Uncertainty of the Perez Anisotropic Illuminance Model

The validation of the illuminance models was accomplished by comparison with mea­sured data from six measurement stations in the northeastern United States. Table 5 in Perez et al. [11] presents detailed site-by-site mean bias and root mean square (RMS) differences between modeled and measured data for the luminance efficacy functions. Note that illuminance measurements are typically accomplished with a photometer, usually a pyranometer with a silicon-based sensor in conjunction with an optical fil­ter that emulates the photopic response function. Besides the contributing factors for uncertainty in these measurements is the accuracy of the filter spectral match to the photopic response [12]. A summarized version of that table is shown in Table 8.6.

The table shows that the basic uncertai...

Read More

Perez Luminous Efficacy Functions

Global, diffuse, and direct luminance efficacy (Ge, De, Ie, respectively) are computed directly from GHI, DHI, and DNI using

Ge = GHI[ai + bi W + ci cos(z) + di Ln(A)] (8.6)

De = DHI[ai, + bi W + ci cos(z) + di Ln(A)] (8.7)

Ie = max(0, DNI[ai + bi W + ci e(573 Z-5) + diA]) (8.8)

where W is the total precipitable water vapor (atm-cm), and the ai, bi, ci, and di depend on the epsilon bins 1 through 8. These are the same epsilon bins as used in Chapter 6, Section 6.4, for the Perez diffuse model for tilted surfaces (also discussed in the next section). The ai… di coefficients for global, diffuse, and direct luminance efficacy and the illuminance at the zenith are presented in tabular form in Appendix F. Functional fits of the efficacy functions, similar to those of Section 6.4 (Equations 6...

Read More


A version of the popular model for computing illuminance values uses luminous efficacy models of Perez et al. [11], which were discussed in Chapter 6. Inputs to the luminous efficacy models are global horizontal radiation, direct beam radiation, diffuse horizontal radiation, and dew point temperature. As in Chapter 6, Section 6.4, where the Perez tilt irradiance model was described, sky conditions were par­titioned according to a clearness parameter epsilon and sky brightness factor A (see Equations 6.13 and 6.14).

є = [(DHI + DNI)/DHI + 1.041z3]/[1 + 1.041z3] (8.4)

where Z is the zenith angle in radians. For Z in degrees, 5.535 10-6 should be used in place of the 1.041 term.

A = m DHI/I0 (8.5)

In this equation, A is the sky brightness factor, with m the airmass and DHI and Io the diffus...

Read More

Exterior Applications

As briefly mentioned in the introduction to this chapter, exterior applications of illu­minance data and models apply mainly to the appearance (to the human eye) of objects outdoors. This may include such applications as the appearance of build­ing facades, display advertisement or informational signs, or menu boards at drive – through establishments. Additional applications include design of automated video and photo image-capturing cameras [12] or the modeling of the readability of a cell phone, tablet computer, and other electronic display screens in varying outdoor conditions. As mentioned in the introduction, there are complex radiance-modeling programs such as RADIANCE [1] and the VELUX Daylight Visualizer software (http://viz. velux...

Read More


8.3.1 Interior Applications

In 2010, buildings in the United States consumed 38% of America’s energy and 68% of its electricity [5] (see the Buildings Energy Data Book, http://buildingsdatabook. eren. doe. gov). The most straightforward application of daylighting is the substitution of daylight for electrical loads for lighting in interior building spaces. This is usu­ally accomplished through window and skylight design and integration into building facades. These applications may also include “light pipe” for collecting and distribut­ing photons from the sky dome to interior spaces [6,7]. Complex daylighting models, such as RADIANCE [1], address daylighting alone. Other total building energy design tools such as Energy-10, developed by the U. S...

Read More

Luminous Efficacy

The specific wavelength dependence of the definition of the luminous intensity and the comment about the greater radiant intensity needed at different wavelengths for equivalent luminous intensity means that the efficiency of the source in “converting” irradiance to illuminance varies with the source spectral distribution. Converting total irradiance in watts per square meter into illuminance values of lux is not simple because of this dependence on the spectral distribution of the source. The ratio of the total luminous intensity to the total irradiance of a source is the luminous efficacy K of the source:

K = Ev/I = (683 J V(X) I(X) dX)/(J I(X) dX) lm/W (8.3)

The luminous efficacy provides a “conversion factor” to convert more readily available (or modeled) irradiance data into illum...

Read More


Previous chapters discussed the modeling of solar components in terms of irradi – ance, or power per unit area. For applications where natural daylight is desired in place of artificial light, the spectral response of the human eye is taken into account. The International Commission on Illumination, known in French as the Commission International de I’Eclairage, or CIE, is the internationally recognized organization devoted to research and standards in the field of illumination. The scientific com­munity recognizes the CIE standard spectral response of the eye for daylight called the photopic response. The spectral response of the eye at night (scoptopic response)


Wavelength, nm

FIGURE 8.1 The photopic response of the human eye as published by the CIE. (Data from SMARTS mode code...

Read More

Introduction to Modeling Daylight

But soft! What light through yonder window breaks?

—William Shakespeare, Romeo and Juliet, Act 2, Scene 2


The previous chapters addressed solar radiation applications that use solar irradiance to produce either electricity (photovoltaics) or heat (solar thermal collectors). This chapter addresses the use of natural daylight in place of artificial light for architec­tural applications...

Read More