Energy and Buildings 138 (2017) 347–354
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Analysis of daylight metrics of side-lit room in Canton, south China: A comparison between daylight autonomy and daylight factor Yu Bian a , Yuan Ma b,∗ a
School of Architecture, State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 501640 Guangdong, China Low-Carbon Ecological Urban & Rural Research Center, College of Architecture & Urban Planning, Guang Dong University of Technology, Guangzhou 510090, Guangdong, China b
a r t i c l e
i n f o
Article history: Received 28 January 2016 Received in revised form 15 December 2016 Accepted 18 December 2016 Available online 24 December 2016 Keywords: Daylight performance metrics Daylight factor Daylight autonomy Side-lit window
a b s t r a c t To ensure sufficient daylight in rooms, daylight performance metrics are the basic references to guide building design or to benchmark a building against another in terms of daylighting in a room. Daylight factor (DF) is the most commonly accepted daylight performance metric, but it has limitations in evaluating the daylighting of a room space in a real daylight climate, as defined under CIE standard overcast sky, while daylight autonomy (DA) is a climate-based performance metric which takes into consideration the regional daylight climate. Based on long-term continuous measurements of daylight illuminance in a test room under real climate, combined with scale model tests under an artificial sky and computational simulations, the quantitative relationship between monthly average daylight illuminance, DF and DA are holistically analyzed in this paper. The result shows that a monthly average daylight illuminance above 300 lx in a room located in Canton requires a DF of no less than 1.8% for north-facing space. Finally, the depth of DA300lx [50%] daylit area for four cardinal directions was proposed in comparison with DF. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Building performance metrics are supposed to be “quality measures” of buildings with respect to their energy efficiency, safety, quality of design, etc. [1]. Criteria of performance metric are vital for judging whether or not a building design meets a certain functional requirement. Moreover, daylighting environments are notoriously difficult to evaluate, for which a series of methods have been proposed including static metrics as well as dynamic metrics, parts of which are not easily accessible for non-professional daylight simulation designers. Side-lit windows are the most widely used glazing openings in various buildings which ensure direct transmission of daylight into buildings, and well-designed side-lit windows could reduce electrical lighting energy consumption and enhance indoor environmental quality. It is estimated that huge amount of energy has been wasted associated with electric lighting during typical daytime working hours (8:00–18:00) partly because the imperfect design of side-lit windows [2], so it is meaningful to analyze the daylight performance metrics of side-lit windows and discuss the
∗ Correspondence to: Guang Dong University of Technology, Yuexiu District, Guangzhou, China. E-mail address:
[email protected] (Y. Ma). http://dx.doi.org/10.1016/j.enbuild.2016.12.059 0378-7788/© 2016 Elsevier B.V. All rights reserved.
criteria of performance metric, especially under regional daylight climate from which building daylighting design will benefit. This article relates a commonly used daylight metric (daylight factor, DF) to a newer, more complex daylight metric (daylight autonomy, DA) with the objective of providing simple DF-based design guidance in Canton, China so as to achieve adequate daylight levels within interior space, particularly, for those who do not have the ability or time to conduct more DAYSIM simulations. Daylight factor (DF) is the most common metric used in actual practice and/or guidelines, which is the ratio of internal illuminance to external horizontal illuminance under an overcast sky defined by the CIE luminance distribution. Although this is a fair model of sky brightness under certain types of dull weather conditions, it is not particularly common [3]. Significant amongst the various reasons for this may be the lack of realism of the standard predictive method: the DF approach [4].
