The effects of deep water cycling on planetary thermal evolution

Abstract

[1] 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.

The thermal evolution of Mars as constrained by paleo-heat flows

“…Our results are also supported by parameterized mantle con vection models that couple convective vigor with the rheologic weakening effect of interior volatiles suggesting that high Urey ra tios are also favored by inefficient cycling of volatiles to and from the mantle (McGovern and Schubert, 1989;Sandu et al, 2011), as might be expected for Mars, which has lacked a plate tectonic cycle to efficiently degas and (especially) replenish the mantle volatiles at least since the early part of the evolution of Mars. Further, High Urey ratios might typify all planets lacking the thermal efficiency of plate tectonics.…”

Earth's evolving stress state and the past, present, and future stability of cratonic lithosphere

“…The greater increase of viscosity over time leads to a greater increase in the convective stress. This qualitative conclusion was robust for a range of varied model parameters (Sandu and Lenardic 2008) and is consistent with an alternative modelling approach that explored the effects of water cycling on planetary evolution. Rather than relying exclusively on a parameterized approach, mantle stress levels can also be explored with numerical simulations that directly solve the coupled conservation of mass, momentum, and energy equations associated with mantle convection.…”

The effects of mantle composition on the peridotite solidus: Implications for the magmatic history of Mars

“…Alkalis, water, and radioactive elements are all incompatible and are therefore extracted by volcanism from the mantle to the crust assuming bulk mantle-melt partition coefficients of D = 0.1 for Na and D = 0.01 for U, Th, K, and water (Salters et al, 2002;Borg and Draper, 2003;Aubaud et al, 2004). Full numerical details of the model are available in Sandu et al (2011) and Sandu and Kiefer (2012). Fig.…”