29 29 4 4 1 bbr T t S a s 31 where a is the planetary albedo σ is the Stefan

29 29 4 4 1 bbr t t s a s 31 where a is the planetary

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( 29 ( 29 4 4 1 bbr T t S a s = - (3.1) where a is the planetary albedo, σ is the Stefan-Boltzmann constant, and T bbr is the effective black-body 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 self-consistently [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)
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