Estimation of obstructed vertical solar irradiation under the 15 CIE Standard Skies

Building and Environment 103 (2016) 123e133

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Estimation of obstructed vertical solar irradiation under the 15 CIE Standard Skies Siwei Lou*, Danny H.W. Li, Joseph C. Lam, Eric W.M. Lee Building Energy Research Group, Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 December 2015 Received in revised form 7 April 2016 Accepted 7 April 2016 Available online 11 April 2016

The estimation of solar heat gain via vertical fenestration is important in energy-efficient building design and operation especially for subtropical Hong Kong. Being one of the most populated cities in the world, buildings in Hong Kong tend to be densely constructed. In this regard, the shading effect of surrounding buildings could significantly limit solar radiation from the sun and sky to the window while certain amount of solar radiation would be reflected from the opposite façades. This paper presents a calculation approach to compute solar radiation on obstructed fenestration for both overcast and non-overcast skies. Performance of the proposed method is evaluated by comparing with simulated results of a sophisticated lighting program and field measurements. The findings are essential for the assessment of both active and passive building energy saving techniques including shading and building integrated photovoltaic systems in metropolitan environment. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Vertical irradiance Obstructions CIE Standard Skies Reflection Simulation

1. Introduction In subtropical Hong Kong, buildings are subjected to substantial cooling requirements throughout most of the year [1,2]. Solar heat gain, particular via vertical windows, presents the major part of the cooling load [3,4]. The estimation of solar heat gain is thus important in the cooling load estimation, air-conditioning system optimizations and energy-efficient building designs [5]. Horizontal solar data from routine meteorological measurements [6e9] are sufficient in studying solar heat gain through horizontal glazing such as skylight. There are greater demands for the knowledge of solar radiation on vertical surfaces [10,11] particularly for high-rise curtain-walling buildings with large window areas. Being one of the most densely populated cities in the world, many building developments in Hong Kong are constructed in densely-built zones. Window façades facing narrow long streets are quite common and long urban canyons are the main Hong Kong skyline features [12]. The shading effects due to surrounding buildings could significantly limit the sunlight and solar radiation from the sun and sky [13]. It indicates that a considerable portion of sunlight and solar radiation of a building surrounded by high-rise

* Corresponding author. E-mail address: [email protected] (S. Lou). http://dx.doi.org/10.1016/j.buildenv.2016.04.005 0360-1323/© 2016 Elsevier Ltd. All rights reserved.

blocks would be reflected from ground and opposite façades [14]. The reflected components can be large under non-overcast skies [15]. The quantification of solar radiation on obstructed vertical fenestration is essential for shading device designs to minimize solar heat gain and the estimation of the power output potential of vertical photovoltaic façade [16]. The estimation of solar radiation in highly obstructed environment tends to be very complex. Many studies tackled this issue [10,17e19] but most of them just considered the geographical information science which estimates solar radiation with the assumption of isotropic diffuse skylight distribution. For building integrated photovoltaic (BIPV) designs and building energy assessments, anisotropic skylight distribution would be more appropriate [20]. Conventionally, such analysis was mainly based on computer simulations [21]. The simulation packages are, however, complicated to use and effort demanding especially when various options and schemes are being analyzed [22]. Manual calculations using algebraic equations in simple computer spreadsheets are more appropriate in evaluating the solar radiation availability at the initial stage of design. Previously, we proposed a number of estimation procedures to estimate the vertical daylight illuminance on obstructed building façades under overcast and non-overcast skies [23,24]. Daylight is the visual part of solar radiation and same approaches can also be applied for the estimation of radiation.

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S. Lou et al. / Building and Environment 103 (2016) 123e133

Nomenclature

EVG,rg

cfrb

RΖ Raf

cfrb0

cfgsun

EHD ENB EVB EVB,rb EVB,rg EVD,avgb EVD,avgg EVD,O EVD,rg EVG,O EVG,rb

Configuration factor indicating the portion of diffuse irradiance reflected by the façade of building that reaches the façade of obstruction Configuration factor indicating the portion of diffuse irradiance reflected by the façade of obstruction that reaches the center of fenestration Configuration factor indicating the portion of direct solar irradiance reflected by the ground that reaches the fenestration Diffuse irradiance on the unobstructed horizontal plane W m
2 Direct normal solar irradiance without obstruction W m
2 Direct solar irradiance from sun W m
2 Direct solar irradiance onto the fenestration, originated from building reflection W m
2 Direct solar irradiance onto the fenestration, originated from ground reflection W m
2 Diffuse irradiance onto the façade of building, originated from sky W m
2 Diffuse irradiance onto the ground under obstruction W m
2 Diffuse irradiance onto the fenestration, originated from sky, under obstruction W m
2 Diffuse irradiance onto the fenestration, originated from ground reflection W m
2 Total solar irradiance on the vertical fenestration, under obstruction W m
2 Total solar irradiance onto the fenestration, originated from building reflection W m
2

This paper proposes a manual calculation approach to estimate the solar irradiance on obstructed building façades under the 15 CIE Standard Sky conditions [25,26], which is reliable for analyzes in initial design stage. The performance of the proposed method is assessed by comparing its results against the results of a sophisticated simulation program namely RADIANCE and field measurements. Features of the findings are discussed.

2. CIE Standard Skies The set of 15 CIE Standard Skies predicts the ratio between luminance at any point of the sky hemisphere to that at the zenith point [23,24]. The same mathematical models can also be used to estimate the ratio between the radiance of an arbitrary sky point (Ra4, W m
2 sr
1) and the radiance at the zenith position (Rz). The standard formula of the ratio is the product of a relative gradation expression 4(Z)/4(0) and a relative scattering indicatrix function f(c)/f(ZS) as given in Eqs. (1)e(3).

