Radiative forcing at high concentrations of well- mixed greenhouse gases

We present new calculations of radiative forcing at very high concentrations of CO2, CH4, and N2O, relevant to extreme anthropogenic climate change and paleoclimate studies. CO2 forcing is calculated over the range 100ppmv to 50,000ppmv, and the maximum forcing is 38.1W m(-2). CH4 and N2O forcings are calculated over the range 100ppbv to 100ppmv and give maximum forcings of 6.66W m(-2) and 22.3W m(-2). The sensitivity of our calculations to spatial averaging and tropopause definition is examined. We compare our results with the simplified expressions reported by Intergovernmental Panel on Climate Change (IPCC) and find significant differences at high greenhouse gas concentrations. We provide new simplified expressions which agree much better with the calculated forcings and suggest that these expressions be used in place of the IPCC expressions. Additionally, we provide meridionally resolved forcings which may be used to force simple and intermediate complexity climate models.