Predictability of Mesoscale Variability in the East Australia Current given Strong Constraint Data Assimilation Hernan G. Arango IMCS, Rutgers John L. Wilkin IMCS, Rutgers Javier Zavala-Garay IMCS, 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 Configuration Resolution0.25x025 degrees Grid64x80x30 DX km DY km DT(1080, 21.6) sec Bathymetry m Decorrelation Scale100 km, 150 m Nouter, Ninner10, 3 OBC HYCOM (years 2001 and 2002) ForcingNOGAPS, daily

IS4DVAR

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

The best fit becomes the reanalysis assimilation window

The final state becomes the IC for the forecast window assimilation windowforecast

The final state becomes the IC for the forecast window assimilation windowforecast 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 variable

Predictability in EAC given IS4DVAR

Days since January 1 st 2001, 00:00:00 XBTs 4DVar Observations and Experiments 7-Day IS4DVAR Experiments E1: SSH, SST E2: SSH, SST, XBT SSH 7-Day Averaged AVISO SST 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 Observations First Guess EAC Incremental 4DVar: Surface Versus Sub-surface Observations

SSH/SST ObservationsROMS IS4DVAR: SSH/SST ROMS IS4DVAR: XBT OnlyFirst Guess EAC Incremental 4DVar: Surface Versus Sub-surface Observations

Observations E1 E2 E1 – E2 SSH Temperature along XBT line EAC Incremental 4DVar (IS4DVAR) 7-Day 4DVar Assimilation cycle E1: SSH, SST Observations E2: SSH, SST, XBT Observations

Quantifying the IS4DVAR fit and forecast skill Close to 1 if the patterns of variability in ROMS are very similar to the patterns of variability in observations. Correlation: Close to 1 if the patterns of variability in ROMS are very similar to the patterns of variability in observations. small if the fit is very good. Root Mean Square (rms): small if the fit is very good. Good fit or forecast skill if correlation are close to 1 and rms close to 0. Good fit or forecast skill if correlation are close to 1 and rms close to 0.

Days since January 1 st 2001, 00:00:00 Lag Forecast Time (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 weeklag = 0lag = 1 weeklag = 2 weekslag = 3 weekslag = 4 weeks lag = -1 weeklag = 0lag = 1 weeklag = 2 weekslag = 3 weekslag = 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 week lag = 0 weeklag = 1 week lag = 2 weekslag = 3 weeks

Ensemble prediction Assimilation of SSH+SST and SSH+SST+XBT gives similar rms and decorrelation maps of SSH when compared with observations Assimilation of SSH+SST and SSH+SST+XBT gives similar rms and decorrelation maps of SSH when compared with observations 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 IC Yes, the resulting analysis is less sensible to errors in the IC We computed the optimal perturbations at day 85 from from the two reanalysis E1 and E2 We computed the optimal perturbations at day 85 from from the two reanalysis E1 and E2 Produced an ensemble (10 members) by perturbing the corresponding IC with the leading optimal perturbations (scaled to represent realistic errors) Produced an ensemble (10 members) by perturbing the corresponding IC with the leading optimal perturbations (scaled to represent realistic errors) E1 OP E2 OP

Ensemble Prediction: E1 15-days forecast1-day forecast8-days forecast

Ensemble Prediction: E2 15-days forecast1-day forecast8-days forecast

Assimilation of subsurface information (XBT) improves predictability Assimilation of subsurface information (XBT) improves predictability Assimilation of subsurface information can help to determine surface information (SSH) Assimilation of subsurface information can help to determine surface information (SSH) In practice it is impossible to observe the subsurface at all model domain, at all times. In practice it is impossible to observe the subsurface at all model domain, at all times. It will be nice to infer the subsurface from surface observations It will be nice to infer the subsurface from surface observations Synthetic XBT (proxies for subsurface temperature and salinity given SSH and SST; provided by Griffin) Synthetic XBT (proxies for subsurface temperature and salinity given SSH and 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+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.

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 enough Assimilation of just surface information is not enough Assimilation of subsurface information help by Assimilation of subsurface information help by improving estimate of the subsurface improving estimate of the subsurface making more stable the system to errors in IC making more stable the system to errors in IC Proxies for subsurface information can be obtained based on surface information, but need lots of subsurface data to construct a robust empirical relationship Proxies for subsurface information can be obtained based on surface information, but need lots of subsurface data to construct a robust empirical relationship The fact that an empirical (linear) relationship exist suggest that there could be a simple dynamical relationships linking the surface with the subsurface variability The fact that an empirical (linear) relationship exist suggest that there could be a simple dynamical relationships linking the surface with the subsurface variability The idea is actually not new (Weaver et al 2006: “multivariate balance operator”) The idea is actually not new (Weaver et al 2006: “multivariate balance operator”)

Future work Include balance terms in the IS4DVAR Include balance terms in the IS4DVAR Improve boundary forcing Improve boundary forcing –Better global forecast and/or boundary conditions –Determine the optimal boundary forcing via “weak constraint” data-assimilation (WS4DVAR) Use of along track SSH data instead of reanalysis Use of along track SSH data instead of reanalysis Use of is4dvar and w4dvar to downscale GCMs climate change projections Use of is4dvar and w4dvar to downscale GCMs climate change projections

Thanks to… David Griffin (CSIRO) for the XBT David Griffin (CSIRO) for the XBT David Robertson (IMCS) for the editing of nice figures David Robertson (IMCS) for the editing of nice figures John Evans (IMCS) for XBT observation files John Evans (IMCS) for XBT observation files