Ra4 f ðcÞ4ðZÞ ¼ f ðZS Þ4ð0Þ RZ 4ðZÞ 4ð0Þ

¼

1 þ a expðb=cos ZÞ 1 þ a exp b

(1)

(2)

Rafi Z ZS

a ab ai aiL aL aS aU aW1 f fiL fN 0

fN fS c cref rb rg

Total solar irradiance onto the fenestration, originated from ground reflection W m
2 Diffuse radiance from sky zenith W m
2 sr
1 Diffuse radiance of an unobstructed sky point at a and f W m
2 sr
1 Diffuse radiance of an unobstructed finite sky element at a and f W m
2 sr
1 Zenith angle of an arbitrary sky point rad Zenith angle of sun rad Altitude angle of an arbitrary sky point rad Obstruction angle of the building rad Altitude angle of the center of a finite sky element rad Low limit altitude angle of a finite sky element rad Lower obstruction angle of the obstructed fenestration rad Altitude angle of the sun rad Upper obstruction angle of the obstructed fenestration rad The angle of the lower boundary of area lit by direct solar irradiance for Case 1 rad Azimuth angle of an arbitrary sky point rad Low limit azimuth angle of a finite sky element rad Azimuth angle of the normal direction of the vertical fenestration rad Azimuth angle of the normal direction of the obstruction rad Azimuth angle of sun rad Scattering angle of an arbitrary sky point rad Scattering angle of the reference sky element rad Reflectance of the building and obstruction Reflectance of the ground

f ðcÞ 1 þ c½expðdcÞ
expðdp=2Þ þ e cos2 c ¼ f ðZS Þ 1 þ c½expðdZS Þ
expðdp=2Þ þ e cos2 ZS

(3)

where a, 4 and Z are the altitude, azimuth and zenith angle of the sky point under consideration (rad), Z ¼ p/2
a; ZS is the zenith angle of the sun; a, b, c, d and e are coefficients, the values of which can be adjusted to describe the sky condition from heavy overcast to clear; c is the shortest angular distance between the sky point and the solar disc, i.e. scattering angle (rad), which can be calculated as:

c ¼ arccosðcos ZS $cos Z þ sin ZS $sin Z$cosj4
4S jÞ

(4)

where 4S is the azimuth angle of the sun. The gradation function (Eq. (2)) describes the sky radiance variation between horizon and zenith. In terms of overcast skies, greater radiance can be found at zenith. The trend is opposite for clear skies. The indicatrix function (Eq. (3)) represents the direct sunlight scattered in the atmosphere, which peaks at the sun position and drops rapidly when the scattering angle increases. By adjusting the value of coefficients from a to e, 15 groups of equations can be generated to denote the radiance distribution of a range of sky conditions, including 5 overcast, 5 partly cloudy and 5 clear skies. The coefficients of the skies and their features are listed in Table 1 [25,26]. 3. Irradiance in obstructed environment An infinite-length urban canyon (as shown in Fig. 1) is used in

S. Lou et al. / Building and Environment 103 (2016) 123e133

125

Table 1 The general features of the 15 CIE Standard Skies. Sky

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Gradation

For indicatrix

Indicatrix group

a

b

c

d

e

4.0 4.0 1.1 1.1 0 0 0 0
1
1
1
1
1
1
1


0.7
0.7
0.8
0.8
1
1
1
1
0.55
0.55
0.55
0.32
0.32
0.15
0.15

0 2 0 2 0 2 5 10 2 5 10 10 16 16 24


1
1.5
1
1.5
1
1.5
2.5
3
1.5
2.5
3
3
3
3
2.8

0 0.15 0 0.15 0 0.15 0.3 0.45 0.15 0.3 0.45 0.45 0.3 0.3 0.15

Type of sky

1 2 1 2 1 2 3 4 2 3 4 4 5 5 6

Classification

Description of luminance distribution

Overcast Overcast Overcast Overcast Overcast Partly cloudy Partly cloudy Partly cloudy Partly cloudy Partly cloudy Clear Clear Clear Clear Clear

Steep gradation, azimuthal uniformity Steep gradation, slight brighten around sun Gentle gradation, azimuthal uniformity Gentle gradation, slight brighten around sun Uniform No gradation, slight brighten around sun No gradation, brighter circumsolar region No gradation, distinct solar corona Sun position shaded/obscured Brighter circumsolar region White-blue sky, distinct solar corona Low turbidity Polluted atmosphere Cloudless turbid sky, broad sun corona White-blue turbid sky, wide sun corona

EVB ¼ ENB cos as cosð4s
4N Þ; when tan as  tan aU cosð4s
4N Þ

Fig. 1. The infinitively long building and obstruction model.

the research. The model represents a typical skyline feature of densely-built cities, which was adopted by many researchers to examine urban daylight and wind environments [14,15,27,28]. As shown in the figure, aU is the upper obstruction angle (rad); aL is the lower obstruction angle (rad); ab is the building obstruction angle (rad); 4N is the azimuth angle of the normal direction of 0 the vertical fenestration (rad) and 4N is the azimuth angle of the normal direction of obstruction (rad). Holistically, solar irradiance on such obstructed vertical fenestration (EVG,O, W m
2) can be given as Eq. (5).

EVG;O ¼ EVB þ EVD;O þ EVG;rb þ EVG;rg

(5)

where EVB is the direct solar irradiance from the sun (W m
2), EVD,O is the diffuse irradiance from the sky (W m
2), EVG,rb is the reflected solar irradiance from the buildings (W m
2) and EVG,rg is the reflected solar irradiance from ground (W m
2). Since the EVB and EVD,O casting onto the fenestration can be significantly obstructed, the reflected components (EVG,rb and EVG,rg) can be a considerable source of solar irradiance.

(6)

where ENB is the direct normal irradiance (W m
2). Eq. (6) indicates that the sun is visible in the window center when tan as  tan aU cosð4s
4N Þ [15]. In this situation, EVB contributes to a major component of the total irradiance onto the vertical fenestration. The critical issue would be the estimation of sky-diffuse vertical irradiance which is partly obstructed by the opposite buildings (EVD,O). The fenestration is insolated with EVD,O under both overcast and non-overcast conditions. Due to the significant forward-casting effect of aerosols in atmosphere, the radiance from sky hemisphere can be quite dissimilar in different directions [29]. This makes the sky to be highly anisotropic and complicated to formulate particularly under non-overcast skies. In the obstructed environment, EVD,O is contributed by the radiance from the part of sky hemisphere visible from the vertical fenestration as given in Eq. (7).

