hans huang: variational data assimilation, snu lecture. june 9th, 20091 da variational data...
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Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 1
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Variational Data Assimilation
Hans Huang
NCAR
Acknowledge: Dale Barker, The WRFDA team, MMM and DATC staff
AFWA, NSF, KMA, CWB, BMB, AirDat
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 2
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• Introduction to data assimilation.• Basics of variational data assimilation.• Demonstration with a simple system.• The WRFDA approach.
Outline
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 3
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Modern weather forecast (Bjerknes,1904)
• Analysis: using observations and other information, we can specify the atmospheric state at a given initial time: “Today’s Weather”
• Forecast: using the equations, we can calculate how this state will change over time: “Tomorrow’s Weather”
Vilhelm Bjerknes (1862–1951)
• A sufficiently accurate knowledge of the state of the atmosphere at the initial time
• A sufficiently accurate knowledge of the laws according to which one state of the atmosphere develops from another.
(Peter Lynch)
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 4
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initial state forecast
Analysis
Model
Model state x, ~107
Observationsyo, ~105-106
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 5
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Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 6
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Assimilation methods
• Empirical methods– Successive Correction Method (SCM)
– Nudging
– Physical Initialisation (PI), Latent Heat Nudging (LHN)
• Statistical methods – Optimal Interpolation (OI)
– 3-Dimensional VARiational data assimilation (3DVAR)
– 4-Dimensional VARiational data assimilation (4DVAR)
• Advanced methods– Extended Kalman Filter (EKF)
– Ensemble Kalman Filter (EnFK)
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 7
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• Introduction to data assimilation.• Basics of variational data assimilation.• Demonstration with a simple system.• The WRFDA approach.
Outline
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 8
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The analysis problem for a given time
Consider a scalar x.
The background (normally a short-range forecast):
xb=xt+b.
The observation:
xr=xt+r.
The error statistics are assumed to be known: < b > = 0, mean error (unbiased), < r > = 0, mean error (unbiased), <b2> = B, background error variance, <r2> = R, observation error variance, <br> = 0, no correlation between b and r ,
where <⋅> is ensemble average.
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BLUE: the Best Liner Unbiased Estimate
The analysis: xa =xt +a.Search for the best estimate: xa=αxb+βxr
Substitute the definitions, we have: α+β=1. <a>=0The variance: A=<a2>=B−2βB+β2 B+R( )
To determine β: dAdβ
=−2B+2β B+R( )=0
we have β= BB+R
The analysis: xa=xb+B
B+Rxr−xb( )
The analysis error variance: A−1=B−1+R−1
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 10
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limB→0
xa =xb
The analysis: xa =xb+B
B+Rxr−xb( )
0 <
BB+R
<1
The analysis error variance: A−1 =B−1 + R−1
limR→0
xa =xr
A < B
A < R
The analysis value should be
between background and
observation.
Statistically, analyses are better than
background.Statistically, analyses are better than
observations!
If B is too small,
observations are less useful.If R can be tuned, analysis
can fit
observations as close as one
wants!
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 11
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3D-Var
The analysis is obtained by minimizing the cost function J , defined as :
J=12
x-xb( )
T
B-1 x-xb( )+
12
x-xr( )
T
R-1 x-xr( )
The gradient of J with respect to x:
′J =B-1 x-xb( )+R-1 x-xr
( )
At the minimum, ′J =0, we have:
xa=xb+B
B+Rxr−xb( )
the same as BLUE.
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 12
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Sequential data assimilation (I)
True states : ..., xi−1t , xi
t , xi+1t , ...
Observations : ..., xi−1r , xi
r , xi+1r , ...
Forecasts : ..., xi−1f , xi
f , xi+1f , ...
Analyses : ..., xi−1a , xi
a, xi+1a , ...
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 13
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Sequential data assimilation (II)
Forecast model:
xi+1t =M xi
t( )+qi
Where qi is the model error.
As qi is unknown and xia is the best estimate of xi
t the forecast
model usually takes the form:
xi+1f =M xi
a( )
OI (and 3DVAR): xb=xif
xia=xi
f +B
B+Rxi
r−xif⎛
⎝⎜⎞⎠⎟
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Sequential data assimilation (III)
4DVAR analysis is obtained by minimizing the cost function J , defined as:
J xi( )=12
xi−xif⎛
⎝⎜⎞⎠⎟
T
B−1 xi−xif⎛
⎝⎜⎞⎠⎟
+12
Mk−1 xi( )−xi+kr⎡
⎣⎢⎤⎦⎥T
R−1 Mk−1 xi( )−xi+kr⎡
⎣⎢⎤⎦⎥
k=0
K∑
where, K is the assimilation window and
M−1 xi( ) = xi
M0 xi( ) = M xi( )
Mk−1 xi( ) = M (M (...M
k
1 24 34 (xi )...))
