11(a). The daylight coefficient approach slightly underestimatesilluminances at a point near the window (C1) and overestimatesthem at the back of the room (C2) for the simulation case withinterior blinds. However, illuminance differences between the day-light coefficient approaches and Radiance are negligibly small sincethe sky was blocked by blinds, causing no influence due to skyluminance distributions.

As shown in Figs. 10(b) and 11(b), the daylight coefficientapproach tends to overestimate illuminance at points C1 and C2.Among the four neighboring sky patches, two were located below

Table 5Coefficient of determination (r2) between illuminance by Radiance and ADSM.

Calculation point Computation method for Case 1

#1 #2 #3 #4

Outdoor 0.998 1.0 1.0 1.0C4 0.826 1.0 0.984 0.996C10 0.945 1.0 0.972 0.992W4 0.812 0.998 0.976 0.976W10 0.939 0.998 0.974 0.976E4 0.861 0.998 0.984 0.992E10 0.953 1.0 0.939 0.937

Where #1: Radiance vs. Skymatching method of ADSM. #2: Radiance vs. Daylight coeffipatch of ADSM. #4: Radiance vs. Daylight coefficient approach with 4 sky patches of AD

the actual sun, providing more lighting to the space than the sun.Therefore, combining the illuminance contributions from the foursky patches results in overestimation of illuminance.

In the sun-matching method, the approximation of a given sunlocation to one of the 55 (or more depending on the location) pre-calculated sun positions caused errors in predicting the illumi-nance contribution from direct sunlight penetration. To achievehigher accuracy in the illuminance prediction from the sun, theseparation of direct and inter-reflected contribution from the sunis desirable.

4.2. Relationship between prediction results of ADSM and Radiance

The relationship between prediction results from the ADSM andRadiance was examined using linear regression analysis andANOVA to correlate the prediction results. For the linear regressionanalysis, the ADSM- and Radiance-computed illuminance levelsduring the entire time period at all calculation points in Figs. 4and 5 were used as independent and dependent variables,respectively.

Table 5 summarizes the coefficient of determination (r2) for thelinear relationship between illuminance generated for all cases.Scatter plots for some selected calculation points (W10, C4) thatindicate the relationship are shown in Figs. 12 and 13. The ANOVAtest results are summarized in Table 6. Overall, the linear correla-tion is strong and all selected regression models were acceptable atthe significance level of 0.01. The coefficient of determination ran-ged from 0.812 to 1.0, indicating that the predictions results of theADSM and Radiance have significant statistical meaning.

For both overhang and blind conditions, the correlationbetween the results from the sky daylight coefficient approachand Radiance is stronger than that between the sky-matchingmethod and Radiance. Moreover, the correlation between theresults of the sun-matching method and Radiance was superiorto any other method that reflects the contribution of the sun toilluminance. The results from the solar daylight coefficient withone or four sky patches show a similar correlation to those fromRadiance.

In addition to the regression analysis, frequency analysis wasconducted for the predicted illuminance from the ADSM and Radi-ance to examine deviation ranges between them. Table 7 showsthe summary of the percent difference of illuminance generatedfrom the ADSM and Radiance. Overall, the daylight coefficientapproach for the sky generated a narrower deviation range com-pared to the sky-matching method. The deviation range was nar-rower from the sun-matching method than from the daylightcoefficient approach for the sun with one or four sky patchesmethod.

For the overhang conditions, 98.91% of the difference fell within10% of the difference range, when the daylight coefficient approachfor the sky was used. When the sky-matching method was

Computation method for Case 2

#5 #1 #2 #3 #4 #5

1.0 0.998 1.0 1.0 1.0 1.01.0 0.998 1.0 0.986 0.992 1.01.0 0.986 1.0 0.978 0.974 1.01.0 0.994 0.998 0.988 0.988 1.01.0 0.976 0.998 0.970 0.884 1.01.0 0.996 0.998 0.984 0.984 1.01.0 0.982 0.998 0.962 0.863 1.0

cient approach of ADSM. #3: Radiance vs. Daylight coefficient approach with 1 skySM. #5: Radiance vs. Sunmatching method of ADSM.

