# Happy 35th birthday, global warming!

It is difficult to determine the significance of the next most important climatic effect induced by man, “dust”, because of uncertainties with regard to the amount, the optical properties and the distribution of man-made particles,

citing a number of papers by Steve Schneider and others. Because he cannot quantify it, he leaves out this effect. Here luck was on Broecker’s side: the warming by other greenhouse gases and the cooling by aerosols largely cancel today, so considering only CO2 leads to almost the same radiative forcing as considering all anthropogenic effects on climate (see IPCC AR4, Fig. SPM.2).

Table 1 of Broecker (1975)

Step 2: Predict future concentrations

To go from the amount of CO2 emitted to the actual increase in the atmosphere, one needs to know what fraction of the emissions remains in the air: the “airborne fraction”. Broecker simply assumed, based on past data of emissions and CO2 concentrations (Keeling’s Mauna Loa curve), that the airborne fraction is a constant 50%. I.e., about half of our fossil fuel emissions accumulates in the atmosphere. That is still a good assumption today, if you look at the observed CO2 increase as fraction of fossil fuel emissions. Broecker calculated that about 35% of the emissions is taken up by the ocean and the other 15% by the biosphere (again not far from modern values, see Canadell et al.). On this basis he argued that if the ocean is the main sink, the airborne fraction would remain almost constant for the decades to come (his calculations extend to the year 2010).

Thus, with a 3% increase in emissions per year and 50% of that remaining airborne, it is easy to compute the increase in CO2 concentrations. He obtains an increase from 295 to 403 ppm from 1900 to 2010. The actual value in 2010 is 390 ppm, a little lower than Broecker estimated because his forecast cumulative emissions were a little too high.

Step 3: Compute the global temperature response

Now we come to the temperature response to increased CO2 concentration. Broecker writes:

The response of the global temperature to the atmospheric CO2 content is not linear. As the CO2 content of the atmosphere rises, the absorption of infrared radiation will “saturate” over an ever greater portion of the band. Rasool and Schneider point out that the temperature increases as the logarithm of the atmospheric CO2 concentration.

Based on this logarithmic relationship (still valid today) Broecker assumes a climate sensitivity of 0.3ºC warming for each 10% increase in CO2 concentration, which amounts to 2.2ºC warming for CO2 doubling. This is based on early calculations by Manabe and Wetherald. Broecker writes:

Although surprises may yet be in store for us when larger computers and better knowledge of cloud physics allow the next stage of modeling to be accomplished, the magnitude of the CO2 effect has probably been pinned down to within a factor of 2 to 4.

The AR4 gives the uncertainty range of climate sensitivity as 2-4.5ºC warming for CO2 doubling, so there still is about a factor of 2 uncertainty and Broecker used a value near the very low end of this uncertainty range. Modern estimates are not only based on model calculations but also on paleoclimatic and modern data; the AR4 lists 13 studies that constrain climate sensitivity in its table 9.3.

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