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7. Discussion, conclusions, and implications
The findings of the present study may be considered surprising in several respects:
(1) The relatively small effective heat capacity of the global ocean that is coupled to the increase in global
mean surface temperature over the five-decade period for which ocean heat content measurements are
available, 14 ± 6 W yr m-2 K-1 (0.44 G J m-2 K-1), equivalent to about 150 m of the world ocean, and the
correspondingly low effective planetary heat capacity C, 16.7 ± 7.0 W yr m-2 K-1 (0.5 ± 0.2 G J m-2 K-1).
(2) The short relaxation time constant of global mean surface temperature in response to perturbations τ, 5
± 1 years; and
(3) The low equilibrium climate sensitivity λs-1 inferred from (1) and (2) as λ τs− =1 /C, 0.30 ± 0.14 K/(W
m-2), equivalent to equilibrium temperature increase for doubled CO2 ∆T2 × = 1.1 ± 0.5 K.
This value is well below current best estimates of this quantity, summarized in the Fourth Assessment Report of the
IPCC <2007> to be "2 to 4.5 K with a best estimate of about 3 K and ... very unlikely to be less than 1.5
K".
This situation invites a scrutiny of the each of these findings for possible sources of error of interpretation
in the present study.
Is the effective heat capacity that is coupled to the climate system, as determined from trends in ocean heat
content and GMST, too low, or too high? For a given relaxation time constant τ, a lower value of C would
result in a greater climate sensitivity, and vice versa. As noted above previous investigators have used similar
considerations to suggest different values for C, in one instance substantially greater than the value reported
17 here (20 - 50 W yr m-2 K-1) and in one instance with a range of a factor of 20, (3.2 - 65 W yr m-2 K-1) that
encompasses the value determined here.
Examination of Figure 4 suggests that it would be hard to justify a slope less than about 8 W yr m-2 K-1. Perhaps
a more fundamental question has to do with the
representativeness of the data that comprise the Levitus et al. <2005> compilation. In this context it might be
noted that Willis et al. <2004> reported an heat uptake rate in the upper 750 meters of the ocean, based on
satellite altimetry as well as in-situ measurements, of 0.86 ± 0.12 W m-2, a factor of 7 greater than the
Levitus et al. <2005> average for 1958-1995; a greater heat uptake rate would result in a greater effective
ocean heat capacity and a lower climate sensitivity. However in a subsequent publication a year later Lyman
et al. <2006> reported a rapid net loss of ocean heat for 2003-2005 that led those investigators to estimate
the heat uptake rate for 1993-2005 as 0.33 ± 0.23 W m-2, a value much more consistent with the long-term
record in the Levitus et al. <2005> data set. The previous instances of several-year periods of net loss of
heat from the ocean exhibited in the Levitus et al. <2005> data and shown in Figure 2 suggest the necessity
of evaluating the effective heat capacity based on a long-term record.
Is the relaxation time constant of the climate system determined by autocorrelation analysis the pertinent
time constant of the climate system? Of the several assumptions on which the present analysis rests, this
would seem to invite the greatest scrutiny. A possible explanation for the short time constant inferred from
the autocorrelation analysis might be that the autocorrelation is dominated by short term variability, such as
that resulting from volcanic eruptions, and that the thermal signal from such a short perturbations would not
be expected to penetrate substantially into the deep ocean. Two considerations would speak against such an
explanation. First, the autocorrelation leading to the 5-year time constant extended out to lag times of 15
years or more with little indication of increased time constant for lag time greater than about 5-8 years
(Figure 6). Also, recent studies with coupled ocean atmosphere GCMs have shown that the thermal signal
from even a short-duration volcanic event is transported into the deep ocean and can persist for decades
; such penetration of the thermal signal from a short-
duration forcing would suggest that the autocorrelation of GMST over a decade or more would be
representative of the longer time constant associated with the coupling to the deep ocean and not reflective
simply of a short time constant associated with the ocean mixed layer.
Finally, as the present analysis rests on a simple single-compartment energy balance model, the question
must inevitably arise whether the rather obdurate climate system might be amenable to determination of its
key properties through empirical analysis based on such a simple model. In response to that question it
might have to be said that it remains to be seen. In this context it is hoped that the present study might
stimulate further work along these lines with more complex models. It might also prove valuable to apply
the present analysis approach to the output of global climate models to ascertain the fidelity with which
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these models reproduce "whole Earth" properties of the climate system such as are empirically determined
here. Ultimately of course the climate models are essential to provide much more refined projections of
climate change than would be available from the global mean quantities that result from an analysis of the
present sort. Still it would seem that empirical examination of these global mean quantities – effective heat
capacity, time constant, and sensitivity – can usefully constrain climate models and thereby help to identify
means for improving the confidence in these models.
The empirical determinations presented here of global heat capacity and of the time constant of climate
response to perturbations on the multidecadal time scale lead to a value of equilibrium global climate
sensitivity of 0.30 ± 0.14 K/(W m-2), where the uncertainty range denotes a one-sigma estimate. This
sensitivity together with the increase in global mean surface temperature over the twentieth century would
imply a total forcing 1.9 ± 0.9 W m-2; although the central value of this range is fairly close to the total
greenhouse gas forcing over this time period, 2.2 W m-2, this result is consistent with an additional forcing
over the twentieth century of –0.30 ± 0.97 W m-2. The rather large uncertainty range could be consistent
with either substantial cooling forcing (-1.3 W m-2) or substantial warming forcing (+ 0.7 W m-2), with
aerosol forcing a likely major contributor. Because of the short response time of the climate system to
perturbations, the climate system may be considered in near steady state to applied forcings and hence,
within the linear forcing-response model, the change in temperature over a given time period may be
apportioned to the several forcings. The estimated increase in GMST by well mixed greenhouse gases from
preindustrial times to the present, 0.7 ± 0.3 K; the upper end of this range approaches the threshold for
"dangerous anthropogenic interference with the climate system," which is considered to be in the range 1 to
2 K .
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