The CSIRO conformal-cubic atmospheric model: APE

simulations

April 2005

John McGregor and Martin Dix

CSIRO Atmospheric Research

Gnomonic-cubic grid and panelsSadourny (MWR, 1972)

Semi-Lagrangian advection study by McGregor (A-O, 1996)

Conformal-cubic grid Devised by Rancic et al., QJRMS 1996

C20 grid shows location of mass variables in CSIRO C-CAM model

Conformal-cubic C48 grid used for AMIP and APE simulations

Resolution is about 220 km

Features of C-CAM dynamics

• 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

Semi-Lagrangian horizontal advection

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).

~0.1 is an off-centering constant used to avoid mountain resonances.

TVD vertical advectionAdvocated 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.

Location of variables in grid cells

All variables are located atthe centres of grid cells.During semi-implicit/gravity-wave calculationsu and v are transformed tothe indicated C-grid locations.

Reversible staggering

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

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

Dispersion behaviour for linearized shallow-water equations

Typical atmosphere case Typical ocean case

Treatment of pressure-gradient terms

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.

Helmholtz solver

3-colour schemeused for solutionof Helmholtzequations

The semi-Lagrangian, semi-implicit method leads to a set ofHelmholtz 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.

a posteriori conservation• 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.

· 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

Physical parameterizations

Observed 1979-95 DJF rainfall

CCAM 1979-95 DJF rainfall CCAM 1979-95 JJA rainfall

AMIP simulation with quasi-uniform 220 km grid Observed 1979-95 JJA rainfall

MPI implementation by Martin Dix

Remapping of off-processor neighbour indices to buffer region

Original

Remapped

Preferred number of processors: 1, 2, 3, 4, 6, 12, 16, 18, 24, …

MPI performance

SX6 N Time Speedup1 30.1 1.02 17.2 1.83 12.2 2.66 7.2 4.5

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 5.512 12.3 10.316 10.6 12.024 6.6 19.354 3.7 34.0

Cherax – SGI Altix N Time Speedup 1 162.0 1.0 2 78.7 2.1 4 36.0 4.5 6 23.7 6.816 9.6 16.824 6.2 26.3

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

Malaysia Calcutta

Obs

C-CAM

Diurnal rainfall behaviour from 10-y RMIP run

Andaman Sea Bay of Bengal

Obs

C-CAM

Diurnal rainfall behaviour from 10-y RMIP run

Zonal winds – control & qobs

Zonal theta – control & qobs

Zonal SST and precip

Convective versus resolved precip

Note: convective fraction is largestadjacent to Equator (except for Flat and Control5N)

Control SST and precip (mm/day)

Peaked SST and precip

Qobs SST and precip

Flat SST and precip

Control5N SST and precip

1KEQ SST and precip

3KEQ SST and precip

3KW1 SST and precip

Hovmöller precip - control & qobs- get mainly westward propagation

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.

Diurnal plots of precip

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

1-month animations of precip

Convective precip mm/day

Total precip mm/day

ape_control_convective.avi ape_control_precip.avi