Demonstration and Comparison of Sequential Approaches for Altimeter Data Assimilation in HYCOM

Demonstration and Comparison of Sequential Approaches for Altimeter Data Assimilation in HYCOM

A. Srinivasan, E. P. Chassignet, O. M. Smedstad, C. Thacker, L. Bertino, P. Brasseur, T. M. Chin,, F.

Counillon, and J. Cummings.

Outline:

Assimilation Schemes

Twin Experiments

Results/Diagnostics

Sequential assimilation schemes for HYCOMSequential assimilation schemes for HYCOM

1. Optimal Interpolation

2. Multivariate Optimal Interpolation(J. Cummings, O.M. Smedstad –NRL)

3. Ensemble Optimal Interpolation & Kalman Filter

(F. Counillon, L. Bertino – NERSC)

4. Ensemble Reduced Order Information Filter

(T. M. Chin, Univ of Miami/JPL)

5. Singular Evolutive Extended Kalman Filter

(P. Brasseur – LEGI, Grenoble)

Multivariate Optimal InterpolationNRL Coupled Data Assimilation System (NCODA)

Multivariate Optimal InterpolationMultivariate Optimal InterpolationNRL Coupled Data Assimilation System (NCODA)NRL Coupled Data Assimilation System (NCODA)

• Oceanographic version of MVOI method used in NWP systems (Daley, 1991)

• Simultaneous analysis of five ocean variables: temperature, salinity, geopotential, and u-v velocity components (T, S, Φ, u, v)

)]([)( 1b

Tb

Tbba xHyRHHPHPxx −++= −

Observation Space Formulationwhere xa is the analysis

xb is the backgroundPb is the background error covarianceR is the observation error covarianceH is the forward operator (spatial interpolation)(xa – xb) is the analyzed increment[y-H(xb)] is the innovation vector (synoptic T, S, u, v observations)

Xa = Xf + α A’A’THT (α HA’A’T HT + εo εo)-1 (Y- HXf)Kalman Gain obs-model

X : model state (η, t, s, u, v, thk); (a: analysis; f: forecast)A’: centered collection of model states (A’=A-A)Y : observationsH : interpolates from model grid to observationεo : Observation errorα : rebalance ensemble variability to realistic level

Ensemble Optimal Interpolation (ENOI)Ensemble Optimal Interpolation (ENOI)

• Covariance are based on an historical ensemble composed of 3 year 10 day model output (106 members) without assimilation

• Covariance are 3D multivariate

• Conservation of the dynamical balance of the model since the update is a linear combination of model state

• Temporal invariance of the covariance matrix, computationally cheap

Ensemble Reduced Order Information Filter (ENROIF)Ensemble Reduced Order Information Filter (ENROIF)

• The ROIF assimilation scheme parameterizes the covariance matrixusing a second-order Gaussian Markov Random Field (GMRF) model

• A sparse auto-regression operator operates on the error in the MRF neighborhood

ej = Σi€Z αijej-i + νj

• The square of the regression operator is the Information Matrix which is the inverse of the covariance Matrix

• Recently replaced the extended KF with ensemble methods to propagate the information matrix.

• Uses a static Information matrix generated using 55 members in all experiments shown here

MRF order 2 Neighborhood

Configuration:• 89° to 98°W Longitude and 8° to 31°N Latitude•1/12° horizontal grid (258x175 pts; 6.5km average spacing)• 20 vertical layers• Forcing from NOGAPS/FNMOC 1999-2000• Monthly River Runoff• Nested within 1/12 N. Atlantic domain• HYCOM V. 2.1.36

Gulf of Mexico Model ConfigurationGulf of Mexico Model Configuration

Synthetic Data Used in the ExperimantsSynthetic Data Used in the Experimants

GOMHYCOM

AssimilationSchemes

Ocean Obs

SST: Ship, Buoy, AVHRR(GAC/LAC), GOES, AMSR-E, AATSR, MSG

SSH: Altimeter (Jason, Envisat, GFO), in situTemp/Salt profiles

Innovations

Restart Files

First Guess

Sequential Analysis-Forecast-Analysis CycleSequential Analysis-Forecast-Analysis Cycle

Communication via restart files

sea surf. height Aug 29, 1999

20N

22N

24N

26N

28N

30N

98W 96W 94W 92W 90W 88W 86W 84W 82W 80W 78W

-100 -80 -60 -40 -20 0 20 40 60 80 100

GOMd0.08ci 2.0 cm

-25.4 to 91.7

sea surf. height Aug 29,1999

20N

22N

24N

26N

28N

30N

98W 96W 94W 92W 90W 88W 86W 84W 82W 80W 78W

-100 -80 -60 -40 -20 0 20 40 60 80 100

REFci 2.0 cm

-14.1 to 88.5

temperature zonal sec. 25.08n Aug 29, 1999

200

400

600

800

0

5

10

15

20

25

30

35 6789

101112

13

14

15

16

17

18

98W 96W 94W 92W 90W 88W 86W 84W 82W 80W 78WREF

temperature zonal sec. 25.08n Aug 29, 1999

200

400

600

800

0

5

10

15

20

25

30

35 6789

101112

13

14

15

16

17

18

6

98W 96W 94W 92W 90W 88W 86W 84W 82W 80W 78WGOMd0.08

Truth and Initial State of Assimilative RunsTruth and Initial State of Assimilative Runs

Truth and Forecast Day 50Truth and Forecast Day 50

RMS Error in SSH ForecastsRMS Error in SSH Forecasts

SST RMS ErrorSST RMS Error

Temperature Vertical Section Forecast Day 50 Temperature Vertical Section Forecast Day 50

Salinity Vertical Section Forecast Day 50Salinity Vertical Section Forecast Day 50

Mean and RMS Error Profiles (T &S) Mean and RMS Error Profiles (T &S)

Mean and RMS Error Profiles (u & v) Mean and RMS Error Profiles (u & v)

0 5 10 15 20 30 35 40 45 50-10

010

Layer-8

0 5 10 15 20 30 35 40 45 50-10

010

Layer-9

0 5 10 15 20 30 35 40 45 50-505

Layer-10

0 5 10 15 20 30 35 40 45 50-505

Layer-11

0 5 10 15 20 30 35 40 45 50-10

010

Layer-12

0 5 10 15 20 30 35 40 45 50-20

020

Layer-13

0 5 10 15 20 30 35 40 45 50-10

010

Layer-14

0 5 10 15 20 30 35 40 45 50-10

010

Layer-15

OI/CHMVOIENOIENROIFTruth

Basin Averaged Change in Layer Thickness

Basin Averaged Layer Thickness Basin Averaged Layer Thickness

Transports across a closed section Transports across a closed section

0 10 20 30 40 50 60 70-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Transports Across 26N

Days

Tran

spor

t (SV

)OI/CHMVOIENOIENROIFOI/CHNew

Transports across a closed section Transports across a closed section