Coastal Ocean Observation Lab

1
Coastal Ocean Modeling, Observation and Prediction
John Wilkin, Hernan Arango, Julia Levin,Javier
Zavala-Garay, Gordon Zhang Regional Ocean
Prediction Scott Glenn, Oscar Schofield, Bob
Chant Josh Kohut, Hugh Roarty, Josh Graver
Coastal Ocean Observation Lab Janice McDonnell
Education and Outreach
Regional Ocean Prediction http//marine.rutgers.e
du/po
Coastal Ocean Observation Lab http//marine.rutger
s.edu/cool
Education Outreach http//coolclassroom.org
Coastal Observation and Prediction Sponsors
2
Integrating Ocean Observing and Modeling Systems
for SW06 Analysis and Forecasting
Coastal Ocean Observation Labhttp//marine.rutger
s.edu/cool/sw06/sw06.htm
Regional Ocean Modeling and Predictionhttp//mari
ne.rutgers.edu/po/sw06

• ROMS model embedded in NCOM or climatology
• WRF and NCEP forcing rivers
• 2-day cycle IS4DVAR assimilation

• gliders and CODAR
• satellite SST, bio-optics
• high-res regional WRF atmospheric forecast
• SW06 ship-based obs.

• Model-based re-analysis of submesoscale ocean
  state
• ROMS/IS4DVAR assimilation plus CODAR,
  Scanfish, moorings, CTDs
• high-res nesting in SW06 center
• ensemble simulations uncertainty instability,
  sensitivity analysis, optimal observations
• Weekly/monthly bulletin ?

3
Regional Ocean Modeling and Predictionfor
Shallow Water 2006

• Rutgers Ocean Modeling and Prediction Group for
  SW06
• Hernan Arango
• John Evans
• Naomi Fleming
• Gregg Foti
• Julia Levin
• John Wilkin
• Javier Zavala-Garay
• Gordon Zhang
• http//marine.rutgers.edu/po/sw06

4
Outline

• Strong constraint 4-dimensional variational data
  assimilation
• some math
• how it works
• SW06 configuration
• some results
• Next steps
• SW06 reanalysis
• Algorithmic tuning, more data, higher resolution
• ensemble simulations
• Forecast and analysis uncertainty and
  predictability
• observing system design

5
Notation

• ROMS state vector
• NLROMS equation form
• 
  
  (1)
• NLROMS propagator form
• Observation at time with observation
  error variance
• Model equivalent at observation points
• Unbiased background state with background
  error covariance

6
Strong constraint 4DVAR
Talagrand
Courtier, 1987, QJRMS, 113, 1311-1328

• Seek that minimizes
• subject to equation (1) i.e., the model dynamics
  are imposed as a strong constraint.
• depends only on
• control variables
• Cost function as function of control variables
• J is not quadratic since M is nonlinear.

7
S4DVAR procedure

• Lagrange function
• 
  
  Lagrange multiplier
• At extrema of , we require
• S4DVAR procedure
• Choose an
• Integrate NLROMS and compute J
• Integrate ADROMS to get
• Compute
• Use a descent algorithm to determine a down
  gradient correction to that will yield
  a smaller value of J

8
xb model state at end of previous cycle, and
1st guess for the next forecast In 4D-VAR
assimilation the adjoint model computes the
sensitivity of the initial conditions to
mis-matches between model and data A descent
algorithm uses this sensitivity to iteratively
update the initial conditions, xa, to minimize
Jb S(Jo)
0 1 2 3
4 time
Observations minus Previous Forecast
Adjoint model integration is forced by the
model-data error
dx
9
Incremental Strong Constraint 4DVAR

(Courtier et al, 1994, QJRMS, 120,
1367-1387
Weaver et al,
2003, MWR, 131, 1360-1378 )

• True solution
• NLROMS solution from Taylor series
• ---- TLROMS Propagator
• Cost function is quadratic now

10
Basic IS4DVAR procedureIncremental Strong
Constraint 4-Dimensional Variational Assimilation

• Choose an
• Integrate NLROMS and save
• (a) Choose a
• (b) Integrate TLROMS
  and compute J
• (c) Integrate ADROMS
  to yield
• (d) Compute
• (e) Use a descent algorithm to
  determine a down gradient correction
  to that will yield a smaller value
  of J
• (f) Back to (b) until converged
• (3) Compute new
  and back to (2) until converged

