Empirical Modeling of TSI: A Critical View

Solar empirical models based on regression of two variability indices for radiation from the photosphere and chromosphere fit total solar irradiance (TSI) observations with accuracy comparable to the precision reported for the observations themselves. However, the physical meaning of the fitting coefficients and their stability during different phases of the solar cycle has not been examined in detail. We test the stability of the coefficients in regression models of the VIRGO TSI observations over the nine years from the minimum of Cycle 23 in 1996 through the maximum to 2005. We also show how the coefficients converge to the ‘`best fit’' using a search in the coefficient space. Analysis of TSI variability in different phases of this cycle shows little change in regression models as long as the time periods used in the regression are long enough to show the slow solar cycle variation in TSI. We extend our analysis to TSI observations from ERB, ACRIM2, ACRIM3, DIARAD, and TIM. The regression models from these time series show large systematic differences in fitting coefficients for the plage and sunspot indices that we used. These differences are significantly larger than the estimated uncertainties in the coefficients and point to the difficulty of combining observations from different instruments to create an accurate composite TSI record over several solar cycles. Our results clearly demonstrate the improvement in precision of TSI measurements from the Nimbus 7 ERB in Cycle 22 to the latest SORCE TIM data in Cycle 23.