ROMS/TOMS European WorkshopROMS/TOMS European WorkshopMaison Jean Kuntzmann, Grenoble, FranceMaison Jean Kuntzmann, Grenoble, France

October 7, 2008October 7, 2008

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M o d e l i n g

ROMS Framework and AlgorithmsROMS Framework and Algorithms

Hernan G. ArangoHernan G. ArangoInstitute of Marine and Coastal SciencesInstitute of Marine and Coastal Sciences

Rutgers University, New Brunswick, NJ, USARutgers University, New Brunswick, NJ, USA

Outline

• Algorithms and Documentation Status

• The Good, The Bad, and The Ugly …

• Advection Operator

• Detiding Algorithm

• Observation Sensitivity

• Balance Operator

• Grid Nesting

The Good… The Bad… The Ugly…

Adjoint Nesting Adjoint Maintenance

Data Assimilation Open Boundaries ROMS Code Divergence

ESMF/MCT Coupling Advection Operator Compiler Bugs

Released Version 3.1 Monotonicity Treatment of Rivers

WikiROMS Documentation Documentation

Forum Activity Wetting and Drying

ROMS Blog Parallel IO

www.myroms.org Grid Generation

Frequent Releases Tutorials

Version Control Post-processing

Copyright/Open Source

Algorithms and Documentation Status

Advection Operator: North Atlantic (DAMEE_4)

Resolution 0.75x0.75 degrees

Grid 128x128x20

DX 40.8 - 95.8 km

DY 43.5 - 102.1 km

DT (5400, 200) sec

Bathymetry ETOPO-5

S-coordinates 5.0 and 0.4

Initial Conditions Levitus (1994), Feb

OBC Levitus (1994)

Forcing COADS, monthly

SSH, Year 10, Winter

Hadv Vadv Hmix

T,S C2 C4 0

u,v U3 C4 0

Hadv Vadv Hmix

T,S C2 C4 50, H-G

u,v U3 C4 0

Hadv Vadv Hmix

T,S U3 C4 0

u,v U3 C4 0

Advection Operator: GOM ¾° resolutionInitial (red) and 10-year (blue) T-S Diagram Curves

Hadv Vadv Hmix

T,S C4 C4 50, H-G

u,v U3 C4 0

Hadv Vadv Hmix

T,S C4 C4 2x1012,B-G

u,v C4 C4 8x1012,B-S

Hadv Vadv Hmix

T,S A4 A4 50, H-G

u,v U3 C4 0

Advection Operator: GOM ¾° resolutionInitial (red) and 10-year (blue) T-S Diagram Curves

Hadv Vadv Hmix

T,S MPDATA MPDATA 0

u,v U3 C4 0

Hadv Vadv Hmix

T,S U3-S U3-S Yes, B-G

u,v U3-S U3-S Yes, B-S

Hadv Vadv Hmix

T,S U3-S U3-S Yes, B-G

u,v U3 C4 0

Advection Operator: GOM ¾° resolutionInitial (red) and 10-year (blue) T-S Diagram Curves

Remarks

• There is excessive numerical, diapycnal mixing in the default

third-order, upstream-bias (U3) scheme.

• The second- and fourth-order centered differences schemes are

dispersive and overshoot.

• The MPDATA (Multidimensional Positive Definite Advection

Transport Algorithm) is monotonic and maintains the extrema.

However, there is some deep-water modification.

• The split schema (QUICK operator is split into advective and

diffusive components) is the best, showing few spurious maxima

and minima. However, the diffusion operator (along

geopotentials) has some stability problems that we need to

address.

ROMS Tides Least-Squares FitA ROMS state variable, , can be represented in terms of its time mean, , plus a set of -tidal harmonics of frequency, .

The unknowns , , and coefficients are evaluated by minimizing the least-squares error function defined by:

Minimization subject to the additional constraints , , result in a linear set of equations:

Least-Squares: Linear Equations System

Tidal Forcing NetCDF File

K1 (23.93 h) P1 (24.07 h) O1 (25.82 h) Q1 (26.87 h)

K2 (11.97 h) S2 (12.00 h) M2 (12.42 h) N2 (12.66 h)

Philippine Archipelago Tides: SSH Amplitude and Phase

B. Zhang

Remarks

• The detiding algorithm (AVERAGES_DETIDE) is working nicely.

• As the number of tidal constituents increases, the time needed

to resolve the beat frequencies increases. That is, the beat

period (sum of all frequencies) becomes longer.

• For example, if only M2 and S2 components are used, the beat

period is around 28-days (spring-neap cycle). Therefore we need

to run for a least 28 days to resolve the harmonic coefficients in

matrix A.

