CSIRO Marine and Atmospheric Research VCAM: the variable-cubic atmospheric model John McGregor Centre for Australian Weather and Climate Research CSIRO/BOM,

CSIRO Marine and Atmospheric Research

VCAM: the variable-cubic atmospheric model

John McGregorCentre for Australian Weather and Climate Research

CSIRO/BOM, Melbourne

PDEs on the SpherePotsdam

26 August 2010


Outline

Formulation of CCAM

Formulation of VCAM

AMIP results and some comparisons


The conformal-cubic atmospheric model

• CCAM is formulated on the conformal-cubic grid

• Orthogonal• Isotropic

Example of quasi-uniform C48 grid with resolution about 200 km


CCAM dynamics• atmospheric GCM with variable resolution (using the Schmidt

transformation)• 2-time level semi-Lagrangian, semi-implicit• total-variation-diminishing vertical advection• reversible staggering

- produces good dispersion properties• a posteriori conservation of mass and moisture

CCAM physics

• cumulus convection:- CSIRO mass-flux scheme, including downdrafts- up to 3 simultaneous plumes permitted

• includes advection of liquid and ice cloud-water- used to derive the interactive cloud distributions (Rotstayn 1997)

• stability-dependent boundary layer with non-local vertical mixing• vegetation/canopy scheme (Kowalczyk et al. TR32 1994)

- 6 layers for soil temperatures- 6 layers for soil moisture (Richard's equation)

• enhanced vertical mixing of cloudy air• GFDL parameterization for long and short wave radiation• Skin temperatures for SSTs enhanced for sunny, low wind speeds


Location of variables in grid cellsAll variables are located atthe centres of quadrilateralgrid cells.

However, during semi-implicit/gravity-wave calculations, u and v are transformed reversibly to the indicated C-grid locations.

Produces same excellent dispersion properties asspectral method (see McGregor, MWR, 2006), but avoids any problems of Gibbs’ phenomena.

2-grid waves preserved. Gives relatively lively winds, and good wind spectra.


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

• gives periodic tridiagonal system - solved iteratively, or by cyclic tridiagonal solver

• excellent dispersion properties for gravity waves, as shown for the linearized shallow-water equations


Dispersion behaviour for linearized shallow-water equations

Typical atmosphere case Typical ocean case

N.B. the asymmetry of the R grid response disappears by alternating the reversing direction each time step,giving same response as Z (vorticity/divergence) grid


MPI performance

Runs on many platforms, including WindowsMostly use 1, 6, 12, 24 processorsbut can use 1, 2, 3, 4, 6, 12, 16, 18, 24, …

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


Conformal-cubic C48 grid used for Australian simulations, Schmidt = 0.3

Resolution over Australia is about 60 km


C48 8 km grid over New Zealand

C48 1 km grid over New Zealand

Grid configurations used to support Alinghi in America’s Cup: 60, 8, 1, kmDigital filter used to provide broadscale fields from prior coarser-resolution run.Successfully use similar procedure for regional climate modelling.

Schmidt transformation can be used to obtain very fine resolution


Original Sadourny C20 grid

Equi-angular C20 grid

Alternative gnomonic grids


Gnomonic grid showing orientation of the contravariant wind components

Illustrates the excellent suitability of the gnomonic grid for reversible interpolation – thanks to smooth changes of orientation


Solution procedure for VCAM

• In the following equations u, v denote wind components in the contravariant direction

• Components in the covariant direction are denoted by uT, vT

• u, vT are the stored variables as they are orthogonal (convenient for physics, displaying wind speed, etc.)

• uses flux form of primitive equations, with gravity-wave terms handled by forward-backward procedure, in conjunction with reversible staggering



Control volume notation for edge lengths and area

v

v

uus/m

s/m

s/m

s/m

Area =(s*s)/(m*m)

Have kept map factor notation but with this interpretation


Some time splitting details

Strang splitting(Almut Gassmann)

* Advection step, typically but not necessarily uses velocities at *


Solution procedure• Start loop

Start Nx(t/N) forward-backward loop Stagger (u, v) +n(t/N) Average ps to (psu, psv) +n(t/N) Calc (div, sdot, omega) +n(t/N) Calc (ps, T) +(n+1)(t/N) Calc phi and staggered pressure gradient terms, then unstagger these Including Coriolis terms, calc unstaggered (u, v) +(n+1)(t/N) End Nx(t/N) loop

• Perform TVD advection (of T, qg, Cartesian_wind_components) using average ps*u, ps*v, sdot from the N substeps

• Calculate physics contributions• End loop

Advection of u and v• As in the semi-Lagrangian advection of CCAM, the two u and v advection

equations are replaced by three equations advecting the corresponding Cartesian wind components uc, vc, wc

• Benefit is that uc, vc, wc are simple variables, essentially behaving as scalars• Then transform these back to u and v


Comparisons with semi-Lagrangian method of CCAM

Advantages• No Helmholtz equation needed• Includes full gravity-wave terms (no T linearization needed)• Mass and moisture conserving• More modular and “simpler”• No semi-Lagrangian resonance issues near steep mountains• Simpler MPI (“computation on demand” not needed) and runs faster

- also MPI results always identical to single processor

Disadvantages• Restricted to Courant number of 1, but OK since grid is very uniform• Some overhead from extra reversible staggering during sub time-steps

(done for Coriolis terms)• Non-hydrostatic version will take more effort


Results for AMIP runs• Unlike CCAM, VCAM

dynamics seems to require hybrid coordinates to reduce spurious oscillations near high terrain (esp. Andes).

• There are less oscillations in PMSL near terrain (top) when using hybrid coordinates for 1-month January runs, with all other settings the same

• Also a clear signal in monthly-averaged omega at 500 hPa (next slide)

hybrid

non-hybrid


500 hPa omega (Jan 1979)

hybrid

non-hybrid


hybrid VCAMCCAM

CCAM CCAM


AMIP 1979-95

CCAM

VCAM

Obs


AMIP 1979-95

CCAM

VCAM

Obs


AMIP 1979-95

CCAM

VCAM

Obs

VCAM rainfall may be better over tropical land masses


AMIP 1979-95

CCAM

VCAM

Obs


wind speeds at 250 hPa

CCAM

VCAM

CCAM

VCAM

DJF MAM

JJA SON


wind speeds top level (4 hPa)

CCAM

VCAM

CCAM

VCAM

DJF MAM

JJA SON


Remaining tasks

• Check extra wind rotation terms in advection (run HS?)

• Check top boundary conditions

• May be able to do Coriolis in “long” time steps

• Finish coding pre-processing and post-processing


Other plans

• Produce non-hydrostatic version

• Couple to PCOM (parallel cubic ocean model) of Motohiko Tsugawa from JAMSTEC


Thank you!

CSIRO Marine and Atmospheric Research VCAM: the variable-cubic atmospheric model John McGregor Centre for Australian Weather and Climate Research CSIRO/BOM,

Documents

csiro marine

atmospheric research

grid waves

climate research csirobom

r grid response

csiro massflux scheme

low wind speeds slide

good dispersion properties