Modeling the development of marine terraces on tectonically mobile rock coasts

A mathematical model was used to study the effect of glacially induced fluctuations in sea level on the formation of wave-cut terraces on tectonically mobile rock coasts. Two deep water wave sets were used to calculate breaker height and depth, which, along with surf zone width, bottom roughness, and the gradient of the submarine slope, dictated the force exerted at the shoreline. An erosional force threshold was employed to represent the variable strength of the rocks. The model also considered tidal range, the time that the water level spent at each intertidal elevation, and the protective effect of debris accumulation at the cliff foot. Three hundred runs were made with constant sea level and with different rates of rising and falling relative sea level. Rates of erosion increased with the rate of rising and falling sea level, but eventually decreased in some runs with very rapid changes in relative sea level. Fifty-five longer runs were also made with a Quaternary sea level model that consisted of 26 glacial cycles representing the period from 2 million to 0.9 million years ago, and nine cycles, of approximately twice the amplitude and wavelength, in the last 0.9 million years. These runs were made on a landmass experiencing slow (0.11 mm yr−1) or fast (0.74 mm yr−1) positive or negative changes in the elevation of the land. It was found that on rising landmasses, erosional coastal terraces are formed during interglacial stages, and on subsiding landmasses during glacial stages. The number of terraces increased with the rate of uplift and subsidence, and with the slope of the hinterland. Terrace gradient increased with tidal range, and decreased with rock resistance. The was an inverse relationship between terrace width and the strength of the rock.