1. AOSN-II in Monterey Bay: Data Assimilation, Adaptive Sampling and Dynamics Pierre F.J. Lermusiaux Harvard University www.deas.harvard.edu/~pierrel Princeton, October 29, 2003 1.AOSN-II: ocean physics scientific background 2.ERROR SUBSPACE STATISTICAL ESTIMATION (ESSE) 3.AUGUST 2003 REAL-TIME EXPERIMENT: Field and error predictions, Data assimilation, Adaptive sampling and Dynamical investigations 4.CONCLUSIONS Collaborators: Wayne G. Leslie, Constantinos Evangelinos, Patrick J. Haley, Oleg Logoutov, Patricia Moreno, Allan R. Robinson, Gianpiero Cossarini (Trieste), X. San Liang, A. Gangopadhay (U-Mass), Sharan Majumdar (U-Miami) AONS-II Team: Cal-Tech, Princeton, MBARI, JPL (ROMS), NRL, NPS, WHOI, SIO, etc

2. Top left – Upwelling State – 23-26 May 1989 – upwelled water from points moves equatorward and seaward – Point Ano Nuevo water crosses entrance to Monterey Bay Top right – Relaxation State – 18 -22 June 1989 – Cal. Crt. anti-cyclonic meander moves coastward Bottom right – Larger regional context – 18 June 1989 – California Current System Conceptual model: Rosenfeld et al., 1994. Bifurcated flow from an upwelling center

3. California Undercurrent RAFOS Floats off Central California [from Garfield et al., 1999]

4. FeatureWidth Location Vertical extent Core Characteristics Scales of Variability References California Current (Mean flow + Southwestward meandering Jet) Mean southward flow between 100–1350 km offshore Inshore edge is 100–150km away from coast Jet location default (Fig. 5 of Brink et al., 1991) 0–500m0–300m, Baroclinic jet’s V_max = 50– 70cm/s; Salinity minimum (32.9psu); Sigma–t = 25 Meandering jet from 39N (Strong) to 30N (Weak) Meander longshore wavelength O (300km); onshore- offshore amplitude O (100–200km); temporal synoptic scales: Eulerian (5 days), Lagrangian (10 days) Brink et al., 1991; Lynn and Simpson, 1987; Chelton, 1984; Ramp (website); Tisch et al., 1992; Chereskin et al., 1998; Miller et al., 1999; Ramp et al., 1997a,b; Collins et al., 2003 Poleward Flows: California Under Current and Inshore Current (Davidson Current) 10-40kmVariable Near Pt. Sur 10- 40km offshore, another branch offshore following 2500m isobath, about 100km offshore 0-300m Offshore and inshore (coastal) Cores! 100–200m. 15–20cm/s. Meanders with what Wavelengths and what time-periods? Ramp et al. (1997a,b); Wooster and Jones (1970); Wickham (1973); Pierce et al., 1999– DSR); Oey, JGR (1999); Swenson and Miller JGR (1996); Huyer et al. DSR (1992); Chavez et al. (1997), Garfield et al., (1999); Collins et al. (1996) Coastal Transition Zone (CTZ) The Coastal Transition Zone is a region offshore of the continental shelf (Brink and Cowles, 1991) where filaments, eddies, upwelling fronts and anomalous pools occur in this eastern boundary current system California Current System: Its Features and Scales of Variability