Z Z EVD;O ¼

Ra4 cos2 a cosð4
4N Þdad4

(7)

Ra4 is the radiance of any unobstructed sky point at altitude a and azimuth 4, which can be determined by the CIE Standard Skies as shown in Eqs. (1)e(3). Since Ra4 is given by complicated expressions, Eq. (7) can hardly be integrated analytically. In this regard, a numerical approach [30] which divides the sky hemisphere into finite elements shall be more applicable for the calculation, by which Eq. (7) can be transferred to Eq. (8) as:

2 EVD;O ¼

n X

6 Ra4i 4

i

2 6 4

4iLZþd4i

3 7 cosð4
4N Þd45

4iL maxðaZiL þdai ;aO Þ

3 7 cos2 ada5

(8)

maxðaiL ;aO Þ

3.1. Direct and diffuse irradiance on vertical surfaces Under non-overcast skies, direct irradiance imposes on the fenestration when the difference between 4s and 4N is less than p/ 2. For the infinite city canyon in Fig. 1, EVB on the center of vertical fenestration can be expressed as:

ðj4iL
4N j < p=2 and 0 < aiL < p=2Þ where Ra4i is the radiance of the ith sky element that varies incrementally between different sky elements; aiL and 4iL are the lower limits of the altitude and azimuth angles for the ith sky element (rad) corresponding to the increments dai and d4i respectively; As shown in Fig. 2 (a), aO is the angle below which the

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S. Lou et al. / Building and Environment 103 (2016) 123e133

sky element is not visible from the fenestration. The values of aO at different j4N
4j and aU are shown in Fig. 2 (b). The finite sky elements and the aforementioned angles are given in Fig. 3. Each sky element visible from the vertical fenestration is calculated as an area in the vertical Waldram Diagram [31]. If the sky element is partly obstructed as the one highlighted in Fig. 3, the area of visible part (P) in the Diagram can be estimated using the Monte Carlo Method [32,33]. It has been proved that dividing the sky hemisphere into 145 elements is sufficient to give acceptable result without imposing unnecessary computation burden [34,35]. The vertical window only views half of the sky and half of the 145 elements should be considered as depicted in Fig. 3. By adding up the result of each sky element, the total irradiance on the fenestration can be calculated accordingly. 3.2. Obstructed vertical sky component The determinations of EVD,O by the numerical approach and CIE Standard Sky models are computation intensive and Rz dependent. To simplify the process, obstructed vertical sky component (OVSC) defined as the ratio of sky-diffuse irradiance on the obstructed vertical plane to the unobstructed diffuse sky irradiance on a horizontal plane under the same sky condition (EVD,O/EHD) is proposed as an effective tool to determine EVD,O. OVSC can be estimated by its angular distance between the normal direction of the plane (fenestration) and the solar disc for a given aU under a particular CIE Standard Sky. The angular distance, namely reference scattering angle (cref), is the shortest angle between the sun and the sky element with 4N at zero altitude as shown in Fig. 4. The cref can stand for many combinations of solar zenith, azimuth and plane normal direction. Owing to the azimuthal uniformity for CIE Standard Skies 1, 3 and 5, the values of OVSC are constants at any cref for a given aU. The results of OVSC of Skies 1, 3 and 5 are listed in Table 2. The OVSC decreases as the aU increase under these three skies. For each of the other 12 CIE Standard Skies at a given aU, the outcomes of OVSC at different cref cluster around a curve, by which the relationship between the two parameters is indicated. Fig. 5 shows the curves of OVSC against cref under CIE Standard Skies 2, 8 and 13 representing respectively the overcast, partly cloudy and clear skies [20,36]. The data in the figure are smoothed by the moving average [37] to highlight the variation of OVSC at different cref. As shown in Table 2 and Fig. 5, the OVSC of these CIE Standard Skies decreases at all cref as aU rises. The reduction of OVSC at sun facing direction (cref < p/2) is larger than those at the sun shaded

Fig. 3. The 145 sky elements, one partly visible element is highlighted in a (a) Perspective view; (b) Plan view.

direction (cref > p/2). For example, when aU changes between 0 and p/9, the OVSC reduces 38% from 0.92 to 0.57 at cref ¼ p/6 while 34% from 0.32 to 0.21 at cref ¼ 5p/6 for Sky 8. Thus the peak of OVSC is shifted to high cref slightly. Less reduction of OVSC is found for overcast Sky 2, which is 24% from 0.51 to 0.39 at cref ¼ p/6. For the heavily obstructed cases when aU ¼ p/3, the OVSCs for all these skies are below 0.1. It indicates that the OVSCs would be quite similar of low values for all the 15 CIE Standard Skies and the variations for OVSCs among all cref are very limited. The variations are 0.09 to 0.06 for Sky 2 and 0.09 to 0.03 for Sky 13. Such features can also be observed for other CIE Standard Skis. In order to establish mathematical expressions of OVSC for computer based calculations with large datasets, regression

Fig. 2. (a) The shape and (b) The value of aO at different jfNef j and obstruction angle.

S. Lou et al. / Building and Environment 103 (2016) 123e133

127

template of curve fitting. The Fourier series was used to represent the moderate ups and downs of OVSC at different cref. As given in Fig. 5, the OVSC drops when aU rises from 0 to p/2. However, for the same increment of aU, the reduction of OVSC is significant for low aU but minor for high aU. Such OVSC variations can also be found at different cref. In this connection, the logistic function was employed to simulate the OVSC at various cref and aU. Coefficients a0, a1, b1, a2, b2, c0, d1, d2 and w are the coefficients. Table 3 summarizes the findings for the 15 CIE Standard Skies. The coefficients of determination (R2) indicate the quality of regressions referring to the results of OVSC without data smoothed. With R2 greater than 0.94 for each regression, it means that at least 94% of the variations for the OVSC can be explained by Eq. (9) and its coefficients. Fig. 4. Angles defining the position of the sun and a reference sky element.

