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Publication Date
1 July 2024

Stabilized Bases for High-Order, Interpolation Semi-Lagrangian, Element-Based Tracer Transport

Subtitle
A method to find stabilized element bases enables extremely efficient tracer transport.
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Example of modifications to a natural basis set (dashed curves) to produce an Islet stabilized basis set (solid curves). Each color corresponds to a basis function in the set.
Science

Tracer transport in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core. Tracers are used in models of atmospheric microphysics and macrophysics, convection, aerosols, and chemistry. Atmosphere models may use from a few to hundreds of tracers. It is important that tracer transport be computed extremely efficiently. 

Impact

As part of developing a method that we call the Interpolation Semi-Lagrangian Element-based Transport (Islet) method, which is used in the E3SM Atmosphere Model, we developed a new procedure to find stabilized interpolation semi-Lagrangian (ISL) basis sets. These enable efficient ISL transport on unstructured element grids. The lowest-order Islet basis set is used in the E3SM Atmosphere Model versions 2 and 3. It is part of a method that speeds up atmosphere tracer transport over version 1 by a factor of six to eight and provides a slightly higher resolution. 

Summary

Advection of trace species, or tracers, also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core. Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods without requiring the solution of a globally coupled system of equations as implicit Eulerian methods do. Thus, to reduce the computational expense of tracer transport, dynamical cores often use SL methods to advect tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. However, unstructured grids, as E3SM uses, are a challenge for ISL methods. We developed an element-based ISL transport method that we call the Interpolation Semi-Lagrangian Element-based Transport (Islet) method, such as for use with atmosphere models discretized using unstructured element-based methods, including the E3SM Atmosphere Model. A core piece of the Islet method is a collection of element basis sets that provide spatial discretization. In contrast to classical ISL methods, the Islet method works on unstructured element grids. The natural element basis sets lead to an unstable ISL method. We developed a procedure to search for modified, stabilized basis sets. The resulting basis sets provide extremely accurate tracer transport and excellent diagnostic values in a number of verification problems. The lowest-order basis set is used in the E3SM Atmosphere Model versions 2 and 3 and is part of the overall transport method that speeds up atmosphere tracer transport over version 1 by a factor of six to eight. 

Point of Contact
Andrew M. Bradley
Institution(s)
Sandia National Laboratories (SNL)
Funding Program Area(s)
Additional Resources:
ALCC (ASCR Leadership Computing Challenge)
Publication