A Two-Way Nested Global-Regional Dynamical Core on the Cubed-Sphere Grid

Abstract A nested-grid model is constructed using the Geophysical Fluid Dynamics Laboratory finite-volume dynamical core on the cubed sphere. The use of a global grid avoids the need for externally imposed lateral boundary conditions, and the use of the same governing equations and discretization on the global and regional domains prevents inconsistencies that may arise when these differ between grids. A simple interpolated nested-grid boundary condition is used, and two-way updates use a finite-volume averaging method. Mass conservation is achieved in two-way nesting by simply not updating the mass field. Despite the simplicity of the nesting methodology, the distortion of the large-scale flow by the nested grid is such that the increase in global error norms is a factor of 2 or less in shallow-water test cases. The effect of a nested grid in the tropics on the zonal means and eddy statistics of an idealized Held–Suarez climate integration is minor, and artifacts due to the nested grid are comparable to those at the edges of the cubed-sphere grid and decrease with increasing resolution. The baroclinic wave train in a Jablonowski–Williamson test case was preserved in a nested-grid simulation while finescale features were represented with greater detail in the nested-grid region. The authors also found that lee vortices could propagate out of the nested region and onto a coarse grid, which by itself could not produce vortices. Finally, the authors discuss how concurrent integration of the nested and coarse grids can be significantly more efficient than when integrating the two grids sequentially.

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

Geoscientific Model Development ◽

10.5194/gmd-7-909-2014 ◽

2014 ◽

Vol 7 (3) ◽

pp. 909-929 ◽

Cited By ~ 26

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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Poster reception---The finite-volume dynamical core on the cubed-sphere

ACM/IEEE SC 2006 Conference (SC'06) ◽

10.1145/1188455.1188634 ◽

2006 ◽

Cited By ~ 3

Author(s):

William Putman

Keyword(s):

Finite Volume ◽

Dynamical Core ◽

Cubed Sphere

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Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow

Computational Geosciences ◽

10.1007/s10596-020-09969-y ◽

2020 ◽

Vol 24 (4) ◽

pp. 1605-1624

Author(s):

Philipp Selzer ◽

Olaf A. Cirpka

Keyword(s):

Finite Element ◽

Velocity Field ◽

Finite Volume Method ◽

Finite Volume ◽

Particle Tracking ◽

Mass Conservation ◽

Velocity Fields ◽

Test Case ◽

Hydraulic Gradients ◽

Volume Method

Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the $\mathcal {RTN}_{0}$ R T N 0 velocity field imposing element-wise mass conservation. Using the conforming velocity field in $\mathcal {RTN}_{0}$ R T N 0 space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the $\mathcal {RTN}_{0}$ R T N 0 -projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.

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Exploring Convection-Allowing Model Evaluation Strategies for Severe Local Storms Using the Finite-Volume Cubed-Sphere (FV3) Model Core

Weather and Forecasting ◽

10.1175/waf-d-20-0090.1 ◽

2021 ◽

Vol 36 (1) ◽

pp. 3-19

Author(s):

Burkely T. Gallo ◽

Jamie K. Wolff ◽

Adam J. Clark ◽

Israel Jirak ◽

Lindsay R. Blank ◽

...

Keyword(s):

Finite Volume ◽

Weather Forecasting ◽

Severe Weather ◽

Receiver Operating Curve ◽

Brier Score ◽

Dynamical Core ◽

Object Based ◽

Verification Methods ◽

Cubed Sphere ◽

Verification Techniques

AbstractVerification methods for convection-allowing models (CAMs) should consider the finescale spatial and temporal detail provided by CAMs, and including both neighborhood and object-based methods can account for displaced features that may still provide useful information. This work explores both contingency table–based verification techniques and object-based verification techniques as they relate to forecasts of severe convection. Two key fields in severe weather forecasting are investigated: updraft helicity (UH) and simulated composite reflectivity. UH is used to generate severe weather probabilities called surrogate severe fields, which have two tunable parameters: the UH threshold and the smoothing level. Probabilities computed using the UH threshold and smoothing level that give the best area under the receiver operating curve result in very high probabilities, while optimizing the parameters based on the Brier score reliability component results in much lower probabilities. Subjective ratings from participants in the 2018 NOAA Hazardous Weather Testbed Spring Forecasting Experiment (SFE) provide a complementary evaluation source. This work compares the verification methodologies in the context of three CAMs using the Finite-Volume Cubed-Sphere Dynamical Core (FV3), which will be the foundation of the U.S. Unified Forecast System (UFS). Three agencies ran FV3-based CAMs during the five-week 2018 SFE. These FV3-based CAMs are verified alongside a current operational CAM, the High-Resolution Rapid Refresh version 3 (HRRRv3). The HRRR is planned to eventually use the FV3 dynamical core as part of the UFS; as such evaluations relative to current HRRR configurations are imperative to maintaining high forecast quality and informing future implementation decisions.

