Summary
We present a generalized theory governing gravitationally self-consistent, spatio-temporal sea-level changes within an ocean-plus-lake system that is intermittently connected by water mass flux across a sill. Our expressions for the change in sea level (defined as the difference in height of the sea surface equipotential relative to the solid surface) hold for any Earth model, and easily incorporate effects of viscoelastic deformation of the solid Earth and perturbations in both the gravitational field and rotation vector (as is now standard in ice-age sea-level calculations). In its most general form, the theory also includes an exact treatment of the evolving shoreline position in both water bodies. Our formalism involves three cases: (1) one global ocean, in which mass transfer may occur between ice sheets and the global ocean; (2) an ocean and lake separated by an exposed sill, in which mass transfer may occur between ice sheets and the global ocean, and between the ocean and lake via evaporative flux; and (3) transitional phases between these two states, when the ocean surface reaches the height of the sill from below (i.e., the sill is breached) or above (the sill is exposed). We illustrate the new theory using examples from the Black Sea flooding during the last deglacial phase (∼10 ka) and sea-level fall in the Mediterranean Sea during the Messinian Salinity Crisis (5.96-5.33 Ma). These examples demonstrate the importance of including the geophysical feedbacks associated with sea-level change in an isolated basin in the dynamics of flooding and desiccation.</jats:p
