Post on 17-Dec-2015
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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.
ROMS data assimilation for ESPreSSO
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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
ROMS data assimilation for ESPreSSO
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Mid-Atlantic Bight ROMS Model for ESPreSSO/IS4DVAR
… ~12 km resolution outer model:NCOMglobal HyCOM/NCODA ROMS MAB-GoM
5 km resolution IS4DVAR model embedded in …
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Mid-Atlantic Bight ROMS
5 km resolution is for IS4DVAR5 km resolution is for IS4DVARcan use 1 km downscale for can use 1 km downscale for forecast, with forward forecast, with forward ecosystem/opticsecosystem/optics
• 3-hour forecast meteorology 3-hour forecast meteorology NCEP/NAMNCEP/NAM
• daily river flow (USGS)daily river flow (USGS)• boundary tides (TPX0.7)boundary tides (TPX0.7)• nested in ROMS MABGOM nested in ROMS MABGOM
V6 (nested in Global-V6 (nested in Global-HyCOM*) HyCOM*) (* which assimilates altimetry)(* which assimilates altimetry)
– nudging in a 30 km boundary nudging in a 30 km boundary zonezone
– radiation of barotropic mode radiation of barotropic mode
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Mid-Atlantic Bight ROMS Model for IS4DVAR
… ROMS MAB-GoM V6 which uses global HyCOM+NCODA boundary data
5 km resolution IS4DVAR model embedded in …
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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.
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IS4DVAR*
• Given a first guess (the forward trajectory)…
• and given the available data…and given the available data…
( )oR x
ox
*Incremental Strong Constraint 4-Dimensional Variational data assimilation
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IS4DVAR
• Given a first guess (the forward trajectory)…
• and given the available data…
• what change (or increment) to the initial what change (or increment) to the initial conditions (conditions (ICIC) produces a new forward trajectory ) produces a new forward trajectory that better fits the observations?that better fits the observations?
ox
( )oR x
( )o oR x x
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The best fit becomes the analysis
assimilation window
ttii = = analysis analysis initial time initial time
ttff = analysis = analysis final time final time
The strong constraint requires the trajectory satisfies the physics in ROMS. The Adjoint enforces the consistency among state variables.
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The final analysis state becomes the IC for the forecast window
assimilation window forecast
ttff = analysis = analysis final time final time
ttff + + = forecast = forecast horizon horizon
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Forecast verification is with respect to data Forecast verification is with respect to data not yet assimilatednot yet assimilated
assimilation window forecast
verification
ttff + + = forecast = forecast horizon horizon
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Basic IS4DVAR procedure:
Lagrange function
Lagrange multiplier
1
( ) ( )N
T ii i i
i
dL J
dt
xx λ N x F
( )i i t F F
( )i i t x x
( ) ( )i it i t λ λ λ
The “best” simulation will minimize L: model model-data misfit is small and model physics are satisfied
1 1
1
1 1( )
2 2b o
NT T
b b i i i i i ii
J J
J x
x x B x x H x y O H x y
J = model-data misfit
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Basic IS4DVAR procedure:
Lagrange function
Lagrange multiplier
1
1
0 ( ) 0
0
0 (0) (0) &(0)
0 ( ) 0 . .( )
ii i
i
TTi
i im m mi
b
dLNLROMS
dt
dLADROMS
dt
Lcoupling of NL AD
Li c of ADROMS
xN x F
λ
λ Nλ H O Hx y
x x
B x x λx
λx
1
( ) ( )N
T ii i i
i
dL J
dt
xx λ N x F
( )i i t F F
( )i i t x x
( ) ( )i it i t λ λ λ
At extrema of L
we require:
The “best” simulation minimizes L:
1
1
1
1( )
2
1
2
b
o
T
b b
J
NT
i i i i i ii
J
J x
x x B x x
H x y O H x y
J = model-data misfit
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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
(0) (0)bx x
[0, ]t
(0)x
[0, ]t
[ ,0]t (0)(0)oJ
λx
1 (0) (0)(0)
J
B x λ
x
(0)x
(0) (0) (0) x x x
( )tx
Out
er-l
oop
(1
0)
Inne
r-lo
op
(3)
NLROMS = Non-linear forward model; TLROMS = Tangent linear; ADROMS = Adjoint
1
1
1
1( )
2
1
2
b
o
T
b b
J
NT
i i i i i ii
J
J x
x x B x x
H x y O H x y
J = model-data misfit
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Adjoint model integration is forced by
the model-data error
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+ (Jo)
Observations minus Previous Forecast
x
0 1 2 3 4 time
previous forecast
xb
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(1) (1) The Adjoint ModelThe Adjoint Model
(2) (2) Empirical statistical correlations to generate Empirical statistical correlations to generate “synthetic XBT/CTD”“synthetic XBT/CTD”
In EAC assimilation get T(z),S(z) from vertical In EAC assimilation get T(z),S(z) from vertical EOFs of historical CTD observations regressed EOFs of historical CTD observations regressed on SSH and SSTon SSH and SST
(3) (3) Modeling of the background covariance matrixModeling of the background covariance matrix e.g. via the hydrostatic/geostrophic relation e.g. via the hydrostatic/geostrophic relation