Table 2 Values of OVSC for CIE Skies 1, 3 and 5 at different aU.

Sky 1 Sky 3 Sky 5

aU ¼ 0

aU ¼ p/6

aU ¼ p/4

aU ¼ p/3

0.380 0.447 0.500

0.245 0.248 0.251

0.157 0.152 0.148

0.077 0.072 0.069

h       OVSC ¼ a0 þ a1 cos cref w þ b1 sin cref w þ a2 cos 2cref w 3 2  i 1 4 5  þ b2 sin 2cref w 1 þ exp c0 þ d1 cref þ d2 aU (9)

3.3. Reflected irradiance from building equations between OVSC and cref at different aU were developed. Due to the accessibility in formulating satisfactory results, Eq. (9) based on the Fourier series and logistic function was used as the

Building and ground surfaces are usually assumed to be perfectly diffusing for the estimation of reflected components. The reflected solar irradiance from opposite building and ground can be

Fig. 5. The smoothed OVSC for CIE Standard Skies 2, 8 and 13.

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S. Lou et al. / Building and Environment 103 (2016) 123e133

Table 3 Coefficients of Eq. (9) for all 15 CIE Standard Skies (0 < aU < p/2). Sky

a0

a1

b1

a2

b2

w

c

d1

d2

R2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.41
2.833 0.540
3.453 0.670
5.990
6.780 0.615
4.976 0.732 0.801 0.949 1.069 1.384 1.503

0 3.200 0 4.037 0 7.074 7.899 0.358 6.230 0.336 0.487 0.575 0.784 0.964 1.255

0 3.256 0 3.807 0 5.798 6.809 0.042 5.061 0.024
0.032
0.166
0.357
0.654
0.833

0 0.129 0 0.03 0
0.383
0.245 0.042
0.306 0.040 0.070 0.092 0.134 0.136 0.148

0
1.415 0
1.73 0
2.721
3.262 0.025
2.511 0.017 0.015
0.011
0.079
0.169
0.259

0 0.432 0 0.418 0 0.379 0.415 1.434 0.387 1.402 1.327 1.203 1.078 0.996 0.973


2.26
2.75
1.44
2.31
1.04
2.22
2.21
2.06
2.02
1.96
1.86
1.73
1.57
1.33
1.14

0
0.09 0
0.06 0
0.08
0.10
0.21
0.07
0.12
0.22
0.17
0.39
0.36
0.62

3.58 4.16 3.12 4.00 3.00 4.18 4.26 4.31 4.59 4.64 4.71 4.87 4.98 5.23 5.32

0.99 0.99 0.99 0.98 1.00 0.98 0.96 0.96 0.97 0.96 0.96 0.95 0.95 0.94 0.94

key elements of the irradiance on the fenestration. Referring to the Tregenza method [15] and the modifications [24], the total reflected irradiance onto fenestration is:

EVB;rb ¼ ENB cos as cosð4s
4N Þr2b cf1 cf2 ðfor Cases B1 and B2Þ (12)



   0 0 0 0 EVD;avgb þEVG;rg r2b cfrb cfrb þ EVD;avgb þEVG;rg rb cfrb þEVB;rb   EVG;rb ¼ 0 1
r2b cfrb cfrb

where cf1 and cf2 are the configuration factors of the first and second reflection according to the laws of radiative heat transfer

(10) Case A: Sun shaded

where:

Sunlit Area (on Obstruction) Case A1 Case A2

0

EVG,rg is: Total irradiance on façade of obstruction, originated from ground (W m
2) EVD,avgb is: Diffuse irradiance on façade of building, originated from sky (W m
2) [23]. 0 EVD,avgb is: Diffuse irradiance on façade of obstruction, originated from sky (W m
2) [23]. EVB,rb is: Reflected direct irradiance (EVB,rb, W m
2) cfrb is: The portion of diffuse irradiance reflected by the building qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi that reaches the façade of obstruction ¼ 1 þ cot2 ab
cot ab 0 cfrb is: The portion of diffuse irradiance reflected by the obstruction that reaches the center of fenestration ¼ 0:5ðsin aU þ sin aL Þ rb is: Reflectance of the building and obstruction Although Eq. (10) was developed for cloudy and clear skies, it can be extended to the overcast skies with EVB,rb ¼ 0. The equation considers maximum 2 times of reflection, since the irradiance from greater times of reflection tend to be too low and it is not worthwhile to have multi-reflection especially for clear skies with large EVB. EVG,rg, as the irradiance onto the fenestration center, is approximated as the irradiance onto the entire façade in Eq. (10). This is because its value tends to be very low compared with EVB and EVD,O due to the low ground reflectance and it is not rewarding to calculate it precisely. Similar approximation is applicable for 0 EVG,rg. For different solar altitudes and orientations in Fig. 6, reflected direct solar irradiance from building (EVB,rb) can be calculated under 4 cases. Similar to Eq. (10), EVB,rb can be expressed by the following equations:

  0 EVB;rb ¼ ENB cos as cos 4s
4N rb cf1 ðfor Cases A1 and A2Þ (11)

φN’

φN

αW1<0 Obstruction

αW1

αW W2

Window

αW1>0 Target Building

(a) Sunlit Area (on Target Building)

Case B: Sun facing

Case B1 Case B2

φN

φN’ αW1<0 Obstruction

Window

W1 αW2 αW

αW1>0

Target Building

(b) Fig. 6. Solar position, sunlit area by the direct solar irradiance and the angular relationship for (a) Cases A1 and A2 and (b) Cases B1 and B2.

S. Lou et al. / Building and Environment 103 (2016) 123e133

[38,39]. It is assumed that the target and opposite buildings are of the same height. The criterion of different cases and the correspondent equation of cf1 and cf2 are summarized in Table 4.

3.4. Reflected irradiance from ground Irradiance reflected by the ground on to the fenestration center (EVG,rg) can be determined as.