1. The CIE standard overcast sky is merely an idealist sky model: Overcast sky type is not unique. The CIE overcast sky is applicable when the complete sky canopy is covered with uniform dark clouds representing heavy overcast sky only [5]. 2. DF is assessed under overcast conditions, no account is made of illuminance from sun and non-overcast skies, and so the daylight
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factor is invariant to building orientation and the location of the room [6]. Daylight autonomy (DA), on the other hand, is a climate-based daylight performance metric which factors in the daylight climate of the building site and fac¸ade orientation. DA is represented as a percentage of annual daytime hours that a given point in space is above a specified illumination level. It is a major innovation since it encompasses specific weather conditions of the geographic location on an annual basis [7]. DA uses work plane illuminance as an indicator of whether sufficient daylight is rendered in a space so that an occupant can work by daylight alone. Required minimum illuminance levels for different space types can be directly taken from reference documents such as “China National Standard of Building Daylighting Design”. DA300lx [50%] represents the percentage of the work plane area that exceeds 300 lx for at least 50% of the annual time. In this paper, under the real daylight climate condition in Canton, the relationship between DF and monthly average daylight illuminance on work task plane were studied and as a conclusion the criteria of DF was proposed. By comparing the measured data in the test room and the software simulation, the results showed that the deviation between simulation and measurement is less than 20%, which is an acceptable result, indicating the validity of the simulation in terms of accuracy. Based on the simulated results, the depth of DA300lx [50%] daylit area in four cardinal orientations were studied, and the comparison between DA300lx [50%], DF, average daylight illuminance in a specific month and annual daylight illuminance were proposed in various orientations. These results could be adopted as design references for the building daylighting design, especially for those non-profession daylighting simulation designers who are familiar with DF as the performance metric. 2. Methodology
Fig. 1. Inside view of test room.
Table 1 Photometric description in test room. Item
Photometric description
GLAZING
Double glazing with Low-E coating: transmittance Tvis = 0.45 Lambertian diffuser with a 0.85 reflectance, White Lambertian diffuser with a 0.85 reflectance, White Lambertian diffuser with a 0.66 reflectance, Medium gray 0.15 specular component, 0.42 reflectance, Dark gray ceramic tile Lambertian diffuser with a 0.78 reflectance, White
INTERIOR WALL CEILING CURTAIN FLOOR PROJECTOR SCREEN
2.1. Test room measurement To study the daylight performance metrics in Canton, a qualified side-lit room space was selected as the test room where the measurements towards daylight illuminance distribution under real daylight climate were taken place. According to Prof. C. F Reinhart: for cities in low latitude in the north hemisphere (e.g. Phoenix, United State), the north facing facade receives little to no direct sunlight [8,9]. A north facing room was selected in this research as a baseline to study the DF criteria and used as the test room to test and verify the simulation program. The test room adopted in this study is a due north facing side-lit room located in Canton, with open surroundings. The dimensions are 7.6 m*3.0 m*2.7 m, the window head height (WHH) is 2.2 m. The room depth is 7.6m, more than 3 times the WHH, which related to the rules of thumb. The window-to-wall ratio (WWR) of the test room is 45%. The outer frame and mullion width are 0.05 m resulting in a frame factor of 18% of the rough opening area of the window (Fig. 1). There are 3 sets of fluorescent grille lamp installed on the ceiling, but turned off during the measurement period. Optical properties of all room components are listed in Table 1. The arrangement of photometers (Sensor Maker/Model: Konica Minolta T-10, Range: 0.01–299,900 lx along with automatic range switching, Accuracy ±5%) is represented in Fig. 2. A total of 24 photometers are settled on the axis of symmetry of the test room and on two equidistant axes at 1 m. Therefore, the photometers are located with a spacing of 1/2 WHH and at a height of a typical work task plane (above the interior floor of 0.75m). The arrangement of photometers had referenced Ho and Chiang’s research work of daylight level distribution in a classroom in Taiwan [10]. All the
Fig. 2. Plan of test room & photometers arrangement.
photometers are wire linked and a string of 24 photometers collect illuminance data every 10 min simultaneously and then recorded in computer. The measurement is processed daily from 8:00AM to 6:00PM, to be consistent with the occupied hours of a typical office room. This occupancy schedule is in agreement with the IESNA’s new Lighting Measurement IES LM-83-12 which promotes climate based daylighting metrics [11]. The study included the daylight illuminance data collected from April 2013 to April 2015, except a few hours or days that the photometers were halt or broken down, a total of 39,000 sets of data based on intervals of 10 min measurement were analyzed in this study.
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Fig. 4. inside view of scale model for DF measurement.
Fig. 3. DF measurement within scale model in wall mirrored artificial sky.
ers of 1 mm acrylic glass (maker: Mitsubishi, T = 0.70) and 1 layer of 1 mm acrylic glass (maker: Mitsubishi, T = 0.90) was used in the model as window glass. multi-way photometers with 8 micro lux sensors (Sensor Maker/Model: Konica Minolta T–10 M, Range: 0.01–299,900 lx along with automatic range switching, Accuracy ±5%) arranged in one row were used to measure the illuminance in the scale model (Fig. 4). All the 24 study points were measured for 3 rounds, and the outcome of DF obtained are shown in Fig. 5. All the DF analyzed in this study come from the measurements in the scale model.
