U. S. Navy Fleet Numerical Weather Central Operational Five-Level Global Fourth-Order Primitive-Equation Model

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  • 1 Fleet Numerical Weather Central, Monterey, Calif. 93940
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Abstract

The U. S. Navy Fleet Numerical Weather Central (FNWC) operational, global, primitive-equation model (GPEM) is described. It is an extension of the Northern Hemisphere model (NHPEM) described by Kesel and Winninghoff. The GPEM uses a staggered, spherical, sigma-coordinate system with real input data which is interpolated to the sigma surfaces. The streamfunction obtained from the solution of the full balance equation is used to determine the initial velocity field. Fourth-order spatial differencing and centered time differencing are used for all the cases described in this paper. In addition to Euler-backward differencing, a combination of Arakawa's Fourier frequency-amplitude modification scheme and three-point method is used to maintain computational stability at each latitude ring. The calculations of the heating and moisture, source-sink terms and friction in the present version of the GPEM are quite similar to the NHPEM. The only substantial change in these computations involves the parameterization of the planetary boundary layer.

The selection of the numerical procedures for the GPEM was based upon four experimental cases: 1) determination of the basic stable time step; 2) use of the Shuman pressure gradient term averaging to allow a longer time step than the one given by the Courant-Friedrichs-Lewy condition; 3) use of Shuman pressure gradient averaging with Robert time filtering to control high-frequency oscillations; and 4) elimination of the Euler-backward time step to control solution separation. A 33% increase in the time step and the removal of the Euler-backward time step, except for the initial time step, has been achieved thus far.

Abstract

The U. S. Navy Fleet Numerical Weather Central (FNWC) operational, global, primitive-equation model (GPEM) is described. It is an extension of the Northern Hemisphere model (NHPEM) described by Kesel and Winninghoff. The GPEM uses a staggered, spherical, sigma-coordinate system with real input data which is interpolated to the sigma surfaces. The streamfunction obtained from the solution of the full balance equation is used to determine the initial velocity field. Fourth-order spatial differencing and centered time differencing are used for all the cases described in this paper. In addition to Euler-backward differencing, a combination of Arakawa's Fourier frequency-amplitude modification scheme and three-point method is used to maintain computational stability at each latitude ring. The calculations of the heating and moisture, source-sink terms and friction in the present version of the GPEM are quite similar to the NHPEM. The only substantial change in these computations involves the parameterization of the planetary boundary layer.

The selection of the numerical procedures for the GPEM was based upon four experimental cases: 1) determination of the basic stable time step; 2) use of the Shuman pressure gradient term averaging to allow a longer time step than the one given by the Courant-Friedrichs-Lewy condition; 3) use of Shuman pressure gradient averaging with Robert time filtering to control high-frequency oscillations; and 4) elimination of the Euler-backward time step to control solution separation. A 33% increase in the time step and the removal of the Euler-backward time step, except for the initial time step, has been achieved thus far.

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