Model Comparison and Model Comparison and Evaluation StudiesEvaluation Studies

Tal Ezer Tal Ezer (with H. Arango & A. Shchepetkin)(with H. Arango & A. Shchepetkin)

TOMS Inaugural Meeting, NCAR, Aug. 23, 2001

• Goal:Goal: to evaluate and test new numerical to evaluate and test new numerical elements in elements in terrain-following ocean models.terrain-following ocean models.

• Why: Why: to help developers in improving codes and to help developers in improving codes and users users in in selecting options and selecting options and parameterizations.parameterizations.

• How:How: by comparing different schemes and by comparing different schemes and parameterizations in POM and ROMS/TOMS.parameterizations in POM and ROMS/TOMS.

• Criteria:Criteria: numerical errors, accuracy, stability, numerical errors, accuracy, stability, compatibility between schemes, computational compatibility between schemes, computational

cost.cost.

Tested ElementsTested Elements

• Advection schemesAdvection schemes

• Time stepping algorithmsTime stepping algorithms

• Pressure gradient schemesPressure gradient schemes

• OthersOthers

Seamount configuration testSeamount configuration testVery steep case h=4050m, w=50km s=0.36, r=14.2

moderately steep h=2700m, w=100km s=0.07, r=2.7

S=max(H/2H)r=max(

grid=(64x64x20), x=8km

Zonal flowZonal flow

Topography Sea surface heightTopography Sea surface height

-50cm

0

+50cm

Effect of advection scheme on model: Surface elevation anomaly

AD

V4-

4th o

rd.

cn

t.A

DV

2-

2n

d o

rd.

cn

t.

AD

V3-

3rd

ord

. u

pst.

POM ROMS

ROMS ROMS

Time-stepping schemesTime-stepping schemes(split mode: baroclinic/internal and (split mode: baroclinic/internal and

barotropic/external)barotropic/external)

POMPOM ROMSROMS

schemescheme Leap-FrogLeap-Frog Predictor-Predictor-CorrectorCorrector

Time-splitting Time-splitting filterfilter

Weights:Weights:

(n-1, n, n+1)(n-1, n, n+1)

AsselinAsselin

((

Adams-MoultonAdams-Moulton

(-1/12, 2/3, (-1/12, 2/3, 5/12)5/12)

Internal-externalInternal-external

CouplingCouplingOnce every Once every internalinternal time time stepstep

Weighted, every Weighted, every externalexternal time time stepstep

Coupling of barotropic (external) and Coupling of barotropic (external) and baroclinic (internal) modes in ROMSbaroclinic (internal) modes in ROMS

DTI

Un+1 =

amUm

Un+½ = bm’Um’

DTE

weights

1<m<N, N=DTI/DTE

Sensitivity to internal (DTI) & external (DTE) time Sensitivity to internal (DTI) & external (DTE) time stepssteps

DTIDTI

DTEDTE180s180s 360s360s 540s540s 720s720s 900s900s 10801080

ss

8s8s 2222 4545 6767 9090 112112

12s12s 1515 3030 4545 6060 7575

16s16s 2222 3434 4545 5656

20s20s 1818 2727 3636 4545

24s24s 1515 2222 3030 3737

26s26s 1919 2525 3232

32s32s 1717 2222 2828

DTIDTI

DTEDTE180s180s 360s360s 540s540s 720s720s 900s900s 10801080

ss

8s8s 2222 4545 6767 9090

12s12s 1515 3030 4545 6060

16s16s 1111 2222 3434 4545

20s20s 99 1818 2727 3636

ROMS

POM

UNSTABLE

STABLE

TDI/DTE

CFL=13s

Computational cost for different Computational cost for different models & parameterizationsmodels & parameterizations

modemode

ll

featuresfeatures CPU (ms)/CPU (ms)/

(Im*Jm*Km*n)(Im*Jm*Km*n)CPU (s)/CPU (s)/

1 day1 day

22ndnd order cent. advection order cent. advection 12.512.5 21.321.3

22ndnd order upstream adv. order upstream adv.

Lin et al. (1994)Lin et al. (1994)13.213.2

POMPOM 33rdrd order upstream adv. order upstream adv.

Smolarkiewicz (1984)Smolarkiewicz (1984)17.117.1

66thth order PG (CPP) order PG (CPP)

Chu & Fan (1998)Chu & Fan (1998)207.4207.4

Z-lev. Interp. PG schemeZ-lev. Interp. PG scheme

Kliem & Pietrzak (1999)Kliem & Pietrzak (1999)40.040.0

22ndnd order cent. Adv. order cent. Adv. 17.317.3 21.621.6

ROMROMSS

44thth order cent. Adv. order cent. Adv. 19.219.2

33rdrd order upstream adv. order upstream adv. 20.020.0

The adjustment process in POM and The adjustment process in POM and ROMS: forced case (zonal flow)ROMS: forced case (zonal flow)

Roms- sensitivity of adjustment procesRoms- sensitivity of adjustment procesto time step choices to time step choices

DTE=12s

DTE=24s

DTI=360s DTI=720s

Pressure Gradient SchemesPressure Gradient SchemesSchemeScheme TypeType ReferenceReference

POM-DJPOM-DJ Standard Density Jacobian Standard Density Jacobian schemescheme

Mellor et al. (1998)Mellor et al. (1998)

POM-CCDPOM-CCD Combined Compact Combined Compact Difference scheme (6Difference scheme (6thth))

Chu & Fan (1997)Chu & Fan (1997)

ROMS-FPJROMS-FPJ Finite-Volume Pressure Finite-Volume Pressure Jacobian schemeJacobian scheme

Lin (1997)Lin (1997)

ROMS-DJROMS-DJ Weighted Density Jacobian Weighted Density Jacobian scheme (scheme (0)0)

Song (1998)Song (1998)

ROMS-WDJROMS-WDJ Weighted Density Jacobian Weighted Density Jacobian scheme (scheme (0.125)0.125)

Song (1998)Song (1998)

ROMS-PJQROMS-PJQ Pressure Jacobian scheme Pressure Jacobian scheme with Quadratic Polynomial with Quadratic Polynomial fitfit

Shchepetkin & Shchepetkin & McWilliams (2001)McWilliams (2001)

ROMS-DJCROMS-DJC Density Jacobian scheme Density Jacobian scheme with Cubic Polynomial fitwith Cubic Polynomial fit

Shchepetkin & Shchepetkin & McWilliams (2001)McWilliams (2001)

Structure ofStructure ofV (cm/s) in ROMS for different V (cm/s) in ROMS for different PG schemes (medium seamount case)PG schemes (medium seamount case)

R-DJ (Vmax=3.7)

R-WDJ (Vmax=0.3)

R-FPJ (Vmax=30)

R-PJQ (Vmax=0.03)

R-DJC (Vmax=0.06)

PG errors- moderately steep seamountPG errors- moderately steep seamount

More model elements and More model elements and schemes need to be testedschemes need to be tested

• Boundary conditionsBoundary conditions

• Data assimilationData assimilation

• Nesting and air-sea coupling Nesting and air-sea coupling

• Horizontal and vertical mixing Horizontal and vertical mixing schemesschemes

• Generalized coordinate system: Generalized coordinate system: comparisons between sigma, z-comparisons between sigma, z-level & isopycnal grids. level & isopycnal grids.