Adjoint Sensitivity Stidues in the Philippine Archipelago Region

– Julia Levin– Hernan Arango– Enrique Curchitser– Bin Zhang

http://www.myroms.org/applications/philex/

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

Outline

• Philippine model setup

• Preliminary model-data comparison

• Adjoint Sensitivity results

• Optimal Perturbations

• Discussion

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

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

Salinity at 10 m depth

Exploratory Cruise (Jun 2007)

Red line ship track

Comparison with CTD: Salinity

Comparison with CTD: Temperature

• 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( , , , , )Tu v T S

( )J

J

J J J J JJ u v T S

u v T S

† † †, , , etcJ J J

u v Tu v T

J

† † † † † †( , , , , )Tu v T S

Motivation: identify observational strategy

Cost function: transport through a cross section over the whole water column averaged over 5 day period.

Adjoint Sensitivity:

1u n dVdt

T

1

2

3

1. Mindoro straight

2. Bohol straight

3. Surigao Straight

4. San Bernardino Straight

4

Variation in Transport through Different Straights

Average Maximum change due to

transport Bathy-metry

Tempe-rature

Velocity Free surface

Salinity Wind stress

Mindoro 0.8 Sv 12% 0.02% 0.14% 0.004% 0.01% 0.00008%

Bohol 0.1 Sv 45% 0.12% 0.04% 0.02% 0.02% 0.0002%

Surigao 0.1 Sv 32% 0.02% 0.12% 0.02% 0.01% 0.00004%

S. Ber-nardino 0.01 Sv 100% 0.2% 0.4% 0.06% 0.04% 0.0008%

Maximum Standard deviation

100 m 2.7 ˚C 0.7 m/s 0.2 m 0.31 psu 0.03

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.

Transport sensitivity to velocity and temperature (Sv)

Optimal Perturbations

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

Optimal perturbations

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

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.

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)