Modeling Solar Radiation at the Earth’s Surface

# Calibration of Solar Radiometers

Since the WRR/WSG is the only reference for solar radiometer calibrations, pyrhe - liometers are calibrated by direct comparison with an ACR traceable to the WRR. The calibration of working pyrheliometers is similar to the transfer of the WRR to working reference absolute cavity radiometers (ASTM 2005a).

The ratio of the voltage signal of a test pyrheliometer to the ACR beam irradiance determines responsivity, Rs, in units of ^VW-1m2. Many data samples through a large range of irradiance levels and solar geometry are collected, and an average responsivity calculated. When such calibrations are performed, the Rs values de­rived are often not flat or uniform, and exhibit some biases, which are discussed below. Some types of pyrheliometer are more sensitive to environmental conditions (mainly temperature and wind) than others. Most often, the average responsivity is divided into the field pyrheliometer voltage signal to produce measured irradi - ance. Characterization of the pyrheliometers is needed to produce data with lower uncertainty.

Pyranometer calibrations are accomplished by applying Eq. (1.1) (ISO 1990; ASTM 2005b). The reference ACR measures the direct beam, just as for the pyrheliometer calibrations. Exposed to the total hemispherical irradiance, G, a pyranometer output signal Vg is generated. If the pyranometer is then shaded by a device subtending the same solid angle as the field of view of the pyrheliometer, the pyranometer responds only to the diffuse sky irradiance, D, generating an output voltage Vd. Equation (1.1) implies that the vertical component of the direct beam is equal to the difference between the total and diffuse sky radiation:

B cos(z) = G - D. (1.3)

If the voltages Vg and Vd are used for G and D, the responsivity of the pyranome­ter, RS can be computed from the vertical component of the direct beam:

Rs =(Vg - Vd)/[Bcos(z)]. (1.4)

It is observed that RS varies during the day, mainly as a function of z. A con­venient single value of RS is obtained for z = 45°, but a more refined method is desirable (see Sect. 6.1). The procedure described above is referred to as “shade - unshade” calibration, and is suitable for calibrating small numbers of pyranometers at a time. Once a “reference” pyranometer is calibrated in this manner, compari­son (ratios) of test and reference pyranometer output voltages can be used to cal­ibrate other pyranometers. However, this simple one-to-one comparison method is not recommended because it results in larger uncertainties (since the characteristic response curves of both pyranometers are most likely different) than either a di­rect shade-unshade calibration or the “component-summation” technique described next.

In the component-summation calibration method, a shade-unshade calibrated pyranometer monitors the diffuse “reference” irradiance, DR. The direct beam is measured with an ACR. The responsivity of pyranometer i, RSi, exposed to global irradiance with voltage output Vgi is computed from:

RSi = Vg,/[B cos(z)+DR]. (1.5)

Responsivities as a function of zenith angle for sample pyrheliometers and pyra­nometers are shown in Figs. 1.6 and 1.7, respectively. Note that these curves are not representative of radiometer make or model, as every instrument has a different in­dividual response curve. Characterization of each pyranometer is needed to produce data with lower uncertainty. We discuss the sources of uncertainty and characteriza­tion of solar radiometers in the next section.

The detailed procedures to correctly calibrate solar radiometers and transfer these calibrations to other instruments are described in national and international stan­dards such as those developed by the American Society for Testing and Materials (ASTM) and the International Standards Organization (ISO) as referenced above.

 Fig. 1.6 Response curves for sample Kipp & Zonen CH1 and Eppley NIP pyrheliometers as a function of zenith angle, resulting from calibration against an ACR

Examples of response-curve characterizations of different pyrheliometers and pyranometers are included on the CD-ROM. These examples include the reports from the Broadband Outdoor Calibration (BORCAL) conducted in 2006 at NREL (‘2006-02_NREL_SRRL_BMS. pdf’) and at the Southern Great Plains Atmospheric Radiation Measurement site (‘2006-02_ARM_SGP_Full. pdf’).

## Modeling Solar Radiation at the Earth’s Surface

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### Foreword

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