ROMS/TOMS European Workshop Maison Jean Kuntzmann, Grenoble, France October 7, 2008

1. ROMS Framework and Algorithms Hernan G. Arango Institute of Marine and Coastal Sciences Rutgers University, New Brunswick, NJ, USA ROMS/TOMS European Workshop Maison Jean Kuntzmann, Grenoble, France October 7, 2008

2. Outline • Algorithms and Documentation Status • The Good, The Bad, and The Ugly … • Advection Operator • Detiding Algorithm • Observation Sensitivity • Balance Operator • Grid Nesting

3. Algorithms and Documentation Status

4. Advection Operator: North Atlantic (DAMEE_4) SSH, Year 10, Winter

5. Advection Operator: GOM ¾° resolution Initial (red) and 10-year (blue) T-S Diagram Curves

6. Advection Operator: GOM ¾° resolution Initial (red) and 10-year (blue) T-S Diagram Curves

7. Advection Operator: GOM ¾° resolution Initial (red) and 10-year (blue) T-S Diagram Curves

8. 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.

9. ROMS Tides Least-Squares Fit A 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:

10. Least-Squares: Linear Equations System

11. Tidal Forcing NetCDF File

12. K2 (11.97 h) S2 (12.00 h) M2 (12.42 h) N2 (12.66 h) K1 (23.93 h) P1 (24.07 h) O1 (25.82 h) Q1 (26.87 h) Philippine Archipelago Tides: SSH Amplitude and Phase B. Zhang

13. 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.

14. 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

15. Philippine Archipelago Forecast Salinity at 10m J. Levin

16. PhilEx 4DVar Assimilation: Salinity J. Levin

17. PhilEx 4DVar Assimilation: Temperature J. Levin

18. Observation Sensitivity Driver

19. 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 a • 4-CPUs Linux box. • Observations: • Satellite SST • Satellite SSH • Shipborne ADCP http://www.myroms.org/ias Arango, Di Lorenzo, Milliff, Moore, Powell, Sheinbaum

20. IAS 4DVar Observation Sensitivity: SSH SSH sensitivity SSH observations 13-20 Apr 2007 13-20 Apr 2007 Arango, Moore, Powell

21. IAS 4DVar Observation Sensitivity: SST SSH sensitivity SSH observations 13-20 Apr 2007 13-20 Apr 2007 Arango, Moore, Powell

22. 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.

23. 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 Z = -300m Z = -300m Z = -300m Z = -300m The cross-covariances are computed from a single sea surface height observation using multivariate physical balance relationships. Arango, Moore, Zavala

24. 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 Z = 0m Z = -300m Z = -300m Z = -300m The cross-covariances are computed from a single temperature observation at the surface using multivariate physical balance relationships. Arango, Moore, Zavala

25. 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 Z = -300m Z = -300m Z = 0m Z = -300m The cross-covariances are computed from a single U-velocity observation at the surface using multivariate physical balance relationships. Arango, Moore, Zavala

26. 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.

27. Nested Grids Types Refinement Composite Mosaics Arango, Warner

28. Nested Grids: Lateral Boundary Conditions Arango, Warner

29. Nested Grid Connectivity 3 2 1 * Who is your parent? To whom are you connected to on ______ boundary edge? Arango, Warner