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 yr31) or fast (0.74 mm yr31) 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. / 2002 Elsevier Science B.V. All rights reserved. 0025-3227 / 02 / $ ^ see front matter / 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 5 3 2 2 7 ( 0 2 ) 0 0 1 8 7 1 Abbreviations: C, coe⁄cient to represent di¡erences in the force exerted at the waterline by plunging, spilling or surging-collapsing breakers; Es, amount of submarine erosion each year (m); Ey, amount of intertidal erosion each year (m); Fb, wave force at the breakers (kg m32) ; g, acceleration due to gravity (m s32) ; h, water depth (m); hb, breaker depth (m); Hb, breaker height (m); Ho, deep water wave height set consisting of ¢ve wave heights Ho1 to Ho5 (m); k, surf attenuation factor related to bottom roughness; L, deep water wavelength (m); M, coe⁄cient (6.5U10310 to 3.25U1038 m3 kg31) to convert the excess surf force into the amount of intertidal erosion during each model iteration; MHWN, mean high water neap tidal level; MHWS, mean high water spring tidal level; MLWN, mean low water neap tidal level; MLWS, mean low water spring tidal level; MT, mean tidal level; Q, a cli¡-foot protection factor related to the amount and persistence of the debris at the cli¡ foot. When Q=0.2, debris accumulation reduces the erosion rate at the cli¡ foot to one-¢fth of the erosion rate of an unprotected cli¡ foot (Q=1); s, submarine erosion depth decay constant (m31) ; Sf , surf force at the waterline (kg m32) ; Sfmin, threshold erosional strength of the rocks (kg m32) ; T, wave period (s); Td, tidal duration value, the time each year that the water level occupies each intertidal elevation (h yr31) ; Tr, spring tidal range (m); W, hourly number of waves of each of the ¢ve deep water heights; Ws, surf zone width (m); L, gradient of the bottom from the breakers to the waterline (‡); N, initial surface gradient (‡); bw, unit weight of sea water (1025 kg m33) * Fax: +1-519-973-7081. E-mail address: [email protected] (A.S. Trenhaile). MARGO 3082 7-6-02 Marine Geology 185 (2002) 341^361 www.elsevier.com/locate/margeo