AOSN-II in Monterey Bay:Data Assimilation, Adaptive Sampling and Dynamics

Pierre F.J. LermusiauxHarvard University

www.deas.harvard.edu/~pierrelPrinceton, October 29, 2003

1. AOSN-II: ocean physics scientific background2. ERROR SUBSPACE STATISTICAL ESTIMATION (ESSE)3. AUGUST 2003 REAL-TIME EXPERIMENT: Field and error predictions, Data

assimilation, Adaptive sampling and Dynamical investigations4. 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

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

California Undercurrent RAFOS Floats off

Central California

[from Garfield et al., 1999]

Feature Width 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)

0–500m 0–300m, 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)

10-40km VariableNear 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

Feature Width Location Vertical extent

Core Characteristics

Scales of Variability

References

Coastal Eddies Less 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 shelf Above 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 Pools 20–30 km wide

Inshore side of upwelled fronts

Less than 60m

Fresh and Cool Weeks Hayward and Mantyla (1990); Strub et al. (1991)

Large Filaments <100km wideextends200km

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/sOnshore speed 69–

92 cm/s

2–4 weeksupwelling ~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 wide50–100km

long

Inshore of baroclinic jets

(upwelling fronts)

Surface –intensified

(High nutrient)

Very cold (10–12C) and highly saline

(>33psu)

6–10 Days All of the above, specially Ramp et al. (1991); Dewey et al. (1991); Hickey, 1998

Mushroom heads T- shaped Instability-generated or wind-forced!

Above seasonal

thermocline (H1/H2 ~

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)

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.

A few AOSN-IIMonterey 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!

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

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)

• 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

CLASSES OF DATA ASSIMILATION SCHEMES

• Estimation Theory (Filtering and Smoothing)1. Direct Insertion, Blending, Nudging2. Optimal interpolation3. Kalman filter/smoother4. Bayesian estimation (Fokker-Plank equations)5. Ensemble/Monte-Carlo methods6. Error-subspace/Reduced-order methods: Square-root

filters, e.g. SEEK7. 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

- Lin, LS/Non-LS- Non-linear, LS/Non-LS

Different goals:

• Field, parameter, structure estimations

•Adaptive modeling, Adaptive sampling

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).

dd

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

Data-Forecast Melding:Minimum Error Variance within Error Subspace

Horizontal Resolution Sensitivity

27 km 9 km 3 km

Representation of Coastal Jets& Coastal Shear Zone Improved

Evaluation of COAMPS WindsFrom Oleg Logoutov and Pierre Lermusiaux, Harvard Univ.

M1

M2 M2

M10-12h

0-12h

72h

72h

0-12h

Atmospheric forcings and oceanic responses during August 2003

Upwelling Relaxation

Atmospheric forcings and oceanic responses during August 2003 (Cont.)

Aug 10: Upwelling Aug 16: Upwelled

Aug 20: Relaxation Aug 23: Relaxed

HOPS AVHRRSST – 21 August

From forecast issued Aug 20 – a posteriori comparison

Surface Temperature: 7 August-23 AugustShows Day/Night Sequence

10m Salinity: 7 August-23 August

7 August-23 AugustIndicates Upwelling/Relaxation Cycle

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- 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

SIO and WHOI Gliders, R/V Pt Sur

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:

RMSE EstimateStandard 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

Bias EstimateHorizontally-averaged data-model differences

Verification data time: Aug 13 Nowcast (Persistence forecast): Aug 11 1-day/2-day forecasts: Aug 12/Aug 13

Quick-Look evaluationof forecast based on

Aug 14 Aircraft SST

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.

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.

Coverage-based covariance: dPc/dt = E Pc + Pc ET – K R KT

Dynamics-based covariance: dPd/dt = DPd + Pd DT – K R KT

Error Covariance: dPe/dt = APe + Pe AT + Q – KR KT

where all K=K(H,R)

Cost function: e.g. find Hi and Ri

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(Pe +Pd + Pc)

dtt

ttPtrMinortPtrMin

f

RiHif

RiHi 0

,,))(())((

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 Fct Salinity Error Fct

Surf. Temperature Fct

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

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

PAA PAO PAB

P = POA POO POB

PBA PBO PBB

Coupled Interdisciplinary Error Covariances

Physics: xO = [T, S, U, V, W]

Biology: xB = [Ni, Pi, Zi, Bi, Di, Ci]

Acoustics: xA = [Pressure (p), Phase ()]

x = [xA xO xB]

xOcO

P = (x – x t ) ( x – x t )Tˆ ˆ

Error Covariance Forecast for 28 August

ESSE T error-Sv

ESSE field and error modes forecast for August 28 (all at 10m)

ESSE S error-Sv

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

3 September 5 September

HOPS AOSN-II nowcast and forecast of surface temperature

issued 3 September.

Real-Time Temperature Error

Forecast for 5 September

• 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