Upload
takoda
View
51
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Regional 4D-Var. Hans Huang NCAR Acknowledgements: NCAR/MMM/DAS USWRP , NSF-OPP, NCAR AFWA , KMA, CWB, CAA, EUMETSAT, AirDat Dale Barker (UKMO), Nils Gustafsson and Per Dahlgren ( SMHI). Outline. 4D-Var formulation and “why regional?” The WRFDA approach - PowerPoint PPT Presentation
Citation preview
Hans Huang: Regional 4D-Var. July 30th, 2012 1
Regional 4D-Var
Hans Huang NCAR
Acknowledgements: NCAR/MMM/DASUSWRP, NSF-OPP, NCARAFWA, KMA, CWB, CAA, EUMETSAT, AirDatDale Barker (UKMO), Nils Gustafsson and Per Dahlgren (SMHI)
Hans Huang: Regional 4D-Var. July 30th, 2012 2
• 4D-Var formulation and “why regional?”
• The WRFDA approach
• Issues specific to regional 4D-Var
• Summary
Outline
Hans Huang: Regional 4D-Var. July 30th, 2012 3
4D-Var
J = Jb + Jo
Jb =12
x0 - xb T B 1 x0 - xb
Jo =12
yk H M k x0 T
R 1 yk H M k x0 k
Hans Huang: Regional 4D-Var. July 30th, 2012 4
Why 4D-Var?
• Use observations over a time interval, which suits most asynoptic data
and uses 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: Regional 4D-Var. July 30th, 2012 5
Why regional?• High resolution model• Regional observation network• Radar data and other high resolution
observing systems (including satellites)• Cloud- and precipitation-affected
satellite observations• Model B with only regional balance
considerations, e.g. tropical B• …
Hans Huang: Regional 4D-Var. July 30th, 2012 6
Regional 4D-Var systems Zupanski M (1993); the Eta model
Zou, et al. (1995); MM5Sun and Crook (1998); a cloud modelHuang, et al. (2002), Gustafsson et al. (2012); HIRLAMZupanski M, et al. (2005); RAMSIshikawa, et al. (2005); the JMA mesoscale modelLorenc, et al (2007); UK Met Office UMTanguay, et al. (2012); Canadian LAM…Huang, et al. (2009); WRF
Hans Huang: Regional 4D-Var. July 30th, 2012 7
HIRLAM tests: 3D-Var vs 4D-Var Nils Gustafsson (SMHI)
• SMHI area, 22 km, 40 levels, HIRLAM 7.2, KF/RK, statistical bal-ance background constraint, reference system background error statis-tics (scaling 0.9), no ”large-scale mix”, 4 months, operational SMHI observations and boundaries
• 3D-Var with FGAT, 40 km increments, quadratic grid, incremental digital filter initialization
• 4D-Var, 6h assimilation window, Meteo-France simplified physics (vertical diffusion only), weak digital filter constraint, no explicit ini-tialization.
• One experiment with one outer loop iteration (60 km increments) and one experiment with two outer loop iterations (60 km and 40 km in-crements)
Hans Huang: Regional 4D-Var. July 30th, 2012 8
Nils Gustafsson
Hans Huang: Regional 4D-Var. July 30th, 2012 9
Nils Gustafsson
Hans Huang: Regional 4D-Var. July 30th, 2012 10
Nils Gustafsson
Hans Huang: Regional 4D-Var. July 30th, 2012 11
Nils Gustafsson
Hans Huang: Regional 4D-Var. July 30th, 2012 12
• 4D-Var formulation and “why regional?”
• The WRFDA approach
WRFDA is a Data Assimilation system built within the WRF software framework, used for
application in both research and operational environments….