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 15
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Sequential data assimilation (IV)
4DVAR (continue)
The gradient of J with respect to x:
′J =B−1 xi−xif⎛
⎝⎜⎞⎠⎟ + M i+ j
T R−1 Mk−1 xi( )−xi+kr⎡
⎣⎢⎤⎦⎥
j=0
k−1∏
k=0
K∑
where, M i+ jT is the adjoint model of M at time step i+ j .
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 16
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Scalar to Vector
From scalar to vector:
Number of grid points ≈ 107 :
x→ x xb → xb
Dimension of B, P ≈ 107x 107Number of observations, 106 :
xr → yo
x−xr → H(x) −yo
Dimension of R ≈ 106x 106
Observation operator H
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 17
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H - Observation operatorH maps variables from “model space” to “observation space” x y
– Interpolations from model grids to observation locations
– Extrapolations using PBL schemes
– Time integration using full NWP models (4D-Var in generalized form)
– Transformations of model variables (u, v, T, q, ps, etc.) to “indirect” observations (e.g.
satellite radiance, radar radial winds, etc.)• Simple relations like PW, radial wind, refractivity, …
• Radar reflectivity
• Radiative transfer models
• Precipitation using simple or complex models
• …
!!! Need H, H and HT, not H-1 !!!
Z =Z(T, IWC,LWC,RWC,SWC)
0
( )( ) ( , ( ))
dTRL B T z dz
dz
νν ν∞ ⎡ ⎤≈ ⎢ ⎥⎣ ⎦∫
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 18
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Level of preprocessing and the observation operator
Phase and amplitude
Ionosphere correctedobservables
Refractivity profiles
Bending angle profiles
Temperature profiles
Raw data:
Frequency relations
Geometry
Abel trasformor ray tracing
Hydrostatic equlibriumand equation of state
H =I
H =H
N
H =H
RH
N
H =H
GH
RH
N
H =H
FH
GH
RH
N
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 19
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Sequential data assimilation
Model: xi+1
f = M x ia( )
OI: xia=xi
f +BHT HBHT + R( )-1
yo - H xi
f( )⎡⎣
⎤⎦
4D-Var: J xi( )=1
2xi -xi
f( )
T
B-1 xi -xif
( )
+1
2H Mk-1 xi( )( )-yi+k
o⎡⎣
⎤⎦
TR -1 H Mk-1 xi( )( )-yi+k
o⎡⎣
⎤⎦
k=0
k∑
′J =B-1 xi -xif
( ) + M i+ jT HTR−1 H Mk−1 xi( )[ ]−yi+k
o⎡⎣
⎤⎦
j=0
k−1∏
k=0
K∑
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 20
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Issues on variational data assimilation
• Observations yo
• Observation operator H
• Observation errors R
• Backgound xb
• Size of B: statistical model and tuning
• Minimization algorithm Quasi−Newton; Conjugate Gradient; …( )
• M and MT : development and validity
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 21
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• Introduction to data assimilation.• Basics of variational data assimilation.• Demonstration with a simple system.
• The WRFDA approach.
Outline
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 22
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Nonlinear equation (NL):
xi+1= axi−xi2=M xi( )
Depending on a,three types of solution are found; steady state; limited cycle; chaotic.
Tangent Linear equations (TL):
xi+1tl = a−2xi
bs( )xitl=Μixi
tl
(linearized around basic state xibs)
Adjoint equation (AD):
xiad= a−2xi
bs( )xi+1ad =Μi
T xi+1ad
Note here for this simple case we have
Μi= ΜiT = a−2xi
bs( )
The Lorenz 1964 equation
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 23
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Issues on data assimilation
for the system based on the Lorenz 64 equation
• Observation operator H =Η =ΗT =1
• Estimate of the true states - generated (with model error!)
• Observation errors xo−xt=σoG
• Size of Β is 1, but B=σb2 still needs attention
• Μ and ΜT : no eort in development but their validity is still a major problem
(model, assimilation window length, ...)
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 24
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Too simple?
Try: Lorenz63 modelTry: 1-D advection equationTry: 2-D shallow water equation…Try: ARW!!!
