Adaptive wavelet simulation of global ocean dynamics using a new Brinkman volume penalization

Kevlahan, Nicholas; Dubos, Thomas; Aechtner, Matthias

doi:10.5194/gmd-8-3891-2015

Cited by 16 publications

(40 citation statements)

References 33 publications

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“…As a next step, we would like to investigate to what extent the results reported here generalize to the SWE on 2D planar domains, or to a global ocean model [27]. Mathematical analysis in such settings is more complicated due to the geometry of the problem, although probably possible for the linearized equations.…”

Section: Discussionmentioning

confidence: 93%

“…Finally, we also intend to investigate optimal placement of observation points in the two-dimensional case including bathymetry effects. As an important enabler for these efforts, our dynamically adaptive wavelet method for the two-dimensional SWE [27] opens up the possibility of adapting the computational grid to improve the accuracy of the assimilation.…”

Section: Discussionmentioning

confidence: 99%

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On the convergence of data assimilation for the one-dimensional shallow water equations with sparse observations

2019

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The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. In particular, the SWE are used to model the propagation of tsunami waves in the open ocean. We consider the associated data assimilation problem of optimally determining the initial conditions for the one-dimensional SWE in an unbounded domain from a small set of observations of the sea surface height and focus on how the structure of the observation operator affects the convergence of the gradient approach employed to solve the data assimilation problem computationally. In the linear case we prove a theorem that gives sufficient conditions for convergence to the true initial conditions. It asserts that at least two observation points must be used and at least one pair of observation points must be spaced more closely than half the effective minimum wavelength of the energy spectrum of the initial conditions. Our analysis is confirmed by numerical experiments for both the linear and nonlinear SWE data assimilation problems which reveal a relation between the convergence rate of gradient iterations and the number and spacing of the observation points. More specifically, these results show that convergence rates improve with increasing numbers of observation points and that at least three observation points are required for the practically useful results. Better results are obtained for the nonlinear equations provided more than two observation points are used. This paper is a first step in understanding the conditions for observability of the SWE for small numbers of observation points in more physically realistic settings.

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Section: Discussionmentioning

confidence: 93%

Section: Discussionmentioning

confidence: 99%

On the convergence of data assimilation for the one-dimensional shallow water equations with sparse observations

2019

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“…The choice of Lagrangian vertical coordinates (rather than mass based) is simple, computationally efficient and especially well suited for ocean modelling since it virtually eliminates numerical vertical diapycnal diffusion, unlike a z coordinate. This will become important when we develop the ocean version of wavetrisk (see Kevlahan et al, 2015). The vertical coordinates are pressure based and may either be evenly spaced or hybrid (σ ).…”

Section: Hydrostatic Dynamical Equations and Ale Vertical Coordinatesmentioning

confidence: 99%

“…We are also developing an ocean variant of wavetrisk that will improve the ALE formulation of the vertical coordinate and use penalization for bathymetry and coastlines. This work builds on the shallow water ocean model we presented in Kevlahan et al (2015).…”

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confidence: 99%

WAVETRISK-1.0: an adaptive wavelet hydrostatic dynamical core

Kevlahan

Dubos

2019

Geosci. Model Dev.

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Abstract. This paper presents the new adaptive dynamical core wavetrisk. The fundamental features of the wavelet-based adaptivity were developed for the shallow water equation on the β plane and extended to the icosahedral grid on the sphere in previous work by the authors. The three-dimensional dynamical core solves the compressible hydrostatic multilayer rotating shallow water equations on a multiscale dynamically adapted grid. The equations are discretized using a Lagrangian vertical coordinate version of the dynamico model. The horizontal computational grid is adapted at each time step to ensure a user-specified relative error in either the tendencies or the solution. The Lagrangian vertical grid is remapped using an arbitrary Lagrangian–Eulerian (ALE) algorithm onto the initial hybrid σ-pressure-based coordinates as necessary. The resulting grid is adapted horizontally but uniform over all vertical layers. Thus, the three-dimensional grid is a set of columns of varying sizes. The code is parallelized by domain decomposition using mpi, and the variables are stored in a hybrid data structure of dyadic quad trees and patches. A low-storage explicit fourth-order Runge–Kutta scheme is used for time integration. Validation results are presented for three standard dynamical core test cases: mountain-induced Rossby wave train, baroclinic instability of a jet stream and the Held and Suarez simplified general circulation model. The results confirm good strong parallel scaling and demonstrate that wavetrisk can achieve grid compression ratios of several hundred times compared with an equivalent static grid model.

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“…Other points to investigate are the impact of variable resolution on propagating waves and the optimal layout to build a multiresolution mesh. A more prospective approach could be the use of an adaptive wavelet method (Kevlahan et al 2015).…”

Section: Challengesmentioning

confidence: 99%