Coastal boulder deposits (CBD), transported by waves at elevations above sea level and substantial distances inland, are markers for marine incursions. Whether they are tsunami or storm deposits can be difficult to determine, but this is of critical importance because of the role that CBD play in coastal hazard analysis. Equations from seminal work by Nott (1997), here referred to as the Nott Approach, are commonly employed to calculate nominal wave heights from boulder masses as a means to discriminate between emplacement mechanisms. Systematic review shows that this approach is based on assumptions that are not securely founded and that direct relationships cannot be established between boulder measurements and wave heights. A test using an unprecedented dataset of boulders moved by storm waves (with associated sea-state data) shows a lack of agreement between calculations and actual wave heights. The equations return unrealistically large heights, many of which greatly exceed sea states occurring during the boulder-moving storms. This underscores the finding that Nott-Approach wave-height calculations are unreliable. The result is general, because although the field data come from one region (the Aran Islands, Ireland), they represent a wide range of boulder masses and topographic settings and present a valid test of hydrodynamic equations. This analysis demonstrates that Nott Approach equations are incapable of distinguishing storm waves from tsunami transport and that wave heights hindcast from boulder masses are not meaningful. Current hydrodynamic understanding does not permit reliable computation of wave height from boulder measurements. A combination of field, numerical, and experimental approaches is required to quantify relationships between wave power and mass transport onshore. Many CBD interpreted as tsunami deposits based on Nott-Approach analysis may in fact have been emplaced during storms and should therefore be re-evaluated. This is especially important for CBD that have been incorporated into long-term coastal risk assessments, which are compromised if the CBD are misinterpreted. CBD dynamics can be better determined from a combination of detailed field measurements, modeling, and experiments. A clearer understanding of emplacement mechanisms will result in more reliable hazard analysis.

Summary: A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is proposed. It is developed for general conforming two‐dimensional triangular meshes and utilizes a slope limiting strategy to accurately model inundation. The method features a nondestructive limiter, which concurrently meets the requirements for linear stability and wetting and drying. It further combines existing approaches for positivity preservation and well balancing with an innovative velocity‐based limiting of the momentum. This limiting controls spurious velocities in the vicinity of the wet/dry interface. It leads to a computationally stable and robust scheme, even on unstructured grids, and allows for large time steps in combination with explicit time integrators. The scheme comprises only one free parameter, to which it is not sensitive in terms of stability. A number of numerical test cases, ranging from analytical tests to near‐realistic laboratory benchmarks, demonstrate the performance of the method for inundation applications. In particular, superlinear convergence, mass conservation, well balancedness, and stability are verified.

Numerical simulations based on solving the 2D shallow water equations using a discontinuous Galerkin (DG) discretisation have evolved to be a viable tool for many geophysical applications. In the context of flood modelling, however, they have not yet been methodologically studied to a large extent. Systematic model testing is non-trivial as no comprehensive collection of numerical test cases exists to ensure the correctness of the implementation. Hence, the first part of this manuscript aims at collecting test cases from the literature that are generally useful for storm surge modellers and can be used to benchmark codes. On geographic scale, hurricane storm surge can be interpreted as a localised phenomenon making it ideally suited for adaptive mesh refinement (AMR). Past studies employing dynamic AMR have exclusively focused on nested meshes. For that reason, we have developed a DG storm surge model on a triangular and dynamically adaptive mesh. In order to increase computational efficiency, the refinement is driven by physics-based refinement indicators capturing major model sensitivities. Using idealised numerical test cases, we demonstrate the model’s ability to correctly represent all source terms and reproduce known variability of coastal flooding with respect to hurricane characteristics such as size and approach speed. Finally, the adaptive mesh significantly reduces computing time with no effect on storm waves measured at discrete wave gauges just off the coast which shows the model’s potential for use as a robust simulation tool for real-time predictions.

This research is to facilitate the current understanding of long wave dynamics at coasts and during on-land propagation; experimental and numerical approaches are compared against existing analytical expressions for the long wave run-up. Leading depression sinusoidal waves are chosen to model these dynamics. The experimental study was conducted using a new pump-driven wave generator and the numerical experiments were carried out with a one-dimensional discontinuous Galerkin non-linear shallow water model. The numerical model is able to accurately reproduce the run-up elevation and velocities predicted by the theoretical expressions. Depending on the surf similarity of the generated waves and due to imperfections of the experimental wave generation, riding waves are observed in the experimental results. These artifacts can also be confirmed in the numerical study when the data from the physical experiments is assimilated. Qualitatively, scale effects associated with the experimental setting are discussed. Finally, shoreline velocities, run-up and run-down are determined and shown to largely agree with analytical predictions.

Non-uniform, dynamically adaptive meshes are a useful tool for reducing computational complexities for geophysical simulations that exhibit strongly localised features such as is the case for tsunami, hurricane or typhoon prediction. Using the example of a shallow water solver, this study explores a set of metrics as a tool to distinguish the performance of numerical methods using adaptively refined versus uniform meshes independent of computational architecture or implementation. These metrics allow us to quantify how a numerical simulation benefits from the use of adaptive mesh refinement. The type of meshes we are focusing on are adaptive triangular meshes that are non-uniform and structured. Refinement is controlled by physics-based indicators that capture relevant physical processes and determine the areas of mesh refinement and coarsening. The proposed performance metrics take into account a number of characteristics of numerical simulations such as numerical errors, spatial resolution, as well as computing time. Using a number of test cases we demonstrate that correlating different quantities offers insight into computational overhead, the distribution of numerical error across various mesh resolutions as well as the evolution of numerical error and run-time per degree of freedom.