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On the sensitivity of hurricane intensity and structure to horizontal tracer advection schemes in FV3

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-20-0331.1 ◽

2021 ◽

Author(s):

Kun Gao ◽

Lucas Harris ◽

Linjiong Zhou ◽

Morris Bender ◽

Matthew Morin

Keyword(s):

Inner Core ◽

Positive Definite ◽

Moisture Distribution ◽

Geophysical Fluid Dynamics Laboratory ◽

Hurricane Intensity ◽

Dynamical Core ◽

Intensity Prediction ◽

Advection Schemes ◽

Structural Differences ◽

Cubed Sphere

AbstractWe investigate the sensitivity of hurricane intensity and structure to the horizontal tracer advection in the Geophysical Fluid Dynamics Laboratory (GFDL) Finite-Volume Cubed-Sphere Dynamical Core (FV3). We compare two schemes, a monotonic scheme and a less diffusive positive-definite scheme. The positive-definite scheme leads to significant improvement in the intensity prediction relative to the monotonic scheme in a suite of five-day forecasts that mostly consist of rapidly intensifying hurricanes. Notable storm structural differences are present: the radius of maximum wind (RMW) is smaller and eyewall convection occurs farther inside the RMW when the positive-definite scheme is used. Moreover, we find that the horizontal tracer advection scheme affects the eyewall convection location by affecting the moisture distribution in the inner-core region. This study highlights the importance of dynamical core algorithms in hurricane intensity prediction.

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

Geoscientific Model Development Discussions ◽

10.5194/gmdd-6-6867-2013 ◽

2013 ◽

Vol 6 (4) ◽

pp. 6867-6925 ◽

Cited By ~ 3

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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A Limited Area Modeling Capability for the Finite‐Volume Cubed‐Sphere (FV3) Dynamical Core and Comparison with a Global Two‐Way Nest

Journal of Advances in Modeling Earth Systems ◽

10.1029/2021ms002483 ◽

2021 ◽

Author(s):

T. L. Black ◽

J. A. Abeles ◽

B. T. Blake ◽

D. Jovic ◽

E. Rogers ◽

...

Keyword(s):

Finite Volume ◽

Limited Area ◽

Dynamical Core ◽

Cubed Sphere

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Performance of the HOMME dynamical core in the aqua-planet configuration of NCAR CAM4: equatorial waves

Annales Geophysicae ◽

10.5194/angeo-29-221-2011 ◽

2011 ◽

Vol 29 (2) ◽

pp. 221-227 ◽

Cited By ~ 6

Author(s):

S. K. Mishra ◽

M. A. Taylor ◽

R. D. Nair ◽

H. M. Tufo ◽

J. J. Tribbia

Keyword(s):

Gravity Waves ◽

Large Scale ◽

Phase Speed ◽

High Order ◽

Equatorial Waves ◽

Climate System Model ◽

Dynamical Core ◽

Model Simulations ◽

High Order Element ◽

Cubed Sphere

Abstract. A new atmospheric dynamical core, named the High Order Method Modeling Environment (HOMME), has been recently included in the NCAR-Community Climate System Model version 4 (CCSM4). It is a petascale capable high-order element-based conservative dynamical core developed on a cubed-sphere grid. We have examined the model simulations with HOMME using the aqua-planet mode of CAM4 (atmospheric component of CCSM4) and evaluated its performance in simulating the equatorial waves, considered a crucial element of climate variability. For this we compared the results with two other established models in CAM4 framework, which are the finite-volume (FV) and Eulerian spectral (EUL) dynamical cores. Although the gross features seem to be comparable, important differences have been found among the three dynamical cores. The phase speed of Kelvin waves in HOMME is faster and more satisfactory than those in FV and EUL. The higher phase speed is attributed to an increased large-scale precipitation in the upper troposphere and a more top-heavy heating structure. The variance of the n=1 equatorial Rossby waves is underestimated by all three of them, but comparatively HOMME simulations are more reasonable. For the n=0 eastward inertio-gravity waves, the variances are weak and phase speeds are too slow, scaled to shallow equivalent depths. However, the variance in HOMME is relatively more compared to the two other dynamical cores. The mixed Rossby-gravity waves are feeble in all the three cases. In summary, model simulations using HOMME are reasonably good, with some improvement relative to FV and EUL in capturing some of the important characteristics associated with equatorial waves.

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A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽

10.3390/w12061639 ◽

2020 ◽

Vol 12 (6) ◽

pp. 1639

Author(s):

Abdelkrim Aharmouch ◽

Brahim Amaziane ◽

Mustapha El Ossmani ◽

Khadija Talali

Keyword(s):

Finite Volume ◽

Coastal Aquifers ◽

Nonlinear Partial Differential Equations ◽

Time Integration ◽

Mass Conservation ◽

Coupled System ◽

Finite Volume Scheme ◽

Time Step ◽

Volume Scheme ◽

Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

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