Category SOLAR RADIATION

Summary and Future Prospects

If you don’t know anything about computers, just remember that they are machines that do exactly what you tell them but often surprise you in the result.

—Richard Dawkins, 1996

9.1 OVERVIEW OF THE MODELING CHAPTERS

The models described in the previous chapters were selected because of the fre­quency of their appearance in the literature (read, “popularity”), ease of use and implementation, and the frequency of questions about their accuracy. All utilize to some extent a subset of the fundamentals of solar radiation described in Chapter

1. These fundamentals include the concepts of solar position, solar time, air mass, solar components, zenith and incidence angles, the atmospheric filter, and clearness index...

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OTHER READING

The International Building Performance Simulation Association is a good resource for past and present efforts regarding daylighting (and building simulation in gen­eral). Its Web site (http://www. ibpsa. org/m_papers. asp, accessed 10 July 2012) provides access to extensive conference proceedings papers addressing daylight modeling and applications to building simulations.

8.6 SUMMARY

Given the large, inefficient loads that artificial lighting involves, daylighting strate­gies can have a significant impact on energy usage. The nonuniform response of the human eye, widely varying solar spectral distribution, and complex spatial distribu­tion of sunlight make the modeling of daylight in the outdoors and especially in interior spaces quite complex...

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Computational Example

In the numerical calculation for standard sky type 11 used in Section 8.5.3, the solar elevation angle 90 – 59.4 = 30.6° (0.534 radians). The air mass m for this geometry is

m = 1.9645. Assume the global irradiance GHI is 425 Wm-2. Using average luminous efficacy of GHI from Table 8.2 (115 lm/W), GHL = 48.875 kLx. From Equation 8.26,

Lgs = -0.323(0.534)4 + 1.486(0.534)3 – 2.581 (0.534)2 + 2.090(0.534) + 0.190 = 0.770

from Equation 8.27,

Gl = m GHL/GoL = (1.964*71.875)/(127.038) = 0.756 and from Equation 8.28,

Ngl = 0.756/0.770 = 0.981

From Equations 8.31 to 8.36, A = 19.767, B = -65.54, C = 84.16, D = -56.999, E = 20.33, and F = 5.635, so

Lz = 1710 lx or 1.710 klx.

To compute the luminance at the same sky patch (c = 5.21° = 0...

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OTHER SKY LUMINANCE DISTRIBUTION MODELS

Many arbitrary sky conditions other than the 15 CIE “standard” conditions occur in nature, so attempts have been made to develop models relating general sky condi­tions to the CIE standard conditions. Examples were developed by Igawa et al. [20] and Darula and Kittler [21]. The approach is generally to relate the ratio of zenith luminance to the global hemispherical or diffuse hemispherical irradiance (GHI, DHI) to establish the zenith illuminance. The issue then becomes which sky type to select and how to modify the sky type to produce the desired general sky luminance distribution. In accordance with Igawa’s approach, the following steps are needed: The authors slightly modified the relation for the CIE standard sky calculation gra­dation and indicatrix functions (Equations 8.19 and 8...

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SKY LUMINANCE MODEL ACCURACY

Lam, Mahdavi, and Pal [18] discussed the accuracy of the CIE and Perez models and three others. They used measured diffuse sky irradiance data to obtain the estimated magnitude of the luminance at the zenith. Their evaluation compared illuminance levels measured inside an actual daylight space and on the roof of the building. The basis of the comparison was the daylight factor, described in Section 8.2.1, derived from the data and the models. These authors found all six of the models had indi­vidual average systematic errors of ±20%. The average systematic bias of all six models was -10%, and all six models had similar random error dispersion of an additional ±20%.

The model with the smallest systematic error was the Perez model, with about -2.5% systematic error...

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Computational Example

We compute an example for 8 a. m. standard time for May 30 at a location of 30° N, 105° W, at an elevation of 100 m above sea level. Assume the distribution desired is for a white-blue sky with distinct corona. From Table 8.7, the model type selected is 11; the gradation function is type IV, and the indicatrix function is type 4. Table 8.10 lists parameters for the computation, including the day angle for the day of the year (DANG) and zenith and azimuth angles of the sun.

TABLE 8.10

Parameters for Example Sky Patch Luminance Computation

Model Gradation Indicatrix Model

No.

Function

a

b

Function

c

d

e

Description

11

IV

-1.0

-0.55

4

10

-3

0.45

White-blue with

broad corona

Station

Annual

Time

Elevation

Press

O3

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CIE Gradation and Indicatrix Functions

The CIE relative luminance distribution models can easily be implemented in either computer program codes or spreadsheet programs such as Excel®. The model is based on a set of six “gradation” curves, describing the change in luminance as a function of solar altitude or zenith angle and six “indicatrix” functions. Indicatrix functions describe the theoretical distortion of the uniform hemispherical luminance spatial distribution on the sky dome (hemisphere) as scattering centers (pollution, aerosols, clouds, etc.) are introduced into the radiation field. Table 8.7 describes the 15 standard distributions in qualitative terms and in terms of the gradation and indi – catrix function appropriate for each standard sky condition.

The gradation functions are of the form

ф^)/ф(0) = [1 + a...

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INTERNATIONAL COMMISSION ON ILLUMINATION MODELS

8.5.1 CIE Standard Sky Models

The CIE has constructed a set of “standard sky conditions” to provide guidance regarding the distribution of sky “brightness” for “energy conscious window design, daylight calculation methods and computer programs as well as for visual comfort and glare evaluations” [15, p. 359], see also [16]. According to Kittler, Perez, and Darula [15], CIE developed a “standard overcast sky” in 1955, and 20 years later established a CIE standard clear sky [17]...

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