2.2. Accessing daylight factors in test room
2.3. Daysim simulation
Following the study by Navarro, Sendra and Barros, one frequently used approach to assessing DF within buildings is by means of the scale model, in which a wall-mirrored artificial sky simulator is applied to reproduce the CIE overcast sky [12,13]. According to Jiangtao Du’s research work on accessing the DF in an atrium building with the measurement in the wall mirrored artificial sky, the accuracy of the artificial sky has been previously contrasted [14]. As can be observed in Fig. 3, a wall mirrored artificial sky was applied, which represents an ideal overcast sky. Its design corresponds with that of a parallelepiped model of the artificial sky, where a constant luminance reflector emits light inside a cube. Upon the reflector, there are 32 fluorescent tubes providing a homogeneous emission of light flux. The walls are mirrors simulating the location of the horizon in the infinite. The scale model in this study is placed on a platform whose height is the bottom of the cube. The actual width of the interior of artificial sky is 2400 mm; the width based on a 1:15 scale model in the artificial sky is 500 mm; The distance between the window aperture and the closet wall of the artificial sky is 950 mm. The scale model was made similar to the test room in order to quantify the DF on the study points, the reflectance of each indoor surface in accordance with the actual test room, 2 lay-
2.3.1. The description of computer model The computer model is created similar to the test room, with trials in this stage aiming to verify the daylighting simulation program “Daysim”, and the model was also adopted to study the daylight autonomy distribution with various orientations. Depending on the shape, size and surface reflectance of the test room, the computer model for the analysis of DF is defined as a room of 3.0 m wide by 7.6 m deep by 2.7 m high. The side-lit window is in rectangular shape, with 0.05 m thick mullion and a glazing transmittance of 0.45. All the optical properties of indoor surfaces are similar with those in the test room, as listed in Fig. 6. The positions of study points are arranged in accordance with those of photometers in the test room. The study points are represented in Fig. 6. 2.3.2. Verification by measurement Radiance has been verified in a number of lighting environments [15,16]. Those investigations showed that Radiance simulations could achieve a high accuracy in typical daylit spaces through comparison between measurement and theoretical analysis. A recent study [17] using Radiance as a benchmark to verify a general approach to computing daylight coefficient sets for rooms employing multiple dissimilar components. These investigations further
Fig. 5. Measured DF on study points.
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Fig. 6. Computer model.
Fig. 7. Comparison between test room measured (m) and Daysim simulated (s) daylight illuminance.
indicated the status of Radiance in the field of daylighting simulation. Daysim, a computational tool for dynamically calculating annual illuminance profiles, has adopted the Radiance algorithms and added two other functions (daylight coefficient and Perez sky model) [18]. In this paper, for side-lit room daylighting, Daysim was regarded as an efficient approach. Daysim/Radiance simulation parameters have a direct influence on the simulation result, therefore, these values need to be calibrated so that the effect of complex fenestration devices will be accurately represented throughout the depth of the reference office [11]. This study compared Daysim simulated values with on-site measured illuminance distributions. However, as the measurements occurred in a real room under a real weather, but the simulations were processed under a typical weather, with weather file drawn from China Standard Weather Data (CSWD), it is obviously that deviation existed in this type of comparison.
Fig. 7 compared the measured (m) and simulated (s) result of average daylight illuminance distribution in December and annual average daylight illuminance distribution; the values are listed in Table 2. comparison between measured and simulated daylight illuminance in the test room shows, the deviation between simulation and measurement is obvious (−37%–22%) in the area close to window, but agreement is particularly critical for values beyond WHH of 1.0 around the 300 lx and this is where the disagreement between simulation and measured values are acceptable (−12.9%–22.4%). Based on the two years measurements of daylight illuminance distribution in test room, the measured DA300lx was shown in Fig. 8. As can be seen from the comparison between the measured and Daysim simulated DA, the mean deviation ≤20%, and at 0.84 times the WHH from the fac¸ade, the simulated DA300lx [50%] demon-
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Table 2 Daysim simulated and test room measured illuminance (lx). Distance to fac¸ade in multiples of WHH
Simulated annual average daylight illuminance
Measured annual average daylight illuminance
Difference between simulation and measurement
Simulated average daylight illuminance in Dec
Measured average daylight illuminance in Dec
Difference between simulation and measurement
0 0.5 1 1.5 2 2.5 3
1258.9 611.2 330.5 232.1 152.1 100.5 96.7
1084.3 594.7 379.3 271.1 196.4 152.8 120.8
16.1% 2.8% −12.9% −14.4% −22.6% −34.2% −20.0%
768.8 467.2 265.3 159.4 96.3 61.8 49.2
625.6 396.3 216.8 161 120.4 96.3 78.1
22.9% 17.9% 22.4% −1.0% −20.0% −35.8% −37.0%
Fig. 8. Comparison between test room measured (m) and Daysim simulated (s) Daylight autonomy.
