On the Accuracy of Deriving Climate Feedback Parameters from Correlations between Surface Temperature and Outgoing Radiation

Abstract

Changes in outgoing radiation are both a consequence and a cause of changes in the earth?s temperature. Spencer and Braswell recently showed that in a simple box model for the earth the regression of outgoing radiation against surface temperature gave a slope that differed from the model?s true feedback parameter. They went on to select input parameters for the box model based on observations, computed the difference for those conditions, and asserted that there is a significant bias for climate studies. This paper shows that Spencer and Braswell overestimated the difference. Differences between the regression slope and the true feedback parameter are significantly reduced when 1) a more realistic value for the ocean mixed layer depth is used, 2) a corrected standard deviation of outgoing radiation is used, and 3) the model temperature variability is computed over the same time interval as the observations. When all three changes are made, the difference between the slope and feedback parameter is less than one-tenth of that estimated by Spencer and Braswell. Absolute values of the difference for realistic cases are less than 0.05 W m?2 K?1, which is not significant for climate studies that employ regressions of outgoing radiation against temperature. Previously published results show that the difference is negligible in the Hadley Centre Slab Climate Model, version 3 (HadSM3).