On the relative influence of heat and water transport on planetary dynamics

The dynamics of a planet and its evolution are controlled to a large extent by its viscosity. In this study, we demonstrate that the dependence of mantle viscosity on temperature and water concentration introduces strong dynamic feedbacks. We derive a dimensionless parameter to quantitatively evaluate the relative strength of those feedbacks, and show that water and heat transport are equally important in controlling present-day dynamics for the Earth. A simple parameterized evolution model illustrates the strong feedbacks and behavior of the system and agrees well with our analytic results. The analysis identifies characteristic times for changes of viscosity, temperature, and water concentration and demonstrates, for time scales greater than a few hundred million years, that the system should either be degassing while warming or regassing while cooling. This yields a characteristic evolution in which, after an initial period of rapid adjustment, the mantle warms while degassing, and subsequently cools rapidly while regassing. As the planet continues to cool, the entire surface ocean may eventually return to the mantle. Our results suggest that a simple relationship may exist between the rate of change of water concentration and the rate of change of temperature in the mantle. This connection is extended by deriving an explicit equation for the Urey ratio that depends on both heat and water transport.

► Dependence of viscosity on temperature and water content creates strong feedbacks.
► The coupling of heat and water transport is addressed analytically.
► A dimensionless parameter quantifies the relative strength of the two feedbacks.
► The heat and water transport feedbacks are equally important for present day Earth.
► An equation is derived that relates heat and water transport to the Urey ratio.