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

For a "reference day" of minimal solar activity between cycles 23 and 24 we compute the brightness temperature from solar spectral irradiance for each wavelength. We consider small variations of irradiance and temperature about the reference day values, and derive linear and quadratic analytic temperature approximations by Taylor expansion about the reference values. To determine approximation accuracy we compare to exact brightness temperatures computed for each day. We find that the linear analytic approximation overestimates, while the quadratic underestimates the exact result. Using R software, we find statistical fit models with minimum root-mean-square-error. We show that the quadratic statistical fit models give the smallest root-mean-square-error, giving results very near the exact.