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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Volume 11, issue 11
Geosci. Model Dev., 11, 4637-4656, 2018
https://doi.org/10.5194/gmd-11-4637-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Geosci. Model Dev., 11, 4637-4656, 2018
https://doi.org/10.5194/gmd-11-4637-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Development and technical paper 22 Nov 2018

Development and technical paper | 22 Nov 2018

Symmetric equations on the surface of a sphere as used by model GISS:IB

Gary L. Russell1, David H. Rind1, and Jeffrey Jonas2 Gary L. Russell et al.
  • 1NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA
  • 2Center for Climate Research, Columbia University, New York, NY 10025, USA

Abstract. Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north–south axis) and a specific angular momentum component that is the product of the velocity component multiplied by the cosine of axis' latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain. Model results are presented for three different initial conditions and five different resolutions.

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This paper presents the Fortran 90 source code for one-layer model GISS:IB on an icosahedral grid. The model solves the shallow water equations on the sphere using three symmetric horizontal components of angular momentum instead of velocity. One-layer shallow water models are a basic building block used in complex global weather and climate models.
This paper presents the Fortran 90 source code for one-layer model GISS:IB on an icosahedral...
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