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A Comparison of Semi-Lagrangian and Eulerian Polar Climate Simulations

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

The differences in the polar lower-troposphere temperature simulated by semi-Lagrangian and Eulerian approximations are examined and their cause is identified. With grids having 8–10 layers below 500 mb, semi-Lagrangian simulations are colder than Eulerian by 2–4 K in the region poleward of 60°N and below 400 mb in winter. Diagnostic calculations with the NCAR CCM3 show that the semi-Lagrangian dynamical approximations tend to produce a cooling relative to the Eulerian at the 860-mb grid level. The difference occurs over land and sea ice where an inversion forms in the atmosphere with its top at the 860-mb grid level. The source of the difference is shown to be the different way the vertical advection approximations treat vertical structures found at the tops of marginally resolved inversions when the vertical velocity is reasonably vertically uniform surrounding the top of the inversion. The Eulerian approximations underestimate the cooling that should occur at the top of the inversion. This is also verified with diagnostic calculations on a grid with substantially increased resolution below 800 mb. On this grid, the adiabatic tendency differences between semi-Lagrangian and Eulerian approximations are small and the two approximations produce the same simulated lower-tropospheric temperature, which is also the same as that produced by the semi-Lagrangian approximations on the coarse grid. Compared to the NCEP reanalysis, the low vertical resolution Eulerian simulated temperature looks better than the semi-Lagrangian, but those approximations produce that “better” simulated temperature by an incorrect mechanism. For practical applications, the Eulerian approximations require higher vertical resolution below 800 mb than usually used today in climate models, but the semi-Lagrangian approximations are adequate on these coarser grids.

Corresponding author address: Dr. David L. Williamson, NCAR, P.O. Box 3000, Climate and Global Dynamics Division, Boulder, CO 80307-3000.

Email: wmson@ucar.edu

Abstract

The differences in the polar lower-troposphere temperature simulated by semi-Lagrangian and Eulerian approximations are examined and their cause is identified. With grids having 8–10 layers below 500 mb, semi-Lagrangian simulations are colder than Eulerian by 2–4 K in the region poleward of 60°N and below 400 mb in winter. Diagnostic calculations with the NCAR CCM3 show that the semi-Lagrangian dynamical approximations tend to produce a cooling relative to the Eulerian at the 860-mb grid level. The difference occurs over land and sea ice where an inversion forms in the atmosphere with its top at the 860-mb grid level. The source of the difference is shown to be the different way the vertical advection approximations treat vertical structures found at the tops of marginally resolved inversions when the vertical velocity is reasonably vertically uniform surrounding the top of the inversion. The Eulerian approximations underestimate the cooling that should occur at the top of the inversion. This is also verified with diagnostic calculations on a grid with substantially increased resolution below 800 mb. On this grid, the adiabatic tendency differences between semi-Lagrangian and Eulerian approximations are small and the two approximations produce the same simulated lower-tropospheric temperature, which is also the same as that produced by the semi-Lagrangian approximations on the coarse grid. Compared to the NCEP reanalysis, the low vertical resolution Eulerian simulated temperature looks better than the semi-Lagrangian, but those approximations produce that “better” simulated temperature by an incorrect mechanism. For practical applications, the Eulerian approximations require higher vertical resolution below 800 mb than usually used today in climate models, but the semi-Lagrangian approximations are adequate on these coarser grids.

Corresponding author address: Dr. David L. Williamson, NCAR, P.O. Box 3000, Climate and Global Dynamics Division, Boulder, CO 80307-3000.

Email: wmson@ucar.edu

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