1 4-Dimensional Variational Assimilation of Satellite Temperature and Sea Level Data in the Coastal Ocean and Adjacent Deep Sea John Wilkin Javier Zavala-Garay Julia Levin and Weifeng Gordon Zhang Institute of Marine and Coastal Sciences Rutgers, The State University of New Jersey New Brunswick, NJ, USA ROMS User Meeting Grenoble, 6-8 October

2 ROMS* models of two Western Boundary Current regimes: East Australian Current (EAC) and Middle Atlantic Bight (MAB) EAC: deep ocean adjacent to narrow continental shelf influenced by proximity of boundary current deep ocean adjacent to narrow continental shelf influenced by proximity of boundary current large (250 km) mesoscale eddies generated locally by boundary current separation process large (250 km) mesoscale eddies generated locally by boundary current separation process 2000 x 1600 km model domain; 25 km resolution 2000 x 1600 km model domain; 25 km resolutionMAB: wide shallow shelf separated from Gulf Stream by the Slope Sea wide shallow shelf separated from Gulf Stream by the Slope Sea Shelf/Slope Front (~0.3 m/s) at shelf edge Shelf/Slope Front (~0.3 m/s) at shelf edge Gulf Stream rings frequently enter Slope Sea and impact shelf Gulf Stream rings frequently enter Slope Sea and impact shelf 800 x 300 km model domain; 5 km resolution 800 x 300 km model domain; 5 km resolution *

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4 NERACOOS Altimetry: Jason-n, ERS

5 NERACOOS Altimetry: Jason-n, ERS MARCOOS CODAR, gliders …

6 IS4DVAR* Given a first guess (the forward trajectory)… and given the available data… and given the available data… *Incremental Strong Constraint 4-Dimensional Variational data assimilation

7 IS4DVAR Given a first guess (the forward trajectory)… and given the available data… what change (or increment) to the initial conditions (IC) produces a new forward trajectory that better fits the observations? what change (or increment) to the initial conditions (IC) produces a new forward trajectory that better fits the observations?

8 The “best fit” becomes the analysis assimilation window t i = analysis initial time t f = analysis final time The strong constraint requires the trajectory satisfies the physics in ROMS. The Adjoint enforces the consistency among state variables.

9 The final analysis state becomes the IC for the forecast window assimilation windowforecast t f = analysis final time t f +  = forecast horizon

10 Forecast verification is with respect to data not yet assimilated assimilation windowforecast verification t f +  = forecast horizon

11 Basic IS4DVAR procedure: Lagrange function Lagrange multiplier The “best fit” simulation will minimize L: model-data misfit is small, and model physics are satisfied J = model- data misfit

12 Basic IS4DVAR procedure: Lagrange function Lagrange multiplier At extrema of L we require: The “best” simulation minimizes L: J = model- data misfit

13 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 Outer-loop (10) Inner-loop (3) NLROMS = Non-linear forward model; TLROMS = Tangent linear; ADROMS = Adjoint J = model- data misfit

14 Adjoint model integration is forced by the model-data error x b = model state (background) at end of previous cycle, and 1 st guess for the next forecast In 4DVAR 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, x a, (analysis) to minimize J b + J o Observations minus previous forecast xx time previous forecast xbxb

15 Three ways: (1) The Adjoint Model (2) Empirical statistical correlations to generate “synthetic XBT/CTD”  In EAC assimilation get T(z),S(z) from vertical EOFs of historical CTD observations regressed on SSH and SST (3) Modeling of the background covariance matrix  e.g. via the hydrostatic/geostrophic relation How is observed information (SLA, SST) transferred to unobserved state variables (velocity) and projected from surface to subsurface?

