Most of the long-term predictions of the shoreline response to sea-level rise are based on simple geometric relationships, namely the conservation of mass and an assumed preservation of subaqueous shapes. Although models based upon these 'Bruun rule' concepts can shed much understanding, geometric, or 'morphokinematic', approaches are appropriate only in certain cases. Accordingly, an understanding of process can be lost as these approaches make predictions of shoreline change that are independent of the rate of sea-level rise, depending only on the total change. For example, geometric models make the same shoreline change predictions regardless of whether a sea-level rise of one meter took decades or millennia. Is the rate of sea-level rise (and not just the current sea level elevation) important?
Theoretical investigations reveal interesting behaviors of two separate (but related) cases where the shoreline responds dynamically to the rate and rate of change of sea-level rise: overwashing barriers and rocky coasts. Overwashing barriers present an apparent paradox. Although higher sea levels should direct sediment offshore due to shoreface oversteepening, non-equilibrium behavior must occur somehow to provide the net onshore sediment flux that would be necessary for a barrier to survive long-term sea-level rise. A simple model suggests that understeepening of the shoreface by overwash causes a long-term net shoreward sediment flux; shoreface response to sea-level rise becomes 'slaved' to the rate and timing of barrier overwash. Simulations suggest that the dynamically coupled shoreface-overwash system can demonstrate surprising long-term behavior. A dynamic response to sea-level rise also can occur when the coast consists of lithified sediment that can be broken down into fine sediment by wave attack. Such coasts are affected more directly by the rate of sea level rise (rather than the location of sea level itself). The behavior of detachment-limited systems can be investigated using a simplistic theoretical framework to understand the relationship between the rate of sea-level rise and the rate of erosion for rocky coasts.