On the corners of the cubed sphere grid †

2021 ◽  
Author(s):  
M. Zerroukat ◽  
T. Allen
Keyword(s):  
Cubed Sphere

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

Diffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model

2009 ◽  
Vol 137 (10) ◽  
pp. 3339-3350 ◽  
Author(s):  
Ramachandran D. Nair
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Water Model ◽  
Order System ◽  
Small Scale ◽  
Shallow Water Model ◽  
First Order ◽  
Advection Diffusion Equation ◽  
Diffusion Scheme ◽  
Cubed Sphere

Abstract A second-order diffusion scheme is developed for the discontinuous Galerkin (DG) global shallow-water model. The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a nonorthogonal curvilinear coordinate system. In the viscous shallow-water model the diffusion terms (viscous fluxes) are approximated with two different approaches: 1) the element-wise localized discretization without considering the interelement contributions and 2) the discretization based on the local discontinuous Galerkin (LDG) method. In the LDG formulation the advection–diffusion equation is solved as a first-order system. All of the curvature terms resulting from the cubed-sphere geometry are incorporated into the first-order system. The effectiveness of each diffusion scheme is studied using the standard shallow-water test cases. The approach of element-wise localized discretization of the diffusion term is easy to implement but found to be less effective, and with relatively high diffusion coefficients, it can adversely affect the solution. The shallow-water tests show that the LDG scheme converges monotonically and that the rate of convergence is dependent on the coefficient of diffusion. Also the LDG scheme successfully eliminates small-scale noise, and the simulated results are smooth and comparable to the reference solution.

A Simple Method to Find a Neighboring Grid Point on the Cubed-sphere

2018 ◽  
Vol 54 (S1) ◽  
pp. 413-419 ◽  
Author(s):  
Ki-Hwan Kim ◽  
Pyoung-Seop Shim ◽  
Seoleun Shin ◽  
Junghan Kim
Keyword(s):  
Grid Point ◽  
Simple Method ◽  
Cubed Sphere

Multi-resolution Hybrid Data Assimilation Core on a Cubed-sphere Grid (HybDA)

2018 ◽  
Vol 54 (S1) ◽  
pp. 337-350 ◽  
Author(s):  
Hyo-Jong Song ◽  
Ji-Hyun Ha ◽  
In-Hyuk Kwon ◽  
Junghan Kim ◽  
Jihye Kwun
Keyword(s):  
Data Assimilation ◽  
Hybrid Data Assimilation ◽  
Hybrid Data ◽  
Cubed Sphere

scholarly journals Hermitian Compact Interpolation on the Cubed-Sphere Grid

2013 ◽  
Vol 57 (1) ◽  
pp. 193-212 ◽  
Author(s):  
Jean-Pierre Croisille
Keyword(s):  
Cubed Sphere

scholarly journals High-Resolution Ensemble HFV3 Forecasts of Hurricane Michael (2018): Rapid Intensification in Shear

2020 ◽  
Vol 148 (5) ◽  
pp. 2009-2032 ◽  
Author(s):  
Andrew T. Hazelton ◽  
Xuejin Zhang ◽  
Sundararaman Gopalakrishnan ◽  
William Ramstrom ◽  
Frank Marks ◽  
...  
Keyword(s):  
Tropical Cyclones ◽  
Early Stage ◽  
Vertical Wind Shear ◽  
Vertical Shear ◽  
Rapid Intensification ◽  
Forecast System ◽  
The Mean ◽  
Cubed Sphere ◽  
Environmental Prediction ◽  
The Relationship

Abstract The FV3GFS is the current operational Global Forecast System (GFS) at the National Centers for Environmental Prediction (NCEP), which combines a finite-volume cubed sphere dynamical core (FV3) and GFS physics. In this study, FV3GFS is used to gain understanding of rapid intensification (RI) of tropical cyclones (TCs) in shear. The analysis demonstrates the importance of TC structure in a complex system like Hurricane Michael, which intensified to a category 5 hurricane over the Gulf of Mexico despite over 20 kt (10 m s−1) of vertical wind shear. Michael’s RI is examined using a global-nest FV3GFS ensemble with the nest at 3-km resolution. The ensemble shows a range of peak intensities from 77 to 159 kt (40–82 m s−1). Precipitation symmetry, vortex tilt, moisture, and other aspects of Michael’s evolution are compared through composites of stronger and weaker members. The 850–200-hPa vertical shear is 22 kt (11 m s−1) in the mean of both strong and weak members during the early stage. Tilt and moisture are two distinguishing factors between strong and weak members. The relationship between vortex tilt and humidification is complex, and other studies have shown both are important for sheared intensification. Here, it is shown that tilt reduction leads to upshear humidification and is thus a driving factor for intensification. A stronger initial vortex and early evolution of the vortex also appear to be the key to members that are able to resist the sheared environment.

scholarly journals A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

2014 ◽  
Vol 7 (3) ◽  
pp. 909-929 ◽  
Author(s):  
J. Thuburn ◽  
C. J. Cotter ◽  
T. Dubos
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Model Comparison ◽  
Mass Conservation ◽  
Time Discretization ◽  
Water Model ◽  
Tracer Transport ◽  
Exact Mass ◽  
Large Wave ◽  
Cubed Sphere

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

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