Earth's Constant Mean Elevation: Implication for Long-Term Sea Level Controlled by Oceanic Lithosphere Dynamics in a Pitman World

摘要

On a spherical Earth, the mean elevation (approximately -2440 m) would be everywhere at a mean Earth radius from the center. This directly links an elevation at the surface to physical dimensions of Earth, including surface area and volume, which are at most very slowly evolving components of the Earth system. Earth's mean elevation thus provides a framework within which to consider changes in height of Earth's solid surface as a function of time. In this article, the focus will be on long-term, nonglacially controlled sea level. Long-term sea level has long been argued to be largely controlled by changes in ocean basin volume related to changes in the area-age distribution of oceanic lithosphere. As generally modeled by Walter Pitman and subsequent workers, the age-depth relationship of oceanic lithosphere, including both the ridge depth and the coefficients describing the age-depth relationship, are assumed constant. This article examines the consequences of adhering to these assumptions when placed within the larger framework of maintaining a constant mean radius of Earth. Self-consistent estimates of long-term sea level height and changes in the mean depth of the oceanic crust are derived from the assumption that the mean elevation and corresponding mean radius are unchanging aspects of Earth's shorter-term evolution. Within this context, changes in the mean depth of the oceanic crust, corresponding with changes in the mean age of oceanic lithosphere, acting over the area of the oceanic crust represent a volume change that is required to be balanced by a compensating equal but opposite volume change under the area of the continental crust. Models of cumulative paleohypsometry derived from a starting glacial isostatic adjustment (GIA)-corrected ice-free hypsometry that conserve mean elevation provide a basis for understanding how these compensating changes impact global hypsometry and particularly estimates of global mean shoreline height. Paleoshoreline height and areal extent of flooding can be defined as the height and corresponding cumulative area of the solid surface of Earth at which the integral of area as a function of elevation, from the maximum depth upward, equals the volume of ocean water filling it with respect to cumulative paleohypsometry. The present height of the paleoshoreline is the height on the GIA-corrected cumulative hypsometry at an area equal to the areal extent of flooding. Paleogeographic estimates of the global extent of ocean flooding from the Middle Jurassic to end Eocene, when combined with conservation of mean elevation and ocean water volume, allow an explicit estimate of the paleoheight and the present height of the paleoshoreline. The best-fitting estimate of the present height of the paleoshoreline, equivalent to a long-term eustatic sea level curve, implies very modest (25 +/- 22 m) changes in long-term sea level above the ice-free sea level height of approximately +40 m. These, in turn, imply quite limited changes in the mean depth of the oceanic crust (15 +/- 11 m) and in the mean age of the oceanic lithosphere (approximate to 62.1 +/- 2.4 My) since the Middle Jurassic.