A Comparison of Primitive-Equation and Semigeostrophic Simulations of Baroclinic Waves

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

In the course of adapting a nonhydrostatic cloud model [or primitive-equation model (PE)] for simulations of large-scale baroclinic waves, we have encountered systematic discrepancies between the PE solutions and those of the semigeostrophic (SG) equations. Direct comparisons using identical, uniform potential vorticity jets show that 1) the linear modes of the PE have distinctively different structure than the SG modes; 2) at finite amplitude, the PE pressure field develops lows that are deeper, and highs that are weaker, than in the SG solution; and 3) the nonlinear PE wave produces a characteristic “cyclonic wrapping” of the temperature contours on both horizontal boundaries and has an associated “bent-back” frontal structure at the surface, while in the SG solutions (for this particular basic state jet) there is an equal tendency to pull temperature contours anticyclonically around highs and cyclonically around lows. An analysis of the vorticity and potential vorticity equations for small Rossby number reveals that the SG model errs in its treatment of terms involving the ageostrophic vorticity. Simulations based on an equation set that includes the leading-order dynamical contributions of the ageostrophic vorticity agree more closely with the PE simulations.

Abstract

In the course of adapting a nonhydrostatic cloud model [or primitive-equation model (PE)] for simulations of large-scale baroclinic waves, we have encountered systematic discrepancies between the PE solutions and those of the semigeostrophic (SG) equations. Direct comparisons using identical, uniform potential vorticity jets show that 1) the linear modes of the PE have distinctively different structure than the SG modes; 2) at finite amplitude, the PE pressure field develops lows that are deeper, and highs that are weaker, than in the SG solution; and 3) the nonlinear PE wave produces a characteristic “cyclonic wrapping” of the temperature contours on both horizontal boundaries and has an associated “bent-back” frontal structure at the surface, while in the SG solutions (for this particular basic state jet) there is an equal tendency to pull temperature contours anticyclonically around highs and cyclonically around lows. An analysis of the vorticity and potential vorticity equations for small Rossby number reveals that the SG model errs in its treatment of terms involving the ageostrophic vorticity. Simulations based on an equation set that includes the leading-order dynamical contributions of the ageostrophic vorticity agree more closely with the PE simulations.

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