NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy

Abstract. The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss–Lobatto–Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

Download Full-text

Two conservative multi-tracer efficient semi-Lagrangian schemes for multiple processor systems integrated in a spectral element (climate) dynamical core

Communications in Applied and Industrial Mathematics ◽

10.1515/caim-2016-0023 ◽

2016 ◽

Vol 7 (3) ◽

pp. 74-98 ◽

Cited By ~ 1

Author(s):

Christoph Erath ◽

Mark A. Taylor ◽

Ramachandran D. Nair

Keyword(s):

Spectral Element Method ◽

Spectral Element ◽

Tracer Transport ◽

Third Order ◽

Dynamical Core ◽

Community Atmosphere Model ◽

High Scalability ◽

Passive Tracers ◽

Cubed Sphere ◽

A Current

Abstract In today’s atmospheric numerical modeling, scalable and highly accurate numerical schemes are of particular interest. To address these issues Galerkin schemes, such as the spectral element method, have received more attention in the last decade. They also provide other state-of-the-art capabilities such as improved conservation. However, the tracer transport of hundreds of tracers, e.g., in the chemistry version of the Community Atmosphere Model, is still a performance bottleneck. Therefore, we consider two conservative semi-Lagrangian schemes. Both are designed to be multi-tracer efficient, third order accurate, and allow significantly longer time steps than explicit Eulerian formulations. We address the difficulties arising on the cubed-sphere projection and on parallel computers and show the high scalability of our approach. Additionally, we use the two schemes for the transport of passive tracers in a dynamical core and compare our results with a current spectral element tracer transport advection used by the High-Order Method Modeling Environment.

Download Full-text

Terascale spectral element dynamical core for atmospheric general circulation models

Proceedings of the 2001 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '01 ◽

10.1145/582034.582052 ◽

2001 ◽

Cited By ~ 26

Author(s):

Richard D. Loft ◽

Stephen J. Thomas ◽

John M. Dennis

Keyword(s):

General Circulation ◽

General Circulation Models ◽

Spectral Element ◽

Dynamical Core ◽

Atmospheric General Circulation ◽

Atmospheric General Circulation Models

Download Full-text

Effect of a High-Order Filter on a Cubed-Sphere Spectral Element Dynamical Core

Monthly Weather Review ◽

10.1175/mwr-d-17-0226.1 ◽

2018 ◽

Vol 146 (7) ◽

pp. 2047-2064 ◽

Cited By ~ 1

Author(s):

Hyun-Gyu Kang ◽

Hyeong-Bin Cheong

Keyword(s):

Baroclinic Instability ◽

Spectral Element ◽

High Order ◽

Local Domain ◽

Step Size ◽

Time Step ◽

Dynamical Core ◽

Time Step Size ◽

Order Filter ◽

Cubed Sphere

Abstract A high-order filter for a cubed-sphere spectral element model was implemented in a three-dimensional spectral element dry hydrostatic dynamical core. The dynamical core incorporated hybrid sigma–pressure vertical coordinates and a third-order Runge–Kutta time-differencing method. The global high-order filter and the local-domain high-order filter, requiring numerical operation with a huge sparse global matrix and a locally assembled matrix, respectively, were applied to the prognostic variables, except for surface pressure, at every time step. Performance of the high-order filter was evaluated using the baroclinic instability test and quiescent atmosphere with underlying topography test presented by the Dynamical Core Model Intercomparison Project. It was revealed that both the global and local-domain high-order filters could better control the numerical noise in the noisy circumstances than the explicit diffusion, which is widely used for the spectral element dynamical core. Furthermore, by adopting the high-order filter, the effective resolution of the dynamical core could be increased, without weakening the stability of the dynamical core. Computational efficiency of the high-order filter was demonstrated in terms of both the time step size and the wall-clock time. Because of the nature of an implicit diffusion, the dynamical core employing this filter can take a larger time step size, compared to that using the explicit diffusion. The local-domain high-order filter was computationally more efficient than the global high-order filter, but less efficient than the explicit diffusion.

Download Full-text

AMIP Simulation with the CAM4 Spectral Element Dynamical Core

Journal of Climate ◽

10.1175/jcli-d-11-00448.1 ◽

2013 ◽

Vol 26 (3) ◽

pp. 689-709 ◽

Cited By ~ 51

Author(s):

K. J. Evans ◽

P. H. Lauritzen ◽

S. K. Mishra ◽

R. B. Neale ◽

M. A. Taylor ◽

...