EVG;rg ¼ EVD;rg þ EVB;rg ¼ 0:5rg EVD;avgg ð1
sin aL Þ þ ENB sin aS rg cfgsun

(13)

where: EVD,rg is: The reflected diffuse irradiance from the ground (W m
2) EVB,rg is: The reflected direct irradiance from the ground, which exists only when the ground is partly exposed to direct sunlight, i.e. Case A2 and B2 (W m
2). EVD,avgg is: The diffuse irradiance received by the ground (W m
2) [23]. rg is: Reflectance of the ground cfgsun is: Configuration factor indicating the portion of direct solar irradiance reflected by the ground that reaches the center of fenestration. It can be determined as: cfgsun ¼ 0:5ðsin aW2
sin aL Þ for cases when sun shines on the obstruction façade aL tan aS Where tan aW2 ¼ tantan ab cosð4S
40N Þ cfgsun ¼ 0:5ð1
sin aW2 Þ for cases when sun shines on the window façade tan aL tan aS Where tan aW2 ¼ tan aS
tan a cosð4
4 Þ b

S

129

model were benchmarked with the simulations. The obstruction angles aU and aL were set as p/6 (30 ) and 0.306p (55 ) to represent the slightly obstructed environments in the higher floors of a building. In terms of the heavily obstructed environments in lower floors, aU and aL were set as p/3 (60 ) and 0.083p (15 ). The infinitely long city canyon with rb ¼ 0.4 and rg ¼ 0.2 [15] was used to reproduce the typical building development conditions, where the building and obstruction were assumed of the same height. The horizontal global and diffuse irradiance recorded every 10 min in our measuring station located in City University of Hong Kong between 2004 and 2005 contribute to the input. The solar position of each measurement was calculated correspondingly. The simultaneously measured unobstructed vertical irradiance in the 4 cardinal directions were used to classify the CIE Standard Skies according to their vertical component ratio and vertical sky component [44e47]. All measurements were made in City University of Hong Kong (22.3 N, 114.2 E). Details of the equipment and data quality control can be found in the earlier publications [36]. Table 5 displays the frequency of occurrence of the classified 15 CIE Standard Skies. As shown in the table, the overcast and partly cloudy skies account for respectively 27.1% and 38.3%. The clear skies represent the remaining 34.6%. Skies 1, 8 and 13 have an individual frequency of occurrence greater than 14%, which represents the typical skies of Hong Kong [20,47]. Among all, Sky 13 was the most representative in Hong Kong with a frequency of 17%. This supports the argument that Hong Kong is currently infamous for its air pollution. The results are in good agreement with previous findings in Hong Kong [47]. The general performance of the proposed model was assessed by the root-mean-square error (RMSE) with respect to the mean simulated irradiance (%RMSE) given in Eq. (14). And the results are summarized in Table 6. A detailed comparison between the results of proposed method and the simulation is given in Fig. 7.

N

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 1 ðEVG;O by the proposed approach
EVG;O by RADIANCEÞ2 N %RMSE ¼ P 1 EVG;O by RADIANCE N

Referring to our previous study [23], EVD,avgg can be approximated as EHD ð1
0:011ab Þ, where ab shall be converted to degree. 4. Model benchmark and results discussion Owing to the development of computer technology, there have been a number of program packages in solar radiation analysis. A comprehensive study was conducted to benchmark the prediction of the proposed model against the well acknowledged simulation program RADIANCE, which has been used by a number of researchers [40e43]. Using the advanced ray-tracing technique, the package is capable of reproducing the real measurement of solar radiation transfer in complexed building environment with high reliability. RADIANCE is updated by the Lawrence Berkeley Laboratory and available in different versions while the version 5.0 on Windows platform was used in present study. A code written in MATLAB 2015b was used to run the simulations repeatedly for different groups of data. The application of the proposed approach was demonstrated by studying some representative cases, i.e. the solar irradiance on the vertical window facing south and north under slight and heavy obstructions for the whole year. The predictions of the proposed

(14)

As demonstrated by Table 6 and Fig. 7, results of the proposed approach were in good agreement with those based on the simulations. The maximum %RMSE was identified as 14.88% for north facing fenestration with moderate obstruction (i.e. aU ¼ p/6). As shown in Fig. 7 (b), the proposed approach tends to overestimate the irradiance compared with simulation. This is due to its great accessibility to the anisotropic diffuse component (EVD,O), which was estimated as the product of the smoothed OVSC by Eq. (9) and EHD by measurement. By integration, there may be more than one unique OVSC under a standard sky at given aU and cref because of the various solar positions may result the same cref. However, the variations are small and thus averaged for simplicity in Fig. 5 and Eq. (9). Given the error in Fig. 7 (b) is acceptable, the averaged values are sufficient and representative. The direct solar irradiance (EVB) is directional, periodical and thus more straightforward in prediction compared with EVD,O. In this connection, the irradiance on the south facing fenestrations in Hong Kong that subject to greater EVB were estimated with more consistency by different approaches. According to Fig. 7 (c) and (d), solar irradiance on the south facing fenestration with aU ¼ p/3 and p/6 could be as great as 400 W m
2 and 700 W m
2, respectively. The high irradiance implies the necessities of employing shading devices to reduce

130

S. Lou et al. / Building and Environment 103 (2016) 123e133

Table 4 Criterions and configuration factor for calculating EVB,rb. Case

Criterion

cf1

cf2

A1

Sun shaded, 0 < tan aS  tan ab cosðfS
f0N Þ Sun shaded, tan aS > tan ab cosðfS
f0N Þ Sun facing, 0 < tan aS  tan ab cosðfS
fN Þ Sun facing, tan aS > tan ab cosðfS
fN Þ

0:5ðsin aU þ sin aW1 Þtan aW1 ¼ ½tan aS =cosðfS
f0N Þ
tan aU

None, not calculated

0:5ðsin aU þ sin aL Þ

None, not calculated

0:5ðsin aU þ sin aW1 Þtan aW1 ¼ ½tan aS =cosðfS
fN Þ
tan aU

0:5ðsin aU þ sin aL Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ cot2 ab
cot ab

0:5ðsin aU þ sin aL Þ

A2 B1 B2

Table 5 Frequency of occurrence for CIE Standard Skies in Hong Kong, 2004e2005. Sky

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

FOC (%)

14.9

5.7

1.6

3.4

1.5

2.7

10.9

14.7

3.6

6.4

6.2

5.5

17

1.4

4.4

Table 6 %RMSE for different facing direction and level of obstruction.

