Predictability of Mesoscale Variability in Predictability of Mesoscale Variability in the East Australia Current given Strong the East Australia Current given Strong

Constraint Data AssimilationConstraint Data Assimilation

Hernan G. ArangoIMCS, Rutgers

John L. WilkinIMCS, Rutgers

Javier Zavala-GarayIMCS, Rutgers

Outline

• East Australia Current (EAC), and ROMS EAC application

• Incremental, Strong-constraint 4- Dimensional Variational (IS4DVAR) data assimilation

• Two applications of IS4DVAR

Reanalysis (assimilation window)

Prediction (forecast window)

• Predictability of mesoscale variability in EAC given IS4DVAR

• Final remarks

• Future work

EAC

East Australia Current Application

-24

-32

-28

-40

-36

-44

-48145 150 155 160 165

Configuration

Resolution 0.25x025 degrees

Grid 64x80x30

DX 18.7 - 29.2 km

DY 23.6 - 30.4 km

DT (1080, 21.6) sec

Bathymetry 16 - 4895 m

Decorrelation Scale 100 km, 150 m

Nouter, Ninner 10, 3

OBCHYCOM (years 2001 and 2002)

Forcing NOGAPS, daily

IS4DVAR

Forward model

Forward model

Forward model

Forward model

IS4DVAR

• Given a first guess (a forward trajectory)Given a first guess (a forward trajectory)

IS4DVAR

• Given a first guess (a forward trajectory)…Given a first guess (a forward trajectory)…

• And given the available data…And given the available data…

IS4DVAR

• Given a first guess (a forward trajectory)…Given a first guess (a forward trajectory)…

• And given the available data…And given the available data…

• What are the changes (or increment) to the IC so What are the changes (or increment) to the IC so that the forward model fits the observations?that the forward model fits the observations?

The best fit becomes the The best fit becomes the reanalysisreanalysis

assimilation window

The final state becomes the IC The final state becomes the IC for the forecast windowfor the forecast window

assimilation window forecast

The final state becomes the IC The final state becomes the IC for the forecast windowfor the forecast window

assimilation window forecast

verification

How IS4DVAR operates

• IS4DVAR tries to minimize a cost function that measures the misfit between model and observations

• The is4dvar tries o find the best road from first guess * to a better initial guess *

• The road might not be very nice because of nonlinearity.

**

*

state

vari

able

state variable

Predictability in EAC given IS4DVAR

Days since January 1st 2001, 00:00:00

XBTs

4DVar Observations and Experiments

7-Day IS4DVAR Experiments

E1: SSH, SSTE2: SSH, SST, XBT

SSH 7-Day Averaged AVISOSST Daily CSIRO HRPT

EAC Incremental 4DVar:Surface Versus Sub-surface Observations

SSH/SST

First Guess

EAC Incremental 4DVar:Surface Versus Sub-surface Observations

SSH/SST

SSH/SST

Observations

First Guess

EAC Incremental 4DVar:Surface Versus Sub-surface Observations

SSH/SST

SSH/SSTSSH/SST

SSH/SST

Observations ROMS IS4DVAR: SSH/SST

ROMS IS4DVAR: XBT OnlyFirst Guess

EAC Incremental 4DVar:Surface Versus Sub-surface Observations

Observations

E1

E2

E1 – E2

SSH

SSH

SSHSSH

Temperature along XBT line Temperature along XBT line

Temperature along XBT line

Temperature along XBT line

EAC Incremental 4DVar (IS4DVAR)

7-Day 4DVar Assimilation cycle

E1: SSH, SST ObservationsE2: SSH, SST, XBT Observations

Quantifying the IS4DVAR fit and forecast skill

•Correlation: Close to 1 if the patterns Close to 1 if the patterns of variability in ROMS are very similar of variability in ROMS are very similar to the patterns of variability in to the patterns of variability in observations.observations.

•Root Mean Square (rms): small if the small if the fit is very good.fit is very good.

• Good fit or forecast skill if correlation Good fit or forecast skill if correlation are close to 1 and rms close to 0.are close to 1 and rms close to 0.

