Quantification of the ocean-continent cistern problem

The ocean basins have almost exactly the correct surface area and average depth to hold Earth’s water. We model the dynamics that is hypothesized to be responsible for this using three materials corresponding to the continent material, earth’s mantle material, and oceanic water.  These are exposed to three processes: continent thickening from forces from mantle convection cells, subaerial continent erosion, and conservation of all materials. A numerical model that includes quantified values of all these features produces ocean, continent, and ocean-mantle surfaces that are relatively flat within certain parameter ranges.  There, they duplicate the well-known double maximum in Earth’s surface area versus elevation (the hypsometric curve). Large values of erosion rates compared to thickening rates produce the result that almost all water resides within the ocean basins. The resulting dimensionless numbers are discussed along with comments about the energy flux ratio between internal heat generation and solar heating.