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 InterpolationMultivariate Optimal InterpolationNRL Coupled Data Assimilation System (NCODA)NRL 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, , u, v)
)]([)( 1b
Tb
Tbba xHyRHHPHPxx
Observation Space Formulationwhere xa is the analysis xb is the background Pb is the background error covariance R is the observation error covariance H 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 + A’A’THT ( HA’A’T HT + o o)-1 (Y- HXf) Kalman Gain obs-model
X : model state (, 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 observationo : Observation error : 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 matrix using a second-order Gaussian Markov Random Field (GMRF) model
• A sparse auto-regression operator operates on the error in the MRF neighborhood ej = i€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 situ Temp/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
35 678
9101112
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 6
7891011
12
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
Tra
ns
po
rt (
SV
)
OI/CHMVOIENOIENROIFOI/CHNew
Transports across a closed section Transports across a closed section
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