Thanks for this analysis, it’s very interesting. You might find it simpler and more accurate to go straight from emissions to warming using the transient climate response to cumulative carbon emissions (TCRE) rather than climate sensitivity, though (see https://en.wikipedia.org/wiki/Transient_climate_response_to_cumulative_carbon_emissions ). A problem with using ECS is that it gives you the warming that occurs after Earth has reached equilibrium with a given CO2 concentration. However, in reality, the CO2 concentration won’t stay constant once we’ve stopped emitting, but will decline as it is slowly taken up by the Earth system. The result found in many Earth system models is that temperatures rise linearly with emissions and once emissions stop, temperatures also stop rising, rather than rising to reach the value implied by the ECS for the peak concentration value (at the point when emissions stop). (Though, temperatures would still rise further if the ECS were very high, since the Earth would be experiencing a much larger radiative forcing in that case.) So I think this would reduce the chance of high temperatures a bit.
Thanks for this analysis, it’s very interesting. You might find it simpler and more accurate to go straight from emissions to warming using the transient climate response to cumulative carbon emissions (TCRE) rather than climate sensitivity, though (see https://en.wikipedia.org/wiki/Transient_climate_response_to_cumulative_carbon_emissions ). A problem with using ECS is that it gives you the warming that occurs after Earth has reached equilibrium with a given CO2 concentration. However, in reality, the CO2 concentration won’t stay constant once we’ve stopped emitting, but will decline as it is slowly taken up by the Earth system. The result found in many Earth system models is that temperatures rise linearly with emissions and once emissions stop, temperatures also stop rising, rather than rising to reach the value implied by the ECS for the peak concentration value (at the point when emissions stop). (Though, temperatures would still rise further if the ECS were very high, since the Earth would be experiencing a much larger radiative forcing in that case.) So I think this would reduce the chance of high temperatures a bit.