Implementation%20and%20Testing%20of%203DEnVAR%20and%204DEnVAR%20Algorithms%20within%20the%20ARPS%20Data%20Assimilation%20Framework

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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

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Outline

• ARPS 4DEnVar framework design
• OSSE for a storm case
• Only Vr
• Vr reflectivity
• Vr reflectivity mass continuity constraint
• Conclusions
• On-going work

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Hybrid En-4DVar (Lorenc 2003, Clayton et al 2012)
Ensemble covariance part
Static B part
Localization matrix
Alpha control variable
Analysis increment and cost function
innovation
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4DEnVar-NPC (Non-Propagation of alpha Control
variable)
Two approximations
(1) Neglecting temporal propagation of alpha
control variable by TLM
AJM avoided !!
(2) Use nonlinear model ensemble forecasts to
replace the temporal propagation of
perturbations by the TLM
TLM avoided !!
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The hybrid 4DEnVAR DA system based on the ARPS
variational DA framework

• 4DEnVar-NPC is adopted as ARPS hybrid variational
  algorithm because
• Adjoint and tangent linear model are not good
  approximations in convective scale DA.
• High resolution observations, like Radar, are
  main observation source for convective DA.
• The alternative observation-space-perturbation-bas
  ed 4DEnVar algorithm(Liu et al 2008, 2009) is
  computationally more expensive.

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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.

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Radar data operators
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EnKF-En4DVar Hybrid
EnKF
En4DVar
Obs
Obs
4D Assimilation Window 1 cycle
t1
t0
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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

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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

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True reflectivity and wind at 850Hpa
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Reflectivity
3DVar VrZ
3DVar Vr
Truth
En3DVar VrZ
En3DVar Vr
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Reflectivity
3DVar VrZ
3DVar Vr
Truth
En3DVar Vr
En3DVar VrZ
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Vertical Velocity
3DVar VrZ
3DVar Vr
Truth
En3DVar VrZ
En3DVar Vr
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Pot. Temp. Pert
3DVar Vr
3DVar VrZ
Truth
En3DVar VrZ
En3DVar Vr
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RMSE for 3DVar-Vr, 3DVar-VrZ, En3dVar-Vr,
En3DVar-VrZ
U
V
3DVar-Vr
3DVar-VrZ
En3dVar-Vr
En3DVar-VrZ
PT
W
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RMSE for 3DVar-Vr, 3DVar-VrZ, En3dVar-Vr,
En3DVar-VrZ
Qh
Qv
Qr
3DVar-Vr
3DVar-VrZ
En3dVar-Vr
En3DVar-VrZ
Qs
Qc
Qi
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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
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w and T
3DVar-CS
3DVar
Truth
En3DVar-CS
En3DVar
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RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar
V
U
W
PT
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RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar
Qr
Qv
Qh
Qs
Qi
Qc
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Divergence Constraint term testwith 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

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Vertical Velocity and T
En3DVar
Truth
En3DVar CSLW
En3DVar CSSW
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RMSE forEn3DVar, En3DVar-CSSW, En3DVar-CSLW
U
V
W
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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)

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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.