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A Data Assimilation System for Costal Ocean Real-Time Predictions

Zhijin Li and Yi ChaoJet Propulsion Laboratory, California Institute of Technology

James C. McWilliams (UCLA), Kayo Ide (UMD)

ROMS Meeting, April 5-8, 2010, Hawaii

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Outline

1. Developed costal ocean data assimilation and forecasting systems

2. Recap on the three-dimensional variational data assimilation

3. A multi-scale three-dimensional variational data assimilation

4. Summary

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2003 Autonomous Ocean Sampling Network (AOSN) Experiment

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

Southern California Bight Real-Time System

Data Assimilation

HF Radar Observation

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Prediction of Drifter Trajectories in the Prince William Sound

Oil Spill: 1989 Exxon Tanker Wreck ,Prince William Sound, Alaska

L0 10kmL1 3.6kmL2 1.2km

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Release time: July 25th, 02 GMT, end time: July 28th, 02 GMT.

Ensemble of Co-located ROMS Simulated Trajectories

PWS 2009 Field Experiment

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Data Assimilation and Forecasting Cycle

3-day forecast

Aug.100Z

Time

Aug.118Z

Aug.112Z

Aug.106Z

Initialcondition

6-hour forecast

Aug.200Z

xa

xf

6-hour assimilation cycle

xxx fa

Time scales comparable with those of the atmosphere

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A There-Dimensional Variational Data Assimilation (3DVAR)

1. Real-time capability

2. Implementation with sophisticated and high resolution model configurations

3. Flexibility to assimilate various observation simultaneously

4. Development for more advanced scheme

(Li et al., 2006, MWR; Li et al., 2008, JGR, Li et al., 2008, JAOT)

),,,,(

)()(21)()(

21min 11

vuSTx

yHxRyHxxxBxxJ TfTf

x

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Weak Geostrophic Constraint:Decomposition of Balanced and Unbalanced Components

TSfTS

aaTSfuv

aTSf

TS

uv

xxxxxxxx

xxx

STvu

x

aaTSuv xxx TS

Guv xx

aTS xxx

TSS xx

Geostrophic balance

Geostrophic sea surface level

ax Ageostrophic streamfunction and velocity potential

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Kronecker Product Formulation of 3D Error Correlations

TTT

GGGG

GGGGC

CCC

CCC

111

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Inhomogeneous and anisotropic 3D correlations

Cross-shore and vertical section salinity correlation

Non-steric SSH correlations

(Li et al., 2008, JGR)

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Assimilation of Multi-Satellite SSTs and SSHs

Infrared and Microwave SST Sea Surface Heights

JASON-1

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Assimilation of Real-Time High Frequency Radar Velocities

Short distance: 100km, res of 1km, 5 MHzLong distance:

200km, res of 5km, 25 MHz

http://www.cocmp.org/

2008-12-08

http://www.sccoos.org/

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Comparison of Glider-Derived Currents (vertically integrated current)

Black: SIO glider; Red: ROMSSALT(PSU)

Performance of ROMS3DVAR: AOSN-II, August 2003

(Chao et al., 2009, DSR)

TEMP(C)

Glider temperature/salinity profiles

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Southern California Coastal Ocean Observing System (SCCOOS)

SIO Glider Tracks

Motivation: assimilating sparse vertical profiles along with high resolution observations for a very high resolution model

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Multi-Scale Data Assimilation: Concept

SL

SL

eeexxx

)()(21)()(

21min

)()(21)()(

21min

11

11

SSSST

SSSfSSS

TfSSx

LLLLT

LLLfLLL

TfLLx

yxHRyxHxxBxxJ

yxHRyxHxxBxxJ

S

L

SL

SL yyyHxy

Background

Observation

Multi-scale DA

(Boer, 1983, MWR)

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Multi-Scale Data Assimilation: Scheme

)()(21)()(

21min 11

ssT

safLa

TafLx

yHxRyHxxxBxxJ

)()(21)()(

21min 11

LLLLT

LLLfLLL

TfLLx

yxHRyxHxxBxxJL

aL

fL

aL xxx

Large Scale

aL

fafL xxx Small Scale

Sparse Obs

High Resolution Obs

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Twin Experiments: Observations

• Model resolution of 1km

• SSTs and surface velocities at 2km by 2km

• T/S profiles

1. at 10km by 60km (ideal)

2. at 10km by 180km (real)

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Root-Mean Squared Errors (RMSEs) at 30m

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Root-Mean Squared Errors (RMSEs)at 50m

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3DVAR

MS3DVAR

NO-DA

RMSEs

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3DVAR

MS3DVAR

NO-DA

RMSEs

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SCB Operational System: 3DVAR vs MS3DVAR

3DVAR

MS3DVAR

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HF Radar and Data Assimilation Analysis Velocities

Standard 3DVAR MS-3DVAR

Correlation RMSE Correlation RMSE

U 0.62 0.13m/s 0.75 0.11m/s

V 0.68 0.11m/s 0.82 0.08m/s

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Summary

A 3DVAR system has been developed with unique formulations for coastal oceans.

The MS3DVAR system has been demonstrated significantly better skill and computational efficiency, and it has been implemented in operational applications.

For more information on real-time data assimilation and forecasting systems: http://ourocean.jpl.nasa.gov

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Backup

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MS3DVAR Work Flow

LS-3DVAR -SS-3DVAR

Increment

Obs (Glider, Satellite, HF radar, etc)

Large Scale (LS) Small Scale (SS)Forecast fx

Large Scale fLx

aS

afL

a xxx aS

fa xxx

aLx

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ETKF vs MS-3DVAR in Twin experiments

• Observations: HF radar velocities and SSTs, along with Sparse T/S profiles

• ETKF continuously reduces RMSEs because of the predicted error covariance, while MS-3DVAR more effectively fit to high resolutions observations at the early stage

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RMSE, ETKF RMSE, MS-3DVAR

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(Lorenc 2003)

A Hybrid Ensemble MS-3DVAR

Applied to the small-scale components