• Issues specific to regional 4D-Var
• Summary
Outline
Hans Huang: Regional 4D-Var. July 30th, 2012 13
WRFDA 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)
• Observations: Conv. + Sat. + Radar (+Bogus)
Hans Huang: Regional 4D-Var. July 30th, 2012 14
www.mmm.ucar.edu/wrf/users/wrfda
Hans Huang: Regional 4D-Var. July 30th, 2012 15
Recent Tutorials at NCAR
1. WRFDA Overview2. Observation Pre-processing3. WRFDA System4. WRFDA Set-up, Run5. WRFDA Background Error Estimations6. Radar Data7. Satellite Data8. WRF 4D-Var9. WRF Hybrid Data Assimilation System10. WRFDA Tools and Verification11. Observation Sensitivity
Practice
1. obsproc
2. wrfda (3D-Var)
3. Single-ob tests
4. Gen_be
5. Radar
6. Radiance
7. 4D-Var
8. Hybrid
9. Advanced (optional)
Hans Huang: Regional 4D-Var. July 30th, 2012 16
Observing System Simulation Experiment (OSSE)2010-09-11-00 +6h precipitation
(IC and BC come from +12h forecast from 2010-09-10-12 NCEP FNL)
Hans Huang: Regional 4D-Var. July 30th, 2012 17
Sample the hourly precipitation obs. based on the NA METAR sta.(2066)
+ random error (<±1 mm)
Hans Huang: Regional 4D-Var. July 30th, 2012 18
4dvar
+6h total precipitation simulations
control
obs
4DVAR Control
“OBS”
Hans Huang: Regional 4D-Var. July 30th, 2012 19
A short list of 4D-Var issues
y 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
M and MT :Ź development and validity (and ensemble approaches)
Minimization algorithm Quasi Newton; Conjugate Gradient;
J =
12
x0 - xb T B 1 x0 - xb 12
yk H M k x0 T
R 1 yk H M k x0 k
Hans Huang: Regional 4D-Var. July 30th, 2012 20
(WRFDA) Observations, y In-Situ:
- Surface (SYNOP, METAR, SHIP, BUOY).- Upper air (TEMP, PIBAL, AIREP, ACARS, TAMDAR).
• Remotely sensed retrievals:- Atmospheric Motion Vectors (geo/polar).- SATEM thickness.- Ground-based GPS Total Precipitable Water/Zenith Total Delay.- SSM/I oceanic surface wind speed and TPW.- Scatterometer oceanic surface winds.- Wind Profiler.- Radar radial velocities and reflectivities.- Satellite temperature/humidity/thickness profiles.- GPS refractivity (e.g. COSMIC).
Radiative Transfer (RTTOV or CRTM):– HIRS from NOAA-16, NOAA-17, NOAA-18, METOP-2– AMSU-A from NOAA-15, NOAA-16, NOAA-18, EOS-Aqua, METOP-2– AMSU-B from NOAA-15, NOAA-16, NOAA-17– MHS from NOAA-18, METOP-2– AIRS from EOS-Aqua– SSMIS from DMSP-16
• Bogus:
– TC bogus.
– Global bogus.
Hans Huang: Regional 4D-Var. July 30th, 2012 21
H 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” ob-
servations (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 !!!
H - Observation operator
Z Z(T , IWC, LWC, RWC,SWC)
0
( )( ) ( , ( )) dTRL B T z dzdz
Hans Huang: Regional 4D-Var. July 30th, 2012 22
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: Regional 4D-Var. July 30th, 2012 23
Radiance Observation Forcing at 7 data slots
H iTRi
1(HiM ix0 di)
Hans Huang: Regional 4D-Var. July 30th, 2012 24
A short list of 4D-Var issues
y 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
M and MT :Ź development and validity (and ensemble approaches)
Minimization algorithm Quasi Newton; Conjugate Gradient;
J =
12
x0 - xb T B 1 x0 - xb 12
yk H M k x0 T
R 1 yk H M k x0 k
Hans Huang: Regional 4D-Var. July 30th, 2012 25
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 Back-ground Errors
B (xb x t )(xb x t )T x'x'T
B x ' x 'T A(x t 2 x t1 )(x t 2 x t1 )T
B x ' x 'T C(x k x )(x k x )T
Hans Huang: Regional 4D-Var. July 30th, 2012 26
Single observation experiment- one way to view the structure of B
The solution of 3D-Var should be
xa xb BHT HBHT R 1y Hxb
Single observation
xa xb Bi b2 o
2 1yi x i
Hans Huang: Regional 4D-Var. July 30th, 2012 27
Pressure,
Temperature
Wind Speed,
Vector,
v-wind component.
