Tsunamis and rapid coastal remodeling: Linking energy and fractal dimension

Tsunamis are one of several processes that contribute to coastal remodeling. This research interpreted geomorphic features over time to better understand if a relationship exists between the flash remodeling of coasts, expressed by bidimensional-fractal dimensions, and known tsunami energy. Fractal geometry analysis, through the box-counting and correlation integral methods, was applied to the physiography of four oceanic coastlands: three in Sumatra, Indonesia, and one in Japan, hit by tsunamis in the last 14 years. Their shoreline fractal dimensions before and after the events and the present-day ones were calculated and compared. Results highlighted any difference or convergence of calculated fractal dimensions. Significant numerical variations of fractal dimensions of the shores before and after each tsunami were registered, and those values gradually decreased post-tsunami. These shorelines, considered stable before tsunamis, increased in physiographic irregularity up to 5-11% immediately after the phenomena; this slowly diminished to 2-5% about 8 to 15 years later; and finally to 3-6% present-day, compared to the pre-event shorelines. Considering these changes of the fractal dimension and the hydrodynamic energy of the tsunami, responsible for the abrupt coastal remodeling, a simple empirical expression and evaluation of the residual resilience is proposed. As a first step, a real physical meaning, in terms of energy, is attributed to the (dimensionless) fractal dimension.