Sky matchingy = 0.8987x + 40.141

R2 = 0.9393

DCAy = 1.034x - 8.7225

R2 = 0.999

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Fig. 12. Correlation between illuminances computed by ADSM and Radiance(Overhang, Point W2).

Sky matchingy = 1.0112x - 4.055

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Fig. 13. Correlation between illuminances computed by ADSM and Radiance (45degree blind, Point C1).


employed, 64.34% of the illuminance difference between the ADSMand Radiance fell within 10% of the percentage difference range.These results imply that the deviation ranges of illuminance gener-ated from Radiance and the ADSM using the sky daylight coeffi-cient approach did not exceed 10%. In addition, the sky daylightcoefficient approach generated illuminance levels closer to thosefrom Radiance.

When the sun-matching method was employed, 90.97% of thedifference fell within the 10% difference range. The percentage dif-ference within the 10% range was 60.53% and 61.27% for the day-light coefficient approach for the sun with one and four skypatches, respectively. Therefore, the sun-matching method wascombined to Radiance most appropriately.

For the blind conditions, the results were similar to those for theoverhang conditions when the contribution of sun to illuminancewas considered. The sun-matching method achieved the closestprediction results to those of Radiance. The application of theone or four sky patches method did not successfully achieve a nar-row range.

When the contribution of sky to illuminance was considered,both the sky-matching method and the sky daylight coefficientapproach achieved a narrow range of deviation from the resultsof Radiance. The percentage difference range within the 10% was89.87% for the sky-matching method and 78.39% for the sky day-light coefficient approach, respectively. This implies that bothmethods achieve prediction results closer to those from Radiance.

In summary, the illuminance values predicted by the ADSM andRadiance were strongly correlated, when the daylight coefficient

approach was used for the sky and the sun-matching method forthe sun, using overhang and blinds. Additionally, these two com-putation algorithms generated the smallest deviation range fromthe predicted illuminance of Radiance.

The sky and the daylight coefficient approach with one or foursky patches for the sun deviated more. Accordingly, the sky day-light coefficient approach and the sun-matching method are rec-ommended for reliable simulations.

Although the illuminance values predicted by the ADSM are notideally equal to those by Radiance under the actual sky conditionsassumed in the present simulations, the ADSM appears to generateeffective predictions for daylight illuminance in space. For addi-tional validation procedure, illuminance from simulations of theADSM and field measurements in real sky and daylight conditionsneed to be examined.

4.3. Outdoor daylight illuminance for sky conditions

The variation of indoor daylight illuminance predicted from theADSMwas compared with actual daylight illuminance measured infield experiments. The field experiments were performed in a full-scale mock-up space that represents a real small private officespace on a daily basis throughout a year.

Among the data monitored during the entire measurementperiods, three days of selected data with clear representative char-acteristics for distinct sky conditions are discussed in this sectionto examine the effect of the sky conditions to the variation of day-light illuminance in an indoor space. Fig. 14 shows the variation of

Table 6Linear relationship between illuminance by Radiance and ADSM for selected calculation points.

Case & point Computation Method Statistics

Variables Unstandardized Coefficients t Sig. ANOVA

B Std. Error

Case 1, W10 #1 (Constant) 40.142 21.90 1.83 0.08 F(37,1) = 572.6r2 = 0.9390, Sig. = 0.00W10 0.899 0.04 23.93 0.00

#2 (Constant) �8.722 3.14 �2.78 0.01 F(37,1) = 36890.8r2 = 0.9990, Sig. = 0.00W10 1.034 0.01 192.07 0.00

#3 (Constant) 16.144 10.64 1.52 0.14 F(37,1) = 1361.2r2 = 0.9750, Sig. = 0.00W10 0.973 0.03 36.89 0.00

