1. Adjoint Sensitivity Stidues in the Philippine Archipelago Region –Julia Levin –Hernan Arango –Enrique Curchitser –Bin Zhang http://www.myroms.org/applications/philex/

2. 1.Understanding of the remote and local factors that control the meso- and submesoscale features in and around the Philippine Archipelago Straits 2.Improve our capability to predict the inherent spatial and temporal variability near the Philippine Straits Motivation

3. Outline Philippine model setup Preliminary model-data comparison Adjoint Sensitivity results Optimal Perturbations Discussion

4. Model Bathymetry: Nested Grids Regional Grid: 5 km grid spacing (200x250x42 points) Contour levels (m): -100 -150 -250 -500 -1000 -2000 -4000 -5000 Philippine Grid: 2 km grid spacing, (480x350x42 points) refined bathymetry

5. ROMS PhilEx 5-km grid and 2 km grid, 42 vertical layers Forcing: NOGAPS 1/2 deg 3 hourly atmospheric forcing, tides from global OTPS model Open boundaries: assimilative HYCOM 1/12 deg model No rivers Boundary Conditions: chapman for free surface, flather for barotropic velocity, clamped for 3d fields GLS mixing Model Setup

6. Salinity at 10 m depth

7. Exploratory Cruise (Jun 2007) Red line ship track

8. Comparison with CTD: Salinity

9. Comparison with CTD: Temperature

10. Consider the model state vector: Consider a function,, defined in terms of space and/or time integrals of. Small changes in will lead to changes in where: Define sensitivity as Can be proven that are solution of the adjoint system Adjoint Sensitivity

11. Motivation: identify observational strategy Cost function: transport through a cross section over the whole water column averaged over 5 day period. Adjoint Sensitivity: 1 2 3 1.Mindoro straight 2.Bohol straight 3.Surigao Straight 4.San Bernardino Straight 4

12. Variation in Transport through Different Straights AverageMaximum change due to transportBathy- metry Tempe- rature VelocityFree surface SalinityWind stress Mindoro0.8 Sv12%0.02%0.14%0.004%0.01%0.00008% Bohol0.1 Sv45%0.12%0.04%0.02% 0.0002% Surigao0.1 Sv32%0.02%0.12%0.02%0.01%0.00004% S. Ber- nardino 0.01 Sv100%0.2%0.4%0.06%0.04%0.0008% Maximum Standard deviation 100 m2.7 ˚C0.7 m/s0.2 m0.31 psu0.03

13. Transport Sensitivity to Bathymetry The plot shows adjoint bathymetry scaled by the difference between real and model bathymetry. Shows spacial distribution of the variation in the transport through four major straights due to bathymetry.

14. Transport sensitivity to velocity and temperature (Sv)

15. Optimal Perturbations Singular vectors of salinity at 5m depth, computed over 5 day period on the regional grid.

16. Optimal perturbations Singular vectors of salinity at 5m depth, computed over 5 day period on the philippine grid.

17. Adjoint sensitivity discussion Adjoint sensitivity analyzes linear problem. Results may depend on a particular time window. Adjoint Sensitivity results agree with optimal perturbation studies. Adjoint sensitivity gives an idea about how to allocate observational resources to observe certain features, while optimal perturbation identifies the fastest growing modes, that need to be controlled. Adjoint sensitivity can be used to identify cause and effect mechanisms for various processes quantitavily.

18. Next Steps Adjoint sensitivity: 1.Adjoint sensitivity of overflows 2.Flow above and below thermocline 3.Age and transient time (sensitivity of passive tracers), Data assimilation (IS4DVAR)