New Absolute Cavity Pyrgeometer Equation by Application of Kirchhoff's Law and Adding a Convection Term

Bruce Forgan, Julian Grobner, Ibrahim Reda

    Research output: Contribution to journalArticlepeer-review


    An equation for the Absolute Cavity Pyrgeometer (ACP) is derived from application of Kirchhoff's law and the addition of a convection term to account for the thermopile being open to the environment, unlike a domed radiometer. The equation is then used to investigate four methods to characterise key instrumental parameters using laboratory and field measurements. The first uses solar irradiance to estimate the thermopile responsivity, the second uses a minimisation method that solves for the thermopile responsivity and transmission of the cavity, and the third and fourth revisit the Reda et al. (2012) linear least squares calibration technique. Data were collected between January and November 2020, when the ACP96 and two IRIS radiometers monitoring terrestrial irradiances were available. The results indicate good agreement with IRIS irradiances using the new equation. The analysis also indicates that while the thermopile responsivity, concentrator transmission and emissivity of an ACP can be determined independently, as an open instrument, the impact of the convection term is minor in steady-state conditions but significant when the base of the instrument is being subjected to rapid artificial cooling or heating. Using laboratory characterisation of the transmission and emissivity, together with use of an estimated solar calibration of the thermopile, generated mean differences of less than 1.5 Wm-2 to the two IRIS radiometers. A minimisation method using each IRIS radiometer as the reference also provided similar results, and the derived thermopile responsivity was within 0.3 μV W-1 m2 of the solar-calibration-derived infrared responsivity estimate of 10.5 μV W-1 m2 estimated using a nominal solar calibration and provide irradiances within ±2 % of the terrestrial irradiance measured by the reference pyrgeometers traceable to the International System of Units (SI). The calibration method using linear least squares regression introduced by Reda et al. (2012) that relies on rapid cooling of the ACP base but utilising the new equation was found to produce consistent results but was dependent on the assumed temperature of the air above the thermopile. This study demonstrates the potential of the ACP as another independent reference radiometer for terrestrial irradiance once the magnitude of the convection coefficient and any potential variations in it have been resolved.

    Original languageAmerican English
    Pages (from-to)727-743
    Number of pages17
    JournalAtmospheric Measurement Techniques
    Issue number3
    StatePublished - 2023

    Bibliographical note

    Publisher Copyright:
    © 2023 Bruce W. Forgan et al.

    NREL Publication Number

    • NREL/JA-1900-85308


    • absolute cavity pyrgeometer
    • Kirchhoff's law
    • linear least squares calibration technique
    • meterology
    • minimisation method
    • radiometer
    • solar irradiance


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