The dynamical system of weathering: deterministic and stochastic analysis

The critical zone is fundamental to human society as it provides most of the ecosystem services such as food and fresh water. However, climate change and intense land use are threatening the critical zone, so that theoretical frameworks, to predict its future response, are needed. In this talk, a new modeling approach to evaluate the effect of hydrologic fluctuations on soil water chemistry and weathering reactions is analyzed by means of a dynamical system approach. In this model, equilibrium is assumed for the aqueous carbonate system while a kinetic law is adopted for the weathering reaction. Also, through an algebraic manipulation, we eliminate the equilibrium reactions and reduce the order of the system. We first analyze the deterministic temporal evolution, and study the stability of the nonlinear system and its trajectories, as a function of the hydro-climatic parameters. By introducing a stochastic rainfall forcing, we then analyze the system probabilistically, and through averaging techniques determine the inter-annual response of the nonlinear stochastic system to the climatic regime and hydrologic parameters (e.g., ET, soil texture). Some fundamental thermodynamic aspects of the chemical reactions are also discussed. By introducing the weathering reaction into the system, any mineral, such as calcium carbonate or a silicate mineral, can be considered.