16 Mid-Atlantic Bight ROMS Model for IS4DVAR 5 km resolution for IS4DVAR 1 km downscale forecast 3-hour forecast meteorology NCEP/NAM 3-hour forecast meteorology NCEP/NAM daily river flow (USGS) daily river flow (USGS) boundary tides (TPX0.7) boundary tides (TPX0.7) nested in ROMS MAB-GoM (which is nested in Global- HyCOM*) nested in ROMS MAB-GoM (which is nested in Global- HyCOM*) – nudging in a 30 km boundary zone – radiation barotropic mode (*which assimilates altimetry)

17 Mid-Atlantic Bight ROMS Model for IS4DVAR ~20 km outer model: ROMS MAB-GoM, or… NCOM or global HyCOM+NCODA 5 km resolution IS4DVAR model embedded in …

18 Mid-Atlantic Bight ROMS Model for IS4DVAR 5 km resolution for IS4DVAR 1 km downscale for forecast EAC eddies are resolved by AVISO multi-satellite SLA MAB SLA is more anisotropic with shorter length scales due to flow-topography interaction Use along-track altimetry: 4DVar uses the data at time of satellite pass 4DVar uses the data at time of satellite pass model “grids” along-track data by simultaneously matching observations and dynamical and kinematic constraints model “grids” along-track data by simultaneously matching observations and dynamical and kinematic constraints need coastal altimetry corrections need coastal altimetry corrections

19 Mid-Atlantic Bight ROMS Model for IS4DVAR Model variance (without assimilation) is comparable to along-track in Slope Sea, but not shelf-break AVISO gridded SLA differs from along-track SLA in Slope Sea (4 cm) and Gulf Stream (10 cm)

20 The altimeter anomalies are with respect to the long-term mean and therefore contain seasonal variability, but this is small compared to the mesoscale in the MAB.

21 ROMS assimilates total SSH. Therefore we need to add a mean dynamic topography (MDT) to the anomaly data prior to assimilation. This MDT is computed by 4DVAR analysis using a regional 3-D T-S climatology computed from historical hydrographic data The altimeter anomalies are with respect to the long-term mean and therefore contain seasonal variability, but this is small compared to the mesoscale in the MAB.

22 Mean Dynamic Topography (MDT) is computed by 4DVAR analysis of a regional 3-D T-S climatology computed from historical hydrographic data. 4DVAR analysis is forced with annual mean meteorology and open boundary conditions.

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25 High frequency variability: model and data issues ROMS includes high frequency variability typically removed in altimeter processing (tides, storm surge) The IS4DVAR cost function, J, samples this high frequency variability, so it must be either (a) removed from the model or (b) included in the data Our approach: Run 1-year ROMS (no assimilation) forced by boundary TPX0.7 tides; compute ROMS tidal harmonics Run 1-year ROMS (no assimilation) forced by boundary 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 data add ROMS tides to de-tided altimeter data thus the observations are adjusted to include model tide thus the observations are adjusted to include model tide assimilate – high frequency mismatch of model and altimeter is minimized and cost function is, presumably, dominated by sub-inertial frequency dynamics assimilate – high frequency mismatch of model and altimeter is minimized and cost function is, presumably, dominated by sub-inertial frequency dynamics

26 High frequency variability: model and data issues The IS4DVAR increment is to the initial conditions of the analysis window, and this itself generates HF variability (inertial oscillations)

27 High frequency variability: model and data issues The IS4DVAR increment is to the initial conditions of the analysis window, and this itself generates HF variability (inertial oscillations) Our approach: Apply a short time-domain filter to IS4DVAR initial conditions Apply a short time-domain filter to IS4DVAR initial conditions Reduces inertial oscillations in the Slope Sea but removes tides Reduces inertial oscillations in the Slope Sea but removes tides Tides recover quickly Tides recover quickly – approach needs refinement – possibly using 3-D velocity harmonic analysis of free running model

