Formulation of a Lateral Sponge Layer for Limited-Area Shallow-Water Models and an Extension for the vertically Stratified Case

Kar, Sajal K.; Turco, R. P.

doi:10.1175/1520-0493(1995)123<1542:foalsl>2.0.co;2

Cited by 12 publications

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“…Maximum values of the sensitivity metric of the relative vorticity near the center of the domain to the 400-hPa v-wind component on the lateral boundaries and on the domain interior (from Errico et al 1993). small scales in the fine-mesh solution near the boundary (Perkey and Kreitzberg 1976;Kar and Turco 1995). For example, in the Perkey and Kreitzberg approach, a wave-absorbing or sponge zone near the lateral boundary prevents internal reflection of outward-propagating waves through an enhanced diffusion as well as truncation of the time derivatives.…”

Section: Summary Of Types Of Lbc Formulationsmentioning

confidence: 99%

A Tutorial on Lateral Boundary Conditions as a Basic and Potentially Serious Limitation to Regional Numerical Weather Prediction

Warner¹,

Peterson²,

Treadon³

1997

Bull. Amer. Meteor. Soc.

401

270

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Limited-area models (LAMs) are presently used for a wide variety of research and operational forecasting applications, and such use will likely expand greatly as the rapid increase in the performance/price ratio of computers and workstations makes LAMs more accessible to novice users. The robustness of these well-tested and documented models will make it tempting for many to consider them as turn-key systems that can be used without any experience or formal training in numerical weather prediction. This paper is intended as a tutorial and caution for such prospective model users, with the specific purpose of illustrating that, in spite of advanced physical-process parameterizations and high resolutions permitted by faster computers, and modern mesoscale data for initial conditions, there is still a basic limitation to predictability with a LAM-lateral boundary conditions (LBC). Illustrations are provided of previous work that show the serious negative effects of LBCs, and guidelines are provided for helping to minimize their negative impact on forecast quality.

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Section: Summary Of Types Of Lbc Formulationsmentioning

confidence: 99%

A Tutorial on Lateral Boundary Conditions as a Basic and Potentially Serious Limitation to Regional Numerical Weather Prediction

Warner¹,

Peterson²,

Treadon³

1997

Bull. Amer. Meteor. Soc.

401

270

View full text Add to dashboard Cite

show abstract

“…The closer a scheme is to the continuous relation of Equation (28), the better is the scheme's dispersion relation. Now, we look into the discrete forms (10), (14), and 15…”

Section: Dispersion Relation Analysismentioning

confidence: 99%

“…Numerical noise usually appears near the Dirichlet boundaries because the boundary values do not match the predicted values of the model due to truncation errors, even though these errors are very small. A sponge boundary treatment [14] is usually used to minimize the spurious wave reflections. In our implementation of the Z-grid models, we used a simple sponge method to avoid the spurious reflections at the north and south boundaries.…”

Section: Modification Of the Test Casesmentioning

confidence: 99%

“…We implemented three Z-grid models to demonstrate the improvement of the new Z-grid model. For the Voronoi Z-grid model, we used the finite volume scheme defined by Equations (10), (14), and (15) by setting w t = w b = 0 and w m = 1, denoted as VORO (Voronoi scheme) hereafter. For the new centroidal Z-grid model, we used w t = w b = 1/8 and w m = 3/4; this scheme is denoted as CENT.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Generalized Z-Grid Model for Numerical Weather Prediction

Xie

2019

Atmosphere

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Z-grid finite volume models conserve all-scalar quantities as well as energy and potential enstrophy and yield better dispersion relations for shallow water equations than other finite volume models, such as C-grid and C-D grid models; however, they are more expensive to implement. During each time integration, a Z-grid model must solve Poisson equations to convert its vorticity and divergence to a stream function and velocity potential, respectively. To optimally utilize these conversions, we propose a model in which the stability and possibly accuracy on the sphere are improved by introducing more stencils, such that a generalized Z-grid model can utilize longer time-integration steps and reduce computing time. Further, we analyzed the proposed model’s dispersion relation and compared it to that of the original Z-grid model for a linearly rotating shallow water equation, an important property for numerical models solving primitive equations. The analysis results suggest a means of balancing stability and dispersion. Our numerical results also show that the proposed Z-grid model for a shallow water equation is more stable and efficient than the original Z-grid model, increasing the time steps by more than 1.4 times.

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“…This integral equation has to be solved numerically (Drazin, 1961;Durran, 1992;Davis, 1999;Kar, 1995).…”

Section: Long's Equation -A Short Overviewmentioning

confidence: 99%

Long's equation in terrain following coordinates

Humi

2009

Nonlin. Processes Geophys.

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Abstract. Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorporates the terrain as part of the differential equation rather than the geometry of the domain. This new formulation enables us to compute analytically steady state gravity wave patterns over complex topography in some limiting cases of the parameters that appear in this equation.

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Formulation of a Lateral Sponge Layer for Limited-Area Shallow-Water Models and an Extension for the vertically Stratified Case

Cited by 12 publications

References 0 publications

A Tutorial on Lateral Boundary Conditions as a Basic and Potentially Serious Limitation to Regional Numerical Weather Prediction

A Tutorial on Lateral Boundary Conditions as a Basic and Potentially Serious Limitation to Regional Numerical Weather Prediction

Generalized Z-Grid Model for Numerical Weather Prediction

Long's equation in terrain following coordinates

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