The effects of deep water cycling on planetary thermal evolution

We use a parameterized convection model to investigate the effects of deep water cycling on the thermal evolution of an Earth-like planet. The model incorporates two water reservoirs, a surface and an interior mantle reservoir. Exchange between the two is calculated using a mantle convection parameterization that allows for temperature-and water-dependent mantle viscosity together with internally self-consistent degassing and regassing parameterizations. The balance between degassing and regassing depends on the average spreading rate of tectonic plates, the amount of water partitioned into melt, the thickness of a mantle melt zone, and of a hydrated layer at the top of subducting plates. Degassing scales with melt zone thickness such that an early period of extensive melting would create a drier and more viscous mantle, shifting the solidus line in a direction that would reduce the melt zone thickness and the rate of mantle heat loss. Coupling a hydrated zone thickness-dependent regassing factor to the model, to mimic water delivery to the mantle via a serpentinized layer, allows for the potential of a reversing point where the overall water flow direction switches from degassing to regassing as the mantle cools. The water effect on viscosity creates a negative feedback that tends to regulate the final amount of water in the mantle so it is not strongly dependent on the initial amount of planetary water. The final amount of water in the surface reservoir is then determined by this feedback effect together with the initial water budget of the entire planet. This implies that if the initial water budget of a planet can be estimated, from planetary formation models, then the volume of surface water can be used to estimate the volume of water in the mantle of an Earth-like planet. Applying this methodology to the Earth leads to predictions for water concentration in the Earth's mantle that are in line with geochemical and petrological constraints.