Days since January 1st 2001, 00:00:00

Days since January 1st 2001, 00:00:00

Lag

Fore

cast

Tim

e (

weeks

)La

g F

ore

cast

Tim

e (

weeks

)

2001 EAC 4DVar Sequential Assimilation: E2

SSH Lag Pattern RMS

SSH Lag Pattern Correlation

0.6

2001 EAC 4DVar Sequential Assimilation: E2

lag = -1 week lag = 0 lag = 1 week lag = 2 weeks lag = 3 weeks lag = 4 weeks

lag = -1 week lag = 0 lag = 1 week lag = 2 weeks lag = 3 weeks lag = 4 weeks

SSH Correlations Between Observations and Forecast

SSH RMS Between Observations and Forecast

rms error normalized by the expected variance in SSH

lag = -1 weeklag = 0 week lag = 1 week lag = 1 weeklag = 2 weekslag = 3 weeks

Ensemble prediction• Assimilation of SSH+SST and SSH+SST+XBT gives similar rms Assimilation of SSH+SST and SSH+SST+XBT gives similar rms

and decorrelation maps of SSH when compared with and decorrelation maps of SSH when compared with observationsobservations

• So does assimilation of XBT help to better predict the SSH?So does assimilation of XBT help to better predict the SSH?• Yes, the resulting analysis is less sensible to errors in the ICYes, the resulting analysis is less sensible to errors in the IC• We computed the optimal perturbations at day 85 from from the We computed the optimal perturbations at day 85 from from the

two reanalysis E1 and E2two reanalysis E1 and E2• Produced an ensemble (10 members) by perturbing the Produced an ensemble (10 members) by perturbing the

corresponding IC with the leading optimal perturbations (scaled corresponding IC with the leading optimal perturbations (scaled to represent realistic errors)to represent realistic errors)

E1 OP

E2 OP

Ensemble Prediction: E1

15-days forecast1-day forecast 8-days forecast

Ensemble Prediction: E2

15-days forecast1-day forecast 8-days forecast

• Assimilation of subsurface information Assimilation of subsurface information (XBT) improves predictability(XBT) improves predictability

• Assimilation of subsurface information can Assimilation of subsurface information can help to determine surface information (SSH)help to determine surface information (SSH)

• In practice it is impossible to observe the In practice it is impossible to observe the subsurface at all model domain, at all times.subsurface at all model domain, at all times.

• It will be nice to infer the subsurface from It will be nice to infer the subsurface from surface observationssurface observations

• Synthetic XBT (proxies for subsurface Synthetic XBT (proxies for subsurface temperature and salinity given SSH and temperature and salinity given SSH and SST; provided by Griffin)SST; provided by Griffin)

Remarks on assimilation of surface (SSH and SST) versus subsurface (XBT) information

Example of synthetic XBT

Comparison between ROMS fit and observed temperature from all XBTs. Note: actual XBT-data was not assimilated, it is

used here to evaluate the quality of the reanalysis.

SSH+SST

SSH+SST

SSH+SST+SynXBT

Comparison between ROMS fit and observed temperature from all XBTs. Note: actual XBT-data was not assimilated, it is used here to evaluate the quality of the reanalysis.

Comparison between ROMS prediction and observed temperature from all XBTs.

Comparison between ROMS prediction and observed temperature from all XBTs.

Comparison between ROMS prediction and observed temperature from all XBTs.

Comparison between ROMS prediction and observed temperature from all XBTs.

Comparison between ROMS prediction and observed temperature from all XBTs.

Final Remarks

• Good ocean state predictions for up to 2 weeks in advance Good ocean state predictions for up to 2 weeks in advance • Assimilation of just surface information is not enoughAssimilation of just surface information is not enough• Assimilation of subsurface information help byAssimilation of subsurface information help by

• improving estimate of the subsurface improving estimate of the subsurface • making more stable the system to errors in ICmaking more stable the system to errors in IC

• Proxies for subsurface information can be obtained based on surface Proxies for subsurface information can be obtained based on surface information, but need lots of subsurface data to construct a robust information, but need lots of subsurface data to construct a robust empirical relationshipempirical relationship

• The fact that an empirical (linear) relationship exist suggest that there The fact that an empirical (linear) relationship exist suggest that there could be a simple dynamical relationships linking the surface with the could be a simple dynamical relationships linking the surface with the subsurface variabilitysubsurface variability

• The idea is actually not new (Weaver et al 2006: “multivariate balance The idea is actually not new (Weaver et al 2006: “multivariate balance operator”)operator”)

Future work

• Include balance terms in the IS4DVARInclude balance terms in the IS4DVAR• Improve boundary forcingImprove boundary forcing

– Better global forecast and/or boundary Better global forecast and/or boundary conditionsconditions

– Determine the optimal boundary forcing via Determine the optimal boundary forcing via “weak constraint” data-assimilation (WS4DVAR)“weak constraint” data-assimilation (WS4DVAR)

• Use of along track SSH data instead of Use of along track SSH data instead of reanalysisreanalysis

• Use of is4dvar and w4dvar to downscale Use of is4dvar and w4dvar to downscale GCMs climate change projectionsGCMs climate change projections

Thanks to…

• David Griffin (CSIRO) for the XBTDavid Griffin (CSIRO) for the XBT

• David Robertson (IMCS) for the David Robertson (IMCS) for the editing of nice figuresediting of nice figures

• John Evans (IMCS) for XBT John Evans (IMCS) for XBT observation filesobservation files