http://www.princeton.edu/~lam/documents/RoyceLam2010.pdf
The difference between the transient and the equilibrium DelTs responses
is attributed to the finite thermal inertia of the Earth system
(Hansen et al., 2005). The Earth receives radiant energy from the Sun,
and emits radiant energy back into space. The mismatch of these two fluxes changes the thermal energy content of the Earth system.
Using a control volume enclosing the Earth (with its boundary surface above the atmosphere), the Earth's energy balance equation is:
dE
dt
= Fin(t) �� Fout(X; Ts; ...); (4)
where E is the stored thermal energy content per unit area of the Earth
(Joules per unit area), and Fin(t) and Fout(X; Ts; ...) are, respectively,
the incoming radiant energy flux from the Sun and the outgoing radiant
energy flux away from the Earth|both fluxes (Joules per year
The Earth system is expected to exhibit a number of different thermal
response time scales depending on the mode of excitation. The governing
equation for Ts(t) is Eq.(7), and the role played by on the
Ts(t) response to either a periodic or a Dirac-delta forcing function
is well known.
The data shown in Figs. 1 and 2 has been t using least squares
to yield values of the transient climate sensitivity ( 2.3C) and
the thermal inertia time scale associated with global warming
(approximately 32 years).
Note that Ts will continue to rise even after X=Xo has been successfully
stabilized at some constant value. For example, if 32
years, then it would take more than six decades after X=Xo is stabilized
in order for Ts to eventually reach 90% of its full equilibrium
rise. When Tau is some multi-decadal number, the Earth's response to
changes of radiative forcing is very sluggish. This sluggishness has
important policy implications.
What is the probability that might be a multi-decadal or even
multi-centurial number? It is not obvious that this question could
ever be answered objectively. The meaningfulness of probability distribution
functions constructed by polling modeling data generated
by computers is still subject to debate. At the present time, the
available observational data do not support subjective assignments of
multi-decadal tau's.