Observed information (e.g. SLA, SST) is transferred tounobserved state variables andprojected from surface to subsurface in 3 ways:
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MAB Satellite Observations for IS4DVAR
5 km resolution for IS4DVAR 1 km downscale for forecast
SST 5-km daily blended MW+IR SST 5-km daily blended MW+IR from NOAA PFEG Coastwatchfrom NOAA PFEG Coastwatch
MAB MAB Sea Level Anomaly (SLA)Sea Level Anomaly (SLA) is is
strongly anisotropic with short strongly anisotropic with short length scales due to flow-length scales due to flow-topography interaction, so use topography interaction, so use along-track altimetry (need along-track altimetry (need coastal altimetry corrections coastal altimetry corrections for shelf data) for shelf data)
• 4DVar uses all data at time of 4DVar uses all data at time of satellite passsatellite pass
• model “grids” data by model “grids” data by simultaneously matching simultaneously matching observations and dynamical observations and dynamical and kinematic constraints and kinematic constraints
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Mid-Atlantic Bight ROMS Model for IS4DVAR
Model variance (without Model variance (without assimilation) is comparable assimilation) is comparable to along-track in Slope Sea, to along-track in Slope Sea, but not shelf-breakbut not shelf-break
AVISO gridded SLA differs AVISO gridded SLA differs from along-track from along-track SLASLA in in Slope Sea (4 cm) and Gulf Slope Sea (4 cm) and Gulf Stream (10 cm)Stream (10 cm)
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All inputs:
NAM Ocean model based open boundary conditionsRiver discharge, temperature (USGS)
Altimetry (via RADS; AVISO gridded)XBT, CTD, ArgoSatellite SST – IR and mWave, passes/blendedHF radar – totals/radialsCabled observatory time series – MVCOGlider CTD (and optics)NDBC buoy time series (T, S, velocity)tide gaugeswavesDrifters - SLDMB and AOML GDP
Delayed modeOleander ADCPscience moorings
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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:
1. ROMS nested in MABGOM V6
2. Free running ROMS initialized with climatology and forced by climatology at the boundaries and mean surface wind stress
3. 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
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Skill of climatologies and MABGOM-V6 at reproducing all XBT/CTD from GTS in 2007-2008 in MAB shelf waters
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Blue – mean of ROMS v6
Red – mean of clim ROMS
Black – mean of assim ROMS
Green - observations
Mean barotropic velocity from ROMS versus mean alongshelf velocity from analysis of mooring observations by Lentz (2008)
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High frequency variability: model and data issues
ROMS includes high frequency variability typically ROMS includes high frequency variability typically removed in altimeter processing (tides, storm surge)removed in altimeter processing (tides, storm surge)
The IS4DVAR cost function, The IS4DVAR cost function, JJ, samples this high , samples this high frequency variability, so it must be either (a) removed frequency variability, so it must be either (a) removed from the model or (b) included in the datafrom the model or (b) included in the data
Our approach:Our approach:• Run 1-year ROMS (no assimilation) forced by boundary Run 1-year ROMS (no assimilation) forced by boundary TPX0.7 tides; compute ROMS tidal harmonics TPX0.7 tides; compute ROMS tidal harmonics • de-tide along-track altimetry (developmental in MAB) de-tide along-track altimetry (developmental in MAB) • add ROMS tides to de-tided altimeter dataadd ROMS tides to de-tided altimeter data• thus the thus the observationsobservations are are adjustedadjusted to include model tide to include model tide
• assimilate – high frequency mismatch of model and assimilate – high frequency mismatch of model and altimeter is minimized and cost function is, presumably, altimeter is minimized and cost function is, presumably, dominated by sub-inertial frequency dynamics dominated by sub-inertial frequency dynamics
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High frequency variability: model and data issues
The IS4DVAR increment is to the initial conditions of The IS4DVAR increment is to the initial conditions of the analysis window, and this itself generates HF the analysis window, and this itself generates HF variability (inertial oscillations)variability (inertial oscillations)
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High frequency variability: model and data issues
The IS4DVAR increment is to the initial conditions of The IS4DVAR increment is to the initial conditions of the analysis window, and this itself generates HF the analysis window, and this itself generates HF variability (inertial oscillations)variability (inertial oscillations)
Our approach:Our approach:
• Apply a short time-domain filter to IS4DVAR initial Apply a short time-domain filter to IS4DVAR initial conditions conditions • Reduces inertial oscillations in the Slope Sea Reduces inertial oscillations in the Slope Sea butbut removes tides removes tides • Tides recover quickly Tides recover quickly
