Harvard University. ASLO, February 21, 2004

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1 Real-Time Error Forecasting, Data Assimilation and Adaptive Sampling in Monterey Bay during AOSN-II using the Error Subspace Statistical Estimation System Wayne G. Leslie, Pierre F.J. Lermusiaux, Constantinos Evangelinos (MIT), Patrick J. Haley, Oleg Logoutov, Patricia Moreno, Allan R. Robinson, Gianpiero Cossarini (Trieste U.), X. San Liang, Sharan Majumdar (U. Miami) ASLO, February 21, AOSN-II: Ocean physics and August 2003 experiment background 2. Error Subspace Statistical Estimation (ESSE) 3. Field/error predictions, Assimilation, Adaptive sampling and Dynamical investigations 4. Conclusions AONS-II Team: Cal-Tech, Princeton, MBARI, JPL (ROMS), NRL, NPS, WHOI, SIO, etc

Current System (CCS) Upwelling/Relaxation at Pt AN/ Pt Sur: Upwelled water advected equatorward and seaward Coastal eddies, jets, squirts, filaments, etc.

2 Regional Features of Monterey Bay and the California Current System and Real-time Modeling Domains (4 Aug. 3 Sep., 2003) HOPS Nested Domains Conceptual model: Rosenfeld et al., Bifurcated flow from an upwelling center Calif. Current System (CCS) Upwelling/Relaxation at Pt AN/ Pt Sur: Upwelled water advected equatorward and seaward Coastal eddies, jets, squirts, filaments, etc. : High submesoscale and mesoscale variability in the CTZ California Undercurrent (CUC): California Current (CC): CC CUC Poleward flow/jet, km offshore, m depth Broad southward flow, km offshore, 0-500m depth

3 Real-time ESSE : AOSN-II Accomplishments 10 sets of ESSE nowcasts and forecasts of temperature, salinity and velocity, and their uncertainties, issued from 4 Aug. to 3 Sep. - Total of 4323 ensemble members: members per day ( state var.) - ESSE fields included: central forecasts, ensemble means, a priori (forecast) errors, a posteriori errors, dominant singular vectors and covariance fields Ensemble of stochastic ocean model predictions - PE of Harvard Ocean Prediction System (HOPS) - Forced by deterministic 3km and hourly COAMPS flux predictions - Oceanic stochastic forcings for sub-mesoscale eddies, BCs and atmos. fluxes ESSE results described and posted on the Web daily - Discussion of predicted errors, fields/features and their dynamics - Outline of uncertainty initialization and forecast procedures - Web:

4 Real-time ESSE : AOSN-II Accomplishments (Cont.) ESSE data assimilation data points per day: ship (Pt. Sur, Martin, Pt. Lobos), glider (WHOI and Scripps) and aircraft SST data, within 24 hours of appearance on data server - Data analyzed and quality controlled daily for real-time forecasts ESSE fields formed the basis for daily adaptive sampling recommendations Adaptive modeling: Oceanic boundary conditions and model parameters for transfer of atmospheric fluxes calibrated and modified in real-time to adapt to evolving conditions 23 sets of real-time OI nowcasts/forecasts (complementary to ESSE) Real-time research work on: stochastic error models, coupled physics-biology, tides, free-surface PE model

5 Oceanic responses and atmospheric forcings during August 2003 Upwelling Relaxation

6 Oceanic responses and atmospheric forcings during August 2003 Aug 10: Upwelling Aug 16: Upwelled Cy. Circ. Bif. Aug 20: Relaxation Aug 23: Relaxed Cy. Circ. Bif.

