Solar Temperature Variations Computed from SORCE SIM Irradiances Observed During 2003 – 2020

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