Nature-based solutions are becoming an increasingly important component of sustainable coastal risk management. For particularly destructive hazards like tsunamis, natural elements like vegetation are often combined with designed elements like seawalls or dams to augment the protective benefits of each component. One example of this kind of hybrid approach is the so-called tsunami mitigation park, which combines a designed hillscape with vegetation. Despite the increasing popularity of tsunami mitigation parks, the protective benefits they provide are poorly understood and incompletely quantified. As a consequence of this lack of understanding, current designs might not maximize the protective benefits of tsunami mitigation parks. Here, we numerically model the interactions between a single row of hills with an incoming tsunami to identify the mechanisms through which the park protects the coast. We initialize the tsunami as an N wave that propagates to shore and impacts the coast directly. We find that partial reflection of the incoming wave is the most important mechanism by which hills reduce the kinetic energy that propagates onshore. The protective benefit of tsunami mitigation parks is thus comparable to that of a small wall, at least for tsunamis with amplitudes that are comparable to the hill height. We also show that hills could elevate potential damage in the immediate vicinity of the hills where flow speeds increase compared to a planar beach, suggesting the need to include a buffer zone behind the hills into a strategic park design.
Numerical weather prediction (NWP) has proven to be computationally challenging due to its inherent multiscale nature. Currently, the highest resolution NWP models use a horizontal resolution of about 10 km. At this resolution many important processes in the atmosphere are not resolved. Needless to say this introduces errors.In order to increase the resolution of NWP models highly scalable atmospheric models are needed.The Non-hydrostatic Unified Model of the Atmosphere (NUMA), developed by the authors at the Naval Postgraduate School, was designed to achieve this purpose.NUMA is used by the Naval Research Laboratory, Monterey as the engine inside its next generation weather prediction system NEPTUNE. NUMA solves the fully compressible Navier-Stokes equations by means of high-order Galerkin methods (both spectral element as well as discontinuous Galerkin methods can be used).Mesh generation is done using the p4est library. NUMA is capable of running middle and upper atmosphere simulations since it does not make use of the shallowatmosphere approximation. This paper presents the performance analysis and optimization of the spectral element version of NUMA. The performance at different optimization stages is analyzed using a theoretical performance model as well as measurements via hardware counters. Machine independent optimization is compared to machine specific optimization using BG/Q vector intrinsics. By using vector intrinsics the main computations reach 1.2 PFlops on the entire machine Mira (12% of the theoretical peak performance). The paper also presents scalability studies for two idealized test cases that are relevant for NWP applications. The atmospheric model NUMA delivers an excellent strong scaling efficiency of 99% on the entire supercomputer Mira using a mesh with 1.8 billion grid points. This allows to run a global forecast of a baroclinic wave test case at 3 km uniform horizontal resolution and double precision within the time frame required for operational weather prediction.
Numerical Weather Prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale e ciently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite di erences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods. Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (2003) [Review of numerical methods for nonhydrostatic weather prediction models Meteorol. Atmos. Phys. 82, 2003], this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.
The fundamental pathways for tropical cyclone (TC) intensification are explored by considering axisymmetric and asymmetric impulsive thermal perturbations to balanced, TC-like vortices using the dynamic cores of three different nonlinear numerical models. Attempts at reproducing the results of previous work, which used the community WRF Model, revealed a discrepancy with the impacts of purely asymmetric thermal forcing. The current study finds that thermal asymmetries can have an important, largely positive role on the vortex intensification, whereas other studies find that asymmetric impacts are negligible.Analysis of the spectral energetics of each numerical model indicates that the vortex response to asymmetric thermal perturbations is significantly damped in WRF relative to the other models. Spectral kinetic energy budgets show that this anomalous damping is primarily due to the increased removal of kinetic energy from the vertical divergence of the vertical pressure flux, which is related to the flux of inertia-gravity wave energy. The increased kinetic energy in the other two models is shown to originate around the scales of the heating and propagate upscale with time from nonlinear effects. For very large thermal amplitudes (50 K), the anomalous removal of kinetic energy due to inertia-gravity wave activity is much smaller, resulting in good agreement between models.The results of this paper indicate that the numerical treatment of small-scale processes that project strongly onto inertia-gravity wave energy can lead to significant differences in asymmetric TC intensification. Sensitivity tests with different time integration schemes suggest that diffusion entering into the implicit solution procedure is partly responsible for the anomalous damping of energy.
The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only.Because the di usion coe cients of the regularization stresses obtained via Dyn-SGS are residual-based, the e ect of the artificial di usion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter.From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly-Smagorinsky SGS model.
We test the behaviour of a unified continuous/discontinuous Galerkin (CG/DG) shallowwater model in spherical geometry with curved elements on three different grids of ubiquitous use in atmospheric modelling: (i) the cubed-sphere, (ii) the reduced latitude-longitude, and (iii) the icosahedral grid. Both conforming and non-conforming grids are adopted including static and dynamically adaptive grids for a total of twelve mesh configurations. The behaviour of CG and DG on the different grids are compared for a nonlinear midlatitude perturbed jet and for a linear case that admits an analytic solution. Because the inviscid solution on certain grids shows a high sensitivity to the resolution, the viscous counterpart of the governing equations is also solved and the results compared. The logically unstructured element-based CG/DG model described in this article is flexible with respect to arbitrary grids. However, we were unable to define a best grid configuration that could possibly minimize the error regardless of the characteristic geometry of the flow. This is especially true if the governing equations are not regularized by the addition of a sufficiently large, fully artificial, diffusion mechanism, as will be shown. The main novelty of this study lies in the unified implementation of two element-based Galerkin methods that share the same numerical machinery and do not rely on any specific grid configuration to solve the shallow-water equation on the sphere.
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