LAUSR

NASA’s Solar Radiation and Climate Experiment (SORCE) Spectral Irradiance Monitor (SIM) instrument produced about 17 years of daily average Spectral Solar Irradiance ( SSI ) data for wavelengths 240 – 2416 nm. We choose a day of minimal solar activity, August 24, 2008 (2008-08-24), during the 2008 – 2009 minimum between Cycles 23 and 24, and compute the brightness temperature ( T o $T_{o}$ ) from that day’s solar spectral irradiance ( SSI o $\mathit{SSI}_{o}$ ). We consider small variations of T $T$ and SSI about these reference values, and derive linear and quadratic analytic approximations by Taylor expansion about the reference-day values. To determine the approximation accuracy, we compare to the exact brightness temperatures T $T$ computed from the Planck spectrum, by solving analytically for T $T$ , or equivalent root finding in Wolfram Mathematica . We find that the linear analytic approximation overestimates, while the quadratic underestimates, the exact result. This motivates the search for statistical “fit” models “in between” the two analytic models, with minimum root-mean-square-error, RMSE. We make this search using open-source statistical R $R$ software, determine coefficients for linear and quadratic fit models, and compare statistical with analytic RMSEs. When only linear analytic and fit models are compared, the fit model is superior at ultraviolet, visible, and near-infrared wavelengths. This again holds true when comparing only quadratic models. Quadratic is superior to linear for both analytic and statistical models, and statistical fits give the smallest RMSEs. Lastly, we use linear analytic and fit models to find an interpolating function in wavelength, useful when the SIM results need adjustment to another choice of wavelengths, to compare or extend to any other instrument. Advantages of the quadratic T $T$ over the exact T $T$ include ease of interpretation, and computational speed.