First approximation sea-level dependent mathematical model for volume eroded and submarine profile development in a semienclosed sea: Kiel Bay, Western Baltic

Abstract

Given a marine basin of near homogeneous lithology, a known sea level curve, and known submarine abrasion rates, a model is developed to estimate the volume of material eroded by marine action. Assumptions of the model are that erosion is effected solely by submarine abrasion, which is assumed known and uniform through time, and that the volume eroded is small relative to the total volume of the basin. The basis of the model is that the volume eroded V, between time limits t1 andt2,is essentially a function of the perimeter length l of the basin, which in turn is time-dependent on the sea level curve, so that $$V = k\int_{t1}^{t2} {l(t)dt} $$ where k is an abrasion rate constant. The model was tested on Kiel Bay, Western Baltic, a shallow semienclosed, essentially nontidal sea, for which considerable data is available. Critical for numerical integration of the model is the k value, representing the volume eroded from the shore normal profile per unit length of shoreline per year. A number of possible k values were utilized, the most likely realizing a total volume eroded over the past 9000 y, since the sea first entered Kiel Bay, of 2.60×109m3. From this model, long-term average vertical submarine abrasion rates for Kiel Bay can be deduced as being between 0.001 and 0.0004 m/y.