Tsunami Modelling with Static and Dynamic Tides in Drowned River Valleys with Morphological Constrictions KAYA M. WILSON 1 and HANNAH E. POWER 1 Abstract—Tsunami modelling is widely used to estimate the potential impacts of tsunamis. Models require a tide input, which can be either static, representing a specific tide level, such as Highest Astronomic Tide or dynamic, which represents a moving tide level. Although commonly used, static tide inputs do not account for tsunami–tide interactions, which are known to be non- linear and more significant in estuaries when compared to the open coast. To demonstrate the differences between tsunami models using static or dynamic tide inputs, a series of models were carried out for two New South Wales estuaries, Sydney harbour and port hacking. Model boundary conditions phased a M W 9.0 Puysegur source tsunami with multiple tide scenarios. Fourteen distinct scenarios with dynamic tides were created by phasing the largest tsunami wave peak at regular intervals across the tidal range. For comparison, static tide models were run using equivalent tide levels. The situations where static tide models provide results comparable or more conservative than dynamic tide models are for the first 1–2 h after tsunami arrival, at high tides, and when com- pared to dynamic falling tides at the same tide level. Differences are most apparent upriver of geomorphological constrictions. The effects of geomorphological constrictions were further examined using idealised model setups with a constriction variable. Results show that constrictions affect downriver maximum water levels, tsunami wave heights, upriver water accumulation and inundation maxima and distributions. These results have implications for estuaries vulnerable to erosion at constriction sites during a tsunami event. Keywords: Tsunami modelling, tide–tsunami interactions, tsunami propagation, Sydney harbour, port hacking, tsunami erosion. 1. Introduction Tsunamis are a global natural hazard and Aus- tralian coastal communities have differing levels of exposure (Davies 2018). In New South Wales (NSW), exposure around estuaries is particularly high, where reduced tidal ranges and protection from wind waves have allowed low-lying development to occur (Hanslow et al. 2018). Geological and historic evidence show that tsunamis have affected NSW in the past (Dominey-Howes 2007). Accounts from the Sydney harbour impacts of the May 1960 Chilean tsunami describe dragged and broken moorings, vessels being swept into bridges by large waves, and extreme currents. Significant scouring and erosion was also reported (Beccari 2009). The 1960 Chilean tsunami was generated by a subduction zone earth- quake, the dominant cause of tsunamis worldwide (UNESCO 2015). Despite the rare occurrence of damaging tsunamis when compared to other hazards, the state of New South Wales (NSW), Australia, identifies tsunamis as a ‘high’ risk hazard due to the potential catastrophic consequences (NSW 2017). Tsunami modelling is used in emergency man- agement to provide a best estimate of potential tsunami impacts. The modelling process typically uses a digital representation of the environment and applies the non-linear shallow water wave equations that have been shown to best represent tsunami behaviour (Synolakis et al. 2008; Titov and Synolakis 1988). Tides can be applied to the models as either a static water level, which represents a constant tide level, such as HAT or Mean Sea Level (MSL) (e.g. Dall’Osso et al. 2014) or as a dynamic rising and falling water level (e.g. Cardno 2013; Wilson et al. 2018). Static tides provide a simpler and easier approach to tsunami modelling and are commonly used. Dynamic tides however, provide a more accu- rate representation of the natural environment and can reduce the limitations of the model (AIDR 2018). When addressing the limitations of tsunami modelling with a static tide, the propagation 1 University of Newcastle, University Drive, Callaghan, NSW 2308, Australia. E-mail: kaya.wilson@newcastle.edu.au Pure Appl. Geophys. Ó 2020 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-019-02411-0 Pure and Applied Geophysics