Continental growth and mantle hydration as intertwined feedback cycles in the thermal evolution of Earth

A model of Earth's continental coverage and mantle water budget is discussed along with its thermal evolution. The model links a thermal evolution model based on parameterized mantle convection with a model of a generic subduction zone that includes the oceanic crust and a sedimentary layer as carriers of water. Part of the subducted water is used to produce continental crust while the remainder is subducted into the mantle. The total length of the subduction zones is calculated from the total surface area of continental crust assuming randomly distributed continents. The mantle viscosity is dependent of temperature and the water concentration. Sediments are generated by continental crust erosion, and water outgassing at mid-oceanic ridges closes the water cycle. We discuss the strongly coupled, non-linear model using a phase plane defined by the continental coverage and mantle water concentration. Fixed points are found in the phase plane at which the rates of change of both variables are zero. These fixed points evolve with time, but in many cases, three fixed points emerge of which two are stable and an intermediate point is unstable with respect to continental coverage. With initial conditions from a Monte-Carlo scheme we calculate evolution paths in the phase plane and find a large spread of final states that all have a mostly balanced water budget. The present day observed 40% continental surface coverage is found near the unstable fixed point. Our evolution model suggests that Earth's continental coverage formed early and has been stable for at least 1.5 Gyr. The effect of mantle water regassing (and mantle viscosity depending on water concentration) is found to lower the present day mantle temperature by about 120 K, but the present day mantle viscosity is affected little. The water cycle thus complements the well-known thermostat effect of viscosity and mantle temperature. Our results further suggest that the biosphere could impact the feedback cycles by its effects on continental weathering and erosion and may be the reason for the present day steady state of continental coverage and mantle water concentration.