Transcript Four-Dimensional Ensemble-Variational (4DEnVAR)

Implementation and Testing of 3DEnVAR and
4DEnVAR Algorithms within the ARPS Data
Assimilation Framework
Chengsi Liu, Ming Xue, and Rong Kong
Center for Analysis and Prediction of Storms
University of Oklahoma
Outline
• ARPS 4DEnVar framework design
• OSSE for a storm case
– Only Vr
– Vr + reflectivity
– Vr + reflectivity + mass continuity constraint
• Conclusions
• On-going work
Hybrid En-4DVar (Lorenc 2003, Clayton et al 2012)
Ensemble covariance part
Static B part
Localization matrix
B  UU
T
 xs  Uv
C  CC
C
Alpha control variable α  

 0
N
 xe   (xbi' C ' αi )
0
α

C
i 1
Analysis increment and cost function
12  22  1
N
 x0  1 x s   2 xe  1Uv   2  (xbi' C ' αi )
I
i 1
1 T
1 T
1
J ( v, α)  v v  α α  [Ht L t x0  dt ]T R 1[Ht L t x0  dt ]
2
2
2 t 1
innovation
4DEnVar-NPC (Non-Propagation of alpha Control
variable)
Two approximations
(1) Neglecting temporal propagation of alpha control variable by TLM
Lt  x e = Lt (
N
 x
i 1
bi
m
N
N
Cαi )  Lt ( xbi Cαi )   (Lt xbi ) Cαi
i 1
N
i 1
αi J (αi )  αi   CT (L t xbi ) Ht T R 1[Ht {(L t xbi ) Cαi }  dt ]
t 1
i 1
AJM avoided !!
(2) Use nonlinear model ensemble forecasts to replace the
temporal propagation of perturbations by the TLM
Lt x  Mt (xbi )  Mt (xb )
'
bi
TLM avoided !!
The hybrid 4DEnVAR DA system based on
the ARPS variational DA framework
•
4DEnVar-NPC is adopted as ARPS hybrid
variational algorithm because:
1. Adjoint and tangent linear model are not good
approximations in convective scale DA.
2. High resolution observations, like Radar, are
main observation source for convective DA.
3. The alternative observation-spaceperturbation-based 4DEnVar algorithm(Liu et
al 2008, 2009) is computationally more
expensive.
The ARPS 4DEnVar characteristics
• 3D-recursive filter is used for ARPS-4DEnVar
localization.
• The capabilities for convective-scale radar DA
( Vr and reflectivity)
• Physical constraint terms (e.g. mass continuity
constraint) can be considered in the cost function.
Radar data operators
RadialVelocity
Vr  u sin  cos   v cos  cos   w sin 
 : elevation angle, : azimuth angle
Reflectivity(Lin et al. 1983; Gilmore et al. 2004; Dowell et al. 2011):
Z e  Z qr  Z qs  Z qh
Z dB  10log10 Z e
Z (qr )  3.63  109 (  qr )1.75
Z (qs )  9.80  108 (  qs )1.75 (drysnow)
Z (qs )  9.80  108 (  qs )1.75 ( wetsnow)
Z (qh )  4.33  1010 (  qh )1.75
EnKF-En4DVar Hybrid
Obs
Obs
Obs
Obs
Obs
Obs
Obs
EnKF
En4DVar
Obs
t0
Obs
4D Assimilation Window – 1 cycle
t1
OSSE for a storm case
• Tested with simulated data from a classic
supercell storm of 20 May 1977 near Del
City, Oklahoma
• Domain : 35 x 35 x 35 grids. 2km
horizontal resolution
• 70-min length of simulation, 5-min cycle
intervene
Error specification:
Smoothed Gaussian obs. error:
rdrstd_vr = 1m/s
rdrstd_zhh=3dBZ
Perturbations added to the sounding (added to whole field):
stdu = stdv = stdw = 2.0 m/s,
stdptprt = 2.0K,
stdqv = stdqc = stdqr = stdqi = stdqs = stdqh = 0.6g/kg,