#4 (Constant) 0.864 11.21 0.08 0.94 F(37,1) = 1465.8r2 = 0.9770, Sig. = 0.00W10 1.063 0.03 38.29 0.00

#5 (Constant) �2.014 1.09 �1.86 0.07 F(37,1) = 138782.3r2 = 1.0, Sig. = 0.00W10 1.001 0.00 372.54 0.00

Case 2, C4 #1 (Constant) �4.054 2.58 �1.57 0.12 F(37,1) = 36230.5r2 = 0.9990, Sig. = 0.00C4 1.011 0.01 190.34 0.00

#2 (Constant) 0.402 1.98 0.20 0.84 F(37,1) = 54956.1r2 = 0.9990, Sig. = 0.00C4 0.956 0.00 234.43 0.00

#3 (Constant) �21.962 14.94 �1.47 0.15 F(37,1) = 2797.8r2 = 0.9870, Sig. = 0.00C4 1.26 0.02 52.90 0.00

#4 (Constant) �10.734 11.58 �0.93 0.36 F(37,1) = 4610.6r2 = 0.9920, Sig. = 0.00C4 1.254 0.02 67.90 0.00

#5 (Constant) �2.889 2.79 �1.04 0.31 F(37,1) = 50554.7r2 = 0.9990, Sig. = 0.00C4 0.999 0.00 224.84 0.00

Where #1: Radiance vs. Skymatching method of ADSM. #2: Radiance vs. Daylight coefficient approach of ADSM. #3: Radiance vs. Daylight coefficient approach with 1 skypatch of ADSM. #4: Radiance vs. Daylight coefficient approach with 4 sky patches of ADSM. #5: Radiance vs. Sunmatching method of ADSM.

Table 7Percent difference of illuminance (X) between Radiance and ADSM.

Percent difference range[%] Case 1 Case 2

1 2 3 4 5 1 2 3 4 5

X < 5 46.15 80.59 33.46 39.97 81.70 76.07 45.91 7.69 3.91 86.455 < X < 10 18.19 18.32 27.07 21.30 9.27 13.80 32.48 12.94 7.08 6.9610 < X < 15 14.29 0.85 16.42 12.53 3.01 7.33 18.44 19.41 11.48 3.5415 < X < 20 8.18 0.12 11.28 8.27 0.00 2.20 3.17 20.51 17.34 0.2420 < X < 25 4.52 0.00 5.39 6.27 0.00 0.49 0.00 14.29 17.46 0.6125 < X < 30 3.30 0.12 3.26 3.76 0.00 0.12 0.00 11.36 12.58 1.71X > 30 5.37 0.00 3.13 7.89 6.02 0.00 0.00 13.80 30.16 0.49

Total 100 100 100 100 100 100 100 100 100 100

Where #1: Radiance - Skymatching method of ADSM. #2: Radiance - Daylight coefficient approach of ADSM. #3: Radiance - Daylight coefficient approach with 1 sky patch ofADSM. #4: Radiance - Daylight coefficient approach with 4 sky patches of ADSM. #5: Radiance - Sunmatching method of ADSM.


outdoor global illuminance and diffuse illuminance, and verticalilluminance measured at the outside of external envelope of themock-up space.

The variation of daylight illuminance on a clear sky day in Juneis shown in Fig. 14(a). The global and diffuse horizontal illumi-nances varied stably, and no significant fluctuation was noticedduring the entire monitoring period. The global and diffuse illumi-nance ranged from 28,720 lx to 85,100 lx and from 15,020 lx to37,600 lx, respectively. The maximum global illuminance occurredat 12:27, when the solar altitude was 75.93�. The differencebetween maximum global and diffuse illuminance was 47,500 lx.

The global vertical illuminance monitored outside the externalenvelope of the mock-up space ranges from 9,060 lx to 42,450 lx.Unlike the global and diffuse illuminance, the maximum verticalilluminance occurred at 10:55, since the mock-up space wasrotated 22� eastward. The variation of vertical illuminance wasstable without any significant fluctuation.

