(
29
( 29
4
4
1
bbr
T
t
S
a
s
=

(3.1)
where
a
is the planetary albedo,
σ
is the StefanBoltzmann constant, and
T
bbr
is the
effective blackbody radiation temperature. The time dependence of the solar constant
S
is fitted with the help of a formula given by Gough [25]. The surface temperature of
the planet
T
s
is related to
T
bbr
by the greenhouse warming factor:
.
T
T
T
bbr
s
∆
+
=
(3.2)
Usually
∆
T
is parameterized as a function of
T
s
and
P
atm
[23, 26].
The total process of weathering embraces first the reaction of silicate minerals with
carbon dioxide, second the transport of weathering products, and third the deposition
of carbonate minerals in sediments. The basic assumptions and limitations of this ap
proach are given in Franck et al. [26]. The weathering rate
F
wr
is a key function in our
model. For any given weathering rate the surface temperature
T
s
and the carbon dioxide
concentration in the soil
P
soil
can be calculated selfconsistently [23, 26, 17].
The main role of the biosphere in the context of our model is to increase
P
soil
in re
lation to the atmospheric carbon dioxide partial pressure and proportional to the bio
logic productivity,
Π
.
Π
is considered to be a function of temperature and carbon
dioxide partial pressure in the atmosphere only.
(
29

+

°
°


=
Π
Π
min
2
1
min
2
max
25
25
1
P
P
P
P
P
C
C
T
atm
atm
s
(3.3)