Accomplishments:

1
ROMS data assimilation for ESPreSSO
Accomplishments
Nested ROMS in larger domain forward
simulation (MABGOM-ROMS) with configuration
suitable for IS4DVAR experimentation.
Considerations boundary conditions, resolution,
computational cost IS4DVAR implemented in
Slope Sea and MAB shelf waters, assimilating SST
and along-track altimeter sea level anomaly
(SLA). Considerations tune IS4DVAR
horizontal/vertical de-correlation scales,
duration of assimilation window, data
preprocessing (error statistics, aliasing, mean
dynamic topography). Used withheld data
to evaluate how well adjoint propagates
information between variables, and in space and
time.
2
ROMS data assimilation for ESPreSSO
Accomplishments

• Full IS4DVAR reanalysis of NJ
  inner/mid-shelf for LaTTE using all data from
  CODAR, 2 gliders, moored current-meters and T/S,
  towed SeaSoar CTD, and satellite SST
• Developed adjoint-based analysis methods for
  observing system design and evaluation
• Have an ESPreSSO ROMS system ready for
  expansion to
• 2006-2008 reanalysis of ocean physics
• introduction of in situ physical data into
  reanalysis
• analyze impact of improved physics on ecosystem
  model
• adjoint/tangent-linear simple optical model,
  with IS4DVAR

3
Mid-Atlantic Bight ROMS Model for ESPreSSO/IS4DVAR
12 km resolution outer model NCOM global
HyCOM/NCODA ROMS MAB-GoM
5 km resolution IS4DVAR model embedded in
4
Mid-Atlantic Bight ROMS

• 5 km resolution is for IS4DVARcan use 1 km
  downscale for forecast, with forward
  ecosystem/optics
• 3-hour forecast meteorology NCEP/NAM
• daily river flow (USGS)
• boundary tides (TPX0.7)
• nested in ROMS MABGOM V6 (nested in
  Global-HyCOM) ( which assimilates altimetry)
• nudging in a 30 km boundary zone
• radiation of barotropic mode

5
Mid-Atlantic Bight ROMS Model for IS4DVAR
5 km resolution IS4DVAR model embedded in
ROMS MAB-GoM V6 which uses global HyCOMNCODA
boundary data
6
Sequential assimilation of SLA and SST
Before attempting assimilation of all in situ
data for a full ESPreSSO reanalysis, we are
assimilating satellite SSH and SST to tune for
the assimilation parameters (horizontal and
vertical de-correlation scales, duration of
assimilation window, etc.) Unassimilated
hydrographic data are used to evaluate how well
the adjoint model propagates information between
variables, and in space and time.
7
IS4DVAR

• Given a first guess (the forward trajectory)
• and given the available data

Incremental Strong Constraint 4-Dimensional
Variational data assimilation
8
IS4DVAR

• Given a first guess (the forward trajectory)
• and given the available data
• what change (or increment) to the initial
  conditions (IC) produces a new forward trajectory
  that better fits the observations?

9
The best fit becomes the analysis
assimilation window
ti analysis initial time
tf analysis final time
The strong constraint requires the trajectory
satisfies the physics in ROMS. The Adjoint
enforces the consistency among state variables.
10
The final analysis state becomes the IC for the
forecast window
assimilation window
forecast
tf analysis final time
tf t forecast horizon
11
Forecast verification is with respect to data not
yet assimilated
assimilation window
forecast
verification
tf t forecast horizon
12
Basic IS4DVAR procedure

• Lagrange function
• Lagrange multiplier

J model-data misfit
The best simulation will minimize L model
model-data misfit is small and model physics are
satisfied
13
Basic IS4DVAR procedure

• Lagrange function
• Lagrange multiplier

J model-data misfit
The best simulation minimizes L
At extrema of L we require
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Basic IS4DVAR procedure

• (1) Choose an
• (2) 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

J model-data misfit
Outer-loop (10)
Inner-loop (3)
NLROMS Non-linear forward model TLROMS
Tangent linear ADROMS Adjoint
15
xb model state (background) at end of previous
cycle, and 1st guess for the next forecast In
4D-Var assimilation the adjoint gives the
sensitivity of the initial conditions to
mis-match between model and data A descent
algorithm uses this sensitivity to iteratively
update the initial conditions, xa, (analysis) to
minimize Jb S(Jo)
xb
previous forecast
0 1 2 3
4 time
Observations minus Previous Forecast
Adjoint model integration is forced by the
model-data error
dx
16
Observed information (e.g. SLA, SST) is
transferred tounobserved state variables
andprojected from surface to subsurface in 3
ways

