Formulating an Energy Balance Model - Climate Change: Identification and Projections - page 52

to keep T E as a parameter to estimate, and limit the series to [1, 10, 100
years]. Finally, the model is therefore written:

⎛ ⎞

c c 1 − c − c

1 2 1 2

T = T +

⎜ ⎜
⎝

+ +

⎟ ⎟
⎠

( S u + S u + S u )

G E 1 1 2 2 3 3

1 + s 1 + 10 s 1 + 100 s

Of course, we checked the robustness of the identification with respect to
the number and the choice of the T i s. The number of parameters to identify
(six, counting T E ) appears to be sufficient for modeling the fundamentals of
the climatic process.

Conversely, we could have attempted to distinguish the terrestrial and
ocean temperatures, or those in the northern and southern hemispheres.
However, firstly, the individual temperature databases only exist from 1850,
and secondly, the ratio of the number of new measurements to the number of
new parameters introduced would lead to an over-parameterization, which is
prohibitive in the context of black box identification. Expect for some minor
variations, regarding the parametrization of G ( s ), the model adopted here
seems to be practically indispensable (and Van Hateren's is very close to it).

Dynamic parameters

The IPCC has introduced a parameter named TCR: Transient Climate
Response. It is defined as the rise in temperature obtained after 70 years, in a
scenario of annual CO 2 increase of 1%. These 70 years correspond to the
duration necessary for a doubling in the concentration of CO 2 (1.01 70 ~ 2).
To date, the equilibrium having not yet been reached, we are thus obviously
left with TCR < S clim .

The TCR parameter is directly proportional to S clim , and the TCR/ S clim
ratio is a complex function of all the temporal and frequential features of
transmittance G ( s ). The smaller it is, the slower the climatic process is to
react to the influence of forcings, whatever they may be: CO 2 , TSI, or AOD.
Using this ratio alone, it is impossible to include all features that are of
interest to us.