Example of B 3D-Var response to a single ps observation
Hans Huang: Regional 4D-Var. July 30th, 2012 28
B from ensemble methodB from NMC method
Examples of B
T increments : T Observation (1 Deg , 0.001 error around 850 hPa)
Hans Huang: Regional 4D-Var. July 30th, 2012 29
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 x t0 12
x t0 xb t0 xg t0 TBo
1 x t0 xb t0 xg t0
x t0 Uv
Jb x t0 12
vn2
n
Hans Huang: Regional 4D-Var. July 30th, 2012 30
WRFDA Background Error Modeling
x 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: Regional 4D-Var. July 30th, 2012 31
WRFDA Background Error Modeling
100
200
300
400
500
600
700
800
900
10000 100 200 300 400 500
Error correlation lengthscale (km)
Pres
sure
(hPa
) uvTpq
x 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: Regional 4D-Var. July 30th, 2012 32
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
Pres
sure
(hPa
)
Mode 1Mode 2Mode 3Mode 4Mode 5
x 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: Regional 4D-Var. July 30th, 2012 33
WRFDA Background Error Modeling
Define control variables:
'
r' = q'/ qs Tb,qb, pb
u ' ' b ' '
Tu ' T ' Tb ' '
psu ' ps ' psb ' '
x 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: Regional 4D-Var. July 30th, 2012 34
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:
b /
Tb T / T T
psb ps / ps ps
b' c '
Tb' (k) G(k,k1) ' (k1)
k1
psb' W (k) ' (k)
k
Hans Huang: Regional 4D-Var. July 30th, 2012 35
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: Regional 4D-Var. July 30th, 2012 36
Single observation experimentThe idea behind single ob tests:
The solution of 3D-Var should be
xa xb BHT HBHT R 1y Hxb
Single observation
xa xb Bi b2 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 1y HMxb
Single observation, solution at observation time
M xa xb MBMT i b
2 o2 1
yi x i
Hans Huang: Regional 4D-Var. July 30th, 2012 37
Analysis increments of 500mb q 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: Regional 4D-Var. July 30th, 2012 38
500mb q increments at 00,01,02,03,04,05,06h to a 500mb T ob at 06h
OBS+
Hans Huang: Regional 4D-Var. July 30th, 2012 39
500mb q difference at 00,01,02,03,04,05,06h from two nonlinear runs (one from background; one from 4D-Var)
OBS+
Hans Huang: Regional 4D-Var. July 30th, 2012 40
500mb q difference at 00,01,02,03,04,05,06h from two nonlinear runs (one from background; one from FGAT)
OBS+
Hans Huang: Regional 4D-Var. July 30th, 2012 41
Jb x0 12
x0 xb T B 1 x0 xb
Jo x0 12
Hkx k yk T R 1 Hkxk yk k1
K
Jc x0 df
2x N 2 xN 2
df T C 1 xN 2 xN 2df
df
2xN 2 fi
i0
N
xi
T
C 1 xN 2 fii0
N
xi
df
2hi
i0
N
xi
T
C 1 hii0
N
xi
where:
hi fi , if i N 2
1 fi , if i N 2
Control of noise: Jc
Hans Huang: Regional 4D-Var. July 30th, 2012 42
0
10000
20000
30000
40000
50000
60000
70000
80000
0 4 9 14 18 23 28 33 37 42iterations
cost
func
tion
JbJoJc
0
10000
20000
30000
40000
50000
60000
70000
80000
0 4 9 14 18 23 28 33 37 42Iterations
cost
func
tion
JbJoJc
Cost functions when minimize
J=Jb
+Jo
Cost functions when minimize
J=Jb+J
o +J
c
df
= 0.1
Hans Huang: Regional 4D-Var. July 30th, 2012 43
3-hour Surface Pressure Tendency
0
2
4
6
8
10
12
14
16
18
20
1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341Time Steps (24 Hours)
DPS
/DT
NoJcDFJcDF(0.1)FGSJcDF(1.0)JcDF(5.0)JcDF(10.0)
Hans Huang: Regional 4D-Var. July 30th, 2012 44
(Dry) Surface Pressure Tendency
DFI No DFI
Hans Huang: Regional 4D-Var. July 30th, 2012 45
• 4D-Var formulation and “why regional?”