North facing South facing

aU ¼ p/3 (heavily obstructed)

aU ¼ p/6 (moderately obstructed)

11.73% 8.91%

14.88% 3.33%

250

150 100 50 R2 = 0.96

0

Simulation (W m-2)

Simulation (W m-2)

200

0 50 100 150 200 Proposed approach (W m-2)

200 150 100 50 0

0 50 100 150 200 250 Proposed approach (W m-2)

(a)

(b)

500

800

400 300 200 100

R2 = 0.99

0

0 100 200 300 400 500 Proposed approach (W m-2) (c)

Simulation (W m-2)

Simulation (W m-2)

R2 = 0.94

600 400 200 R2 = 1.00

0

0 200 400 600 800 Proposed approach (W m-2) (d)

Fig. 7. Solar irradiance predicted by the proposed approach against the RADIANCE simulation, when the fenestration is (a) Facing north, aU ¼ p/3; (b) Facing north, aU ¼ p/6; (c) Facing south, aU ¼ p/3; (d) Facing south, aU ¼ p/6.

S. Lou et al. / Building and Environment 103 (2016) 123e133

25%

%RMSE

implicated the potential of adopting sun-tracking devices in the south facing fenestrations to maximize the solar energy collection in Hong Kong, especially in upper floors with less obstruction.

Frequency of occurrence < 1.5%

20%

131

15% 10%

5. Field measurement and validation

5% 0% 1

2

3

4

5

6 7 8 9 10 11 12 13 14 15 CIE Standard Skies

Fig. 8. %RMSE of the proposed method in different CIE Standard Skies.

excessive heat gain, as well as the potential of building integrated photovoltaic system application to harvest solar energy. The %RMSEs for the 15 CIE Standard Skies under all aforementioned obstruction environments are given in Fig. 8. Skies with frequency of occurrence less than 1.5% were greyed out. It can be found that the %RMSE was generally lower than 20% except Sky 14. For the three Hong Kong Representatives Skies, the %RMSEs were 16.5%, 12.5% and 14% for Skies 1, 8 and 13, respectively. The model performs slightly better for cloudy skies than overcast and clear skies. The uncertainty may be the low direct irradiance in overcast skies and the adverse diffuse radiance gratitude near the sun (corona effect) for clear skies. An advantage of the proposed approach is that the direct, diffuse and reflected vertical irradiance can be calculated separately. Fig. 9 identifies the contribution and significance of each component in different conditions. As shown, the reflected irradiance from the opposite building (EVG,rb) and ground (EVG,rg) were very important when the fenestration is heavily obstructed. The reflected components on the north and south facing windows with aU ¼ p/3 represent respectively 73% and 47% of the total irradiance. When aU ¼ p/6 (moderately obstructed) the EVB and EVD,O were respectively the most important components for the fenestrations facing south and north. The prevalence of EVB

EVG,rg 22.2%

EVG,rb 49.9%

The proposed approach was used to estimate the vertical solar irradiance on the 3rd Floor (aU ¼ 45.7, aL ¼ 16.7 ) and 9th Floor (aU ¼ 26.6 , aL ¼ 39.5 ) of an obstructed building (4N ¼ 10 ) located at the university campus. Fig. 10 shows the building layout. It can be observed that the skyline is not exactly of infinite-length city canyon but such layout is sufficient for model validation. The north facing building was selected to testify the performance in unfavourable conditions. The reflectance values of building and ground were respectively 0.34 and 0.2 as referred to our previously study [24]. The estimation was based on the horizontal and vertical solar irradiance measurements in our measuring station [36] and the results were compared with field measurements by a photodiodebased portable solar power meter (SPM-1116SD). The data collected at 3rd Floor were acquired from 9:00 to 12:00 on 30 March and between 15:20 and 15:50 on 31 March 2016. The measurements at 9th Floor were conducted from 12:40 to 14:00 on 30 March and between 12:40 and 15:10 on 31 March 2016. The recorded readings covered overcast, partly cloudy and clear skies. After the routine quality control [48], 104 and 102 sets of data respectively for the 3rd and 9th Floors were adopted for analysis. Fig. 11 presents the occurrence of the identified skies. During the period of measurement, not all the 15 CIE Standard Skies were identified. However, the most representative overcast, partly cloudy and clear skies of Hong Kong (i.e. Skies 1, 8 and 13) were frequently recognized. Fig. 12 exhibits the plots of fieldmeasured and proposed approach results for the 3rd and 9th Floors. The results estimated by the proposed approach are quite close to the measured data. The errors may largely be due to the

EVB 10.0%

EVG,rb 43.8%

EVD,O 18.0%

EVD,O 47.2%

(a)

(b) EVB 36.1%

EVG,rg 23.7%

EVG,rg 3.0% EVB 6.0%

EVB 50.7%

EVG,rg 1.5% EVG,rb 14.0%

EVG,rb 22.1% EVD,O 18.1%

(c)

EVD,O 33.8%

(d)

Fig. 9. Percentage of irradiance components when the fenestration is (a) Facing north, aU ¼ p/3; (b) Facing north, aU ¼ p/6; (c) Facing south, aU ¼ p/3; (d) Facing south, aU ¼ p/6.

132

S. Lou et al. / Building and Environment 103 (2016) 123e133

50

3rd Floor

40

9th Floor

30 20 10 0 1

2

7

8

13

15

CIE Standard Sky

Calculated (W m−2)

Fig. 11. The sky types for the measured case in different floors.

