GSI-based EnKF-Var hybrid data assimilation system:
implementation and test for hurricane prediction
Xuguang Wang, Xu Lu, Yongzuo Li, Ting Lei
University of Oklahoma, Norman, OK
In collaboration with
Mingjing Tong , Vijay Tallapragada, Dave Parrish, Daryl Kleist
NCEP/EMC, College Park, MD
Jeff Whitaker, Henry Winterbottom
NOAA/ESRL, Boulder, CO
1
GSI-based Hybrid EnKF-Var DA system
Wang, Parrish, Kleist, Whitaker 2013, MWR
EnKF
Whitaker et al. 2008,
MWR
EnKF
analysis 2
member 2
forecast
member k
forecast
control
forecast
Ensemble
covariance
GSI-ACV
Wang 2010, MWR
data assimilation
EnKF
analysis k
control
analysis
Re-center EnKF analysis ensemble
to control analysis
EnKF
analysis 1
member 1
forecast
member 1
analysis
member 1
forecast
member 2
analysis
member 2
forecast
member k
analysis
member k
forecast
control
forecast
First guess
forecast 2
GSI hybrid for GFS:
GSI 3DVar vs. 3DEnsVar Hybrid vs. EnKF
 3DEnsVar Hybrid was
better than 3DVar due to
use of flow-dependent
ensemble covariance
 3DEnsVar was better
than EnKF due to the use
of tangent linear normal
mode balance constraint
Wang, Parrish, Kleist and
Whitaker, MWR, 2013
3
GSI hybrid for GFS:
3DEnsVar vs. 4DEnsVar
•
GSI-4DEnsVar: Naturally extended from and unified with GSIbased 3DEnsVar hybrid formula (Wang and Lei, 2014, MWR, in
press).

Add time dimension in 4DEnsVar

J x1' , α  1 J1   2 J e  J o
1 T
1
1 T
1
 1 x1' B static x1'   2 αT C1α  t 1 ( yto '-Ht xt ) T R -t1 ( yto '-Ht xt )
2
2
2
K

xt  x   α k  (x ek )t
'
'
1

k 1
B stat 3DVAR static covariance; R observation error covariance; K ensemble size;
C correlation matrix for ensemble covariance localization; xek kth ensemble perturbation;
x1' 3DVAR increment; x ' total (hybrid) increment; y o ' innovation vector;
H linearized observation operator; 1 weighting coefficient for static covariance;
 2 weighting coefficient for ensemble covariance; α extended control variable.
4
GSI hybrid for GFS:
3DEnsVar vs. 4DEnsVar
Results from Single Reso. Experiments

4DEnsVar improved general global
forecasts

4DEnsVar improved the balance of
the analysis

Performance of 4DEnsVar degraded
if less frequent ensemble
perturbations used

4DEnsVar approximates nonlinear
propagation better with more
frequent ensemble perturbations

