Formulating an Energy Balance Model - Climate Change: Identification and Projections - page 41

4

Formulating an Energy Balance Model

4.1. State models and transmittance

The first energy balance models appeared in the 1960s [ADE 64,
BUD 69, SEL 69]. Typically, these models are based on the Stefan-
Boltzmann law of radiation and on one-dimensional heat diffusion
equations, according to latitude [GHI 76, NOR 75]. Other models, even
more rudimentary, use single thermal inertia whose energy evolves
depending on the planet's global energy balance. It is with this type of
models - only a little more complex - that we will process here, and they are
particularly suitable for identification.

The reader who is familiar with systems theory will excuse us for giving
a brief presentation of the concepts of state and transmittance, using a
suitable introductive example. We can imagine our planet reduced to its
simplest form: a global thermal inertia (or heat capacity) I G , brought to a
homogenous temperature T G by a balance of radiative flows (index R for Φ

R

radiative) :

where:

Φλ =− x + α u ,

R G

- u is the variation of the solar constant in relation to its nominal value;

is a
coefficient called radiative forcing, which depends on the coefficient of
terrestrial reflection (albedo);

- is the flow of “radiative forcing” received from the sun, and α

u

α