Post on 26-Jan-2016
description
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