A COMPARISON OF SEMI-LAGRANGIAN AND EULERIAN POLAR CLIMATE SIMULATIONS

The differences in the polar lower-troposphere temperature simulated b y semi-Lagrangian and Eulerian approximations are examined and their c ause is identified. With grids having 8-10 layers below 500 mb, semi-L agrangian simulations are colder than Eulerian by 2-4 K in the region poleward of 60 degrees N and below 400 mb in winter. Diagnostic calcul ations with the NCAR CCM3 show that the semi-lagrangian dynamical appr oximations tend to produce a cooling relative to the Eulerian at the 8 60-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 lev el. The source of the difference is shown to be the different way the vertical advection approximations treat vertical structures found at t he tops of marginally resolved inversions when the vertical velocity i s reasonably vertically uniform surrounding the top of the inversion. The Eulerian approximations underestimate the cooling that should occu r at the top of the inversion. This is also verified with diagnostic c alculations on a grid with substantially increased resolution below 80 0 mb. On this grid, the adiabatic tendency differences between semi-la grangian and Eulerian approximations are small and the two approximati ons produce the same simulated lower-tropospheric temperature, which i s 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, th e 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.