Assimilation related parameters
inflation factor 1.07 (i.e., 7%)
localization function (Gaspari and Cohn 1999),
cut-off radius = 6km for hori/vert..
hradius = 1.643km for hori. /vert. influence radius for arps3dvar.
Experiment Design
• ARPS 3DVar and ARPS En3DVar with full
ensemble covariance
– Only Vr
– Vr + Z
– Vr + Z + mass continuity constraint
– Vr + Z + mass continuity constraint and model error
True reflectivity and wind at 850Hpa
Reflectivity
3DVar
Vr
3DVar
Vr+Z
Truth
En3DVar En3DVar
Vr+Z
Vr
Reflectivity
3DVar
Vr
3DVar
Vr+Z
Truth
En3DVar En3DVar
Vr
Vr+Z
Vertical Velocity
3DVar 3DVar
Vr+Z
Vr
Truth
En3DVar
Vr
En3DVar
Vr+Z
Pot. Temp. Pert
3DVar
Vr
3DVar
Vr+Z
Truth
En3DVar En3DVar
Vr+Z
Vr
RMSE for
3DVar-Vr, 3DVar-Vr+Z, En3dVar-Vr, En3DVar-Vr+Z
U
V
3DVar-Vr
3DVar-Vr+Z
En3dVar-Vr
En3DVar-Vr+Z
W
PT
RMSE for
3DVar-Vr, 3DVar-Vr+Z, En3dVar-Vr, En3DVar-Vr+Z
Qv
3DVar-Vr+Z
Qr
Qh
Qc
Qi
3DVar-Vr
En3dVar-Vr
En3DVar-Vr+Z
Qs
Mass Continuity Constraint Test
Exp 1 : 3DVar Vr + Z
Exp 2 : 3DVar Vr + Z + Constraint
Exp 3 : En3DVar Vr + Z
Exp 4 : En3DVar Vr + Z + Constraint
w and T
3DVar
3DVar-CS
Truth
En3DVar En3DVar-CS
RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar
U
W
V
PT
RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar
Qv
Qs
Qr
Qh
Qc
Qi
Divergence Constraint term test
with model error
• Model error is introducing by using a
different microphysical scheme in DA
– Truth simulation: Ice microphysics (LINICE)
– DA: WRF WSM6 scheme (WSM6WR)
• Smaller and larger weights for constraint
term are tested (CSSW, CSLW)
• Both Vr and Z data
Vertical Velocity and T
Truth
En3DVar
En3DVar En3DVar
CSLW
CSSW
RMSE for
En3DVar, En3DVar-CSSW, En3DVar-CSLW
U
V
W
Summary
• 3DEnVar/4DEnVar algorithms are being implemented within the ARPS
variational DA framework, coupled with the ARPS EnKF system;
• The systems can assimilate both radar Vr and Z data;
• Cycled DA OSSEs were performed to compare performances of 3DVar and
En3DVar, assimilating Vr and both Vr and Z;
• Much better state analyses were obtained using En3DVar assimilating both Vr
and Z data;
• Adding Z in 3DVAR improved very little (hydrometero classification of Gao
and Stensrud 2012 should help – not shown);
• Mass continuity constraint hurts En3DVar analyses, and improves w analysis in
3DVar with a perfect model;
• Analysis errors are much larger in the presence of mirophysics-related model
error – adding mass continuity improves results slightly.
• 3DEnVar and EnKF results similar for single time analysis; cycled results to be
compared (using deterministic background forecasts in EnKF)
On-going Research
• ARPS 4DEnVar is being tested with OSSEs;
• Time localization is being considered on 4DEnVar;
• The 4DEnVar results will be compared with 3DEnVar and
4DEnSRF;
• Potential benefits of EnVar for assimilating
attenuated X-band reflectivity will be evaluated.
• Will include other data sources and test with real
cases.
• The entire system will directly support WRF
model also. The EnKF system already does.