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whose coefficients combine the set of inertias and thermal exchange
coefficients, by analogy with complex impedance
Z
(
s
) of an electric
network, function of elementary components
R, L, C.
Reverting back now to the balance of flows
. However complex the
Φ
R
may be, it can always be developed in a linear
function
Φ
(
u
,
u
,
u
,
x
)
R
1
2
3
approximation:
Φ
~
α
u
+
α
u
+
α
u
−
λ
x
R
1
1
2
2
3
3
G
-
are coefficients of radiative forcing;
α
,
α
,
α
1
2
3
- the products
are flows of radiative forcing;
α
u
,
α
u
,
α
u
1
1
2
2
3
3
-
the sum
is the total radiative forcing;
Q
=
α
u
+
α
u
+
α
u
1
1
2
2
3
3
- the term
is a global climatic feedback.
−
λ
x
G
gives the sum of various elementary reactions. Some
are stabilizing, in counter-reaction and have a positive sign in
The coefficient
λ
G
λ
.
Destabilizing reactions act with a negative sign: an initial deviation on
x
leads to an increase of
G
, which in turn causes an increase of
x
, and so on,
Φ
R
hence the divergence.
Eliminating
, the equations are combined:
Φ
R
I
(
s
)
s
x
=
α
u
+
α
u
+
α
u
−
λ
x
G
1
1
2
2
3
3
G
Hence:
1
x
=
(
α
u
+
α
u
+
α
u
)
1
1
2
2
3
3
λ
+
sI
(
s
)
G
G
λ
α
α
α
Setting down
and
, finally gives:
Gs
()
=
G
S
=
1
,
S
=
2
,
S
=
3
1
2
3
λ
+
sIs
()
λ
λ
λ
G
G
G
G
x
=
G
(
s
)
(
S
u
+
S
u
+
S
u
)
1
1
2
2
3
3
where
here is a transmittance of a unit of static gain:
.
G
(
s
)
G
(
0
)
=
1
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