  In this paper we present a series of models for the deep water cycle on
super-Earths experiencing plate tectonics. The deep water cycle can be modeled
through parameterized convection models coupled with a volatile recycling
model. The convection of the silicate mantle is linked to the volatile cycle
through the water-dependent viscosity. Important differences in surface water
content are found for different parameterizations of convection. Surface oceans
are smaller and more persistent for single layer convection, rather than
convection by boundary layer instability. Smaller planets have initially larger
oceans but also return that water to the mantle more rapidly than larger
planets. Super-Earths may therefore be less habitable in their early years than
smaller planets, but their habitability (assuming stable surface conditions),
will persist much longer.