28 High frequency variability: model and data issues Without a subsurface synthetic-CTD relationship, the adjoint model can erroneously accommodate too much of the SLA model-data misfit in the barotropic mode This sends gravity wave at along the model perimeter Our approach: Repeat (duplicate) the altimeter SLA observations at t = -6 hour, t=0 and t = +6 hour but with appropriate time lags in the added tide signal Repeat (duplicate) the altimeter SLA observations at t = -6 hour, t=0 and t = +6 hour 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 of the sub-tidal altimeter SLA data We are effectively acknowledging the temporal correlation of the sub-tidal altimeter SLA data

29 High frequency variability: model and data issues Our approach: Repeat (duplicate) the altimeter SLA observations at t = -6 hour, t=0 and t = +6 hour but with appropriate time lags in the added tide signal Repeat (duplicate) the altimeter SLA observations at t = -6 hour, t=0 and t = +6 hour 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 of the sub-tidal altimeter SLA data We are effectively acknowledging the temporal correlation of the sub-tidal altimeter SLA data

30 Other possible HF issues: Should we include sea level air pressure in ROMS and attempt to model the inverse barometer response? Should we include sea level air pressure in ROMS and attempt to model the inverse barometer response? What about remote HF variability from coastal trapped waves? What about remote HF variability from coastal trapped waves? – regional MOG2D? – regional MOG2D? High frequency variability: model and data issues

31 Sequential assimilation of SLA and SST Before attempting assimilation of COOS observatory in situ data for a full reanalysis, we are assimilating satellite data (SSH and SST) to tune for the assimilation parameters (e.g., horizontal and vertical de-correlation scales, assimilation window, etc.). We use the unassimilated hydrographic data to evaluate how well the adjoint model is propagating information between variables, and in space and time. This experiment also serves as a prototype for a real-time forecast system.

32 Sequential assimilation of SLA and SST Reference time is days after 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.

33 Sequential assimilation of SLA and SST First AW (0<=t<=3 days) Observed SST ROMS SST and currents at 200 m

34 Sequential assimilation of SLA and SST Second AW (3<=t<=6 days) Observed SST ROMS SST and currents at 200 m

35 Sequential assimilation of SLA and SST Second AW (3<=t<=6 days) Observed SST ROMS SST and currents at 200 m Jason-1 data

36 Sequential assimilation of SLA and SST Second AW (3<=t<=6 days) Observed SST ROMS SST and currents at 200 m Jason-1 data XBT transect (NOT assimilated)

37 Sequential assimilation of SLA and SST ROMS-IS4DVAR fits reasonably well the assimilated observations (SST and SSH), but how well does it represent unassimilated data? ROMS solutions along the transect positions [lon,lat,time]

38 Sequential assimilation of SLA and SST ROMS-IS4DVAR fits reasonably well the assimilated observations (SST and SSH), but how well does it represent unassimilated data? ROMS solutions along the transect positions [lon,lat,time]

39 Future work Evaluation of the forward model shows significant forecast skill error due to biases in the boundary and surface forcing. We will therefore use climatology as an additional data source in the assimilation procedure. After bias correction, we will assimilate all the available COOS data (CODAR surface currents, glider T-S, CTD, XBT, moorings) for 2006 to produce a MAB reanalysis. In a true operational forecast system the state of the atmosphere and boundary forcing is not known in advance, so we are developing techniques to produce adjoint-based ensemble techniques that will allow us to place error bars to the forecast.

40 Summary Assimilation of gridded AVISO SLA is not appropriate in MAB because of length/time scales of variability and anisotropy Assimilation of along-track SSH successful but requires consideration of … – – tidal signal in data-model (lest it dominate cost function) – – time filtering IS4DVAR increment to reduce inertial oscillations – – time correlation of SLA obs to suppress waves in adjoint solution Subsurface projection (in addition to Adjoint) is in development using multi-variate background covariance – – Less straightforward than in EAC … – – Shelf/Slope Front and shelf mean circulation reach seafloor so geostrophic balance must acknowledge the bathymetry ROMS User Meeting Grenoble, 6-8 October