TLNMC improved global forecasts
Wang, X. and T. Lei, 2014: GSI-based four dimensional ensemble-variational (4DEnsVar) data
assimilation: formulation and single resolution experiments with real data for NCEP Global
Forecast System. Mon. Wea. Rev., in press.
5
GSI hybrid for GFS:
3DEnsVar vs. 4DEnsVar
16 named storms in Atlantic
and Pacific basins during
2010
6
Approximation to nonlinear propagation
–3h increment
propagated by
model integration
4DEnsVar
(hrly pert.)
4DEnsVar
(2hrly pert.)
3DEnsVar
Hurricane Daniel 2010
*
-3h
time
0
3h
7
Verification of hurricane track forecasts
•
•
•
•
3DEnsVar outperforms GSI3DVar.
4DEnsVar is more accurate than 3DEnsVar after the 1-day forecast lead time.
Negative impact if using less number of time levels of ensemble perturbations.
Negative impact of TLNMC on TC track forecasts.
8
Development and research of GSI based
Var/EnKF/hybrid for regional modeling system
GSI-based
Var/EnKF/3D4DHybrid
GFS
WRF-NMMB
WRF ARW
HurricaneWRF (HWRF)
Poster: Johnson et al.
“Development and Research of
GSI based Var/EnKF/hybrid
Data Assimilation for
Convective Scale Weather
Forecast over CONUS.”
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GSI hybrid for HWRF
Hurricane Sandy, Oct. 2012
 Complicated evolution
 Tremendous size
 147 direct deaths
across Atlantic Basin
 US damage $50 billion
New York State before and after
nhc.noaa.gov
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Experiment Design
• Model: HWRF
Sandy
2012
•Observations: radial velocity
from Tail Doppler Radar (TDR)
onboard NOAA P3 aircraft
• Initial and LBC ensemble: GFS
global hybrid DA system
• Ensemble size: 40
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Experiment Design
• Model: HWRF
Oper.
HWRF
•Observations: radial velocity
from Tail Doppler Radar (TDR)
onboard NOAA P3 aircraft
• Initial and LBC ensemble: GFS
global hybrid DA system
• Ensemble size: 40
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TDR data distribution (mission 1)
P3 Mission 1
13
Verification against SFMR wind speed
Last Leg
14
Comparison with HRD radar wind analysis
15
Comparison with HRD radar wind analysis
S
N
16
Track forecast (RMSE for 7 missions)
17
Experiments for 2012-2013 seasons
Correlation between HRD radar wind analysis and
analyses from various DA methods
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
Hybrid
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
GSI3DVAR
Case#
Hybrid-GFSENS
18
ISSAC 2012 (mission 7)
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Verification against SFMR and flight level data
Experiments for 2012-2013 season
Track
MSLP
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Two-way Dual Resolution Hybrid for
HWRF
9km
•3km movable nest ingests
9km HWRF EnKF ensemble
•Two-way coupling
3km
•Tests with IRENE 2011
assimilating airborne radar
data
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Two-way Dual resolution hybrid
Summary and ongoing work
GFS
a. GSI-based 4DEnsVar for GFS improved global forecast and TC forecast.
b. The analysis generated by 4DEnsVar was more balanced than 3DEnsVar.
c. the performance of 4DEnsVar was in general degraded when less
frequent ensemble perturbations were used.
d. The tangent linear normal mode constraint had positive impact for global
forecast but negative impact for TC track forecasts.
e. Preliminary tests showed positive impact of the temporal localization on
the performance of 4DEnsVar.
HWRF
a. The GSI-based hybrid EnKF-Var data assimilation system was expanded to HWRF.
b. Various diagnostics and verifications suggested this unified GSI hybrid DA system
provided more skillful TC analysis and forecasts than GSI 3DVar and than HWRF
GSI hybrid ingesting GFS ensemble.
c. Airborne radar data improved TC structure analysis and forecast, TC track and
intensity forecasts. Impact of the data depends on DA methods.
d. Dual-resolution (3km-9km) two way hybrid for HWRF showed promising results.
e. Developing/enhancing 4DEnsVar hybrid and assimilation of other airborne data
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and other data from NCEP operational data stream for HWRF.
Development and Research of GSI-based Var/EnKF/hybrid DA
for Convective Scale Weather Forecasts over CONUS
Poster: Johnson, Wang, Lei, Carley, Wicker, Yussouf, Karstens
•
Outer Domain
– assimilate operational
conventional surface and
mesonet observations,
RAOB, wind profiler, ACARS,
and satellite derived winds
every 3 hours to define
synoptic/mesoscale
environment
•
Inner Domain
– assimilate velocity and
reflectivity from NEXRAD
radar network every 5 min
during last 3hr cycle
4 km
12 km
Johnson, Wang et al. 2014
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Precipitation forecast skill averaged over 10 complex,
convectively active cases
• GSI-EnKF forecasts are more skillful than GSI-3DVar
forecasts for all thresholds and lead times.
• Benefits of radar data are more pronounced assimilated by
GSI-EnKF than GSI-3DVar.
26
May 8th 2003 OKC Tornadic Supercell
1hr forecast from 22Z
GSI hybrid
GSI hybrid
Ref and vorticity at 1 km
Lei, Wang et al. 2014
W and Vort. at 4 km
27
DA cycling configuration (mission 1)
Cold Start
GSI3DVar
OBS
Spin-up Forecast
Deterministic Forecast
DA Cycle
OBS
Hybrid
Spin-up Forecast
Deterministic Forecast
Ensemble Perturbation
OBS
HWRF EnKF
Deterministic Forecast
Ensemble
Spin-up Forecast
DA Cycle
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DA cycling configuration (mission 1)
OBS
Hybrid-GFSENS
Spin-up Forecast
Deterministic Forecast
Ensemble Perturbation
GFS ENS
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GSI-based Hybrid EnKF-Var DA system
•
•
(4D)EnKF: ensemble square root filter interfaced with GSI
observation operator (Whitaker et al. 2008)
GSI-3DEnsVar: Extended control variable (ECV) method
implemented within GSI variational minimization (Wang 2010,
MWR):
J x1' , α   1 J1   2 J e  J o



1 ' T 1 '
1 T 1
1 o'
' T
 1 x1 B x1   2 α C α  y  Hx R 1 y o '  Hx'
2
2
2
K

x  x   α k  x ek
'
'
1
k 1


Extra term associated with
extended control variable
Extra increment associated
with ensemble
30