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Ming Ji and Ferdinand Baer

Abstract

A three-dimensional scale index based on spherical domain and quasigeostrophic scale analysis indicates a truncation limit of global atmospheric models that includes both horizontal and vertical dimensions. Applying such a scale index, a numerical experiment is designed using a simplified adiabatic version of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM0B) to examine, incorporating nonlinear dynamics alone, whether an optimal horizontal resolution for a nine-vertical-level (modes) global general circulation model can be achieved. In establishing appropriate vertical modes that can be uniquely scaled and are independent and physically relevant, an optimal distribution of levels, which has been developed, is utilized in the experiment.

The experimental results, which consist of a total of 110 individual integrations of the CCM0B with ten initial states for each of six horizontal truncations, appear to agree with the conclusions implied by the above referenced three-dimensional scale index; that is, a consistent horizontal resolution for a nine-vertical-level model should be in the range of triangular truncation T25 to T30 to yield optimal prediction results, considering, however, only the nonlinear dynamical aspect. It should be noted that due to the simplifications and idealizations made to carry out our experiment, additional studies under more realistic atmospheric conditions are necessary and are encouraged based on the results presented herein to further validate the existence of the consistency of three-dimensional model resolutions.

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Ferdinand Baer and Yuejian Zhu

Abstract

The National Center for Atmospheric Research Community Climate Model 1 was used as an experimental prediction model to assess the value of reassigning model levels in the vertical based on an optimizing hypothesis. The model was considered for T31 horizontal truncation and 12 vertical levels. The levels were relocated in a model called test, and the model with the conventional levels was denoted standard. Both models were integrated for 5 days with six independent initial states, and the results were composited. Analyses of the composites for both models were compared to actual observations. The results of the experiments indicate that the barotropic component of the flow was predicted with equal quality by both models but that the baroclinic component was predicted better by the test model. This observation may be explained by the increased fidelity of the vertical structure in the test model, since it has more resolution in the stratosphere.

Additional analyses were performed using a hypothesized three-dimensional scale index that relates the vertical to the horizontal truncation. The results of those analyses were sufficiently suggestive to encourage further studies to find optimum truncation in all three dimensions simultaneously.

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Bradley A. Ballish and Ferdinand Baer

Abstract

Various normal-mode initialization techniques are applied to a simple 12-level linear model with boundary layer friction, and results are compared to exact solutions of the model. It is found that Machenhauer's initialization scheme gives an approximate solution to the initialization of ageostrophic circulations due to friction; however, all or almost all vertical modes must be initialized and a moderate number of iterations are required. Second-order Baer-Tribbia initialization is found to be less effective than several iterations of the Machenhauer procedure. An iterative initialization based on bounded derivative theory and requiring the second time derivatives of the gravity modes to vanish gives excellent results, but a simple iterative scheme to achieve this diverges with moderate friction. The successful application of these procedures to the initialization of ageostrophic circulations due to friction in numerical weather prediction models will require careful utilization of, and possibly improved, iterative methods to achieve convergence and stability.

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Ferdinand Baer, Houjun Wang, Joseph J. Tribbia, and Aimé Fournier

Abstract

As an effort toward improving climate model–component performance and accuracy, an atmospheric-component climate model has been developed, entitled the Spectral Element Atmospheric Climate Model and denoted as CAM_SEM. CAM_SEM includes a unique dynamical core coupled at this time to the physics component of the Community Atmosphere Model (CAM) as well as the Community Land Model. This model allows the inclusion of local mesh refinement to seamlessly study imbedded higher-resolution regional climate concurrently with the global climate. Additionally, the numerical structure of the model based on spectral elements allows for application of state-of-the-art computing hardware most effectively and economically to produce the best prediction/simulation results with minimal expenditure of computing resources. The model has been tested under various conditions beginning with the shallow water equations and ending with an Atmospheric Model Intercomparison Project (AMIP)-style run that uses initial conditions and physics comparable to the CAM2 (version 2 of the NCAR CAM climate model) experiments. For uniform resolution, the output of the model compares favorably with the published output from the CAM2 experiments. Further integrations with local mesh refinement included indicate that while greater detail in the prediction of mesh-refined regions—that is, regional climate—is observed, the remaining coarse-grid results are similar to results obtained from a uniform-grid integration of the model with identical conditions. It should be noted that in addition to spectral elements, other efficient schemes have lately been considered, in particular the finite-volume scheme. This scheme has not yet been incorporated into CAM_SEM. The two schemes—finite volume and spectral element—are quasi-independent and generally compatible, dealing with different aspects of the integration process. Their impact can be assessed separately and the omission of the finite-volume process herein will not detract from the evaluation of the results using the spectral-element method alone.

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Houjun Wang, Joseph J. Tribbia, Ferdinand Baer, Aimé Fournier, and Mark A. Taylor

Abstract

The authors describe a recent development and some applications of a spectral element dynamical core. The improvements and development include the following: (i) the code was converted from FORTRAN 77 to FORTRAN 90; (ii) the dynamical core was extended to the generalized terrain-following, or hybrid η, vertical coordinates; (iii) a fourth-order Runge–Kutta (RK4) method for time integration was implemented; (iv) moisture effects were added in the dynamical system and a semi-Lagrangian method for moisture transport was implemented; and (v) the improved dynamical core was coupled with the Community Atmosphere Model version 2 (CAM2) physical parameterizations and Community Land Model version 2 (CLM2) in such a way that it can be used as an alternative dynamical core in CAM2. This spectral element version of CAM2 is denoted as CAM-SEM. A mass fixer as used in the Eulerian version of CAM2 (CAM-EUL) is also implemented in CAM-SEM. Results from multiyear simulations with CAM-SEM (coupled with CLM2) with climatology SST are also presented and compared with simulations from CAM-EUL. Close resemblances are shown in simulations from CAM-SEM and CAM-EUL. The authors found that contrary to what is suggested by some other studies, the high-order Lagrangian interpolation (with a limiter) using the spectral element basis functions may not be suitable for moisture and other strongly varying fields such as cloud and precipitation.

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