Methodology and calculator for high precision regression fits of pyranometer angular responsivities and the associated uncertainties. (September 2015) - Boyd, Matthew
Highlights: Regression algorithms are proposed for angular pyranometer calibration factors. Single polynomial regression fits of responsivities and uncertainties are created. The regression functions include extrapolations to 0° and 90° incidence angles. The functions can be calculated with a custom free software tool. The functions closely fit calibration data from a range of pyranometer models. Abstract: An easy to implement method for accurately utilizing pyranometer incidence angle dependent calibration factors, or responsivities (μV/W/m 2 ), 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° and 90°, 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 R 2 values greater than 0.98.