Formulating an Energy Balance Model - Climate Change: Identification and Projections - page 45

where the three transmittances G i ( s ), and their respective static gains
, SS are free from any a priori constraints. We will recover a similar

expression, using the generalization of our introductive example - which
already contained the beginnings of EBM. Eventually, the structure above
will be assigned with a restriction which seems minor, but is essential for
ensuring the identification approach is carried out correctly.

, , S

1 2 3

of the radiative energy
flows entering and leaving at the TOA (Top-Of-Atmosphere). This makes
the difference between the solar flow incident, and the flows reflected and
re-emitted, both by the whole atmosphere and the surfaces of the ocean and
land. All these flows are caused by climatic machinery, localized in the
atmosphere and its immediate contact surface with the continents and
oceans. The balance results from causes

Let us now consider the instantaneous balance Φ

R

uu , known as radiative forcing
input, and from the global temperature anomaly

, , u

1 2 3

, then x = T − T

G E

. Thanks to mixing caused by atmospheric circulation,
it can be accepted that this function takes on value instantaneously (in less
than one year).

Φ = Φ ( u , u , u , x )

R R 1 2 3

The atmospheric mass also exchanges energy with continental surfaces
(very little since the ground is an excellent thermal insulator), and especially
with the enormous ocean mass. This is organized into different temperature
and salinity layers, which float, circulate and slide under and over each
other, very rarely mixing together. The state of the climate system can
therefore not be reduced to the deviation x . The differences in temperature
between the various layers compared to their own equilibrium temperature
also needs to be included. As a result, the whole system is modeled using a
system of differential equations based on the thermal inertias of the various
layers, and the coefficients of resistance or thermal conduction which govern
the energy flows exchanged according to temperature differences.

d

For a single thermal inertia I G , we used , or its equivalent

I x = Φ

G R

dt

1

transmittance formulation,

x = Φ

. In the presence of a number of

R

sI

G

thermal inertias in a situation of linear interactions, an expression of the form

1

, would be used, where is a complex thermal inertia x = Φ

I G ( s )

R

sI

G s

( )