• (1) The Adjoint Model
• (2) Empirical statistical correlations to
  generate synthetic XBT/CTD
• In EAC assimilation get T(z),S(z) from vertical
  EOFs of historical CTD observations regressed on
  SSH and SST
• (3) Modeling of the background covariance matrix
• e.g. via the hydrostatic/geostrophic relation

17
MAB Satellite Observations for IS4DVAR

• SST 5-km daily blended MWIR from NOAA PFEG
  Coastwatch
• MAB Sea Level Anomaly (SLA) is strongly
  anisotropic with short length scales due to
  flow-topography interaction, so use along-track
  altimetry (need coastal altimetry corrections for
  shelf data)
• 4DVar uses all data at time of satellite pass
• model grids data by simultaneously matching
  observations and dynamical and kinematic
  constraints

5 km resolution for IS4DVAR 1 km downscale
for forecast
18
Mid-Atlantic Bight ROMS Model for IS4DVAR
Model variance (without assimilation) is
comparable to along-track in Slope Sea, but not
shelf-break AVISO gridded SLA differs from
along-track SLA in Slope Sea (4 cm) and Gulf
Stream (10 cm)
19
All inputs NAM Ocean model based open
boundary conditions River discharge, temperature
(USGS) Altimetry (via RADS AVISO gridded) XBT,
CTD, Argo Satellite SST IR and mWave,
passes/blended HF radar totals/radials Cabled
observatory time series MVCO Glider CTD (and
optics) NDBC buoy time series (T, S,
velocity) tide gauges waves Drifters - SLDMB and
AOML GDP Delayed mode Oleander ADCP science
moorings
20
Assimilation of hydrographic climatology for
mean dynamic topography (altimetry) removing
model bias

• Bias in the background state adversely affects
  how IS4DVAR projects model-data misfit across
  variables and dimensions
• We assimilate a high-resolution (2-5 km)
  regional temp/salt climatology to (i) produce a
  Mean Dynamic Topography (SSH) consistent with
  model physics, and (ii) to remove bias
• Climatology computed by weighted least squares
  (Dunn et al. 2002, JAOT) from all available T-S
  data (NODC, NMFS) prior to 2006 (Naomi Fleming)
• Three simulations
• ROMS nested in MABGOM V6
• Free running ROMS initialized with climatology
  and forced by climatology at the boundaries and
  mean surface wind stress
• ROMS with climatology initial/boundary/forcing
  and assimilation of climatology over a 2-day
  window

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Skill of climatologies and MABGOM-V6 at
reproducing all XBT/CTD from GTS in 2007-2008 in
Slope Sea
23
Skill of climatologies and MABGOM-V6 at
reproducing all XBT/CTD from GTS in 2007-2008 in
MAB shelf waters
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Mean barotropic velocity from ROMS versus mean
alongshelf velocity from analysis of mooring
observations by Lentz (2008)
Blue mean of ROMS v6 Red mean of clim
ROMS Black mean of assim ROMS Green -
observations
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High frequency variability model and data
issues
ROMS includes high frequency variability
typically removed in altimeter processing (tides,
storm surge) The IS4DVAR cost function, J,
samples this high frequency variability, so it
must be either (a) removed from the model or (b)
included in the data

• Our approach
• Run 1-year ROMS (no assimilation) forced by
  boundary TPX0.7 tides compute ROMS tidal
  harmonics
• de-tide along-track altimetry (developmental in
  MAB)
• add ROMS tides to de-tided altimeter data
• thus the observations are adjusted to include
  model tide
• assimilate high frequency mismatch of model
  and altimeter is minimized and cost function
  is, presumably, dominated by sub-inertial
  frequency dynamics

31
High frequency variability model and data
issues
The IS4DVAR increment is to the initial
conditions of the analysis window, and this
itself generates HF variability (inertial
oscillations)
32
High frequency variability model and data
issues
The IS4DVAR increment is to the initial
conditions of the analysis window, and this
itself generates HF variability (inertial
oscillations)

