model comparison and evaluation studies tal ezer (with h. arango & a. shchepetkin) toms...
DESCRIPTION
Tested Elements Advection schemes Advection schemes Time stepping algorithms Time stepping algorithms Pressure gradient schemes Pressure gradient schemes Others OthersTRANSCRIPT
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
ADV4
- 4th o
rd. c
nt.
ADV2
- 2nd
ord
. cnt
.
ADV3
- 3rd
ord
. up
st.
POM ROMS
ROMS ROMS
Time-stepping schemesTime-stepping schemes(split mode: baroclinic/internal and (split mode: baroclinic/internal and
barotropic/external)barotropic/external)
POMPOM ROMSROMSschemescheme Leap-FrogLeap-Frog Predictor-Predictor-
CorrectorCorrectorTime-splitting Time-splitting
filterfilterWeights: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-externalCouplingCoupling
Once 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
DTIDTIDTEDTE
180s180s 360s360s 540s540s 720s720s 900s900s 10801080ss
8s8s 2222 4545 6767 9090 11211212s12s 1515 3030 4545 6060 757516s16s 2222 3434 4545 565620s20s 1818 2727 3636 454524s24s 1515 2222 3030 373726s26s 1919 2525 323232s32s 1717 2222 2828
DTIDTIDTEDTE
180s180s 360s360s 540s540s 720s720s 900s900s 10801080ss
8s8s 2222 4545 6767 909012s12s 1515 3030 4545 606016s16s 1111 2222 3434 454520s20s 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 21.321.322ndnd 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 schemeKliem & Pietrzak (1999)Kliem & Pietrzak (1999)
40.040.0
22ndnd order cent. Adv. order cent. Adv. 17.317.3 21.621.6ROMROM
SS44thth 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 ReferenceReferencePOM-DJPOM-DJ Standard Density Jacobian Standard Density Jacobian
schemeschemeMellor 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.