As shown in Fig. 14(b), the daylight illuminance on a partlycloudy sky day in March fluctuated significantly during short-time periods. The global illuminance ranged from 14,200 lx to95,750 lx and the diffuse illuminance ranged from 9,560 lx to86,600 lx. The maximum variation ranges of the global and the dif-fuse illuminance for a monitoring interval were 58,910 lx and45,730 lx, respectively.

The vertical illuminance arriving at the external envelope ran-ged from 6,917 lx to 93,500 lx during the entire monitoring period.Like the global and the diffuse illuminance, the variation of illumi-nance was very unstable, with a maximum fluctuation range of62,640 lx. The changes of illuminance indicate that the sky condi-tions were not stable and caused significant illuminancefluctuation.

The daylight illuminance under overcast sky in September isshown in Fig. 14(c). The global illuminance varied from 1,734 lxto 15,080 lxwith a stable pattern during themonitoring period. Dif-fuse illuminance also showed a similar variation pattern to that ofglobal illuminance. For instance, the maximum illuminance fluctu-ation of the global and the diffuse illuminance for a monitoringinterval was 2,060 lx and 1,844 lx. The vertical illuminanceincreases to 5,341 lx from 920 lx. The variation pattern was alsostable, similarly to the global and diffuse illuminance. Therefore,the difference in the contribution of the global and the diffuse illu-minance was not significant under overcast sky conditions.

4.4. Difference between illuminance from ADSM and fieldmeasurements

The illuminance data predicted from the ADSM computationalgorithm were compared with field measurement data measured

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Fig. 14. Variation of outdoor daylight illuminance for sky conditions.

Table 8ADSM algorithms for combination of sun and sky.

Algorithm Computationalgorithm for sky

Computation algorithm for sun

I Daylight coefficientapproach (DCA)

Daylight coefficient approach with 1sky patch (DCA-1 patch)

II Daylight coefficientapproach (DCA)

Daylight coefficient approach with 4sky patch (DCA-4 patch)

III Daylight coefficientapproach (DCA)

Sun-matching

IV Sky-matching Daylight coefficient approach with 1sky patch (DCA-1 patch)

V Sky-matching Daylight coefficient approach with 4sky patch (DCA-4 patch)

VI Sky-matching Sun-matching

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Measured DCA+DCA 1 patchDCA+DCA 4 patch DCA+Sunmatch

(a) ADSM for sky: Daylight coefficient approach, ADSM for sun: Three methods

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Measured Skymatch+DCA 1 patchSkymatch+DCA 4 patch Skymatch+Sunmatch

(b) ADSM for sky: Sky matching method, ADSM for sun: : Three methods

Fig. 15. Comparison of measured illuminance and computed illuminances usingADSM for a point at desktop (Clear sky, June/20, Desktop 2.1 m).


in a full-scale mock-up model in order to validate the predictionaccuracy of the ADSM. In this study, daylight illuminance wasmonitored at two positions on the desktop height and at one posi-tion on the ceiling, as shown in Fig. 7.

The daylight illuminance consists of the simultaneous effect ofthe direct component (the sun) and the diffuse component (thesky). However, the computation algorithms of ADSM developedin this study considered the effects of the sun and sky separatelyto compute the final daylight illuminance under given sky condi-tions. Accordingly, to compare the final illuminance from theADSM with the field measurements, the computation algorithmsfor the sun and the sky of the ADSM are combined to represent

the complete effect of the sun and the sky on daylight illuminanceat each measurement point.

The combination of each algorithm used for the computation ofilluminance is summarized in Table 8. Six computation algorithmsare considered to generate illuminance by the sun and the sky,according to the combination of algorithms. For the contributionof the sky to daylight illuminance, the daylight coefficientapproach for sky and sky-matching algorithm were employed.For the effect of the sun on daylight illuminance, the sun-matching method, the daylight coefficient approach for the sun


with one sky patch (DCA-1) and four sky patches (DCA-4) wereused.

