Ensemble Kalman Filtering in the MITgcm with DART

Ensemble Kalman Filtering in the MITgcm with DART

MIT, Sep 22, 2008

o SIO: Ibrahim Hoteit Bruce Cornuelle

o NCAR: Jeffrey Anderson Tim Hoar Nancy Collins

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o Tropical Pacific 1/3 degree and 1/6 degree

o CalCOFI 1/10 degreeo Gulf of Mexico 1/10 degreeo San Diego region 1 kmo Taiwan region (to come) All with ECCO-adjoint

assimilation

… Ensemble Kalman Filtering

Regional MITgcm Assimilation at SIO

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o What For?o Ensemble Kalman Filteringo Pros & Conso Data Assimilation Research Testbed

-- DARTo DART implementation with MITgcmo An Example of Fit

Outline

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What For?■ The BP – Scripps GOM project:

o Predict the front of the loop current in the Gulf of Mexico

o Deploy gliders and HF radars and use data assimilation

o 1/10o Gulf of Mexico MITgcm forced by ECCO

■ Ensemble Kalman Filtering with MITgcm: o No update of the background covariance in the

adjoint method o Proved better for forecasting o Add new assimilation capability to MITgcm

(complement adjoint?)

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Analysis Step

Ensemble Kalman Filtering (EnKF)

Forecast Step • Correct forecast

• Update error covariance

• Kalman Gain

P P Pa f f fk k k k kG H

• Integrate analysis

• Update error covariance

, 1 1 , 1P P Qf a Tk k k k k k kM M 1P [ P R ]f T f T

k k k k k k kG H H H

[ ]a f fk k k k k kx x G y H x

, 1 1f ak k k kx M x

■ EnKFs: Represent uncertainties about the state estimate by an ensemble of points

Integrate ensemble with

ModelP =

Cov(ensemble)

Kalman FilterEnsemble Kalman Filter

■ Easily portable■ Provide estimates of the background

covariance matrix■ Offers more flexibility from an OI to Ensemble Kalman

filters

Pros & Cons

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■ Rank deficient Localization and Inflation are needed!

■ A software facility employing different EnKFs

■ DART is designed so that incorporating new models and observations requires minimal coding of a small set of interface routines

■ Advanced localization/inflation schemes■ Operationally used with CAM and WRF at

NCAR, MA2 at GFDL, and elsewhere …

Data Assimilation Research Testbed --DART

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DART Implementation with MITgcm

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■ No modification to the MITgcm■ Scaling of DART parallel algorithm is

independent of model■ Enabled for assimilation of most ocean data

sets

MITgcmIntegrate ensemble in time

DATA

DARTUpdate

ensemble with Data

INTERFACE

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An Example of Fit

Pseudo-DATA Posterior

July 1st, 1996

12 weeks later

Prior

30 members

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■ The machinery is now working

■ Early testing shows good fit

■ ... Will be tested with real data

Thank you

To conclude