Adjoint Sensitivity Stidues in the Philippine
Archipelago Region
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Julia Levin
Hernan Arango
Enrique Curchitser
Bin Zhang
http://www.myroms.org/applications/philex/
Motivation
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
Outline
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•
•
•
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Philippine model setup
Preliminary model-data comparison
Adjoint Sensitivity results
Optimal Perturbations
Discussion
Model Bathymetry: Nested Grids
Philippine Grid: 2 km grid spacing,
(480x350x42 points) refined bathymetry
Regional Grid: 5 km grid spacing
(200x250x42 points)
Contour levels (m): -100 -150 -250 -500 -1000 -2000 -4000 -5000
Model Setup
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
Salinity at 10 m depth
Exploratory Cruise (Jun 2007)
Red line ship track
Comparison with CTD: Salinity
Comparison with CTD: Temperature
Adjoint Sensitivity
• Consider the model state vector:
  (u, v, T , S ,  )T
• Consider a function, J ( ), defined in terms of space
and/or time integrals of  .
• Small changes
where:
 in  will lead to changes  J in J
 J 
 J 
 J 
 J 
 J 
 J     u     v     T     S    
 u 
 v 
 T 
 S 
  
J  †  J  †  J 

†
• Define sensitivity as u    , v    , T  
 , etc
 u 
 v 
 T 
• Can be proven that 
of the adjoint system
†
 (u , v , T , S ,  ) are solution
†
†
†
†
† T
Adjoint Sensitivity:
Motivation: identify observational strategy
4
Cost function: transport through a cross
section over the whole water column
averaged over 5 day period.
1
3
2
1
T
u

n
dVdt

1. Mindoro straight
2. Bohol straight
3. Surigao Straight
4. San Bernardino
Straight
Variation in Transport
through Different Straights
Average
Maximum change due to
transport
Bathymetry
Temperature
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. Bernardino
0.01 Sv
100%
0.2%
0.4%
0.06%
0.04%
0.0008%
100 m
2.7 ˚C
0.7 m/s
0.2 m
0.31 psu
0.03
Maximum
Standard
deviation
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
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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)