Among all data, the comparison between the measured and thecomputed daylight illuminance at each given point on someselected days in each season is shown in Figs. 15–17. As shownin Fig. 15, the variation pattern of the desktop illuminance fromthe ADSM and measurements under a clear sky day in June wassimilar with no significant difference during the entire studyperiod.

Overall, the illuminance from the field measurements waslower than the predicted illuminance, which was computed bythe combination of the ADSM algorithms for the sun and sky.The computation algorithms I (daylight coefficient approach forsky and DCA-1 for sun) and II (daylight coefficient approach forsky and DCA-4 for sun) provided closer illuminance to the mea-sured illuminance as compared to algorithm III (daylight coeffi-cient approach for sky and sun-matching method for sun).

The sun-matching algorithm used for the calculation of daylightilluminance did not function effectively in the combination of com-putation algorithms for the sky, such as the sky daylight coefficientapproach and sky-matching method. The daylight coefficientapproach with one or four sky patches for the sun predicted illumi-nance effectively.

It seems that, under clear sky conditions, the sky was domi-nated by the strong direct component of the sun, but the indoor

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(b) ADSM for sky: Sky matching method, ADSM for sun: Three methods

Fig. 16. Comparison of measured illuminance and computed illuminances usingADSM for a point on desktop (Partly cloudy sky, Mar/11, Desktop 3.9 m).

illuminance was controlled by a shading device that blocks theincoming direct component. Consequently, the daylight coefficientapproach with sky patches appears to be effective to predict day-light illuminance.

Fig. 16 shows the variation of desktop illuminance 3.9 m fromthe internal envelope during a day in March. The illuminance vari-ation pattern was not significantly different from that of the clearsky day, except in the morning from 8:00 to 8:40. Overall, the pre-dicted illuminances were greater than those of measurements.

The solar daylight coefficient approach with one or four skypatches reduced the deviations from the measured illuminance,when it was used with computation algorithms for sky. As withclear sky conditions, the computation algorithms I, II, IV, and Vgenerated a smaller deviation from measured illuminance in aday in March.

Fig. 17 shows the illuminance variation at the center of the ceil-ing for an overcast sky day in September. The illuminances com-puted using all six ADSM algorithms were higher than themeasured illuminances. The six combinations of the ADSM didnot provide any significant differences in the computedilluminance.

It appears that the sun-matching method did not produce widerdeviation ranges than the other algorithms, since the effect of thedirect sun was minimized under overcast sky conditions. In theabsence of the sun, the sky luminance has more influence than

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(b) ADSM for sky: Sky matching method, ADSM for sun: Three methods

Fig. 17. Comparison of measured illuminance and computed illuminances usingADSM for a point on ceiling (Overcast sky, Sep/19, Ceiling 2.1 m).

Table 9Linear correlation between measured and simulated illuminance.