strates to be, 15.1% more than what the measured demonstrates at 0.73 times the WHH from facade. Based on comparisons with the test room measurement, the simulations prove to be a satisfying variation of DA. Daysim can achieve a −37%–22% agreement result in the process of predicting daylight levels in rooms located in Canton. The divergence could be mainly explained by the weather data divergence between the real weather and typical weather data (source: CSWD), geometric and photo metric divergence between the test room and scale model, and some errors that may have occurred in the measuring processes [19,20]. To conclude the Daysim simulations have been verified at certain level (−37%–22%) by the measurements for a north fac¸ade exposed largely to diffuse sky condition, and can therefore be used for further analysis of buildings under construction and those yet to be constructed in Canton. 3. Analysis of criteria of performance metrics 3.1. Criteria of daylight factor in Canton, south China At present, the DF represent the most widely used metric in the evaluation of daylighting. An accurate criteria of daylight factor based on rigorous experiment under the regional daylight climate is the baseline to guide the building daylighting design. In this study, that criteria is developed from more than 38,000 sets of daylight illuminance data, which were collected from 2013 to 2015. According to the statistics of daylight illuminance on 24 study points in the test room for 2 years, the relative values(monthly average value/annually average value) of monthly average daylight
illuminance in the test room were shown in Fig. 9. As can be concluded from the result, the monthly daylight illuminance in Canton varies significantly, with the average daylight illuminance in April, June, July, August, September and October surpassing the annual average level and falling under the latter in other months. The daylight performs obviously higher in June, July, August and September than in other months, among which the daylight illuminance in July is the highest in a typical year, which is 43% more than the annual average level, and the daylight performs weakly in January and December, with the weakest in December–the average daylight illuminance in December is less than half of that in July, about 63% of annual level, meaning that the daylight condition in December is the worst in a typical year in Canton, so the average daylight illuminance in December was adopted to define the criteria for the daylight factor metric. To define the criteria of daylight factor metric in Canton, the average daylight illuminance in December was selected to compare with the DF, because the daylight illuminance in December is the lowest in a typical year in Canton, south China. Fig. 10 and Table 3 shows the relationship between average daylight illuminance in Table 3 Comparing DF with monthly or annually average daylight illuminance. Average daylight illuminance in December(lx)
Daylight factor(%)
Annual average daylight illuminance(lx)
75 150 300 500 750
0.5 0.9 1.8 3.0 4.5
130 297 533 826 1273
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Fig. 9. Relative value of monthly average daylight illuminance measured in test room.
Fig. 10. Relationship between average daylight illuminance (test room measured) and DF (scale model tested).
Table 4 Comparing daylight factor and daylight autonomy in four cardinal directions. Orientation Metric
North
East
South
West
DA300lx DF (%) Distance to fac¸ade in multiple of WHH
50% 1.52 0.84
50% 1.35 0.90
50% 1.20 1.05
50% 1.35 0.90
December/annual and DF, as we can see from Table 4, in Canton, the average daylight factor in the test rooms have a proportional relationship with the daylight level on the work task plane, average daylight illuminance Eavg = 166.67*DF. To have a monthly daylight
illuminance of no less tan 300 lx, the required daylight factor in a north facing room space should be no less than 1.8%. Correspondingly, for a monthly daylight illuminance of no less than 500 lx, the threshold of daylight factor in a north facing room space should be up to 3.0%. 3.2. Comparison between DA and DF in side-lit room in Canton Based on observances of the sky luminance distribution in Canton, south China, DF could not well reflect the real daylight condition in south China as defined under diffused skylight, therefore the climate-based metric DA is more applicable in South China, andthe DA values studied in this article are that in unoccupied space.
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Fig. 11. Daysim simulated DA 300 lx for varying fac¸ade orientation.
