Continental insulation, mantle cooling, and the surface area of oceans and continents

It is generally assumed that continents, acting as thermal insulation above the convecting mantle, inhibit the Earth's internal heat loss. We present theory, numerical simulations, and laboratory experiments to test the validity of this intuitive and commonly used assumption. A scaling theory is developed to predict heat flow from a convecting mantle partially covered by stable continental lithosphere. The theory predicts that parameter regimes exist for which increased continental insulation has no effect on mantle heat flow and can even enhance it. Partial insulation leads to increased internal mantle temperature and decreased viscosity. This, in turn, allows for the more rapid overturn of oceanic lithosphere and increased oceanic heat flux. Depending on the ratio of continental to oceanic surface area, global mantle heat flow can remain constant or even increase as a result. Theoretical scaling analyses are consistent with results from numerical simulations and laboratory experiments. Applying our results to the Earth we find, in contrast to conventional understanding, that continental insulation does not generally reduce global heat flow. Such insulation can have a negligible effect or even enhance mantle cooling, depending on the magnitude of the temperature dependence of mantle viscosity. The theory also suggests a potential constraint on continental surface area. Increased surface area enhances the subduction rate of oceanic lithosphere. If continents are produced in subduction settings this could enhance continental growth up to a critical point where increased insulation causes convective stress levels to drop to values approaching the lithospheric yield stress. This condition makes weak plate margins difficult to maintain which, in turn, lowers subduction rates and limits the further growth of continents. The theory is used to predict the critical point as a function of mantle heat flow. For the Earth's rate of mantle heat loss, the predicted continental surface area is in accord with the observed value.