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 25
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• Introduction to data assimilation.• Basics of variational data assimilation.• Demonstration with a simple system.• The WRFDA approach.
WRFDA is a Data Assimilation system built within
the WRF software framework, used for application in both research and operational environments….
Outline
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 26
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WRF-Var (WRFDA) Data Assimilation Overview
• Goal: Community WRF DA system for • regional/global, • research/operations, and • deterministic/probabilistic applications.
• Techniques: • 3D-Var• 4D-Var (regional)• Ensemble DA, • Hybrid Variational/Ensemble DA.
• Model: WRF (ARW, NMM, Global)• Support: WRFDA team
• NCAR/ESSL/MMM/DAG• NCAR/RAL/JNT/DATC
• Observations: Conv.+Sat.+Radar
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 27
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WRFDA Observations In-Situ:
- Surface (SYNOP, METAR, SHIP, BUOY).- Upper air (TEMP, PIBAL, AIREP, ACARS,
TAMDAR). Remotely sensed retrievals:
- Atmospheric Motion Vectors (geo/polar).- Ground-based GPS Total Precipitable Water.- SSM/I oceanic surface wind speed and TPW.- Scatterometer oceanic surface winds.- Wind Profiler.- Radar radial velocities and reflectivities.- Satellite temperature/humidities.- GPS refractivity (e.g. COSMIC).
Radiative Transfer:- RTTOVS (EUMETSAT).- CRTM (JCSDA).
2004082600 ~ 2004092812
Threshold = 5.0mm
TIME
3 6 9 12 15 18 21 240.0
0.2
0.4
0.6
0.8
1.0
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Th
reat
Sco
re
Bias
KMA Pre-operational Verification:
(with/without radar)
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 28
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Assume background error covariance estimated by model perturbations x’ :
Two ways of defining x’:
The NMC-method (Parrish and Derber 1992):
where e.g. t2=24hr, t1=12hr forecasts…
…or ensemble perturbations (Fisher 2003):
Tuning via innovation vector statistics and/or variational methods.
Model-Based Estimation of Climatological Background Errors
€
€
B0 = (xb − x t)(xb − x t)T ≈ x' x'T
€
B0 = x'x'T ≈ A(x t 2 − x t1)(x t 2 − x t1)T
€
B0 = x'x'T ≈ C(x k − x )(x k − x )T
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 29
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Single observation experiment- one way to view the structure of B
The solution of 3D-Var should be
€
xa = xb + BHT HBHT + R[ ]−1
y − Hxb[ ]
Single observation
€
xa − xb = Bi σ b2 + σ o
2[ ]
−1yi − x i[ ]
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 30
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Pressure,Temperature
Wind Speed,Vector,
v-wind component.
Example of B 3D-Var response to a single ps observation
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 31
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-20 -15 -10 -5 0 5 10 15 20
X GRID
5
10
15
20
25
-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.91
-20 -15 -10 -5 0 5 10 15 20
X GRID
5
10
15
20
25
-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.91
CV5-ENS
-20 -15 -10 -5 0 5 10 15 20
X GRID
5
10
15
20
25
-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.91
CV5-NMC
-20 -15 -10 -5 0 5 10 15 20
X GRID
5
10
15
20
25
-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.91
B from ensemble methodB from NMC method
Examples of BT increments : T Observation (1 Deg , 0.001 error around 850 hPa)
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 32
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Sensitivity to Forecast Error Covariances in Antarctica(Rizvi et al 2006)
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
May 2004
bias/RMSE (K)
60km Verification (vs.
radiosondes)T+24hr Temperature
GFS-based
errors
WRF-based
errors
20km Domain2
60km Domain 1
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 33
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Define preconditioned control variable v space transform
where U transform CAREFULLY chosen to satisfy Bo = UUT .
Choose (at least assume) control variable components with uncorrelated errors:
where n~number pieces of independent information.
Incremental WRFDA Jb Preconditioning
€
Jb δx t0( )[ ] =1
2δx t0( ) − xb t0( ) − xg t0( )[ ]{ }
TBo
−1 δx t0( ) − xb t0( ) − xg t0( )[ ]{ }
€
δx t0( ) = Uv
€
Jb δx t0( )[ ] =1
2vn
2
n∑
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 34
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WRFDA Background Error Modeling
€
δx t0( ) = Uv = UpUvUhv
Uh: RF = Recursive Filter,
e.g. Purser et al 2003
Uv: Vertical correlations
EOF Decomposition
Up: Change of variable,
impose balance.