140

250

120

200

100 80 60

R2 = 0.78

40

40 60 80 100 120 140 Measured (W m−2)

Calculated (W m−2)

Number of data sets

Fig. 10. The site layout of the residence buildings for measurement.

irradiance on the obstructed vertical plane to that on the unobstructed horizontal plane was proposed. The OVSCs for the 15 CIE Standard Skies at a variety of obstruction angles were determined using the numerical approach. The OVSC reduces in the obstructed environment, especially for sun-facing surfaces (reference scatting angle < p/2) under clear skies. The performance of the proposed approach was benchmarked with those estimated by the RADIANCE simulation program. It was found that the results of the proposed model were in good agreement with those simulated findings. For the north facing vertical fenestration with an upper obstruction angle (aU) of p/3 and p/6, the %RMSEs were 11.73% and 14.88%, respectively. Due to the prevalence of direct solar irradiance, the %RMSE for the south facing surface was just 3.33% when aU ¼ p/6. For Skies 1, 8 and 13 which are the Hong Kong Representative Skies, the %RMSEs were found to be 16.5%, 12.5% and 14%, respectively. The model was applied to different obstructed fenestrations in Hong Kong. It has been found that when aU ¼ p/3, the reflected irradiance accounts for 72% and 46% for the north- and south-facing surfaces, respectively. When aU ¼ p/6, the major component for northand south-facing façades were respectively sky diffuse and direct beam irradiance. The proposed approach was applied to the low and high floors of an obstructed building in Hong Kong and the results were evaluated with short-term field measurements. The %RMSE of low and high floors are 11.5% and 9.6%. The findings indicate the proposed approach is reliable and can be helpful for

150 100 50

R2 = 0.94

0 0

(a)

50 100 150 200 250 Measured (W m−2) (b)

Fig. 12. Solar irradiance predicted by the proposed approach against the measurement, for (a) 3rd Floor, aU ¼ 45.7, aL ¼ 16.7 ; (b) 9th Floor, aU ¼ 26.6 , aL ¼ 39.5

difference between actual and modelled luminance distribution of classified skies, the imperfectly diffusing building and ground surfaces, and the irregular skyline patterns. The %RMSEs at 3rd and 9th Floors with respect to the measured data were estimated to be 11.5 and 9.6%, respectively. In general, the predicted results were in reasonably good agreement with the corresponding measured data and the proposed approach is considered applicable to heavily obstructed environments. 6. Conclusions An approach for estimating the solar irradiance on the obstructed vertical fenestrations under the 15 CIE Standard Skies was established. Numerical methods to determine the diffuse irradiance on the fenestrations under different obstruction angles were evolved. To simplify the calculations, the obstructed vertical sky component (OVSC) defined as the ratio of diffuse

architects and engineers to analyse the direct, diffuse and reflected components of solar irradiance for passive architectural designs and active solar energy applications. The systematic long-term field measurements will be conducted in near future. Acknowledgements The work described in this paper was fully supported by a General Research Fund from the Research Grant Council of the Hong Kong SAR, China [Project no. 9041777 (CityU 116312)]. Siwei LOU was supported by a City University of Hong Kong studentship. References [1] J.C. Lam, K.K.W. Wan, L. Yang, Sensitivity analysis and energy conservation measures implications, Energy Convers. Manage 49 (2008) 3170e3177. [2] J.C. Lam, Energy analysis of commercial buildings in subtropical climates,

S. Lou et al. / Building and Environment 103 (2016) 123e133 Build. Environ. 35 (2000) 19e26. [3] J.C. Lam, Residential sector air conditioning loads and electricity use in Hong Kong, Energy Convers. Manage 41 (2000) 1757e1768. [4] D.H.W. Li, J.C. Lam, S.L. Wong, Daylighting and its effects on peak load determination, Energy 30 (10) (2005) 1817e1831. [5] T.T. Chow, G.Q. Zhang, Z. Lin, C.L. Song, Global optimization of absorption chiller system by genetic algorithm and neural network, Energy Build. 34 (2002) 103e109. [6] HKO, 24-Hour Time Series of Solar Radiation [Internet], Hong Kong Observertory, Hong Kong, 2015 [cited 2015 Oct 25] Available from, http://www.hko. gov.hk/wxinfo/ts/display_element_solar_e.htm. [7] D.H.W. Li, S.W. Lou, J.C. Lam, An analysis of global, direct and diffuse solar radiation, Energy Procedia 75 (2015) 388e393. [8] S.L. Wong, K.K.W. Wan, D.H.W. Li, J.C. Lam, Generation of typical weather years with identified standard skies for Hong Kong, Build. Environ. 56 (2012) 321e328. [9] J.C. Lam, D.H.W. Li, Study of solar radiation data for Hong Kong, Energy Convers. Manag. 37 (3) (1996) 343e351. [10] T.R. Tooke, N.C. Coops, A. Christen, A point obstruction stacking (POSt) approach to wall irradiance modeling across urban environments, Build. Environ. 60 (2013) 234e242. [11] D.H.W. Li, J.C. Lam, Evaluation of slope irradiance and illuminance models against Hong Kong data, Build. Environ. 35 (6) (2000) 501e509. [12] L. Chen, E. Ng, X. An, C. Ren, M. Lee, U. Wang, Z. He, Sky view factor analysis of street canyons and its implications for daytime intra-urban air temperature differentials in high-rise, high-density urban areas of Hong Kong: a GIS-based simulation approach, Int. J. Climatol. 32 (2012) 121e136. [13] D.H.W. Li, S.L. Wong, Daylighting and energy implications due to shading effects from nearby buildings, Appl. Energy 84 (2007) 1199e1209. [14] J. Strømann-Andersen, P.A. Sattrup, The urban canyon and building energy use: urban density versus daylight and passive solar gains, Energy Build. 43 (2011) 2011e2020. [15] P.R. Tregenza, Mean daylight illuminance in rooms facing sunlit streets, Build. Environ. 30 (1995) 83e89. [16] D.H.W. Li, T.N.T. Lam, W.W.H. Chan, A.H.L. Mak, Energy and cost analysis of semi-transparent photovoltaic in office buildings, Appl. Energy 86 (2009) 722e729. [17] F. Antonanzas-Torres, F.J. Martinez-de-Pison, J. Antonanzas, O. Perpinan, Downscaling of global solar irradiation in complex areas in R, J. Renew. Sustain. Energy 6 (2014) 063105. [18] R. Dubayah, P.M. Rich, Topographic solar radiation models for GIS, Int. J. Geogr. Inf. Syst. 9 (4) (1995) 405e419. [19] J. Corripio, Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous terrain, Int. J. Geogr. Inf. Sci. 17 (1) (2003) 1e23. [20] E. Ng, V. Cheng, A. Gadi, J. Mu, M. Lee, A. Gadi, Defining standard skies for Hong Kong, Build. Environ. 42 (2007) 866e876. [21] E. Nault, G. Peronato, E. Rey, M. Andersen, Review and critical analysis of early-design phase evaluation metrics for the solar potential of neighborhood designs, Build. Environ. 92 (2015) 679e691. [22] P.J. Jones, D. Alexander, A. Marsh, J. Burnett, Evaluation of methods for modelling daylight and sunlight in high rise Hong Kong residential buildings, Indoor Built Environ. 13 (2004) 249e258. [23] D.H.W. Li, G.H.W. Cheung, J.C. Lam, Simple method for determining daylight illuminance in a heavily obstructed environment, Build. Environ. 44 (2008) 1074e1080. [24] D.H.W. Li, G.H.W. Cheung, K.L. Cheung, T.N.T. Lam, Determination of vertical daylight illuminance under non-overcast sky conditions, Build. Environ. 45 (2010) 498e508. [25] CIE, Spatial Distribution of Daylight - CIE Standard General Sky, Standard, CIE

