Dimensions of continents and oceans -- water has carved a perfect cistern

Abstract The ocean basins have almost exactly the correct surface area and average depth to hold Earth's water. This study asserts that three processes are responsible for this. First, the crust is thickened by lateral compression from mountain formation. Second, Earth's continental crust is leveled by erosion. Third, due to the efficiency of erosion, the average elevation is a few hundred meters above sea level. A theoretical fluid model, suggested partly by laboratory experiments, includes an ocean of specified depth. The resulting continents are tabular (that is, their elevation view is rectangular). The surface lies above sea level, contributing to a well-known double maximum in Earth's elevation corresponding to continents and ocean basins. Next, a simple hydrostatic balance between continent and ocean gives average depth and area of present oceans and continents within 33%. Further calculations with a suitable correction to fit present Earth cover a wide range of possible crust volumes for earlier Earth. With the present water volume, ocean area always exceeds 25% of the globe. For all possible water volumes, average continental crust thickness always exceeds 23.4 km. This may explain why cratons have thicknesses comparable to younger crust so that they are found on Earth's surface today. Therefore, mountain building and erosion have enabled water to carve its own cistern in the form of the accumulated ocean basins. The wide range of areas and depths of oceans and continents found here can constrain models of early earth. Similar calculations can be done for earthlike planets as well.