5. FeatureWidth Location Vertical extent Core Characteristics Scales of Variability References Coastal EddiesLess than 100 km South of promontories of C. Mendocino and Pt. Arena Up to 300m (Bucklin, 1991) Cool, Saline and nutrient-rich water relative to the warmer and less saline jet and offshore waters Temporal scales ~40–60 days Hayward and Mantyla (1990); Bucklin (1991); Hickey, 1998. Coastal jets along Upwelling fronts Narrow ~10–40km Over the shelfAbove the halocline (   < 26.5) Energetic, Vm = 1m/sec Active to Relaxation periods (weeks) Huyer et al. (1991); Smith and Lane (1991); Pierce et al. (1991); Allen et al. (1991); Kosro et al. (1991); Strub et al. (1991); Rosenfeld et al. CSR (1994); Chavez et al. (1997); Huyer (1983); Washburn et al. (1991) Anomalous Pools20–30 km wide Inshore side of upwelled fronts Less than 60m Fresh and CoolWeeksHayward and Mantyla (1990); Strub et al. (1991) Large Filaments <100km wide extends 200km offshore Recurrent off Pt. Arena (inshore of baroclinic jets) Surface- intensified ~100m and below Cool (12–13C) Salty (32.7–33psu) Offshore speed 60– 87 cm/s Onshore speed 69– 92 cm/s 2–4 weeks upwelling ~40 m/day; subduction ~25 m/day Bernstein et al. (1977); Traganza et al. (1980, 1981); Flament et al. (1985); Abbott and Zion (1987); Brink (1991); Strub et al. (1991); Mackas et al. (1991); Ramp et al. (1991); Dewey et al. (1991); Kadko et al. (1991); Chavez et al. (1991); Chereskin and Niiler (1994–DSR) Squirts (smaller filaments) 30km wide 50–100km long Inshore of baroclinic jets (upwelling fronts) Surface – intensified (High nutrient) Very cold (10–12C) and highly saline (>33psu) 6–10 DaysAll of the above, specially Ramp et al. (1991); Dewey et al. (1991); Hickey, 1998 Mushroom headsT- shapedInstability- generated or wind-forced! Above seasonal thermocline (H 1 /H 2 ~ 1/50) Ageostrophic and asymmetric 1–3 days to develop; 3–5 days to diffuse Ikeda and Emery (1984); Sheres and Kenyon (1989); Smith et al. (1991); Mied (1990); Mied et al. (1991); Munk (2000)

6. TEAM AOSN-II Science Objectives Long-Term Objective: Develop an Adaptive Coupled Observation/Modeling Prediction System able to provide an accurate 3 to 5 day forecast of interdisciplinary ocean fields (physical, biological, chemical, etc.) including, importantly, marine biology events, such as bioluminescence blooms, red tide events, or the health of important stages in the food chain. Current Year Objectives: To study processes and conduct science important to above long-term objectives To do this while exploiting the coupled observation/modeling prediction system to conduct science that cannot otherwise be conducted. To study the onset, development, and variability of a 3-D upwelling Center off Point Año Nuevo and in Monterey Bay. To further study the Center’s ecosystem response: physics, chemistry, and biology (including bioluminescence). To understand the California current system and its interactions with coastal circulation, biological dynamics, and advection of the Center.

7. A few AOSN-II Monterey Bay Physical Oceanography Open Questions Is the Monterey Sub-marine Canyon responsible in any way to the introduction of upwelled water in the Bay? What are the dynamical controls of the predominantly cyclonic circulation in the Bay: winds, tidal residuals, seasonal heating, fresh-water influx, topography?.How baroclinic is the Monterey Bay Circulation? Internal Rossby radius of deformation increases from 1-2km at the coast to 10-15 km offhore. What is the intern-annual variability in Monterey Bay? We found that no data in historical databases matched the August 2003 data!

9. Error Subspace Statistical Estimation (ESSE) Uncertainty forecasts (with dynamic error subspace, 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

10. HOPS/ESSE– AOSN-II Accomplishments 23 sets of real-time nowcasts and forecasts of temperature, salinity and velocity released from 4 August to 3 September 10 sets of real-time ESSE forecasts issued over same period: total of 4323 ensemble members (stochastic model, BCs and forcings) Forecasts forced by 3km and hourly COAMPS flux predictions Adaptive sampling recommendations suggested on a routine basis Web: http://www.deas.harvard.edu/~leslie/AOSNII/index.html for daily distribution of forecasts, scientific analyses, data analyses, special products and control-room presentations Assimilated ship (Pt. Sur, Martin, Pt. Lobos), glider (WHOI and Scripps) and aircraft SST data, within 24 hours of appearance on data server (after quality control)

11. 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 Ocean Regions and Experiments/Operations for which ESSE has been utilized in real-time

