Optimal Spectral Element Methods
Abstract
The Spectral Element dynamical core for the Community Atmospheric Model (CAM-SE) is a pseudo-spectral model in which derivative estimates are obtained from the Galerkin method applied to Legendre polynomial basis functions. Unfortunately, as variability approaches the scale of an element (e.g. 4 grid points), these estimates become thoroughly inaccurate. The accuracy of the model is further limited by aliasing errors which result from carrying out nonlinear calculations using grid point values. The damping processes that must be added to compensate for these errors do not fully eliminate their effects and act to reduce the information content of the model grid point values, resulting in a lower effective model resolution. To address these fundamental limitations of the Legendre-Galerkin spectral element method, the origin of the derivative errors is examined and optimal spectral element methods for atmospheric variability are introduced. The optimal estimation of derivative values and corresponding interpolation functions together with the introduction of a more suitable set of basis functions lead to a framework for carrying out fully spectral calculations within each element. With the increased accuracy of derivative estimates and elimination of aliasing effects, the need for artificial damping processes can be minimized to achieve a higher effective model resolution, maximizing the information content of model grid point values. In addition, quantitative measures of variability which cascade down to sub-grid scales through nonlinear processes are then also available for input to sub-grid parameterizations and to more effectively enforce conservation principles. These provide a means by which the sub-grid parameterizations can be optimized to systematically improve the fidelity of the model representation.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFM.A31A0011C
- Keywords:
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- 3336 Numerical approximations and analyses;
- ATMOSPHERIC PROCESSESDE: 3337 Global climate models;
- ATMOSPHERIC PROCESSES