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The OR-WA coastal ocean forecast system

Initial hindcast assimilation tests

Goals for the COMT project:

- DA in presence of the Columbia River- Develop the OR-WA forecast model- Try the ensemble-based covariance for

the initial conditions (the hybrid Ens-4DVAR)

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8 Jan, 2009 27 June, 2009 8 June, 2009

SST (the plume is relatively colder in winter, warmer in summer)

(no DA)

(1) AVHRR (2) model, no CR (3) model, CR (3) minus (2)

SST, May 2009

(no DA)

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Meridional wind stress (ROMS)

Salinity at z=-2 m(obs, model no-CR,model CR)

Temperature at z=-2 m

Time series, mooring NH10 location (44.65N):

(data: courtesy M. Levine, P. M. Kosro, C. Risien)

(no DA)

Initial DA testAvailable data

(assimilated as daily ave.)

- AVHRR SST- HF radar surface velocities- Alongtrack SSH (minus mean along the track)

6/22/2009 6/23 6/24

6/25 6/26 6/27Assimilation window: 22-24 Juneforecast: 25-27 June

6

→ min

Day-night composite AVHRR SST

HF radar daily ave maps (P. M. Kosro)

4DVAR = dynamically based time- and space- interpolation of data

analysisforecast

timepresent- 3 days

Along-track altimetry(AVISO)

forecast (prior)

- Assimilate data in a 3-day interval (TL&ADJ AVRORA)- De-tide the prior- Correct initial conditions in the recent past- Run forecast model (ROMS) with improved initial conditions

3-day averaged RMSE

priorinverse (std. dev. error in SST: 1.5C)inverse (std. dev. error in SST: 0.5C)

analysis forecast

Representer method details:

hbPbbbf

hPb

txuLdh

CRP

bb

xrbxuxu

TT

PRIOR

d

k

K

kkk

PRIORINV

2

1)(

),(

)0,()0,()0,(1

correction = linear combination of representers. K= total number of data

R=representer matrix (all representers sampled at all data locations)

To find b, solve the linear system (or, minimize the quadratic functional f(b))

To obtain a representer: 1 ADJ + 1 TL model runCGM: Solve Pb=h iteratively

CGM: search for “P”-orthogonal (conjugate) directions p1, p2,…

On each iteration, minimize f(b) over a span of {pk}

piPpj=0 (ij)

Preconditioning: provide a matrix A that is easy to invert, s.t.A-1/2P A-1/2 is better conditioned than P.

CGM only requires A-1z

Egbert’s preconditioning (may be found in Bennett’s textbook):

Compute a subset of representers directly

Form the preconditoining matrix from the computed representers

ADJ

TL

ADJ

TL

ADJ

TL

…

A ADJ

TL

CGM (each step requires 1 ADJ and 1 TL run)

“Inner loop” convergence for a given choice of model and data error variances:

No preconditioning

“Re-orthogonalization” of pk

Preconditioning w/ A=Cd (Carrier et al., 2014)

Preconditioning with 280 representers

hPbCRP d ,

2

2

2

2

h

hPb

hbPbbbf TT 2

1)(

(K=50,191)

Model vs/ data errors:The IC error covariance: based on the balanced operator (Weaver et al. (2005))dSST=0.5C

Model error std. dev.

Assumed data error std. dev

SST (C) 0.42 1.5

SSH (m) 0.03 0.01

u,v (m/s) 0.03 0.03for data error std. dev.:SST 1.5C, SSH 0.03 mSST 0.5C, SSH 0.03 mSST 0.5C, SSH 0.01 m

RMS (Rjj)