69values of γ and κ is presented. Two additional model output terms, the climate feed-
back parameter (λ) and Equilibrium Climate Sensitivity (ECS), both of which are
found from γ, are described. Finally, a metric for model performance, χ^2 , which
plays an important role for the projections of ΔT, is defined.
The value of κ found using the OHC record for the upper 700 m of the world’s
oceans, averaged from six studies, is 0.62 W m−^2 °C−^1 (bottom panel, Fig. 2.4). As
stated in Sect. 2.2.1.1, the calculation of κ considers the increase in temperature for
depths below 700 m by scaling observations from the upper part of the ocean. Of the
six OHC datasets, Ishii and Kimoto ( 2009 ) results in the smallest value for κ (0.43 W
m−^2 °C−^1 ) and Gouretski and Reseghetti ( 2010 ) leads to the largest value (1.52 W
m−^2 °C−^1 ). All of the values of κ found using various time series for OHC fall within
the range of empirical estimates and coupled ocean-atmosphere model behavior that
is shown in Fig. 2 of Raper et al. ( 2002 ). As such, the representation of ocean heat
export in the EM-GC framework is realistic, given the present state of knowledge.
If the true value of κ changes over time, then our projections of ΔT based on an
assumption of constant κ will require modification. Past measurements of OHC are
too uncertain to infer, from the prior record, whether κ has changed. The nearly fac-
tor of 3 difference in κ inferred from various, credible estimates of OHC is certainly
much larger than any reasonable change in κ that could have occurred during the
time of OHC observations.
The value of γ found for the EM-GC simulation shown in Fig. 2.5 is 0.49. This
means the increase in RF of climate due to GHGs, tropospheric aerosols, and land
use change from 1860 to present must be increased by ~50 % (i.e., multiplied by
1.49) to obtain best fit to observed ΔT. In other words, the sum of all climate feed-
backs must be positive. Model parameter γ represents the sensitivity of climate to
all of the feedbacks that occur in response to the perturbation to RF at the tropo-
pause induced by humans, and is related to the climate feedback parameter λ via:
1
1
1
+=
-
=
=+
å
g
l
ll
ll lP
whereAll ClimateFeedbacks
ie.. WATERVAPORCLOOUDS++llLAPSE RATE SURFACEREFLECTIVITY+etc.(2.5)
This formulation for the relation between γ and λ is commonly used in the climate
modeling community (see Sect. 8.6 of IPCC ( 2007 )). We record λ rather than γ on
all of the EM-GC ladder plots (Figs. 2.4 and 2.5) because λ is more directly compa-
rable to GCM output, such as that in Table 9.5 of IPCC ( 2013 ).
Equilibrium climate sensitivity (ECS) is also given on the top rung of the EM-GC
ladder plots. This metric represents the increase in ΔT of the climate system after it
2.2 Empirical Model of Global Climate