Implementation and Testing of 3DEnVAR and 4DEnVAR Algorithms within the ARPS Data Assimilation Frame...
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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. Outline. ARPS 4DEnVar framework design OSSE for a storm case Only Vr

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Chengsi Liu, Ming Xue, and Rong Kong Center for Analysis and Prediction of Storms

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Chengsi liu ming xue and rong kong center for analysis and prediction of storms

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

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

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


4denvar npc n on p ropagation of alpha c ontrol variable

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 !!


The hybrid 4denvar da system based on the arps variational da framework

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-based 4DEnVar algorithm(Liu et al 2008, 2009) is computationally more expensive.


The arps 4denvar characteristics

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

Radar data operators


Enkf en4dvar hybrid

EnKF-En4DVar Hybrid

Obs

Obs

Obs

Obs

Obs

Obs

Obs

EnKF

En4DVar

Obs

Obs

4D Assimilation Window – 1 cycle

t1

t0


Osse for a storm case

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


Experiment design

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

True reflectivity and wind at 850Hpa


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

Reflectivity

3DVar

Vr+Z

3DVar

Vr

Truth

En3DVar

Vr+Z

En3DVar

Vr


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

Reflectivity

3DVar

Vr+Z

3DVar

Vr

Truth

En3DVar

Vr

En3DVar

Vr+Z


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

Vertical Velocity

3DVar

Vr+Z

3DVar

Vr

Truth

En3DVar

Vr+Z

En3DVar

Vr


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

Pot. Temp. Pert

3DVar

Vr

3DVar

Vr+Z

Truth

En3DVar

Vr+Z

En3DVar

Vr


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

RMSE for

3DVar-Vr, 3DVar-Vr+Z, En3dVar-Vr, En3DVar-Vr+Z

U

V

3DVar-Vr

3DVar-Vr+Z

En3dVar-Vr

En3DVar-Vr+Z

PT

W


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

RMSE for

3DVar-Vr, 3DVar-Vr+Z, En3dVar-Vr, En3DVar-Vr+Z

Qh

Qv

Qr

3DVar-Vr

3DVar-Vr+Z

En3dVar-Vr

En3DVar-Vr+Z

Qs

Qc

Qi


Mass continuity constraint test

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


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

w and T

3DVar-CS

3DVar

Truth

En3DVar-CS

En3DVar


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar

V

U

W

PT


Chengsi liu ming xue and rong kong center for analysis and prediction of storms

RMSE for 3DVar-CS, 3DVar, En3DVar-CS, En3DVar

Qr

Qv

Qh

Qs

Qi

Qc


Divergence constraint term test with model error

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


Vertical velocity and t

Vertical Velocity and T

En3DVar

Truth

En3DVar

CSLW

En3DVar

CSSW


Rmse for en3dvar en3dvar cssw en3dvar cslw

RMSE forEn3DVar, En3DVar-CSSW, En3DVar-CSLW

U

V

W


Summary

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

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.


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