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Methodology and Calculator for High Precision Regression Fits of Pyranometer Angular Responsivities and the Associated Uncertainties



Matthew T. Boyd


An easy to implement method for accurately utilizing pyranometer incidence angle dependent calibration factors, or responsivities (uV/W/m2), along with the associated uncertainties has been developed. This method uses algorithms for creating single polynomial functions dependent on the incidence angle to characterize both the pyranometer responsivity and the upper prediction interval of the associated standard uncertainties. Single polynomial functions are easier to implement in spreadsheet software and programming environments than the simpler to formulate piecewise polynomials and splines. The polynomials are of high degree, extrapolated to 0 degrees and 90 degrees, and solved using robust techniques to avoid oscillations and overshoots, which can occur when using other interpolation methods. A free software tool was created that calculates the functions using the algorithms presented in this paper, and it was tested on the calibrated responsivities and uncertainties of 40 pyranometers representing six (6) different models. All of the obtained fits closely represent the data with R2 values greater than 0.98.
Solar Energy


Pyranometer, Responsivity, Incidence Angle, Uncertainty
Created June 23, 2015, Updated February 19, 2017