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Publication Date
16 August 2022

Islet: Interpolation Semi-Lagrangian Element-Based Transport

Subtitle
A method for a three-grid atmosphere model enables extremely efficient, ultra-high-resolution tracer transport.
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Example of tracer transport at multiple resolutions. The velocity data (representing the dynamics) and time steps are the same in each case. Time proceeds left to right. Resolution increases top to bottom. The exact solution at the final time (right column) is the same as the initial condition (left column).
Science

Advection of trace species, or tracers, in models of the atmosphere and other physical domains is an important and 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 tens to hundreds of tracers. Thus, it is important that tracer transport be computed extremely efficiently.

Impact

We developed a method that we call the Interpolation Semi-Lagrangian Element-based Transport (Islet) method for use in the E3SM Atmosphere Model. The Islet method uses three grids: a dynamics grid, a physics parameterizations grid, and a tracer grid supporting the use of our new Islet bases. Each grid's subelement structure is independently configurable. These separate grids permit the dynamics, tracer transport, and physics parameterizations each to be as efficient as possible, leading to an overall atmosphere simulation that is extremely efficient. The lowest-order Islet transport method is used in the E3SM Atmosphere Model version 2. It speeds up atmosphere tracer transport over version 1 by a factor of six to eight and provides slightly higher resolution. Higher-order variants could be used to better resolve and maintain filamentary structures in tracers while using the same dynamics and physics parameterization configurations, as shown in the bottom row of the figure.

Summary

Advection of trace species, or tracers, also called tracer transport, in models of the atmosphere and other physical domains is an important and 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 extremely efficient SL methods. We developed a finite-element ISL transport method that we call the Interpolation Semi-Lagrangian Element-based Transport (Islet) method, such as for use with atmosphere models discretized using the spectral element method, including the E3SM Atmosphere Model. The Islet method uses three grids that share an element grid: a dynamics grid supporting, for example, the Gauss-Legendre-Lobatto basis of degree three; a physics parameterizations grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting the use of Islet bases, with the particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of verification problems. The lowest-order Islet transport method is used in the E3SM Atmosphere Model version 2 and 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
Funding Program Area(s)
Publication