A numerical model of the evolution of ocean sulfate and sedimentary sulfur during the last 800 million years

A reservoir model describing the time evolution of the sedimentary cycle of sulfur over the past 800 my has been developed. As a first approximation, the ocean sulfate concentration is assumed to be time-independent. With this assumption, the model is integrated backward in time and a new initialization procedure is derived in order to calculate the present state of the system which must be compatible with both observational data and model equations. The effects of a variation of the present state of the cycle on its past evolution are investigated. It is found that, when the present gypsum reservoir content is too low or when the weathering rate constants are too high, no acceptable solution can be obtained for the evolution of the cycle, since one reservoir is forced to depletion. The sensitivity of the model to the mean isotopic composition of the sedimentary system and to the fractionation factor during pyrite formation is also studied.Moreover, a model with time-dependent ocean sulfate concentration was developed. The existence of an acceptable solution appears to be linked to the steady state hypothesis for ocean sulfate, since a model with no acceptable steady state solution may be integrated until t = −800 my without any problem of reservoir depletion when the time-dependent equations are used.A tentative evolution of the ocean sulfate concentration is calculated. It is shown that this concentration is negatively correlated to the δ³⁴S of seawater sulfate. The carbon cycle is modelled in order to compare the calculated δ¹³C of carbonate deposits to the observational data.