Implitcation of a Power-Law Climate Response Function

Abstract:

A study of global mean temperature is presented assuming that the climate response function to anthropogenic forcing is a power law. This general form allows for long-range dependancies with only 3 parameter while remaining within the linear forcing paradigm. This establish a one-to-one relation between the scaling exponent H and the ratio of the Transient Climate Response, TCR, and the Equilibrium Climate Sensitivity, ECS. The scaling exponent of the power law is estimated by a regression of temperature as a function of forcing and by a spectral analysis of the temperature and the forcing. We consider for the analysis 5 different datasets of historical global mean temperature and 100 CMIP5 RCP runs distributed among the 4 scenarios. We find that the error function for the estimate on historical temperature is very wide and thus, many scaling exponent can be used without meaningful changes in the fit residuals of historical temperatures; their response in the year 2100 on the other hand, is very broad. CMIP5 runs allow a narrower estimate of H which can then be used to estimate the ECS by dividing the TCR estimated from the historical data.