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 35
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WRFDA Background Error Modeling
100
200
300
400
500
600
700
800
900
1000
0 100 200 300 400 500
Error correlation lengthscale (km)
Pressure (hPa)
u
v
T
p
q
€
δx t0( ) = Uv = UpUvUhv
Uh: RF = Recursive Filter,
e.g. Purser et al 2003
Uv: Vertical correlations
EOF Decomposition
Up: Change of variable,
impose balance.
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 36
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WRFDA Background Error Modeling
100
200
300
400
500
600
700
800
900
1000-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Eigenvector Amplitude
Pressure (hPa)Mode 1Mode 2Mode 3Mode 4Mode 5
€
δx t0( ) = Uv = UpUvUhv
Uh: RF = Recursive Filter,
e.g. Purser et al 2003
Uv: Vertical correlations
EOF Decomposition
Up: Change of variable,
impose balance.
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 37
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WRFDA Background Error Modeling
Define control variables:
€
ψ '
€
r' = q'/ qs Tb,qb, pb( )
χu ' = χ '− χ b ' ψ '( )
Tu ' =T '−Tb ' ψ '( )
psu ' =ps '−psb ' ψ '( )
€
δx t0( ) = Uv = UpUvUhv
Uh: RF = Recursive Filter,
e.g. Purser et al 2003
Uv: Vertical correlations
EOF Decomposition
Up: Change of variable,
impose balance.
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 38
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WRFDA Statistical Balance Constraints
• Define statistical balance after Wu et al (2002):
• How good are these balance constraints? Test on KMA global model data. Plot correlation between “Full” and balanced components of field:
€
€
χb • χ / χ • χ
€
Tb • T / T • T
€
psb • ps / ps • ps
€
χb' = cψ '
€
Tb' (k) = G(k,k1)ψ ' (k1)
k1∑
€
psb' = W (k)ψ ' (k)
k∑
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 39
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WRF 4D-Var milestones
2003: WRF 4D-Var project.
2004: WRF SN (simplified nonlinear model).
Modifications to WRF 3D-Var.
2005: TL and AD of WRF dynamics.
WRF TL and AD framework.
WRF 4D-Var framework.
2006: The WRF 4D-Var prototype.
Single ob and real data experiments.
Parallelization of WRF TL and AD.
Simple physics TL and AD.
JcDF
2007: The WRF 4D-Var basic system.
2008: Further optimization and testing
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 40
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Basic system: 3 exes, disk I/O, parallel, full dyn, simple phys, JcDF
NL(1),…,NL(K)
TL(1),…,TL(K)
AF(K),…,AF(1)
AD00
WRF
WRF_NL
WRF_TL
WRF_AD
VAR
Outerloop
Mk
dk
Innerloop
U
UT
call
call
call
TL00
Ry1
…
yK
xb
I/O
WRFBDY B
WRF+ BS(0),…,BS(N)
MkT
HkT
Mk
Hk
xn
TLDF
WRFINPUT
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 41
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Why 4D-Var?• Use observations over a time interval,
which suits most asynoptic data and use tendency information from observations.
• Use a forecast model as a constraint, which enhances the dynamic balance of the analysis.
• Implicitly use flow-dependent background errors, which ensures the analysis quality for fast developing weather systems.
• NOT easy to build and maintain!
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 42
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QuickTime™ and aTIFF (Uncompressed) decompressor
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QuickTime™ and aTIFF (Uncompressed) decompressor
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QuickTime™ and aTIFF (Uncompressed) decompressor
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QuickTime™ and aTIFF (Uncompressed) decompressor
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Radiance Observation Forcing at 7 data slots
€
H iTRi
−1(HiM iδx0 − di)
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 43
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Single observation experimentThe idea behind single ob tests:
The solution of 3D-Var should be
€
xa = xb + BHT HBHT + R[ ]−1
y − Hxb[ ]
Single observation
€
xa − xb = Bi σ b2 + σ o
2[ ]
−1yi − x i[ ]
3D-Var 4D-Var: H HM; H HM; HT MTHT
The solution of 4D-Var should be
€
xa = xb + BMTHT H MBMT( )HT + R[ ]−1
y − HMxb[ ]
Single observation, solution at observation time
€
M xa − xb( ) = MBMT
( )i
σ b2 + σ o
2[ ]
−1yi − x i[ ]
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 44
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Analysis increments of 500mb from 3D-Var at 00h and from 4D-Var at 06h
due to a 500mb T observation at 06h
++
3D-Var 4D-Var
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 45
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500mb increments at 00,01,02,03,04,05,06h to a 500mb T ob at 06h
OBS+
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 46
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500mb difference at 00,01,02,03,04,05,06h from two nonlinear runs (one from background; one from 4D-Var)
OBS+
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 47
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500mb difference at 00,01,02,03,04,05,06h from two nonlinear runs (one from background; one from FGAT)
OBS+
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 48
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Real Case: Typhoon HaitangExperimental Design (Cold-Start)
• Domain configuration: 91x73x17, 45km
• Period: 00 UTC 16 July - 00 UTC 18 July, 2005• Observations from Taiwan CWB operational database.• 5 experiments are conducted:
FGS – forecast from the background [The background fields are 6-h WRF forecasts from National Center for Environment Prediction (NCEP) GFS analysis.]