• I recommend you have a single NetCDF for tidal forcing and

save a copy before using the detiding option since this algorithm

add new variables to it.

PhilEx Real-Time Predictions

• ONR-DRI in the

Philippine Archipelago• Real-time forecasts to

support the PhilEx

Exploratory Cruise.• Coarse (~5 km) and

fine (~2 km) grid

resolution.• Initial and lateral

boundary conditions

from 1/12 HyCOM with

NCODA.• Forcing from NOGAPS

½, 3-hours forecast• Tides from global

OTPS model• Sequential 9-day

forecast cycles without

data assimilation

http://www.myroms.org/philex

Philippine Archipelago

Forecast Salinity at 10m

J. Levin

PhilEx 4DVar Assimilation: Salinity

J. Levin

PhilEx 4DVar Assimilation: Temperature

J. Levin

Observation Sensitivity Driver

Intra-America Sea (IAS)• Real-time forecasts

onboard the RCCL vessel Explorer of the Seas.

• Running continuously since January 17, 2007 to present. Fully automatic since end of February 2007.

• IS4DVAR, 14-day sequential data assimilation cycles.

• 50 ensembles members per week running on a4-CPUs Linux box.

• Observations:

• Satellite SST

• Satellite SSH

• Shipborne ADCP

http://www.myroms.org/ias

Arango, Di Lorenzo, Milliff, Moore, Powell, Sheinbaum

IAS 4DVar Observation Sensitivity: SSH

SSH observations SSH sensitivity

13-20 Apr 2007 13-20 Apr 2007

Arango, Moore, Powell

IAS 4DVar Observation Sensitivity: SST

13-20 Apr 2007 13-20 Apr 2007

SSH observations SSH sensitivity

Arango, Moore, Powell

Remarks

• We are still developing and fine tuning this algorithm

(OBS_SENSITIVITY).

• The mathematical formulation is similar to that of Zhu and

Gelaro (2008).

• It is a powerful tool to quantify the sensitivity of the IS4DVAR

system to the observations.

• It can help us to determine the type of measurements that need

to be made, where to observe, and when: Adapting Sampling.

IS4DVAR Balanced Operator Covariances: EAC

The cross-covariances are computed from a single sea surface height observation using multivariate physical balance relationships.

Free-surface(m)2

Temperature(Celsius)2

Salinity(nondimensional)2

U-velocity(m/s)2

V-velocity(m/s)2

Z = -300m Z = -300m Z = -300m Z = -300m

Arango, Moore, Zavala

IS4DVAR Balanced Operator Covariances: EAC

Free-surface(m)2

Temperature(Celsius)2

Salinity(nondimensional)2

U-velocity(m/s)2

V-velocity(m/s)2

The cross-covariances are computed from a single temperature observation at the surface using multivariate physical balance relationships.

Z = 0m Z = -300m Z = -300m Z = -300m

Arango, Moore, Zavala

IS4DVAR Balanced Operator Covariances: EAC

Free-surface(m)2

Temperature(Celsius)2

Salinity(nondimensional)2

U-velocity(m/s)2

V-velocity(m/s)2

The cross-covariances are computed from a single U-velocity observation at the surface using multivariate physical balance relationships.

Z = -300m Z = -300m Z = 0m Z = -300m

Arango, Moore, Zavala

Remarks

• We are still developing and fine tuning this algorithm

(BALANCE_OPERATOR).

• The approach is similar to that proposed by Weaver et al.

(2006).

• This is a multivariate approach to constraint the background and

model error covariances in the 4DVar system using linear

balance relationships (T-S empirical relationships, linear

equation of state, hydrostatic and geotrophic balances).

• It allows the unobserved variables information to be extracted

from directly observed quantities.

• State vector is split between balanced and unbalanced

components.

Nested Grids Types

Refinement

Mosaics

Composite

Arango, Warner

Grid

(ng)

Free-surface 2D Momentum 3D Momentum Tracers

West

East

No

rth S

ou

th W

est

East

No

rth S

ou

th W

est

East

No

rth S

ou

th W

est

East

No

rth S

ou

th

1

2

3

N: Nested C: Closed

F: Flather M: Clamped

G: Gradient P: Periodic

R: Radiation D: Reduced

H: Chapman

Nested Grids: Lateral Boundary Conditions

Arango, Warner

Grid

(ng)P* West East North South

1 0 2 0 0 0

2 1 0 1 0 0

3 1 1 1 1 1

* Who is your parent? To whom are you connected to on ______ boundary edge?

1

32

Nested Grid Connectivity

Arango, Warner