A physical model for the rate of coastal tafoni development

To explain the temporal change in growth rates of tafoni on homogeneous, insoluble rocks, modeling is carried out based on a formulated relationship for weathering-induced reduction of rock strength. The model is expressed by z = z(c)(1 - root t*/t), where z is the depth of tafoni, z(c) is the ultimate depth, t is the time, and t* is the time lag. Application of the model to the Pacific coast of Japan reveals that (1) the model accurately describes tafoni development, (2) average growth rates presented by most previous studies are underestimated, and (3) an exponential decrease in growth rates stems from strength reduction by inherent rock weathering.