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Topography on a rocky planet would raise land above its hypothetical oceans. The planet's land/ocean fraction emerges in a compromise between the amount of liquid water on its surface and the amplitude of its hypsometry. Although ocean volumes code complex and stochastic stories, topography—at least in certain forms—seems deterministically tractable. Dynamic topography is the surface expression of mantle convection; it should dominate a planet’s long-wavelength relief so long as the interior is geodynamically active, and is freely obtained from any numerical convection model as a function of the mantle Rayleigh number. New scaling relationships are developed for dynamic topography on stagnant lid planets, using 2D numerical models with temperature-dependent viscosity. These scalings are applied to 1D thermal evolution models to estimate how RMS topography varies with exoplanetary observables over a wide parameter space. Finally, via spectral analysis, RMS amplitudes are converted to ocean basin volumes on a sphere. This calculated surface water holding capacity increases less steeply with planet mass than does the amount of water itself from a naive mass-volume relationship. Early results suggest that dynamic topography could be sufficient to avert a waterworld on planets with less than ~0.0001 wt% surface water, depending on planet mass.

Islands in a black sky: Towards scaling relationships for dynamic topography and land propensity on rocky planets