Correlation between continent area and elevation

This presentation is motivated by the following questions: (1) What factors determine the mean elevation and thickness of an individual continent? (2) How to explain the positive correlation between the mean height and area of individual continent? (3) Given total continental crust volume, what determines the mean thickness (and hence total area) of all continents? For example, Mean thickness of all continents is about 41 km. Mean land elevation is 874 m, and mean elevation of all continents (including land areas and continental shelves and slopes to 1000 meters below sea level) is about 800 m. Could mean continental thickness have doubled and continental area have halved in the geologic past? I present a first-order model to address these issues assuming that continental mean height is the steady state height controlled by uplift and erosion. The model predicts that it takes longer time to erode a larger continent. Hence mean continental height at steady state increases as continental area increases. This prediction is consistent with the general trend between present-day continental elevation and area (except for Antarctica), and can fit the trend well. This is the first time the relation between continental area and mean elevation is quantitatively explained. The model is further applied to investigate variations of mean thickness of continental crust over the last 600 Myr over which the continental crust mass and seawater volume are assumed to be constant. Because a change in the number of continents leads to change in the area of continents, it is predicted that the mean continental thickness increases as the number of continents decreases. Nevertheless, the thickness variation is small, amounts to about 10% from one continent to six continents. Change in the number of continents leads to a sea level fluctuation of about 0.3 km, with the lowest sea level coinciding with times of supercontinents. This prediction is consistent with prominent lows in sea level curves at the times of Pangea and Rodinia. It is concluded that the number of continents played a major role in Phanerozoic sea level changes.