Sky ADSM Algorithm Desk 2.1 m Desk 3.9 m Ceiling 2.1 m

r2 ANOVA r2 ANOVA r2 ANOVA

Clear sky I 0.809 F(435,1) = 1837.45Sig. = 0.00

0.835 F(435,1) = 2204.23Sig. = 0.00

0.845 F(435,1) = 2359.39Sig. = 0.00

II 0.830 F(435,1) = 2115.46Sig. = 0.00

0.866 F(435,1) = 2816.92Sig. = 0.00

0.861 F(435,1) = 2681.93Sig. = 0.00

III 0.800 F(435,1) = 1731.41Sig. = 0.00

0.835 F(435,1) = 2142.30Sig. = 0.00

0.863 F(435,1) = 2738.84Sig. = 0.00

IV 0.782 F(435,1) = 1557.42Sig. = 0.00

0.810 F(435,1) = 1854.75Sig. = 0.00

0.816 F(435,1) = 1919.33Sig. = 0.00

V 0.803 F(435,1) = 1767.49Sig. = 0.00

0.844 F(435,1) = 2347.56Sig. = 0.00

0.830 F(435,1) = 2124.71Sig. = 0.00

VI 0.795 F(435,1) = 1681.06Sig. = 0.00

0.834 F(435,1) = 2173.03Sig. = 0.00

0.859 F(435,1) = 2641.19Sig. = 0.00

Partly Cloudy I 0.851 F(435,1) = 2476.81Sig. = 0.00

0.879 F(435,1) = 3157.07Sig. = 0.00

0.873 F(435,1) = 2971.87Sig. = 0.00

II 0.861 F(435,1) = 2696.17Sig. = 0.00

0.900 F(435,1) = 3916.27Sig. = 0.00

0.882 F(435,1) = 3257.85Sig. = 0.00

III 0.850 F(435,1) = 2459.15Sig. = 0.00

0.856 F(435,1) = 2570.2Sig. = 0.00

0.886 F(435,1) = 3371.99Sig. = 0.00

IV 0.820 F(435,1) = 1970.72Sig. = 0.00

0.848 F(435,1) = 2424.19Sig. = 0.00

0.835 F(435,1) = 2191.23Sig. = 0.00

V 0.828 F(435,1) = 2093.89Sig. = 0.00

0.869 F(435,1) = 2876.62Sig. = 0.00

0.843 F(435,1) = 2324.34Sig. = 0.00

VI 0.761 F(435,1) = 1384.12Sig. = 0.00

0.841 F(435,1) = 2292.74Sig. = 0.00

0.862 F(435,1) = 2714.94Sig. = 0.00

Overcast sky I 0.750 F(435,1) = 1304.37Sig. = 0.00

0.732 F(435,1) = 1184.26Sig. = 0.00

0.766 F(435,1) = 1416.94Sig. = 0.00

II 0.754 F(435,1) = 1333.34Sig. = 0.00

0.740 F(435,1) = 1235.55Sig. = 0.00

0.771 F(435,1) = 1465.04Sig. = 0.00

III 0.581 F(435,1) = 602.26Sig. = 0.00

0.621 F(435,1) = 710.74Sig. = 0.00

0.604 F(435,1) = 663.06Sig. = 0.00

IV 0.905 F(435,1) = 4137.69Sig. = 0.00

0.891 F(435,1) = 3533.93Sig. = 0.00

0.922 F(435,1) = 5148.31Sig. = 0.00

V 0.908 F(435,1) = 4273.37Sig. = 0.00

0.896 F(435,1) = 3751.73Sig. = 0.00

0.926 F(435,1) = 5449.93Sig. = 0.00

VI 0.907 F(435,1) = 4220.70Sig. = 0.00

0.895 F(435,1) = 3684.95Sig. = 0.00

0.915 F(435,1) = 4693.41Sig. = 0.00


the case with the sun. The sky luminance distribution used for thedaylight coefficient method was the same as that derived from thePerez model using measured irradiance, whereas the sky-matchingmethod estimated the illuminance based on representative skies.Therefore, the daylight coefficient approach was more accuratethan the sky-matching method for the computation of illuminanceunder overcast sky conditions.

In this study, the relationship between illuminance levels fromfield measurements and simulations from the ADSM were ana-lyzed using linear regression in order to examine how they corre-lated mutually. The coefficients of determination (r2) for the linearrelationship between the illuminance levels were examined todetermine appropriate prediction algorithms of the ADSM. More-over, prediction models indicating the relationship were testedusing ANOVA with a significance level of 0.01.

For the regression analysis, the illuminance data obtainedthrough the field measurements were used as an independent vari-able. The illuminance from the ADSM, which is combined with twoalgorithms representing the sun and sky, was used as a dependentvariable. Table 9 summarizes the linear relationships between day-light illuminance from measurements and the ADSM simulations,and ANOVA test results. Fig. 18 shows selected scatter plots thatindicate the linear relationships between the variables of the desk-top and the ceiling under given sky conditions.

