The CSIRO conformal-cubic atmospheric model: APE simulations

1. The CSIRO conformal-cubic atmospheric model: APE simulations John McGregor and Martin Dix CSIRO Atmospheric Research April 2005

2. Gnomonic-cubic grid and panels Sadourny (MWR, 1972) Semi-Lagrangian advection study by McGregor (A-O, 1996)

3. Conformal-cubic gridDevised by Rancic et al., QJRMS 1996 C20 grid shows location of mass variables in CSIRO C-CAM model

4. Conformal-cubic C48 grid used for AMIP and APE simulations Resolution is about 220 km

5. 2-time level semi-Lagrangian, semi-implicit total-variation-diminishing vertical advection reversible staggering has very good dispersion properties a posteriori conservation of mass and moisture Features of C-CAM dynamics

6. Method is illustrated for the T equation Vertical advection is evaluated separately in a split manner at the beginning and end of each time step. Remainder of equation is evaluated along the trajectory Values at the departure points are found using bi-cubic interpolation (McGregor, MWR,1996). e ~0.1 is an off-centering constant used to avoid mountain resonances. Semi-Lagrangian horizontal advection

7. Advocated by Thuburn (1993). The TVD method combines low-order (upstream) and high-order fluxes, using a flux-limiter C, Non-negative and conserving (for equations expressed in flux form). Uses the monotonized centred (MC) flux-limiter (Van Leer, 1977) where r is a smoothness variable, calculated from the advected field. Find in C-CAM that TVD handles tropopause temperature gradients much better than semi-Lagrangian vertical advection. TVD vertical advection

8. Location of variables in grid cells All variables are located at the centres of grid cells. During semi-implicit/ gravity-wave calculations u and v are transformed to the indicated C-grid locations.

9. Where U is the unstaggered velocity component and u is the staggered value, define (Vandermonde formula) accurate at the pivot points for up to 4th order polynomials solved iteratively, or by cyclic tridiagonal solver excellent dispersion properties for gravity waves, as determined from the linearized shallow-water equations Reversible staggering

10. Transformation of 2, 3, 4, 6-grid waves

11. Dispersion behaviour for linearized shallow-water equations Typical atmosphere case Typical ocean case

12. The reversible staggering technique allows a consistent, accurate calculation of pressure gradient terms. For example, in the staggered u equation the RHS pressure gradient term is first evaluated at the staggered position, then transformed to the unstaggered position for calculation of the whole RHS advected value on the unstaggered grid. That whole term is then transformed to the staggered grid, fully consistent with the subsequent implicit evaluation of the LHS on the staggered grid. Treatment of pressure-gradient terms

13. The semi-Lagrangian, semi-implicit method leads to a set of Helmholtz equations for each of the vertical modes, on a 5-point stencil. The Helmholtz equations are usually solved by simple successive over-relaxation. A vectorized solution is achieved by solving successively on each of the following 3 sets of sub-grids. A conjugate-gradient solver is also available. Helmholtz solver 3-colour scheme used for solution of Helmholtz equations

14. a posteriori conservation of mass and moisture “global” scheme simultaneously ensures non-negative values during each time step applies correction to changes occurring during dynamics (including advection) correction is proportional to the “dynamics” increment, but the sign of the correction depends on the sign of the increment at each grid point. a posteriori conservation

15. Physical parameterizations · cumulus convection: -new CSIRO mass-flux scheme, including downdrafts - N.B. runs for APE use relatively large settings for entrainment and detrainment, increasing the fraction of resolved tropical rainfall. · includes advection of liquid and ice cloud-water -used to derive the interactive cloud distributions · stability-dependent boundary layer and vertical mixing with non-local option - enhanced vertical mixing of cloudy air (replaces shallow convection) · GFDL parameterization for long and short wave radiation · NO horizontal diffusion (apart from that inherent in SL advection) - gravity-wave drag scheme · diurnally varying skin temperatures for SSTs (not done for APE runs) N.B. the APE simulations started from an interpolated restart file of an AMIP run

16. AMIP simulation with quasi-uniform 220 km grid Observed 1979-95 JJA rainfall Observed 1979-95 DJF rainfall CCAM 1979-95 DJF rainfall CCAM 1979-95 JJA rainfall

17. MPI implementation by Martin Dix Remapped Original Remapping of off-processor neighbour indices to buffer region Preferred number of processors: 1, 2, 3, 4, 6, 12, 16, 18, 24, …

18. APAC SC N Time Speedup 1 127.1 1.0 2 65.0 2.0 3 44.6 2.9 4 34.7 3.7 6 23.0 5.5 12 12.3 10.3 16 10.6 12.0 24 6.6 19.3 54 3.7 34.0 MPI performance Cherax – SGI Altix N Time Speedup 1 162.0 1.0 2 78.7 2.1 4 36.0 4.5 6 23.7 6.8 16 9.6 16.8 24 6.2 26.3 SX6 N Time Speedup 1 30.1 1.0 2 17.2 1.8 3 12.2 2.6 6 7.2 4.5

19. Xie-Arkin Precip for JJA Xie-Arkin Precip for DJF 10-y C-CAM/RMIP2 Precip for JJA 10-y C-CAM/RMIP2 Precip for DJF

20. Diurnal rainfall behaviour from 10-y RMIP run Obs C-CAM Calcutta Malaysia

21. Diurnal rainfall behaviour from 10-y RMIP run Obs C-CAM Bay of Bengal Andaman Sea

22. Zonal winds – control & qobs

23. Zonal theta – control & qobs

24. Zonal SST and precip

25. Convective versus resolved precip Note: convective fraction is largest adjacent to Equator (except for Flat and Control5N)

26. Control SST and precip (mm/day)

27. Peaked SST and precip

28. Qobs SST and precip

29. Flat SST and precip

30. Control5N SST and precip

31. 1KEQ SST and precip

32. 3KEQ SST and precip

33. 3KW1 SST and precip

34. Hovmöller precip - control & qobs- get mainly westward propagation

35. Balances of P-E and UV P-E vs convergence of the atmospheric moisture flux. Diffs may be due to SL diffusion Surface stress vs convergence of the atmospheric momentum flux.

36. Diurnal plots of precip Local time of precip is derived from zonal mean of 6-hourly output for each grid point

37. 1-month animations of precip Convective precip mm/day Total precip mm/day