Error Subspace Statistical Estimation (ESSE) Uncertainty forecasts (dynamic error subspace and adaptive error learning) Ensemble-based (with nonlinear and stochastic

7 Error Subspace Statistical Estimation (ESSE) Uncertainty forecasts (dynamic error subspace and adaptive error learning) Ensemble-based (with nonlinear and stochastic model) Multivariate, non-homogeneous and non-isotropic DA Consistent DA and adaptive sampling schemes Software: not tied to any model, but specifics currently tailored to HOPS

8 Ocean Regions and Experiments/Operations for which ESSE has been utilized in real-time Strait of Sicily (AIS96-RR96), Summer 1996 Ionian Sea (RR97), Fall 1997 Gulf of Cadiz (RR98), Spring 1998 Massachusetts Bay (LOOPS), Fall 1998 Georges Bank (AFMIS), Spring 2000 Massachusetts Bay (ASCOT-01), Spring 2001 Monterey Bay (AOSN-2), Summer 2003

9 Atmospheric fluxes from 3km and hourly COAMPS (J. Doyle, NRL): Winds Sensitivity to horizontal resolution 27 km 9 km 3 km 3km improves Representation of Coastal Jets & Coastal Shear Zone Our evaluations: e.g. Buoy winds (blue) vs COAMPS 72h forecasts (red dots) M1 72h M2 72h

10 RMSE Estimate Standard deviations of horizontally-averaged data-model differences Verification data time: Aug 13 Nowcast (Persistence forecast): Aug 11 1-day/2-day forecasts: Aug 12/Aug 13

11 Bias Estimate Horizontally-averaged data-model differences Verification data time: Aug 13 Nowcast (Persistence forecast): Aug 11 1-day/2-day forecasts: Aug 12/Aug 13

12 IC, Aug 12 2-day, central fct 2-day fct, ens mean Ensemble Mean and Central Forecast Issued in real-time

13 ESSE Surface Temperature Error Standard Deviation Forecasts Aug 10 Aug 11 Aug 12 Aug 9 12: start of Upwelling Aug 24 Aug 27 Aug 28 End of Relaxation Upwelling period

14 ESSE Surface Temperature Error Standard Deviations: Before and After ESSE data assimilation Prior: Aug 21 Posterior: Aug 21

15 ESSE/ETKF schemes for adaptive sampling Adaptive Sampling: Use forecasts and their uncertainties to predict most useful observational system in space (locations/paths) and time (frequencies) Dynamics: dx =M(x)dt+ dη η~ (0, Q) Measurement: y = H(x) + ε ε ~ (0, R) Non-lin. Err. Cov.: Linearized Err. Cov. : dp / dt=< ( x xˆ)( M( x) M(ˆ)) x T >+< ( M( x) M(ˆ)( x x xˆ ) T > + Q dp / dt= AP+ PA T + Q Metric or Cost function: e.g. Find H i and R i Min Hi, Ri trpt ( ( f)) such that or Min HiRi, t t f 0 trpt ( ( )) dt ETKF: Use linearized error cov. eq. Replace effect of transfer matrix A by a single priori ensemble ESSE: Use exact nonlinear err. cov. For every choice of adaptive strategy, an ensemble is computed

16 Quantitative Adaptive Sampling via ESSE - Select sets of candidate sampling regions and variables that satisfy operational constraints - Forecast reduction of errors for each set based on a tree structure of small ensembles and data assimilation - Optimization of sampling plan: select sequence of subregions/variables which maximize the nonlinear error reduction at t f (trace of ``information matrix at final time) or over [t 0, t f ]

Position and strength of meander were very uncertain (e.g. T and S error St. Dev., based on 450 2-day fcsts).

17 Real-time Adaptive Sampling Pt. Lobos Surf. Temperature Fcst. Large uncertainty forecast on 26 Aug. related to predicted meander of the coastal current which advected warm and fresh waters towards Monterey Bay Peninsula. Position and strength of meander were very uncertain (e.g. T and S error St. Dev., based on day fcsts). Different ensemble members showed that the meander could be very weak (almost not present) or further north than in the central forecast Sampling plan designed to investigate position and strength of meander and region of high forecast uncertainty. Temperature Error Fcst. Salinity Error Fcst.

18 Adaptive sampling helps correcting data and model errors Real-time Temp 2.5 day Fcst for Aug 26 Aug 26, Calibrated Temp (up to SST) As above, but DA of calibrated data during Aug Lesson Learned: Real-time calibration of multi-sensors (and of multi-models) is essential!