The results indicate that the regression models for each skycondition were acceptable with a significance level of 0.01. In allthe cases considered in correlation analysis, the coefficient of

determination ranged from 0.581 to 0.926. In the majority of casesexcept three cases under overcast sky conditions, strong linearcorrelations existed between the illuminance from measurementand the ADSM simulations. When the algorithm III was used underovercast sky conditions, the correlation was relatively weak.

As an additional procedure for the validation of the ADSM sim-ulation results, statistical frequency analysis was performed for theentire illuminance dataset including both measurements and sim-ulations. Percent differences between the illuminance from mea-surements and simulations were calculated for each skycondition. Tables 10–12 summarize the percent differences forthe illuminance on the desktop and the ceiling.

For clear and partly cloudy sky conditions, narrower percentdifferences ranges were given by the algorithms I, II, IV, and V thanby the algorithms III and VI that employed the sun-matchingmethod. For example, 76.1% and 76.8% of the differences fall withinthe 5% range, when algorithm II was used under partly cloudy skyconditions for the desktop and the ceiling, respectively. This resultimplies that deviation between illuminance from the ADSM andfield measurements did not usually exceed 10%.

For overcast sky conditions, a wider range of percentagedifference occurred compared to that under clear and partlycloudy sky conditions. The percentage difference did not showsignificant variation between the six algorithms. For instance, thepercentage difference that falls within 5% range was from 31.9%to 38.1%. This implies that there was only a small portion of thedeviation between the simulated and the measured illuminance

Algorithm Iy = 0.6394x + 339.02

R2 = 0.809

Algorithm IIy = 0.6516x + 329.79

R2 = 0.830

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Algorithm IAlgorithm II

(a) Desktop at 2.1 m under clear sky

Algorithm Iy = 0.7053x + 164.79

R2 = 0.879

Algorithm IIy = 0.7194x + 157.45

R2 = 0.900

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Algorithm IAlgorithm II

(b) Desktop at 3.9 m under partly cloudy sky

Algorithm IVy = 1.2876x + 4.5217

R2 = 0.922

Algorithm Vy = 1.3026x + 3.0276

R2 = 0.926

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Algorithm IVAlgorithm V

(c) Ceiling at 2.1m under overcast sky

Fig. 18. Linear relationship between measured and simulated illuminance byADSM.


within the 5% range, as compared to the clear and partly cloudyconditions.

In summary, strong linear correlation existed between the illu-minance from measurement and the ADSM simulations. The devi-ation range between the illuminance from the ADSM andmeasurement decreased using the computation algorithm I, II, III,and IV under clear and partly sky conditions. The deviationbetween the illuminance levels did not show differences betweenthe six computation algorithms under overcast sky conditions.The analysis results indicate that the computation results from

the ADSM simulation were consistent with the results of the fieldmeasurements. It appears that the ADSM simulation generatedreliable predictions of the daylight illuminance.

5. Conclusions

Various ADSM computation algorithms were examined to pre-dict the indoor daylight illuminance for a space with shadingdevices. The daylight illuminance computed by the ADSM undervarious daylight conditions were compared with the illuminancevalues obtained from Radiance and field measurements. The sum-mary of findings is as follows:

1. Strong linear correlations existedbetween thepredicteddaylightilluminance levels by the ADSM and Radiance under diverse skyconditions based on weather data. The daylight coefficientapproach for sky and the sun-matching algorithms for the sungenerated narrower deviation ranges from the predicted illumi-nance by Radiance. This result indicates that the two ADSM algo-rithms are recommended for reliable predictions in simulations.

2. The predicted illuminance from ADSM was higher than that ofthe field measurements under all sky conditions except somecases under partly cloudy sky conditions. The computationresults of the ADSM are consistent with the results of field mea-surements for the majority of time periods, although the consis-tency changes according to the sky conditions.