Keyword(s):

Spectral Element Method ◽

Spectral Element ◽

System Model ◽

Energy Spectra ◽

Model Intercomparison ◽

Climate System Model ◽

Dynamical Core ◽

Intercomparison Project ◽

Cubed Sphere ◽

Mean Square Errors

Abstract The authors evaluate the climate produced by the Community Climate System Model, version 4, running with the new spectral element atmospheric dynamical core option. The spectral element method is configured to use a cubed-sphere grid, providing quasi-uniform resolution over the sphere and increased parallel scalability and removing the need for polar filters. It uses a fourth-order accurate spatial discretization that locally conserves mass and total energy. Using the Atmosphere Model Intercomparison Project protocol, the results from the spectral element dynamical core are compared with those produced by the default finite-volume dynamical core and with observations. Even though the two dynamical cores are quite different, their simulated climates are remarkably similar. When compared with observations, both models have strengths and weaknesses but have nearly identical root-mean-square errors and the largest biases show little sensitivity to the dynamical core. The spectral element core does an excellent job reproducing the atmospheric kinetic energy spectra, including fully capturing the observed Nastrom–Gage transition when running at 0.125° resolution.

Download Full-text

CAM-SE–CSLAM: Consistent Coupling of a Conservative Semi-Lagrangian Finite-Volume Method with Spectral Element Dynamics

Monthly Weather Review ◽

10.1175/mwr-d-16-0258.1 ◽

2017 ◽

Vol 145 (3) ◽

pp. 833-855 ◽

Cited By ~ 10

Author(s):

Peter Hjort Lauritzen ◽

Mark A. Taylor ◽

James Overfelt ◽

Paul A. Ullrich ◽

Ramachandran D. Nair ◽

...

Keyword(s):

Finite Volume ◽

Search Algorithm ◽

Control Volume ◽

Spectral Element ◽

Volume Transport ◽

Finite Volume Scheme ◽

Tracer Transport ◽

Courant Number ◽

Dynamical Core ◽

Community Atmosphere Model

An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), and the SE dynamical core is the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model–Spectral Elements (CAM-SE). The primary motivation for coupling CSLAM with CAM-SE is to accelerate tracer transport for multitracer applications. The coupling algorithm result is an inherently mass-conservative, shape-preserving, and consistent (for a constant mixing ratio, the CSLAM solution reduces to the SE solution for air mass) transport that is efficient and accurate. This is achieved by first deriving formulas for diagnosing SE airmass flux through the CSLAM control volume faces. Thereafter, the upstream Lagrangian CSLAM areas are iteratively perturbed to match the diagnosed SE airmass flux, resulting in an equivalent upstream Lagrangian grid that spans the sphere without gaps or overlaps (without using an expensive search algorithm). This new CSLAM algorithm is not specific to airmass fluxes provided by CAM-SE but applies to any airmass fluxes that satisfy the Lipshitz criterion and for which the Courant number is less than one.

Download Full-text

Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model

The International Journal of High Performance Computing Applications ◽

10.1177/1094342017736373 ◽

2017 ◽

Vol 33 (2) ◽

pp. 268-284 ◽

Cited By ~ 2

Author(s):

Katherine J Evans ◽

Richard K Archibald ◽

David J Gardner ◽

Matthew R Norman ◽

Mark A Taylor ◽

...

Keyword(s):

Shallow Water ◽

Message Passing Interface ◽

Spectral Element ◽

Processing Unit ◽

Spectral Order ◽

Dynamical Core ◽

Computational Performance ◽

Implicit Solvers ◽

Trade Offs ◽

Atmosphere Model

Explicit Runge–Kutta methods and implicit multistep methods utilizing a Newton–Krylov nonlinear solver are evaluated for a range of configurations of the shallow-water dynamical core of the spectral element community atmosphere model to evaluate their computational performance. These configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to the largest problem sizes. This analysis is performed within the shallow-water dynamical core option of a full climate model code base to enable a wealth of simulations for study, with the aim of informing solver development within the more complete hydrostatic dynamical core used for climate research. The limitations and benefits to using explicit versus implicit methods, with different parameters and settings, are discussed in light of the trade-offs with Message Passing Interface (MPI) communication and memory and their inherent efficiency bottlenecks. Given the performance behavior across the configurations analyzed here, the recommendation for future work using the implicit solvers is conditional based on scale separation and the stiffness of the problem. For the regionally refined configurations, the implicit method has about the same efficiency as the explicit method, without considering efficiency gains from a preconditioner. The potential for improvement using a preconditioner is greatest for higher spectral order configurations, where more work is shifted to the linear solver. Initial simulations with OpenACC directives to utilize a Graphics Processing Unit (GPU) when performing function evaluations show improvements locally, and that overall gains are possible with adjustments to data exchanges.

Download Full-text