The Daysim simulations had been verified by the measurements in chapter 2.3. The computer model adopted to study the daylight autonomy for four cardinal orientations is identical with the one in the verification study but with varying orientations. Similarly, the study points arranged in the computer model are also identical with the arrangement in the test room. With this model, the daylight illuminance were generated via Daysim simulation and then the illuminance data above 300 lx was processed to ratio of occurrence. Fig. 11 shows the daylight autonomy distributions along the center lines of the test room facing four cardinal directions in Canton. Up to a distance of 1/2 window head height, the daylight autonomies are nearly identical, showing that right near a window there is plenty of daylight for any fac¸ade orientation. Differences appear deeper in space, with the south-facing space receiving most daylight, the DA300lx [50%] appeared at 1.05 times the window head height from fac¸ade. The west-facing space receives almost identical daylight as its east-facing counter part due to the assumed occupancy pattern from 8:00 to 18:00, and the DA300lx [50%] in west-facing space and east-facing space appeared at 0.90 times the window head height from fac¸ade; The north facing space receives the minimum daylight in four cardinal directions, the DA300lx [50%] appeared at%0.84 times the window head height from fac¸ade. Fig12 shows DF distribution in the test room, and the distance to fac¸ade where the DA300lx [50%] occurs for the four orientations are indicated. DF for an overcast sky is not dependent on orientation, so the relationship between distance to fac¸ade and DF for various orientations are identical. To compare the DF and DA in Canton, the DF which measured with a scale model in the artificial sky and the Daysim simulated daylight autonomy (DA300lx [50%])were adopted in this section of the study. The results shown in Table 4 indicates that, for a north facing fac¸ade in Canton, DA300lx [50%] pronounced at the 0.84times of window head height where the daylight factor is 1.36%, for the east facing fac¸ade the DA300lx [50%] pronounced at the 0.90 times of window head height where the daylight factor is 1.35%, for the south facing fac¸ade the DA300lx [50%] pronounced at the 1.20 times of window head height where the daylight factor is 1.20%, for the west facing fac¸ade the DA300lx [50%] pronounced at the 0.90 times of window head height where the DF is 1.35%. For most of architect and parts of building engineering consultant, DA is not a familiar daylight performance metric to access, so the corresponding DF was listed in this study to help them analyze the daylight cases
Fig. 12. Scale model tested DF in artifical sky.
in Canton, and also could be used as a reference in other projects based in south China area. 4. Conclusion Some conclusions that can be drawn from this study include: (1) It has been found that there is an agreement (deviation <20%) between the test room measured DA and the simulated value from the Daysim for a north facing side-lit room under the daylight climate in Canton, South China, particularly within the distance from fac¸ade of window head height. (2) The test room measured daylight levels in December is the lowest in an actual year, which is 63% of the annual average daylight level in Canton, China. (3) The scale model tested DF levels have a proportional relationship with the test room measured daylight level on the work task plane. The former is derived from a parallelepiped artificial sky, and a monthly average daylight level of no less than 300 lx requires a daylight factor of 1.8%, correspondingly, 500 lx requires a daylight factor of 3.0% for a north facing fac¸ade.
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(4) DA is a more applicable daylight performance metric than DF, as the former factors in the regional daylight climate and fac¸ade orientation. DA distribution in the test room varies significantly in four cardinal directions in the distance from fac¸ade surpassing 1/2 WHH in Canton. In this case study, the test room with a double glazing low-E window, the glazing transmittance of which is 0.45. The simulation results indicate that southfacing space receives most daylight, with the DA300lx [50%] pronounced at 1.05 times the window head height from fac¸ade. The west-facing space receives almost identical daylight with its east-facing, with both pronounced at 0.90 times the window head height from fac¸ade; The north facing space receives the minimum daylight in four cardinal directions, the DA300lx [50%] pronounced at 0.84 times the window head height from fac¸ade. (5) Comparing the scale model tested DF under artificial sky and daysim simulated DA in Canton, for a north facing fac¸ade in Canton, DA300lx [50%] pronounced at where the daylight factor is 1.52%, for the east facing fac¸ade the DA300lx [50%] pronounced at where the daylight factor is 1.35%, for the south facing fac¸ade the DA300lx [50%] pronounced at where the daylight factor is 1.20%, for the west facing fac¸ade the DA300lx [50%] pronounced at where the daylight factor is 1.35%; These conclusions are obviously limited to measurement in the test room with an unobstructed window and free from shading facilities under the real weather in actual years (2014–2015). The test room with various glazing, fac¸ade types and blind systems should also be investigated to find the average daylight levels in daylit rooms. These issues will be studied in future work. Acknowledgments The work was supported by China National Key Research and Development Program (Project No. 2016YFC0700205), National Natural Science Foundation of China (Project No. 51208205), autonomous research project of State Key Laboratory of Subtropical Building Science (2015ZC15). We are thankful to Dr. Alstan Jakubiec for his valuable advises and improving the quality of paper. References [1] C.F. Reinhart, C.J. Mardaljevic, Z. Rogers, Dynamic daylight performance metrics for sustainable building design, Leukos 3 (1) (2006) 1–20. [2] A. Shehabi, N. DeForest, A. McNeil, et al., The light harvesting potential of dynamic daylighting windows, Energy Build. 66 (2013) 415–423.
