Modeling of Geochemical Cycles: Phosphorus as an Example

Analysis of various transient situations in a geochemical cycle helps to focus attention on those physical and chemical mechanisms that are more important to the understanding of the cycle. The geochemical cycle of an element can be modeled as a system of n reservoirs (each of mass Mi) and interreservoir fluxes (F ij , in units of mass/time; i, j = 1, ..., n). Transient states of the geochemical cycle have been treated by a simple model based on first-order fluxes d M i d t = ∑ i k j i M j - M i ∑ i k i j where k ij are rate constants (time-1). The phosphorus cycle was used as an example, and the following two transient states were considered: (1) Cessation of photosynthetic productivity on Earth (doomsday scenario)—in this scenario, phosphorus from the dead biota would be redistributed among other reservoirs within 200 years. The most significant result of such a redistribution is an increase in the dissolved phosphorus content of surface ocean layer, making the phosphorus concentration throughout the ocean more uniform than at present. (2) Man's use of phosphorus from mining at an exponentially increasing rate (industrial scenario)— an accelerated rate of mining and fertilizer use that adds phosphorus to land and streams may, during the next 60 years, result in significant increases in the oceanic biomass (40 percent) and in the dissolved phosphorus content of surface ocean water (30 percent). According to the model, restoration of the earlier conditions (that is, those of the present day) will take 150 years.