3. Except three cases for overcast sky conditions, strong correla-tion existed between the illuminance from the ADSM and fieldmeasurements for all sky conditions. Except the three cases,coefficients of determination (r2) ranged from 0.732 to 0.926and the regression models for correlation were effective underthe significance level of 0.01. For the clear and partly cloudysky conditions, the daylight coefficient approach for sky of theADSM generated stronger correlation to measurement data,but the sky-matching algorithm yielded stronger correlationto the field data under the overcast sky condition.

4. Daylight coefficient approach for sky effectively contributed toreducing difference between predicated and measured illumi-nance, when the approach was employed with computationalgorithms of ADSM for the sun under clear and partly cloudyskies. In addition, the sun-matching method did reduce the dif-ference between the simulated and the measured illuminanceeffectively, when the method was used in combination withalgorithms for the sky. Under overcast sky conditions, no signif-icant reduction of the difference between simulated and mea-sured illuminance was observed according to the computationalgorithms.

6. Limitations and future works

In this study, the daylight illuminance predicted by the ADSMsimulations was compared with those of Radiance and field mea-surements in order to determine the computation accuracy of theADSM. The computation results of the ADSM, Radiance, and fieldmeasurements were not ideally equal under given conditions ofdaylight and shading devices conditions.

The field measurements were performed in a different site thanthat of computer simulations due to several limitations such asresearch funding and administration support. The different sitemay affect the prediction results, but the ADSM tends to providereliable prediction results under daylight conditions. Test resultsat an equal building site would be beneficial for future study. Also,more diverse shading device conditions should be examined forADSM prediction, which is developed in this study.

Table 10Percent difference of illuminance (X) between measured and simulated illuminance under clear sky.

Position ADSM Algorithm Percent difference range [%]

X < 5 5 < X < 10 10 < X < 15 15 < X < 20 20 < X < 25 25 < X < 30 X > 30 Total

Desk 2.1 m I 60.1 33.9 4.6 1.1 0.2 0.0 0.0 100II 61.0 33.5 4.8 0.5 0.2 0.0 0.0 100III 33.5 48.2 10.6 4.4 1.1 2.3 0.0 100IV 57.6 34.2 4.6 1.1 0.2 0.0 2.3 100V 57.6 33.9 5.5 0.5 0.2 0.5 1.8 100VI 33.9 48.4 9.6 4.6 3.4 0.0 0.0 100


Ceiling 2.1 m I 58.7 38.1 3.0 0.2 0.0 0.0 0.0 100II 59.9 37.6 2.3 0.0 0.2 0.0 0.0 100III 37.6 40.4 14.2 5.0 2.8 0.0 0.0 100IV 54.6 39.4 3.4 0.2 0.0 0.0 2.3 100V 55.5 37.8 3.9 0.2 0.7 0.0 1.8 100VI 33.9 43.1 14.9 4.8 3.2 0.0 0.0 100

Table 11Percent difference of illuminance (X) between measured and simulated illuminanceunder partly cloudy sky.


X < 5 5 < X < 10 10 < X < 15 15 < X < 20 20 < X < 25 25 < X < 30 X > 30 Total




Table 12Percent difference of illuminance (X) between measured and simulated illuminanceunder overcast sky.


X < 5 5 < X < 10 10 < X < 15 15 < X < 20 20 < X < 25 25 < X < 30 X > 30 Total






Conflict of interest

We authors disclose any actual or potential conflict of interestincluding any financial, personal or other relationships with otherpeople or organizations within three years of beginning the sub-mitted work that could inappropriately influence, or be perceivedto influence, our work.

Acknowledgments

This research was supported by the Basic Science Research Pro-gram through the National Research Foundation of Korea (NRF)funded by the Ministry of Science, ICT and Future Planning (NRF-2014R1A2A1A11051162).

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