[26] [27]

[28]

[29] [30]

[31]

[32] [33]

[34] [35] [36] [37]

[38] [39] [40]

[41]

[42] [43] [44] [45]

[46] [47] [48]

133

Central Bureau, Vienna, Austria, 2003. Report No. S 011/E:2003/ISO 15469: 2003(E). R. Kittler, S. Darula, R. Pereze, A Set of Standard Skies. Polygrafia SAC, Polygrafia SAC, Bratislava, 1998. L.G. Algeciras JAR Consuegra, A. Matzarakis, Spatial-temporal study on the effects of urban street configurations on human thermal comfort in the world heritage city of Camagüey-Cuba, Build. Environ. 101 (2016) 85e101. ~o, Numerical analysis of the M.J.N. Oliveira Pan~ ao, H.J.P. Gonçalves, P.M.C. Ferra street canyon thermal conductance to improve urban design and climate, Build. Environ. 44 (2009) 177e187. R. Kittler, M. Kocifaj, S. Darula, Daylight Science and Daylighting Technology, Springer Science & Business Media, New York, 2012. D.H.W. Li, N.T.C. Chau, K.K.W. Wan, Predicting daylight illuminance and solar irradiance on vertical surfaces based on classified standard skies, Energy 53 (2013) 252e258. Waterslade, Waldram Diagram [Internet], Waterslade, Oxford, 2001 [cited 2015 Jul 23]. Available from, http://www.waterslade.com/resources/ waldram_diagrams/waldrams.htm. G.J. Borse, Numerical Methods with Matlab, PWS Publishing Company, Boston, MA, 1997. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes the Art of Scientific Computing, third ed., Cambridge university press, Cambridge, UK, 2007. P. Tregenza, M. Wilson, Daylight Coefficients and Numerical Models, Routledge, Oxon; New York, 2011. P.R. Tregenza, The sensitivity of room daylight to sky brightness, Archit. Sci. Rev. 42 (1999) 129e132. D.H.W. Li, H.L. Tang, Standard skies classification in Hong Kong, J. Atmos. Sol.Terr. Phys. 70 (2008) 1222e1230. Mathworks, Curve Fitting Toolbox User's Guide [Internet], The MathWorks, Inc., Natick, MA, 2015 [cited 2015 Jul 27]. Available from, http://www. mathworks.com/help/pdf_doc/curvefit/curvefit.pdf. IES., Lighting Handbook Reference & Application, Illuminating Engineering Society of North America, New York, 1993. J.R. Howell, R. Siegel, M.P. Menguc, Thermal radiation Heat Transfer, fifth ed., CRC Press, Boca Raton, FL, 2011. E. Ng, A study on the accuracy of daylight simulation of heavily obstructed buildings in Hong Kong, in: Proceedings of the International Building Performance Simulation Association Conference, 2001, pp. 1216e1222. August 13-15; Rio de Janeiro, Brazil. D.H.W. Li, E.K.W. Tsang, An analysis of measured and simulated daylight illuminance and lighting savings in a daylit corridor, Build. Environ. 40 (2005) 973e982. J. Mardaljevic, Validation of a lighting simulation program under real sky conditions, Light. Res. Technol. 27 (1995) 181e188. C.F. Reinhart, M. Andersen, Development and validation of a Radiance model for a translucent panel, Energy Build. 38 (2006) 890e904. K. Alshaibani, Finding frequency distributions of CIE Standard General Skies from sky illuminance or irradiance, Light. Res. Technol. 43 (2011) 487e495. K. Alshaibani, Determination of CIE Standard General Sky from Horizontal and Vertical Illuminance/Irradiance, World Renewable Energy Congress (WRECX), Glasgow, Scotland, 2008. D.H.W. Li, K.L. Cheung, H.L. Tang, C.C.K. Cheng, Identifying CIE Standard Skies using vertical sky component, J. Atmos. Sol. Terr. Phys. 73 (2011) 1861e1867. D.H.W. Li, T.C. Chau, K.K.W. Wan, A review of the CIE general sky classification approaches, Renew. Sustain. Energy Rev. 31 (2014) 563e574. CIE, Guide to Recommended Practice of Daylight Measurement, Technical report, central bureau of the CIE, Vienna, Austria, 1994. Report No. CIE 108e1994.