AVN- forecast from the NCEP AVN analysis 3DVAR – forecast from WRF-Var3d using FGS as background FGAT - forecast from WRF-Var3dFGAT using FGS as
background
4DVAR – forecast from WRF-Var4d using FGS as background
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 49
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Typhoon Haitang 2005
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 50
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A KMA Heavy Rain Case
Period: 12 UTC 4 May - 00 UTC 7 May, 2006
Assimilation window: 6 hours
Cycling (6h forecast
from previous cycle as
background for analysis) All KMA operational data
Grid : 60x54x31
Resolution : 30km
Domain size: the same as the
KMA operational 10km domain.
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 51
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Precipitation Verification
0.1 mm Precipitation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
3 6 9 12 15 18 21 24
FCST Time (hours)
CSI3dvar4dvar
5mm Precipitation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
3 6 9 12 15 18 21 24
FCST Time (Hours)
CSI3dvar4dvar
15 mm Precipitation
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
3 6 9 12 15 18 21 24
FCST Time (Hours)
CSI3dvar4dvar
25 mm Precipitation
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
3 6 9 12 15 18 21 24
FCST Time (Hours)
CSI3dvar
4dvar
Hans Huang: Variational Data Assimilation, SNU lecture. June 9th, 2009 52
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Test domain: AFWA T8 45-km
Domain configurations:• 2007-08-15-00 to 2007-08-21-00 • Horizontal grid: 123 x 111 @ 45 km grid spacing, 27
vertical levels• 3/6 hours GFS forecast as FG • Every 6 hours
Observations used:sound sonde_sfc
synop geoamv
airep pilot
ships qscat
gpspw gpsref
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00 h 12 h 24 h
RMSE Profiles at Verification Times (U,V)
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00 h 12 h 24 h
RMSE Profiles at Verification Times (T,Q)
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The first radar data assimilation experiment using WRF 4D-Var (OSSE)
TRUTH ----- Initial condition from TRUTH (13-h forecast initialized at 2002061212Z from AWIPS 3-h analysis) run cutted by ndown,
boundary condition from NCEP GFS data. NODA ----- Both initial condition and boundary condition from NCEP
GFS data.3DVAR ----- 3DVAR analysis at 2002061301Z used as the initial
condition, and boundary condition from NCEP GFS. Only Radar radial velocity at 2002061301Z assimilated (total # of data points = 65,195).
4DVAR ----- 4DVAR analysis at 2002061301Z used as initial condition, and boundary condition from NCEP GFS. The radar radial velocity at 4 times: 200206130100, 05, 10, and 15, are assimilated (total # of data points = 262,445).
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TRUTH NODA
4DVAR3DVAR
Hourly precipitation ending at 03-h forecast
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TRUTH NODA
3DVAR 4DVAR
Hourly precipitation ending at 06-h forecast
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Real data experiments
QuickTime™ and a decompressor
are needed to see this picture.
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• Introduction to data assimilation.• Basics of variational data assimilation.• Demonstration with a simple system.• The WRFDA approach:
• y, H, H, HT
• B• M, M, MT
• 4D-Var
Summary
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A short list of
variational data assimilation issues
• yo observations, preprocessing, quality control
• H new observation types, improving operators
• R observational errors, tuning, correlated observational errors
• xb improve models (an important part of DA!!)
• B Statistical models, flow-dependent features
• Minimization algorithm Quasi−Newton; Conjugate Gradient; …( )
• M and MT : development and validity (and ensemble approaches)
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www.mmm.ucar.edu/wrf/users/wrfda