#### Transcript ROMS-ESPreSSO-Wilkin-201008

ROMS data assimilation for ESPreSSO 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 decorrelation 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. 1 ROMS data assimilation for ESPreSSO 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 2 Mid-Atlantic Bight ROMS Model for ESPreSSO/IS4DVAR 5 km resolution IS4DVAR model embedded in … … ~12 km resolution outer model: NCOM global HyCOM/NCODA ROMS MAB-GoM 3 Mid-Atlantic Bight ROMS 5 km resolution is for IS4DVAR can use 1 km downscale for forecast, with forward ecosystem/optics • 3-hour forecast meteorology • • • NCEP/NAM daily river flow (USGS) boundary tides (TPX0.7) nested in ROMS MABGOM V6 (nested in GlobalHyCOM*) (* which assimilates altimetry) – nudging in a 30 km boundary zone – radiation of barotropic mode 4 Mid-Atlantic Bight ROMS Model for IS4DVAR 5 km resolution IS4DVAR model embedded in … … ROMS MAB-GoM V6 which uses global HyCOM+NCODA boundary data 5 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. 6 IS4DVAR* R(xo ) xo • Given a first guess (the forward trajectory)… • and given the available data… *Incremental Strong Constraint 4-Dimensional Variational data assimilation 7 IS4DVAR R(xo ) xo R(x o x o ) • 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? 8 The best fit becomes the analysis assimilation window ti = analysis initial time tf = 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 window tf = analysis final time forecast tf + t = forecast horizon 10 Forecast verification is with respect to data not yet assimilated assimilation window forecast verification tf + t = forecast horizon 11 Basic IS4DVAR procedure: dx L J (x) λ i N(xi ) Fi dt i 1 N Lagrange function Lagrange multiplier J = modeldata misfit T i Fi F(it ) xi x(it ) λ i λ (ti ) λ (it ) N 1 1 T T 1 J ( x) x xb B x xb H i xi y i O 1 H i xi y i 2 i 1 2 Jb Jo The “best” simulation will minimize L: model model-data misfit is small and model physics are satisfied 12 Basic IS4DVAR procedure: Fi F(it ) dx L J (x) λ Ti i N(xi ) Fi dt i 1 N Lagrange function xi x(it ) J ( x) Lagrange multiplier λ i λ (ti ) λ (it ) J = modeldata misfit 1 T x x b B 1 x x b 2 Jb N 1 2 H x i i 1 y i O 1 H i x i y i T i Jo The “best” simulation minimizes L: At extrema of L we require: L 0 λ i L 0 xi dλ N T 1 i λ H O Hxm y m i im dt x dxi N(xi ) Fi 0 dt NLROMS T L 0 B 1 x(0) xb λ (0) x(0) L 0 λ (t ) 0 x(t ) ADROMS coupling of NL & AD i.c. of ADROMS 13 Basic IS4DVAR procedure: (1) Choose an x(0) xb (0) (2) Integrate NLROMS t [0,t ] and save x(t ) (a) Choose a x(0) J = modeldata misfit Inner-loop (3) Outer-loop (10) (b) Integrate TLROMS t [0,t ] and compute J (c) Integrate ADROMS t [t , 0] to yield J o λ (0) x(0) J (d) Compute B 1 x(0) λ (0) x(0) J ( x) 1 T x x b B 1 x x b 2 Jb N 1 2 H x i 1 i y i O 1 H i x i y i T i Jo (e) Use a descent algorithm to determine a “down gradient” correction to x(0) that will yield a smaller value of J (f) Back to (b) until converged (3) Compute new x(0) x(0) x(0) and back to (2) until converged NLROMS = Non-linear forward model; TLROMS = Tangent linear; ADROMS = Adjoint14 xb = model state (background) at end of previous cycle, and 1st guess for the next forecast xb In 4D-Var assimilation the adjoint gives the sensitivity of the initial conditions to mismatch between model and data previous forecast 0 1 2 3 4 time Observations minus Previous Forecast A descent algorithm uses this sensitivity to iteratively update the initial conditions, xa, (analysis) to minimize Jb+ S(Jo) x Adjoint model integration is forced by the model-data error 15 Observed information (e.g. SLA, SST) is transferred to unobserved state variables and projected from surface to subsurface in 3 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 16 MAB Satellite Observations for IS4DVAR 5 km resolution for IS4DVAR 1 km downscale for forecast SST 5-km daily blended MW+IR from NOAA PFEG Coastwatch MAB Sea Level Anomaly (SLA) is strongly anisotropic with short length scales due to flowtopography interaction, so use along-track altimetry (need coastal altimetry corrections for shelf data) • 4DVar uses all data at time of • satellite pass model “grids” data by simultaneously matching observations and dynamical and kinematic constraints 17 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) 18 All inputs: NAM Ocean model based open boundary conditions River discharge, temperature (USGS) Altimetry (via