12. CLASSES OF DATA ASSIMILATION SCHEMES Estimation Theory (Filtering and Smoothing) 1.Direct Insertion, Blending, Nudging 2.Optimal interpolation 3.Kalman filter/smoother 4.Bayesian estimation (Fokker-Plank equations) 5.Ensemble/Monte-Carlo methods 6.Error-subspace/Reduced-order methods: Square-root filters, e.g. SEEK 7.Error Subspace Statistical Estimation (ESSE): 5 and 6 Control Theory/Calculus of Variations (Smoothing) 1.“Adjoint methods” (+ descent) 2.Generalized inverse (e.g. Representer method + descent) Optimization Theory (Direct local/global smoothing) 1.Descent methods (Conjugate gradient, Quasi-Newton, etc) 2.Simulated annealing, Genetic algorithms Hybrid Schemes Combinations of the above - Lin - Lin., LS - Linear, LS - Non-linear, Non-LS - Non-linear, LS/Non-LS - (Non)-Linear, LS -Non-linear, LS/Non-LS - Lin, LS - Lin, LS/Non-LS - Non-linear, LS/Non-LS Different goals: Field, parameter, structure estimations Adaptive modeling, Adaptive sampling

14. Initialization of the Dominant Error Covariance Decomposition Dominant uncertainties: missing or uncertain variability in IC, e.g.~smaller mesoscale variability Approach: Multi-variate, 3D, Multi-scale ``Observed'' portions: directly specified and eigendecomposed from differences between the initial state and data, and/or from a statistical model fit to these differences ``Non-observed'' portions: Keep ``observed'' portions fixed and compute ``non-observed'' portions from ensemble of numerical (stochastic) dynamical simulations See: Lermusiaux et al (QJRMS, 2000) and Lermusiaux (JAOT, 2002).

15. d

16. Hovmoller diagram (t,y) Sample effects of sub-grid-scale internal tides: difference between non-forced and forced model Uncertainties Due to Un-resolved Processes: Stochastic forcing model of sub-grid-scale internal tides

17. Data-Forecast Melding: Minimum Error Variance within Error Subspace

20. Horizontal Resolution Sensitivity 27 km9 km3 km Representation of Coastal Jets & Coastal Shear Zone Improved

21. Evaluation of COAMPS Winds From Oleg Logoutov and Pierre Lermusiaux, Harvard Univ. M1 M2 M1 0-12h 72h 0-12h

22. Atmospheric forcings and oceanic responses during August 2003 Upwelling Relaxation

23. Atmospheric forcings and oceanic responses during August 2003 (Cont.) Aug 10: Upwelling Aug 16: Upwelled Aug 20: Relaxation Aug 23: Relaxed

24. HOPSAVHRR SST – 21 August From forecast issued Aug 20 – a posteriori comparison

25. Surface Temperature: 7 August-23 August Shows Day/Night Sequence

26. 10m Salinity: 7 August-23 August

27. 7 August-23 August Indicates Upwelling/Relaxation Cycle

28. Multi-scale Modeling and Data Assimilation Issues Data -Multiscale data density -Multi-sensor, multi-scale data (inter)-calibration issues Modeling -More than 500 simulations for model calibrations prior to experiments -Due to climatic variations, 4 sets of initial conditions: none matched -Domains: see http://oceans.deas.harvard.edu/haley/AOSN2/Domains/domains.html http://oceans.deas.harvard.edu/haley/AOSN2/Domains/domains.html -Vertical grid discretization (grids + slope) -Sub-grid-scale parameterizations -Open boundary conditions (see movie), nesting ESSE -Started 4 days later than OI because: wait for in-situ data -Stopped for 5 days because: proposals, OBC, surface mixing layer parameterization (heat and wind forcings) -Improved cshell management

29. SIO and WHOI Gliders, R/V Pt Sur

31. Aug 7-9 Drifter Path Simulation and its Uncertainty 5 an hour earlier than the real deployment time 5 at the real deployment time 5 an hour later than the real deployment time. Each set of 5 were placed in a "cross" pattern Note the daily cycle! Modulates/feads a northward coastal rim current! To predict the path of the real drifter deployed by F. Chavez and provide an estimate of uncertainty in this prediction, 15 simulated drifters were deployed in the HOPS simulation:

32. 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

33. 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

34. Quick-Look evaluation of forecast based on Aug 14 Aircraft SST

35. Comparison of 19 August nowcast with CODAR mapped data shows good qualitative agreement. N-S flow at mouth of bay and general cyclonic circulation within the bay are reproduced.

