Jidong Gao and David StensrudJidong Gao and David Stensrud

Some OSSEs on Assimilation of Radar Data with a Hybrid 3DVAR/EnKF Method

OUTLINEOUTLINE

Why hybrid 3(4)DVAR/EnKF ?Why hybrid 3(4)DVAR/EnKF ?

Brief description of the method.Brief description of the method.

OSSEs with a supercell storm.OSSEs with a supercell storm.

Conclusion.Conclusion.

Goal: To test if the hybrid 3DVAR/EnKF scheme is good for convective scale DA and WoF

strategy

Why hybrid 3(4)DVAR/EnKF ?EnKF can use statistical info. more effectively by, providing flow-dependent background error covariances. model errors can be handled by multi-physics ens. but may contain sampling error due to small ens. size.

3(4)DVAR can use model’s dynamic info. more effectively by, adding model equations as strong & weak constraints. sampling error in static bkgrd. error statistics can be small. but does not carry bkgrd. error coaraince B through cycles so

B is not explicitly flow-independent.

Hybrid 3(4)DVAR/EnKF may combine dynamic and statistical information in an optimal way.

111 1

2 22T

TT b b

cJ H H J v v x x y x x yR

Hybrid 3DVAR/EnKF Formulation(Lorenc 2003, QJ; Buehner 2005, QJ; Wang et al.2007, MWR)

The cost function in preconditioned incremental form:

vis 3DVAR control variables; is extended control variables

When β1 =1, β2 =0, a pure 3(4)DVAR method;

When β1 =0, β2 =1, a method equivalent to an EnKF method;

In between, a hybrid method with different combinations.

1 2 1

β1 is weighting for static B; β2 is weighting for ens. Pe

1/ 2 1/ 2

1 2 x v eB P

Illustration of Hybrid 3(4)DVAR/EnKF

mem 2 forecast

mem 1 forecast

mem N forecast

mem 1 analysis

mem 2 analysis

mem N analysis

Control forecast

Why extra control forecast ?

Gao and Xue, Hybrid EnKF, dual-resolution (2008, MWR)

EnKF analysis

update only

3DEnVAR analysis

inflation, or relaxing

to prior

1bx

' ' '1 2, ,.. Nx x x

ax x

2bx

bNx

'2 2a xx x

'aN Nxx x

bxa bx x x

'1 1a xx x

?bx

OSSEs with a Simulated Supercell Storm

• A truth simulation is created using ARPS with the Del City supercell sounding.

• The model domain: 57 x 57 x 16 km3.

• Horizontal: x = 1 km, vertical: z = 500 m.

• Both Vr and Z are assimilated at 5 min intervals, similar to Gao and Stensrud (2012, JAS).

List of OSSEs

Exp. No Description

1 Single-observation experiment

2 OSSEs as a function of ens. size and coeff. for ens. covariance β2.

3 OSSEs as a function of number of alpha control variables

1.Single observation experiment

put Vr = 34 m/s within the storm

with N=50 ens. members

β2=1, full ens. covariance

Increments for α in response to the single ob.

Same pattern but with different values

for every member

-0.321 -0.628

0.213 0.610

allows each ensemble member to give the different degree of contribution to the analysis.

Derived analysis Increments for some model variables

Different flow-dependent structure

for every variable.

1/ 2( ) ex P

2. OSSE Experiments

A function of

ens. size N = 5, 10, 50, 100

& β2=0.0, 0.2, 0.5, 0.8, 1.0

The rms errors for the analysis and forecast cycles

red, green, blue, purple and baby-blue lines are corresponding

to weighting value of ensemble covariance with

β2 = 0.0, 0.2, 0.5, 0.8, and 1.0 respectively.

N=5

N=50

N=10

N=100

-8.37 -10.65

-9.31 -8.95

-8.68 -5.89

V (vectors), θ (contours), and simulated reflectivity Z (shaded

contours) at surface for:

(a)β2=0.2;

(b)β2=0.5;

(c) β2=0.8;

(d)β2=1.0.

All experiments

with 100 ensemble members.

All exp. are pretty close to the truth simulations!

-8.70 -8.55

-8.38 -7.17

Truth simulation: -8.37

3. OSSE Experiments for the size of extra control variables

A function of ensemble size, dimensions of coordinates, number of analysis variables.

1.Control Exp: a function of ensemble size and 3D of coordinates.

2.2D Exp: a function of ensemble size and horizontal 2D of coordinates.

3.Big size: a function of ensemble size and 3D and also number of analysis variables.

The rms errors for the analysis and forecast cycles

In each panel, red, green and blue lines are corresponding to CtrCV, BigCV; and 2dCV exp. respectively.

SummaryThe hybrid 3DVAR/EnKF allows each ens. member to give the different degree of contribution to the analysis through ens. derived covariance.

Even with a very small ens. size, the hybrid method performs better than pure 3DVAR. More weighting should be given to ens. derived covariance.

The best results are obtained when the number of the augmented control vectors is a function of the ensemble size and 3 dimensions of coordinates.

Future work Test the hybrid scheme with a small ensemble size, and dual-resolution strategy (Gao and Xue 2008, MWR) for the purpose of greatly reducing the computational cost for WoF project.