1 A Three-Dimensional Variational Data Assimilation in Support of Coastal Ocean Observing Systems Zhijin Li and Yi Chao Jet Propulsion Laboratory Jim McWilliams.

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A Three-Dimensional Variational Data Assimilation in Support of Coastal Ocean Observing Systems

Zhijin Li and Yi ChaoJet Propulsion Laboratory

Jim McWilliams and Kayo Ide

UCLA

ROMS User Workshop, October 2, 2007, Los Angeles

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Integrated Ocean Observing System (IOOS):Modeling, data assimilation, forecasting and adaptive sampling

Theoretical Understanding &

NumericalModels

Products

Users:Managers

Education & Outreach

Observations(satellite, in situ)

Feedback & Adaptive Sampling

Information

Data Assimilation

Observing System Design

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Outline

1. Real-time Regional Ocean Modeling System (ROMS)

2. Three-dimensional variational data assimilation

3. Assimilated observations

4. Evaluation of analyses and forecasts

5. Observing system experiments (OSE)

6. Relocatability

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Coupled with Tides

Sea Surface M2 Tidal Currents

ROMS Simulation HF Radar Obs

RMS Error of SSHs

Tide Gauge

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Regional Ocean Modeling System

(ROMS): From Global to Regional/Coastal

12-km

Multi-scale (or “nested”) ROMS modeling

approach is developed in order to simulate the 3D ocean at the spatial scale (e.g., 1.5-km) measured by in situ and remote

sensors

1.5-km5-km15-kmModeling Approach

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Data Assimilation

Analysis

Forecast

Processing

Observations

When the numerical model is so good as its predictionis superior to the climatological (almanac) forecast

Model

Data Assimilation

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ROMS Analysis and Forecast Cycle:Incremental 3DVAR

Aug.100Z

Time

Aug.118Z

Aug.112Z

Aug.106Z

Initialcondition

6-hour forecast

Aug.200Z

xa

xf

3-day forecast

y: observationx: model

6-hour assimilation cycle

)()(2

1)()(

2

1min 11 yHxRyHxxxBxxJ TfTf

x

xxx fa

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Why a There-Dimensional Variational Data Assimilation

• Real-time capability• Implementation with sophisticated and high

resolution model configurations• Flexibility to assimilate various observation

simultaneously• Development for more advanced scheme

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3DVAR: Weak Geostrophic Constraint and Hydrostatic Balance

TSfTS

aaTSfuv

aTSf

TS

uv

xx

xxx

xxx

x

x

x

S

T

v

u

x

aaTSuv xxx TS

Guv xx

aTS xxx

TSS xx

Geostrophic balance

Vertical integral of the hydrostatic equation

ax ageostrophic streamfunction and velocity potential

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Inhomogeneous and anisotropic 3D Global Error Covariance

Cross-shore and vertical section salinity correlation

SSH correlations

Kronecker Product

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Assimilated observations:Satellite infrared SSTs

NOAA GOES

NOAA AVHRR

Infrared, High resolutionCloud contamination

Microwave, Low resolution (25km)No cloud contamination

NASA AquaAMSR-E

NASA TRIMMTMI

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Assimilated observations:Satellite SSHs along track

JASON-1

Resolution: 120km cross track, 6km along track

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Integrated Ocean Observing Systems

0

100

200

300

400

500

600

700

800

900

213

215

217

219

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223

225

227

229

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239

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Year Day

Nu

mb

er o

f C

asts

/Day

<55

<110

<220

<440

<1100

T/S profiles from gliders Ship CTD profiles Aircraft SSTs AUV sections

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Assimilated Current Observations

Acoustic Doppler Current Profiler (ADCP)

BottomShipboard Buoy

High Frequency Radar Mapped 2D surface current

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3DVAR with First Guess at Appropriate Time (FGAT)

fttt

tt

ttt

tftt

Ttt

ttt

tfttt

Tt

xxx

yHxxHRyHxxHxBxJ

000

0

0

0

0

0

000

2

1

2

1

12

1

2

1

1

2

1

2

1

3.5DVar

If ,0 tt xx FDAT 3DVar is equivalent to 4DVar

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ROMS Performance Against Assimilated Data

August 2006 Mean

Temperature (C)

Salinity (PSU)

All Gliders Mean Diff RMS Diff

-0.3 0.3 0.0 0.75

-0.1 0.1 0.0 0.20

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Comparison of Glider-Derived Currents (vertically integrated current)

AOSN-II, August 2003 Black: SIO glider; Red: ROMS

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Forecast CorrelationPredictability during AOSN-II

Note: because gliders are moving, one cannot estimate the persistence

RMSE

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Observing System Experiment (OSE)

– Typically aimed at assessing the impact of a given existing data type on a system

– Using existing observational data and operational analyses, the candidate data are either added to withheld from the forecast system

– Assessing the impact

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Observing System Experiment (OSE):Glider Data Denial Experiment

Temperature Salinity

1st week 2nd week

CalPoly SIO WHOI

w/o CalPoly glider

with CalPoly glider

RMS Error

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HF radar

ROMS without HF radar data assimilation

ROMS with HF radar data assimilation

Impact of HF Radar

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Southern California Coastal Ocean Observing System (SCCOOS)

http://ourocean.jpl.nasa.gov/SCB

Southern California Bight

US WEST COAST

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Real-Time SCCOOS Data Assimilation and Forecasting System

http://ourocean.jpl.nasa.gov/SCB

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Evaluation with HF radar velocities

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Toward a Relocatable ROMS Forecasting System:Demonstration for Prince William Sound, Alaska

9-km

1-km3-km