The E3SM Nonhydrostatic Dynamical Core Formulation

  • August 18, 2020
  • Home Page Feature,Science and Technical Highlights
  • A core component of E3SM’s new cloud resolving atmosphere model.

    The Science

    Energy consistent discretizations have proven useful in guiding the development of numerical methods for simulating fluid dynamics. They ensure that the discrete method does not have any spurious sources of energy, which can lead to unstable and unrealistic simulations. In this research, scientists provide an energy consistent discretization of the equations used by global models of the Earth’s atmosphere.  The software component which solves these dynamical equations in a global model is referred to as its dynamical core.  The dynamical core simulates the time evolution of the winds, temperature and pressure throughout the atmosphere.

    The Impact

    This new dynamical core is being used in E3SM’s nonhydrostatic cloud-resolving modeling project.  The project together with DOE’s upcoming Exascale supercomputers will allow scientists to resolve the convective processes responsible for storm systems, removing a large source of uncertainty in climate change projections.


    baroclinic instability

    A baroclinic instability test case used to confirm the energy conservation properties of the new discretization. Shown is the relative vorticity at 750 hPa at day 15.

    To test the energy conservation properties of the new dynamical core, the researchers used a baroclinic instability test case shown in the figure above.  In this test case, the atmosphere is initialized with a geostrophically balanced flow with a small perturbation in the northern hemisphere.  This instability grows quickly, forming a realistic meandering jet stream and associated eddies.  Analysis of the results of this test case verified the correctness of the dynamical core’s software implementation of the energy consistent discretization.


    This research provides an energy-consistent discretization of the nonhydrostatic equations for use in global models of the Earth’s atmosphere.  The discretization was implemented in a new dynamical core for DOE’s Energy Exascale Earth System Model (E3SM).  The discretization is written in terms of standard variables in spherical coordinates and supports a wide variety of terrain-following vertical coordinates. It can be used with any horizontal discretization that has a discrete version of the integration-by-parts identity. The new discretization preserves the Hamiltonian structure of the original differential equations. It is coupled with mimetic numerical methods which leads to an energy consistent discretization. The discretization ensures no spurious sources of energy, resulting in improved stability and accuracy.



    • The U.S. Department of Energy Office of Science, Biological and Environmental Research supported this research as part of the Earth System Modeling Program Area through the Energy Exascale Earth System Model (E3SM) project.


    • Mark Taylor, Sandia National Laboratories
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