19 ESSE DA properties: Error covariance function predicted for 28 August T0m-T0m T0m-S0m T0m-U0m T0m-Psi

20 ESSE Field and Error Modes Forecast for August 28 (all at 10m) T S ESSE T error-sv ESSE S error-sv

21 Two 6-day model runs Temp. at 10 m T section across Monterey-Bay No-tides Tidal effects Vert. Reyn. Stress Horiz. Momen. Stress

22 Dominant dynamical balances for initial biogeochemical fields/parameters Balance subject to observed variables and parameters constraints

23 Surface CHL forecast (hindcast) Starts from balanced IC on Aug 4 Then, 13 days of physical DA Forecast of 3-5 days afterwards CHL Aug 20 CHL Aug 21 CHL Aug 22 CHL Aug 20, 20:00 GMT

24 CONCLUSIONS: ESSE in Monterey Bay-CCS in August 2003 Consistent fully nonlinear ensemble-based Daily real-time predictions of field and errors Data assimilation Adaptive sampling Dynamical analyses The successions of upwelling and relaxed states impact uncertainties In upper layers, uncertainty scales generally smaller during relaxation than during upwelling Descriptive physical dynamics Confirmed Pt AN << Pt Sur upwelling and are in phase Daily cycles matter: e.g. modulate downwelling-driven northward coastal jets Observed bifurcation (separatrix /LCS front) at Monterey Bay Peninsula Cyclonic circulation in the Bay favored when: Local upwellings at Pts. AN/Sur join, along-shelf upwelling, warm croissant along Monterey Bay coastline Ongoing research - Finalize evaluation of error forecasts and stochastic error models - Tidal effects matter: regional-scale offshore, (sub)-mesoscale in the Bay - Coupled physical-biological data calibration, adjustments and data assimilation - Re-analysis ESSE fields and errors

25 EXTRA VUGRAFS

26 ESSE DA properties: Error covariance function predicted for 28 August T0m-T30m T0m-S30m T0m-U30m T0m-Psi

27 T-T T-S T-U T-Psi

28 Observed Tidal Effects Temperature at M1 CODAR Velocity Tidal-series least-square fit to data: For T at 300m, 10-30% total amp. For U,V at 0m, 20-40% total amp.

Modeling of tidal effects in HOPS Obtain first estimate of principal tidal constituents via a shallow water model 1. Global TPXO5 fields (Egbert, Bennett et al.) 2.

29 Modeling of tidal effects in HOPS Obtain first estimate of principal tidal constituents via a shallow water model 1. Global TPXO5 fields (Egbert, Bennett et al.) 2. Nested regional OTIS inversion using tidal-gauges and TPX05 at open-boundary Used to estimate hierarchy of tidal parametrizations : i. Vertical tidal Reynolds stresses (diff., visc.) K T = α u T 2 and K=max(K S, K T ) ii. Modification of bottom stress τ =C D u S+ u T u S iii. Horiz. momentum tidal Reyn. stresses Σ ω (Reyn. stresses averaged over own T ω ) iv. Horiz. tidal advection of tracers ½ free surface v. Forcing for free-surface HOPS full free surface

30 Daily Average of RHS Terms: Residuals vs. Order of Magnitude Mass. Bay: Aug 21, 1998 Monterey Bay: Aug 04, 2003 Surface Surface Residuals Bottom Bottom Surface Surface Order of magnitude Bottom Bottom Cape Cod Cape Ann 100km offshore Monterey

Harvard University AMS Annual Meeting, Seattle, WA, January 13, 2004

Harvard University AMS Annual Meeting, Seattle, WA, January 13, 2004 Application of the ESSE System to Real-Time Error Forecasting, Data Assimilation and Adaptive Sampling off the Central California Coast during AOSN-II: Pierre F.J. Lermusiaux, Wayne G. Leslie, Constantinos