Formulating an Energy Balance Model - Climate Change: Identification and Projections - page 53

Nevertheless, the collection of all the characteristics of G ( s ) must be
reduced to the most pertinent. This is why we prefer to associate the
following two dynamic features to the transmittance G ( s ):

- A global time constant T clim , defined as the final delay (or lag) for the
response to a ramp input:

1( ) − Gs

⎛ ⎞

T = lim

⎠

⎜ ⎟

c lim

S

s → 0

⎝

of high and low frequency sensitivities: more precisely, the
“high frequency” considered will be that of the Schwabe cycles ( f = 1/11
years), which is effectively high at the time scale of the climate. This is
expressed as:

- The ratio

ρ

ρ = G ( j 2 π / 11 ) / G ( 0

We will use this coefficient particularly for solar irradiance. If we note
S irr 11 the sensitivity to the frequency , this will be given by f = 1 / 11

S irr = ρ S

. This ratio will be small (around 0.1 or less), but not negligible.

11 2