36. Interdisciplinary Adaptive Sampling Use predictions and their uncertainties to alter the observational system in space (locations/paths) and time (frequencies) for physics, biology and/or acoustics. Locate regions of interest, based on: Uncertainty values (error variance, higher moments, pdf’s) Interesting physical/biological/acoustical phenomena (feature extraction, Multi-Scale Energy and Vorticiy analysis) Maintain synoptic accuracy Plan observations under operational, time and cost constraints to maximize specific information content: e.g. minimize uncertainty at final time or over the observation period.

38. Coverage-based covariance:dP c /dt = E P c + P c E T – K R K T Dynamics-based covariance:dP d /dt = DP d + P d D T – K R K T Error Covariance:dP e /dt = AP e + P e A T + Q – KR K T where all K=K(H,R) Cost function: e.g. find H i and R i Dynamics: dx/dt =Ax +  ~ (0, Q) Measurement:y = H x +  ~ (0, R) Definition of metric for adaptive sampling: Illustration for linear systems In realistic cases, need to account for: Nonlinear systems and large covariances => use ESSE Operational constraints Multiple objectives and integration, e.g. Min tr(P e +  P d +  P c )

39. Real-time Adaptive Sampling – Pt. Lobos 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 450 2-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 FctSalinity Error Fct Surf. Temperature Fct

40.  Real-time 3-day forecast of cross- sections along 1 ship-track (all the way back to Moss Landing)  Such sections were provided to R/V Pt Lobos, in advance of its survey

41.  Real-time 3-day forecast of the expected errors in cross-sections along 1 ship- track (all the way back to Moss Landing)  Such error sections were provided to R/V Pt Lobos, in advance of its survey

42. P AA P AO P AB P = P OA P OO P OB P BA P BO P BB Coupled Interdisciplinary Error Covariances Physics: x O = [T, S, U, V, W] Biology: x B = [N i, P i, Z i, B i, D i, C i ] Acoustics: x A = [Pressure (p), Phase (  )] x = [x A x O x B ] xOxO cOcO P =   (x – x t ) ( x – x t ) T  ˆˆ

43. Error Covariance Forecast for 28 August

44. ESSE T error-Sv ESSE field and error modes forecast for August 28 (all at 10m) ESSE S error-Sv

45. http://people.deas.harvard.edu/~leslie/AOSNII/Aug22/ESSE/esse_product.html This one focuses on data assimilation: ESSE Second Initialization Aug 21 ESSE Forecast for Aug 24 Example of ESSE daily web-pages

46. 3 September 5 September HOPS AOSN-II nowcast and forecast of surface temperature issued 3 September. Real-Time Temperature Error Forecast for 5 September

47. Monterey Bay-CCS in August 2003 (Daily real-time ESSE for 1 month, error prediction, DA, adaptive sampling) –Two successions of upwelling (Pt. S, Pt. AN) states and relaxed states Specific Processes: –Local upwellings at Pts AN/Sur join, along-shelf upwelling, warm croissant along Monterey Bay coastline: favors cyclonic circulation in the Bay (limited tidal effects) –Relaxation process very interesting: release of kinetic energy, creation of wild N(z) profile, lots of baroclinic instability potential, internal jets, squirts, filaments, eddies –Others: Daily cycles, LCS front/ bifurcation (separatrix) at Monterey Bay Peninsula Future research –Summarize/study dynamical findings in Monterey Bay, including CCS interactions/fluxes –Skill evaluation of fields/errors with classic and new generic/specific metrics –Predictability studies, ensemble properties (mean, mpf, std, sv, etc), energetics –ESSE system: Grid computing, XML, visualization, Bayesian assimilation CONCLUSIONS: Present and Future