• The WRFDA approach
• Issues specific to regional 4D-Var
• Summary
Outline
Hans Huang: Regional 4D-Var. July 30th, 2012 46
Issues specific to regional 4D-Var
Control of lateral boundaries.
Control of the large scales or coupling to a large scale model?
Mesoscale balances.
Hans Huang: Regional 4D-Var. July 30th, 2012 47
Options for LBC in 4D-Var(Nils Gustafsson)
1. Trust the large scale model providing the LBC.
Apply relaxation toward zero on the lateral boundaries during the integration of the TL and AD models in regional 4D-Var.
This, however, will have some negative effects:
• Larger scale increments as provided via the background error constraint may be filtered during the forward TL model
integration.
• Observations close the the lateral boundaries will have reduced effect. In particular, information from observations
downstream of the lateral boundaries and from the end of the assimilation window will be filtered due to the adjoint
model LBC relaxation.
2. Control the lateral boundary conditions.
Hans Huang: Regional 4D-Var. July 30th, 2012 48
Control of Lateral Boundary Conditions
in 4DVAR
(JMA, HIRLAM and WRF)
1) Introduce the LBCs at the end of the data assimilation window as assimilation control variables (full model state =
double size control vector)
2) Introduce the adjoints of the Davies LBC relaxation scheme and the time interpolation of the LBCs
3) Introduce a “smoothing and balancing” constraint for the LBCs into the cost function to be minimized
J = Jb
+ Jo
+ Jc + J
lbcwhere
J lbc =
12
xlbc - xlbcb T Blbc
1 xlbc - xlbcb
Hans Huang: Regional 4D-Var. July 30th, 2012 49
Hans Huang: Regional 4D-Var. July 30th, 2012 50
Hans Huang: Regional 4D-Var. July 30th, 2012 51
Problems with Control of LBC
• Double the control vector length• Pre-conditioning; LBC_0h and LBC_6h are
correlated• Relative weights for Jb and Jlbc??
Hans Huang: Regional 4D-Var. July 30th, 2012 52
Control of “larger” horizontal scales in re-gional 4D-Var
Per Dahlgren and Nils Gustafsson• There are difficulties to handle larger horizontal scales in regional 4D-Var
• Observations inside a small domain may not provide information on larger horizontal scales
• The assimilation basis functions (via the background error constraint) may not represent larger scales properly .
• Possibilities in handling the larger horizontal scales:
- Via the LBC in the forecast model only; Depending on the cycle for refreshment of LBC, one may miss important
advection of information over the LBC
- Via ad hoc techniques for mixing in information from a large scale data assimilation (applied in HIRLAM).
- Via a large scale error constraint - Jls
Hans Huang: Regional 4D-Var. July 30th, 2012 53
A large scale error constraint - Jls
Add a large scale constraint Jls
to the regional 4D-Var cost function:
J = Jb + J
o + J
c + J
lbc + J
lswhere
• Has been tried in ALADIN 3D-Var with xls
being a global analysis from the same observation time. In this case one needs to, at
least in principle, use different observations for the global and regional assimilations
• Is being tried in HIRLAM 4D-Var with xls
being a global forecast valid at the start of the assimilation window.
For both applications one needs to check that (x-xb) and (x-xls
) are not too strongly correlated!
J ls =
12
x - xls T Bls 1 x - xls
Hans Huang: Regional 4D-Var. July 30th, 2012 54
Forecast Impact
Verification Against Observations
MSLP Temperature
• Upper air, MSLP: Very good
• Surface parameters: Unchanged
Hans Huang: Regional 4D-Var. July 30th, 2012 55
• 4D-Var formulation and “why 4D-Var?”
• Why regional? (high resolution; regional observation network;…)
• The WRFDA approach: Jb; J
o; J
c
• Regional 4D-Var issues: Jlbc
, Jls
Summary