Modelling the sedimentary signature of long waves on coasts: implications for tsunami reconstruction David Pritchard a, ⁎, Laura Dickinson b a Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland b Division of Civil Engineering, University of Dundee, Dundee DD1 4HN, Scotland ABSTRACT ARTICLE INFO Article history: Received 7 August 2007 Received in revised form 19 February 2008 Accepted 13 March 2008 Keywords: Tsunami Sediment transport Event deposits We describe a process-based mathematical model of suspended and bedload sediment transport under long, non-breaking waves on a plane beach, and we use this model to investigate the relationship between the hydrodynamics of run-up and run-down and the resulting erosive and depositional ‘signature’ which the wave leaves. In particular, we compare the results of our ‘forward’ model with several recently proposed methods for reconstructing tsunami hydrodynamics from their deposits. We find that sediment transport, both as bedload and in suspension, is strongly controlled by asymmetries in the direction of maximum velocity; in the latter case it is also affected by settling lag, especially around the point of maximum run-up. The combination of these effects appears to preclude simple methods of reconstructing tsunami hydrodynamics from the large-scale features of their signatures; however, our results suggest some promising avenues for further investigation. © 2008 Elsevier B.V. All rights reserved. 1. Introduction and motivation The need for improved methods to assess the vulnerability of coastlines to tsunami inundation has been recognised by natural hazards researchers for some years, and was brought to wider public notice by the devastating Indian Ocean tsunami of 26 December 2004. Much attention has focused on the construction of systems which can detect tsunamis before they reach the shore (see e.g. Bernard et al. 2006), and on the development of increasingly detailed and accurate numerical models of tsunami inception and propagation (e.g. Lynett and Liu 2005). For long-term planning, it is also important to assess the danger which coasts face from especially large, rare events, often with a return timescale longer than the available records. Predicting the frequency of these events is a serious challenge for models based on historical data, although suggestive results have been obtained (Burroughs and Tebbens, 2005); meanwhile, the origins of such tsunamis may be poorly known or understood, and it becomes necessary to quantify this uncertainty in direct simulations (Geist and Parsons, 2006). The only direct evidence of the scale and frequency of extreme tsunamis comes from the sedimentary ‘signatures’ which they leave on the shore. The identification of paleotsunami deposits has developed sub- stantially in the twenty years since the pioneering work of Atwater (1987) and Dawson et al. (1988). Much attention recently has focused on rocky shorelines, with considerable controversy over the inter- pretation of anomalous features such as megaclasts and erosion marks on rock platforms (e.g. Bryant, 2001; Felton and Crook, 2003), and debate continues over whether the effects on rocky coasts of tsunamis can be distinguished from those of large storm surges. On sandy and muddy shores, where transport processes are better understood, there is less controversy, but distinguishing between the deposits of tsunamis and storm surges remains a key issue (Morton et al., 2007). Distinguishing between tsunamigenic and storm-surge deposits is a particular case of a sedimentological inverse problem, to be contrasted with the ‘forward problem’ usual in coastal engineering, where the deposit of an event is predicted from a simulation of that event. A more specific inverse problem is that of reconstructing the hydrodynamics of a tsunami, including run-up distance and flow velocities, from its deposit. Dawson and Shi (2000) note the difficulty of such reconstruction; however, attempts have recently been made by several authors (Jaffe and Gelfenbaum 2007; Soulsby et al, 2007; Smith et al., 2007; Moore et al., 2007), building on detailed surveys carried out in the near aftermath of events. We will discuss the physical basis of these reconstructions, in the light of our ‘forward’ results, below. There is a well-developed body of work (see Synolakis and Bernard, 2006) on the hydrodynamics of tsunami run-up and run-down, employing reduced dynamical models such as the shallow-water equations. Although there are also well-established coastal engineer- ing models which may be used to predict sediment transport under such hydrodynamics, few attempts have been made to use this modelling framework to constrain what can be deduced about a tsunami from its deposit. Possible reasons for this include the difficulty of developing numerical methods which function well close to a moving shoreline, and the perception that hydrodynamical and sedimentary processes are likely to be highly site-specific. However, Sedimentary Geology 206 (2008) 42–57 ⁎ Corresponding author. Fax: + 44 141 548 3345. E-mail address: dtp@maths.strath.ac.uk (D. Pritchard). 0037-0738/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sedgeo.2008.03.004 Contents lists available at ScienceDirect Sedimentary Geology journal homepage: www.elsevier.com/locate/sedgeo