PUMA, Spectral Transform Dynamical Core of the Planet Simulator

Institution: University of Hamburg, Germany

Model Metadata

• Metadata Entry Form
• View Metadata

Description:

The Portable University Model of the Atmosphere (PUMA) is the dynamical core of the climate model PlanetSimulator [Fraedrich et al. 2005, Fraedrich 2012] and it is based on the multi-level spectral hydrostatic model described by Hoskins and Simmons (1975). Model fields are represented in terms of spherical harmonics subject to a triangular trunction and the spectral transform method enables an efficient calculation of nonlinear products [Orszag 1970 and Eliasen et. al 1970]. The model employs a semi-implicit time integration method for making the treatment fast gravity wave tendencies more efficient. The vertical coordinate is sigma (pressure divided by surface pressure) and the vertically discretized equations conserve total energy and mass.

Typical horizontal resolutions, physics and dynamics time steps, and dissipation coefficients:

PUMA uses spherical harmonics as basis functions. The truncation of the spectral representation is triangular at a maximum total wavenumber M (referred to as TM). The computational mode of the semi-implicit time integration scheme is damped by a Robert-Asselin filter using the filtering coefficient 0.02. 6th order hyperdiffusion prevents the emergence of Gibbs phenomena.

Information on the computational grid:

PUMA computes nonlinear products on a Gaussian grid. The number of longitudes results from the formula 3M+1 where M denotes the total wavenumber at which triangular truncation takes place. The figure shows the gridpoints for a triangular truncation at total wavenumber 85 (T85).

---

References:

• PUMA homepage

• Eliasen,E., B. Machenhauer, and E. Rasmussen,1970: On a Numerical Method for Integration of the Hydrodynamical Equations with a Spectral Representation of the Horizontal Fields. Inst. of Theor. Met. Univ. Copenhagen.
• Fraedrich, K., E. Kirk, U. Luksch, and F. Lunkeit, 2005: The Portable University Model of the Atmosphere (PUMA): Storm track dynamics and low frequency variability. Meteorol. Zeitschrift, 14, 735-745.
• Fraedrich, K., 2012: A suite of user-friendly global climate models: Hysteresis experiments. Eur. Phys. J. Plus, 127, 53, DOI 10.1140/epjp/i2012-12053-7.
• Hoskins, B.J., and A. J. Simmons, 1975: A multi-layer spectral model and the semi-implicit method. Quart. J. Roy. Meteor. Soc., 101, 637–655.
• Orszag, S. A., 1970: Transform Method for the Calculation of Vector-Coupled Sums: Application to the Spectral Form of the Vorticity Equation. J. Atmos. Sci. , 27, 890–895.

Name of the DCMIP Modeling Mentor: PUMA will be featured as a remotely-participating model. The model experiments will be conducted by Thomas Frisius at the University of Hamburg, Germany.