Formulating an Energy Balance Model - Climate Change: Identification and Projections - page 44

A complex system can result from the parallel association of a number of
first order transmittances, or in series, or in feedback loops. The state
becomes a vector (

{ }

) Generalizing for nonlinear cases, the
equations of state remain similar to what we presented:

x = x , 1 " x , , x

n

. dx / dt = f ( x , u )

The global coupled atmosphere-ocean General Circulation Models
(GCMs) result from physical laws of continuum mechanics (fluid mechanics
and thermodynamics). They are described by a huge number of first order
nonlinear state equations, resulting from their finite elements discretization.
Their simulation requires gigantic calculation resources 2 .

For the purposes of identification, we are looking instead for a minimal
representation which is able to account for the input-output behavior of the
process. This is the case for the more or less simplified energy balance
models, such as the MAGGIC model [MEI 11], which has been extensively
used by the IPCC since AR3, and also for the production of the RCPs (see
9.1). The number of finite elements of which they are made can be reduced
to a few hundred, a few dozen, a few units, or even a single unit, like in our
introduction model. The fundamental climatic concepts of radiative forcing,
equilibrium sensitivity and climatic feedback, widely used by the IPCC, are
inherent to this type of model.

4.2. Structure of an energy balance model

In a strictly black box context, the LTI model of a climatic process with
inputs (log-CO 2 , irradiance, volcanism) and output u , u , u x = T − T

1 2 3 G E

would be written in the more general form:

x = G ( s ) u + G ( s ) u + G ( s ) u

1 1 2 2 3 3

2 CNRM-CERFACS simulations require the use of 12 nodes (out of 32) of 8 processors of an
NEC SX8 calculator from Météo-France working full-time for one and a half years, and a
volume of data to process and store of around 400 To (400 thousand billion octets). IPSL
simulations require the use of 3 nodes (out of 10) of 16 processors of an NEC SX9 calculator
of the national apparatus for intensive calculations (GENCI) and a volume of data of 2 Po
(2 million billion octets). A significant amount of national calculation power is therefore
taken up by speculative climatic research, which is a different activity to short-term weather
forecasting, also consuming large amount of calculation capacity.