A Similarity Law for Sandy Tsunami Deposits

Herein, a basic relation between tsunami size and sandy tsunami deposits, i.e., a similarity law for sandy tsunami deposits, was derived by integrating the advantages of empirical and theoretical inverse modeling and forward modeling. Two concepts were introduced: (a) defining the involved deposition distance (L_d) based on the pickup and settling of sediments during the tsunami run-up and (b) systematically deriving the relation between the physical quantities involved in tsunami deposit formation and tsunami height based on the tsunami sediment transport theory. Similarity law derivation involved considering continuous sediment pickup at the sediment source. The effects of various uncertainties associated with tsunami deposits, such as those related to topography, land use, and sediment properties, were aggregated into a relation coefficient a*. Consequently, two similarity law models—a low-order model that does not consider the change in suspended-load concentration due to the relative advection of sediment to subsequent flows and a high-order model that considers this aspect—were proposed. If a* was determined based on known information (e.g., relation between the L_d and inundation distance of a known tsunami event), the similarity law could be applied to giant tsunamis without determining the parameters related to uncertainties. To verify the concepts, the results obtained using the similarity law were compared with those from numerical simulations reflecting the assumptions imposed on the similarity law. The similarity law was found to be reasonable. Overall, this research is expected to contribute to more accurate estimation of the sizes of past giant tsunamis and similar future tsunamis.