[3] P.R. Tregenza, The daylight factor and actual illuminance ratios, Lighting Res. Technol. 12 (2) (1980) 64–68. [4] J. Mardaljevic, A. Nabil, The useful daylight illuminance paradigm: a replacement for daylight factors, Energy Build. 38 (2006) (905-903). [5] T. Muneer, Solar irradiance and illuminance models for Japan I: sloped surfaces, Light. Res. Technol. 27 (1995) 209–222. [6] A. Nabil, J. Mardaljevic, Useful daylight illuminance: a new paradigm for assessing daylight in buildings, Lighting Res. Technol. 37 (1) (2005) 41–59. [7] C.F. Reinhart, O. Walkenhorst, Dynamic RADIANCE-based daylight simulations for a full-scale test office with outer venetian blinds, Energy Build. 33 (7) (2001) 683–697. [8] Christoph F. Reinhart, Daylighting Handbook, 2013, pp. 91–95. [9] C.F. Reinhart, A simulation-based review of the ubiquitous window-head-height to daylit zone depth rule of thumb, in: Proceedings of Buildings Simulation 2005, Montreal, Canada, 2005, pp. 15–18. [10] Ming-Chin Ho, Che-Ming Chiang, Optimal sun-shading design for enhanced daylight illumination of subtropical classrooms, Energy Build. 40 (10) (2008) 1844–1855. [11] Christoph F. Reinhart, J. Alstan Jakubiec, Diego Ibarra, Definition of a reference for standardized evaluations of dynamic fac¸ade and lighting technologies, Proceedings of BS2013 (2013) 3645–3652. [12] J. Navarro, J.J. Sendra, C. Barros, Design and calculation method for natural lighting in architecture, in: Proceedings of the 3rd European Conference on Architecture: Solar Energy in Architecture and Urban Planning, Florence, Italy, May, 1993, pp. 371–373. [13] I. Acosta, J. Navarro, J.J. Sendra, Towards an analysis of daylighting simulation software, Energies 4 (7) (2011) 1010–1024. [14] Jiangtao Du, Steve Sharples, The variation of daylight levels across atrium walls: reflectance distribution and well geometry effects under overcast sky conditions, Sol. Energy 85 (2011) 2085–2100. [15] J. Mardaljevic, Validation of a lighting simulation program under real sky conditions, Lighting Res. Technol. 27 (4) (1995) 181–188. [16] M. Fontoynont, P. Laforgue, R. Mitanchey, M. Aizlewood, J. Butt, W. Carroll, et al. IEA SHC Task 21: validation of daylighting computer programs -ECBCS Annex 29; Nov (1999). [17] A. Laouadi, C.F. Reinhart, D. Bourgeois, Efficient calculation of daylight coefficients for rooms with dissimilar complex fenestration systems, J. Build. Perform. Simul. 1 (2008) 3–15. [18] C.F. Reinhart, J. Wienold, The daylighting dash board: a simulation-based design analysis for daylit spaces, Build. Environ. 46 (2) (2011) 386–396. [19] J. Du, S. Sharples, Assessing and predicting average daylight factors of adjoining spaces in atriumbuildings under overcast sky, Build. Environ. 46 (2011) 2142–2152. [20] M. Aizlewood, J. Butt, K. Isaac, P. Littlefair, Daylight in atria: a comparison of measurement, theory and simulation, in: Proceedings Lux Europa, Netherlands: Amsterdam, 1997.