RADS; AVISO gridded) XBT, CTD, Argo Satellite SST – IR and mWave, passes/blended HF radar – totals/radials Cabled observatory time series – MVCO Glider CTD (and optics) NDBC buoy time series (T, S, velocity) tide gauges waves Drifters - SLDMB and AOML GDP Delayed mode Oleander ADCP science moorings 19 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 20 21 Skill of climatologies and MABGOM-V6 at reproducing all XBT/CTD from GTS in 2007-2008 in Slope Sea 22 Skill of climatologies and MABGOM-V6 at reproducing all XBT/CTD from GTS in 2007-2008 in MAB shelf waters 23 24 25 26 27 Mean barotropic velocity from ROMS versus mean alongshelf velocity from analysis of mooring observations by Lentz (2008) Blue – mean of ROMS v6 Red – mean of clim ROMS Black – mean of assim ROMS Green - observations 28 29 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 • de-tide along-track altimetry (developmental in MAB) • add ROMS tides to de-tided altimeter data • 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 30 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) 31 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 • Reduces inertial oscillations in the Slope Sea but removes tides • Tides recover quickly – approach needs refinement – possibly using 3-D velocity harmonic analysis of free running model 32 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 gh 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 • These data cannot easily be matched by a gh wave • We are effectively acknowledging the temporal correlation of the sub-tidal altimeter SLA data 33 High frequency variability: model and data issues gh 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 • These data cannot easily be matched by a gh wave • We are effectively acknowledging the temporal correlation of the sub-tidal altimeter SLA data 34 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. 35 Sequential assimilation of SLA and SST • 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. 36 37 38 Sequential assimilation of SLA and SST Assimilation window (3<=t<=6 days) Observed SST ROMS SST and currents at 200 m XBT transect (NOT assimilated) Jason-1 data 39 Sequential assimilation of SLA and SST ROMS solutions along the transect positions [lon,lat,time] 40 Sequential assimilation of SLA and SST ROMS-IS4DVAR fits the surface observations (SST and SSH), but how well does it represent unassimilated subsurface data? ROMS solutions along the transect positions [lon,lat,time] 41 Forward model Assimilation of SST and SSH (no climatology bias correction) depth (m) depth (m) 42 ROMS data assimilation for ESPreSSO 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 43 IS4DVAR data assimilation LaTTE: The Lagrangian Transport and Transformation Experiment system set-up: • • • • • resolution: forcing: rivers: DA window: period: 2.5km NAM model output USGS Hudson & Delaware gauges 3 days Apr. 10 – Jun 6, 2006 algorithm: Incremental Strong-constraint 4DVAR types and numbers of obs. (Courtier et al, 1994, QJRMS; Weaver et al, 2003, MWR; Powell et al, 2008, Ocean Modelling) 1 Nobs 1 J (Hi Φ y i )T O1 (Hi Φ y i ) φT0 B1φ0 2 i 0 2 44 ---- reduction of misfit 2006-04-20 06:57:36 IS4DVAR result model evolution of cost function observation 45 IS4DVAR result ---- forecast skills skill = 1 RMSafterDA RMSbeforeDA RMSafterDA RMSbeforeDA 1-CC afterDA 1-CC beforeDA 46 Adjoint sensitivity results J SST J day 0 J J J J u (0) T (0) (0) h (0) u (0) T (0) (0) h (0) Upstream temperature Density Surface current J X 104 105 2 10 4 X 2 1 J X (C 2 ) X 2 10 4 105 X SSH Viscosity Diffusion 3 105 1 0.3 101 102 105 106 2 10 5 3 107 105 3 107 47 Ensemble measure of the influence of glider MURI track at the end of the glider mission t 2 1 2 2 dLdt Cost function: J ( T T ) ( S S ) L(t2 t1 ) t1 L Covariance between J and temperature, cov( J , T ( x, y, z, t )), reflects the influence of glider observation, as plotted in the right. t: the finish time of a glider mission. 48 Ensemble measure of the influence of glider MURI track 5 days after the glider mission t: 5 days after the mission is finished. 49 Observation evaluation (T T )2 ( S S )2 1 J dtdV V t V t OT OS Assuming: model error ~ ocean state anomaly glider (T T )2 ( S S )2 1 J dtdV V t V t OT OS Mooring observation window forecast window 50 Observation evaluation (cont’d) northerly wind southerly wind (T T )2 ( S S )2 1 J dtdV V t V t OT OS observation window forecast window 51