71The EM-GC simulation in Fig. 2.4 has χ^2 = 1.52. In the world of physics, this
would be termed a reasonably good model simulation. Such an impression is also
apparent based on visual inspection of the red and black curves on the top rung of
Fig. 2.4. The EM-GC simulation in Fig. 2.5 has χ^2 = 0.81, which is an exceptionally
good simulation both in the literal interpretation of χ^2 , as well as visual inspection
of Fig. 2.5. For the quantitative assessments of the amount of global warming that
can be attributed to humans, as well as the projections of future global warming,
EM-GC simulations are weighted by 1/χ^2 , such that the better the goodness of fit
(i.e., the smaller the value of χ^2 ) the larger the weight. Chapter 7 of Taylor ( 1982 )
provides a description of the utility of this weighting approach.
2.2.1.3 The Degeneracy of Earth’s Climate
Figure 2.9 shows simulations of Earth’s climate that differ only due to choice of
ΔRF due to tropospheric aerosols. Figure 2.9a shows results for AerRF 2011 of
−0.4 W m−^2 (upper limit of IPCC ( 2013 ) likely range), −0.9 W m−^2 (IPCC best
estimate), and −1.5 W m−^2 (lower limit of IPCC likely range). For each simulation,
the upper rung of a typical EM-GC ladder plot is shown, but with ΔT projected into
the future. Projections use values of λ and κ associated with each simulation,
together with RCP 4.5 for GHG abundances and aerosol precursor emissions. Each
simulation uses the OHC record based on the average of the six studies shown in
Fig. 2.8. For our projections of ΔT, the only term considered is ΔTHUMAN (Eq. 2.4):
i.e., we assume that the future change in temperature will be based on GHG warm-
ing and aerosol cooling from RCP 4.5, climate feedback, and ocean heat export. It
is also assumed that natural factors such as ENSO, solar, and volcanoes will have no
influence on future temperature. The second rung of Fig. 2.9 shows ΔTHUMAN as well
as the contributions from individual terms (here the OHE term is not shown for clar-
ity because it is small and nearly the same for each simulation^18 ). The GMST expe-
rienced in 2015 was unusually large due to the effect of ENSO, which is illustrated
by inclusion of the ENSO rung for Fig. 2.9b.^19
Figure 2.9 shows that the climate record can be fit nearly equally well using the
EM-GC approach for two contrasting scenarios:
(1) tropospheric aerosols have had little overall effect on prior climate due to a near
balance of cooling (primarily sulfate aerosols) and heating (primarily black car-
bon aerosols) and the climate feedback (numerical value of λ) needed to fit
observed ΔTi is small (Fig. 2.9a).
(^18) Time series of ocean heat export (OHE) appear on the next figure, which illustrates the sensitivity
of the EM-GC model to choice of data set for ocean heat content (OHC).
(^19) The ENSO rungs for Fig. 2.9a, c are nearly identical to Fig 2.9b and is only shown once
2.2 Empirical Model of Global Climate