• Our approach
• Apply a short time-domain filter to IS4DVAR
  initial conditions
• Reduces inertial oscillations in the Slope Sea
  but removes tides
• Tides recover quickly
• approach needs refinement possibly using 3-D
  velocity harmonic analysis of free running
  model

33
High frequency variability model and data
issues
Without a subsurface synthetic-CTD relationship,
the adjoint model can erroneously accommodate too
much of the SLA model-data misfit in the
barotropic mode This sends gravity wave at
along the model perimeter

• Our approach
• Repeat (duplicate) the altimeter SLA
  observations at t -6 hour, t0 and t
  6 hour but with appropriate time lags in
  the added tide signal
• These data cannot easily be matched by a
  wave
• We are effectively acknowledging the temporal
  correlation of the sub-tidal altimeter SLA
  data

34
High frequency variability model and data
issues

• Our approach
• Repeat (duplicate) the altimeter SLA
  observations at t -6 hour, t0 and t
  6 hour but with appropriate time lags in
  the added tide signal
• These data cannot easily be matched by a
  wave
• We are effectively acknowledging the temporal
  correlation of the sub-tidal altimeter SLA
  data

35
Sequential assimilation of SLA and SST
Before attempting assimilation of all in situ
data for a full ESPreSSO reanalysis, we are
assimilating satellite SSH and SST to tune for
the assimilation parameters (horizontal and
vertical de-correlation scales, duration of
assimilation window, etc.) Unassimilated
hydrographic data are used to evaluate how well
the adjoint model propagates information between
variables, and in space and time.
36
Sequential assimilation of SLA and SST

• Reference time is days after 01-01-2006
• 3-day assimilation
• window (AW)
• Daily MWIR blended SST (available real
  time)
• SSH Dynamic topography ROMS tides
  Jason-1 SLA (repeated three times)
• For the first AW we just assimilate SST to
  allow the tides to ramp up.

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Sequential assimilation of SLA and SST
Assimilation window (3lttlt6 days)
ROMS SST and currents at 200 m
Observed SST
XBT transect (NOT assimilated)
Jason-1 data
40
Sequential assimilation of SLA and SST
ROMS solutions along the transect positions
lon,lat,time
41
Sequential assimilation of SLA and SST
ROMS-IS4DVAR fits the surface observations (SST
and SSH), but how well does it represent
unassimilated subsurface data?
ROMS solutions along the transect positions
lon,lat,time
42
Forward model
Assimilation of SST and SSH (no climatology bias
correction)
depth (m)
depth (m)
43
ROMS data assimilation for ESPreSSO
Accomplishments

• Have a system ready for
• introduction of in situ physical data into
  reanalysis
• 2006-2008 reanalysis of ocean physics
• analysis of impact of improved physics on
  ecosystem (fasham) and optical models
• construction of adjoint/tangent-linear of optical
  model, and subsequent addition of optical data to
  cost function and full IS4DVAR

44
IS4DVAR data assimilation

• LaTTE The Lagrangian Transport and
  Transformation Experiment
• system set-up
• resolution 2.5km
• forcing NAM model output
• rivers USGS Hudson Delaware gauges
• DA window 3 days
• period Apr. 10 Jun 6, 2006
• algorithm
• Incremental Strong-constraint 4DVAR
• (Courtier et al, 1994, QJRMS Weaver et al,
  2003, MWR
• Powell et al, 2008, Ocean Modelling)

types and numbers of obs.
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IS4DVAR result ---- reduction of misfit
2006-04-20 065736
evolution of cost function
model
observation
46
IS4DVAR result ---- forecast skills
47
Adjoint sensitivity results
day 0
Upstream temperature Density Surface current SSH Viscosity Diffusion
1 0.3
2 1

48
Ensemble measure of the influence of glider MURI
track at the end of the glider mission

• Cost function
• Covariance between J and temperature,
• ,
• reflects the influence of glider
  observation, as plotted in the right.
• t the finish time of a glider mission.

49
Ensemble measure of the influence of glider MURI
track 5 days after the glider mission

• t 5 days after the mission is finished.

50
Observation evaluation
Assuming model error ocean state anomaly
51
Observation evaluation (contd)
southerly wind
northerly wind