– – approach needs refinement approach needs refinement – possibly using 3-D velocity harmonic analysis of– possibly using 3-D velocity harmonic analysis of free running model free running model
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High frequency variability: model and data issues
Without a subsurface Without a subsurface synthetic-CTD synthetic-CTD relationship, the adjoint model can relationship, the adjoint model can erroneously accommodate too much of erroneously accommodate too much of the SLA model-data misfit in the the SLA model-data misfit in the barotropic modebarotropic mode
This sends gravity wave at along the This sends gravity wave at along the model perimeter model perimeter
Our approach:Our approach:
• Repeat (duplicate) the altimeter SLA observations at Repeat (duplicate) the altimeter SLA observations at t = -6 hour, t=0 and t = +6 hourt = -6 hour, t=0 and t = +6 hour but with appropriate time lags in the added tide signal but with appropriate time lags in the added tide signal • These data cannot easily be matched by a wave These data cannot easily be matched by a wave • We are effectively acknowledging the temporal correlation We are effectively acknowledging the temporal correlation of the sub-tidal altimeter SLA data of the sub-tidal altimeter SLA data
gh
gh
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High frequency variability: model and data issues
Our approach:Our approach:
• Repeat (duplicate) the altimeter SLA observations at Repeat (duplicate) the altimeter SLA observations at t = -6 hour, t=0 and t = +6 hourt = -6 hour, t=0 and t = +6 hour but with appropriate time lags in the added tide signal but with appropriate time lags in the added tide signal • These data cannot easily be matched by a wave These data cannot easily be matched by a wave • We are effectively acknowledging the temporal correlation We are effectively acknowledging the temporal correlation of the sub-tidal altimeter SLA data of the sub-tidal altimeter SLA data
gh
gh
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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.
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Sequential assimilation of SLA and SST
• Reference time is days after 01-01-2006
• 3-day assimilation
window (AW)
• Daily MW+IR 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 (3<=t<=6 days)
Observed SST ROMS SST and currents at 200 m
Jason-1 data
XBT transect(NOT assimilated)
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Sequential assimilation of SLA and SST
ROMS solutions along the transect positions [lon,lat,time]
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Sequential assimilation of SLA and SST
ROMS solutions along the transect positions [lon,lat,time]
ROMS-IS4DVAR fits the surface observations (SST and SSH), but how well does it represent unassimilated subsurface data?
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Forward model
Assimilation of SST and SSH (no climatology bias correction)
depth (m)
depth (m)
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Accomplishments:
* Have a system ready for:
1. introduction of in situ physical data into reanalysis
2. 2006-2008 reanalysis of ocean physics
3. analysis of impact of improved physics on ecosystem (‘fasham’) and optical models
4. construction of adjoint/tangent-linear of optical model, and subsequent addition of optical data to cost function and full IS4DVAR
ROMS data assimilation for ESPreSSO
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IS4DVAR data assimilationLaTTE: 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)
1 10 0
0
1 1( ) ( )
2 2
obsNT T
i i i ii
J
HΦ y O H Φ y φ B φ
type
s an
d nu
mbe
rs o
f obs
.
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IS4DVAR result ---- reduction of misfit
evolution of cost function
200
6-04
-20
06:
57:3
6
observation
mod
el
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IS4DVAR result ---- forecast skills
afterDA
beforeDA
1-CC
1-CCafterDA
beforeDA
RMS
RMSafterDA
beforeDA
RMSskill = 1
RMS
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Adjoint sensitivity results
J SST
Upstream temperature
DensitySurface current
SSH Viscosity Diffusion
1 0.3
2 1
X
(0) (0) (0) (0)(0) (0) (0) (0) h
h
J J J JJ u T
u T
J X
X
2( )J
X CX
410
42 10
510
510
42 10
110
52 10
53 10
210
73 10
510
510
610
73 10
day 0
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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.
2
1
2 2
2 1
1( ) ( )
( )
t
t L
J T T S S dLdtL t t
cov( , ( , , , ))J T x y z t
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Ensemble measure of the influence of glider MURI track 5 days after the glider mission
t: 5 days after the mission is finished.
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Observation evaluation
2 21 ( ) ( )
T SV t
T T S SJ dtdV
V t
O O
glider
observation window forecast window
Mooring
2 21 ( ) ( )
T SV t
T T S SJ dtdV
V t
O OAssuming: model error ~
ocean state anomaly
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Observation evaluation (cont’d)2 21 ( ) ( )
T SV t
T T S SJ dtdV
V t
O O
observation window forecast window
sout
herly
w
ind
nort
herly
w
ind