11
Basic IS4DVAR procedureIncremental Strong
Constraint 4-Dimensional Variational Assimilation

• Choose an
• Integrate NLROMS and save
• (a) Choose a
• (b) Integrate TLROMS
  and compute J
• (c) Integrate ADROMS
  to yield
• (d) Compute
• (e) Use a descent algorithm to
  determine a down gradient correction
  to that will yield a smaller value
  of J
• (f) Back to (b) until converged
• (3) Compute new
  and back to (2) until converged

12
Conjugate Gradient Descent

(Long Thacker, 1989, DAO, 13,
413-440)

• Expand step (5) in S4DVAR procedure and step (e)
  in IS4DVAR procedure
• Two central component (1) step size
  determination (2) pre-conditioning (modify the
  shape of J )
• New NLROMS initial condition
  ----
  step-size (scalar)
• ---- descent direction
• Step-size determination
• (a) Choose arbitrary step-size and compute
  new , and
• (b) For small correction, assume the
  system is linear, yielded by any step-size
  is
• (c) Optimal choice of step-size is the
  who gives
• Preconditioning
• 
  define

13
Background Error Covariance Matrix (Weaver
Courtier, 2001, QJRMS, 127, 1815-1846 Derber
Bouttier, 1999, Tellus, 51A, 195-221)

• Split B into two parts
• (1) unbalanced component Bu
• (2) balanced component Kb
• Unbalanced component
  ---- diagonal matrix of background error standard
  deviation
• ---- symmetric matrix of
  background error correlation
• for preconditioning,
• Use diffusion operator to get C1/2
• assume Gaussian error statistics, error
  correlation
  
• the solution of diffusion equation
  over the interval
  with is
• ---- the
  solution of diffusion operator

14
(No Transcript)
15
The adjoint solution gives sensitivity of SST in
the marked area to SST over the a 5-day
assimilation interval for steady downwelling and
upwelling winds
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
SW06 Model Domains
ROMS LATTE outer boundary
ROMS SW06 outer boundary
Harvard Box (100kmx100km)
20

• ROMS SW06
• 5-km grid for IS4DVAR testing
• Forcing
• NCEP-NAM and WRF USGS Hudson River OTPS
  tides
• Open boundaries NCOM and LG climatology
• 2-day assimilation cycle
• 20-km horizontal and 5-m vertical length scales
  in background error covariance
• Data
• gliders, CTDs, XBTs, Knorr thermosalinograph,
  daily best-SST composite, AVISO SSH

21
(No Transcript)
22
Salt 5m
Salt 30m
Temp 30m
23
(No Transcript)
24
(No Transcript)
25
Forecast skill in 2-day interval when initial
conditions are adjusted using IS4DVAR
Simple forecast No data assimilation
26
Mesoscale prediction test caseEast Australian
Current

• IS4DVAR assimilation
• daily SST (CSIRO)
• SSH (AVISO)
• VOS XBT Tasman Sea
• Javier Zavala-Garay
• John Wilkin
• Hernan Arango

• Adjoint adjusts all state variables, not just
  those observed
• Singular vectors of the tangent linear model give
  most unstable modes of variability
• Optimal perturbations for ensemble simulation
• Predictability limits

27
East Australian Current
28
(No Transcript)
29
East Australian Current Color ensemble mean.
Contours individual ensemble members. Black SSH
observations
Assimilating SSHSSTXBT
Assimilating SSHSST
30
Optimal Perturbation Analysis
Vertical Structure of SV1
Perturbation after 10 days
Singular Vector 1
After assim. SSHSSTXBT
After assim SSHSST
31
(No Transcript)
32
Now what ?

• SW06 reanalysis of sub-mesoscale ocean state
• IS4DVAR algorithmic tuning
• forecast cycle length background error
  covariance (preconditions
  conjugate gradient search)
• More data
• CODAR, moorings, shipboard ADCP
• Higher resolution
• Ensemble simulations
• forecast skill quantify predictability analysis
  uncertainty
• MURI COMOP
• Observing system design
• Physics information

33
Mixing of the Hudson and Raritan Rivers
Visible RGB
Detritus Absorption
PhytoplanktonAbsorption
SeaWiFS chlorophyll