They combined simple energy balance considerations with a physical assumption for the way water vapour is transported, and separated the contributions of surface heating from solar radiation and from increased greenhouse gases in the atmosphere to obtain the two sensitivities. (geoengineeringwatch.org)
However, even if ENSO or the PDO could be considered partially chaotic, I am certain that the longer timescale climate variations are still controlled by energy balance considerations and therefore would still be considered deterministic. (hannahlab.org)
I will repeat that the non-linear mechanism is something I have inferred from energy balance considerations, i.e. it is not necessarily part of the conjecture as it is stated. (gfdl.noaa.gov)