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 uncertainty of the model is on the order of ±6.0% to ±10.0% for luminance efficacy over all conditions, and the zenith luminance model is accurate to at best about ±25%. Evaluation of the Perez model as well as six other, some more complex, models, with up to 324 independent coefficients or parameters, and four independent data sets [13, 14], was in agreement with the assessment with the average mean bias error (MBE) of about ±3% in Table 8.6. All seven models

TABLE 8.6

Mean Bias and Root Mean Square Error Percentages for Perez Model at Five Sites and Three Sky Conditions

MBE Range (%) RMSE Range (%)

Sky

Global

Direct

Diffuse

Global

Direct

Diffuse

Overcast

-1.3 to +1.2

n/a

-1.1 to +1.1

3.5 to 5.7

n/a

2.7 to 6.1

Intermediate

-1.3 to +3.8

-4.3 to +1.2

-1.1 to +3.8

2.7 to 3.7

9.8 to 14.0

5.0 to 9.1

Clear

-1.2 to +1.6

-1.3 to +1.3

-1.4 to +3.5

1.9 to 3.3

4.0 to 5.7

10.2 to 17.3

Average (all)

-1.2 to +1.2

-1.6 to +1.5

-1.1 to +2.3

2.9 to 4.3

5.6 to 9.5

5.9 to 10.6

Overcast

Intermediate

All

Sky

MBE

RMSE

MBE

RMSE

MBE

RMSE

Zenith luminance

-9.0 to + 3.0

17.6 to 25.9

-2.3 to 4.9

21.9 to 29.4

0.3 to 3.6

21.5 to 30.6

Source: Sandia National Laboratory, data from the development and verification of the Perez diffuse radiation model. Contractor Report Sand88-7030, Sandia National Laboratories, Albuqurque,

NM. http://prod. sandia. gov/techlib/access-control. cgi/1988/887030.pdf.

evaluated had MBEs within this range. However, the RMS errors for all seven mod­els ranged from ±27% to ±62%, averaging about ±40%. Some of the additional RMS error is attributed to differing instrumentation (Sky scanners using photopic filters, rather than photometers) used at some stations to provide the illuminance data used in the validation.

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