1 accomplishments: * nested roms in larger domain forward simulation (mabgom-roms) with...

11

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

22

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


33

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 …

44

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

55

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 …

66

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.

77

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

88

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

99

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.

1010

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

1111

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

1212

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

1313


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


1414


(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


15

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

1616

(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:

1717

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

1818

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)

1919

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

2020

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

2222

Skill of climatologies and MABGOM-V6 at reproducing all XBT/CTD from GTS in 2007-2008 in Slope Sea

2323

Skill of climatologies and MABGOM-V6 at reproducing all XBT/CTD from GTS in 2007-2008 in MAB shelf waters

2828

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)

3030

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

3131


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)

3232


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

3333


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


• 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

3434



• 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

3535


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.

3636


• 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.

3939


Assimilation window (3<=t<=6 days)

Observed SST ROMS SST and currents at 200 m

Jason-1 data

XBT transect(NOT assimilated)

4040


ROMS solutions along the transect positions [lon,lat,time]

4141


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?

4242

Forward model

Assimilation of SST and SSH (no climatology bias correction)

depth (m)

depth (m)

4343

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


44

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

.

45

IS4DVAR result ---- reduction of misfit

evolution of cost function

200

6-04

-20

06:

57:3

6

observation

mod

el

46

IS4DVAR result ---- forecast skills

afterDA

beforeDA

1-CC

1-CCafterDA

beforeDA

RMS

RMSafterDA

beforeDA

RMSskill = 1

RMS

47

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

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.

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

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

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

51

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

1 accomplishments: * nested roms in larger domain forward simulation (mabgom-roms) with...

Documents

is4dvar roms data assimilation

nested roms

resolution is4dvar model

available data

situ data

withheld data

espresso slide

is4dvar roms mabgom