Determination of Earths transient and equilibrium climate sensitivities from observations over the twentieth century: Strong dependence on assumed forcing
Relations among observed changes in global mean surface temperature, ocean heat content, ocean heating rate, and calculated radiative forcing, all as a function of time over the twentieth century, that are based on a two-compartment energy balance model, are used to determine key properties of Earth's climate system. The increase in heat content of the world ocean, obtained as the average of several recent compilations, is found to be linearly related to the increase in global temperature over the period 1965-2009; the slope, augmented to account for additional heat sinks, which is an effective heat capacity of the climate system, is 21.8 {+-} 2.1 W year m{sup -2} K{sup -1} (one sigma), equivalent to the heat capacity of 170 m of seawater (for the entire planet) or 240 m for the world ocean. The rate of planetary heat uptake, determined from the time derivative of ocean heat content, is found to be proportional to the increase in global temperature relative to the beginning of the twentieth century with proportionality coefficient 1.05 {+-} 0.06 W m{sup -2} K{sup -1}. Transient and equilibrium climate sensitivities were evaluated for six published data sets of forcing mainly by incremental greenhouse gases and aerosols over the twentieth century as calculated by radiation transfer models; these forcings ranged from 1.1 to 2.1 W m{sup -2}, spanning much of the range encompassed by the 2007 assessment of the Intergovernmental Panel on Climate Change (IPCC). For five of the six forcing data sets, a rather robust linear proportionality obtains between the observed increase in global temperature and the forcing, allowing transient sensitivity to be determined as the slope. Equilibrium sensitivities determined by two methods that account for the rate of planetary heat uptake range from 0.31 {+-} 0.02 to 1.32 {+-} 0.31 K (W m{sup -2}){sup -1} (CO{sub 2} doubling temperature 1.16 {+-} 0.09-4.9 {+-} 1.2 K), more than spanning the IPCC estimated 'likely' uncertainty range, and strongly anticorrelated with the forcing used to determine the sensitivities. Transient sensitivities, relevant to climate change on the multidecadal time scale, are considerably lower, 0.23 {+-} 0.01 to 0.51 {+-} 0.04 K (W m{sup -2}){sup -1}. The time constant characterizing the response of the upper ocean compartment of the climate system to perturbations is estimated as about 5 years, in broad agreement with other recent estimates, and much shorter than the time constant for thermal equilibration of the deep ocean, about 500 years.