An Efficient Ensemble Data Assimilation Approach and Tests

with Doppler Radar Data

Jidong Gao Ming Xue

Center for Analysis and Prediction of Storms,

University of Oklahoma, Norman

Research Goals

• To develop an efficient ensemble Kalman filter (EnKF) method for high-resolution NWP, by using a dual resolution approach.

• To evaluate the efficiency and accuracy of the method through OSSEs, with simulated radar radial velocity data for a supercell storm.

Introduction• EnKF was first introduced by Evensen (1994)

and has become very popular in recent years

• Recently, the EnKF method has been successfully applied to the radar data assimilation problem (e.g., Snyder and Zhang 2003; Zhang et al. 2004; Dowell et al. 2004; Tong and Xue 2005).

• Effective assimilation of radar data is essential for initializing convective-scale NWP models

Radar Data Assimilation• The EnKF data assimilation method is especially

suitable for radar data assimilation because

– Radar only observes Vr and Z, and data coverage is usually incomplete

– All other variables have to be ‘retrieved’– EnKF ‘retrieves’ the unobserved variables via background

error covariance obtained through a forecast ensemble

• But, EnKF is expensive, because of the need for running a usually rather large ensemble of forecasts and analyses

• In this work, we propose a dual-resolution (DR) hybrid ensemble DA strategy, with the goal of improving the EnKF efficiency

• With the method, an ensemble of forecasts and analyses is run at a lower resolution (LR), while a single system of analysis and forecast is performed at a higher resolution (HR)

• The LR forecast ensemble provides estimated background error covariance for the HR analysis

• The HR forecast is used to replace or partially adjust the mean of the LR analysis ensemble

The Methodology

LR

EnK

F A

nalysis

LR E

nKF

Analysis

LR E

nKF

Analysis

HR EnKF

Single higher-resolution analysis and forecast

Lower-resolution analysis and forecast ensemble

covarian

ce rep

lace m

ean

covarian

ce co

varianc

e

replace

mean

replace

mean

HR EnKFHR EnKF

OSSEs with a Simulated Supercell Storm

• A truth simulation is created using ARPS with the Del City supercell sounding, at x = 2 km

• The model domain: 92 x 92 x 16 km3.

• LR has x=4 km, HR has x=2 km

• z = 500 m.

•Vr data collected at grid point locations are assimilated, at 5 min intervals

•20 ensemble members are used

List of EnKF OSSEs

Experiment Description

EXP1 Single-reslution EnKF at HR (2 km)

EXP2 Single-resolution EnKF at LR (4 km)

EXP3 Dual-resolution hybrid EnKF (2 & 4 km)

RMS Errors of the Analyses for the Three Experiments

HR EnKF (EXP1)

LR EnKF (EXP2)

DR EnKF (EXP3)

’(contours), Z(color shades) and Vh (vectors) at Surface

Truth

EXP2

LR-EnKF

EXP1

HR-EnKF

EXP3

DR-EnKF

’, Z and Vh at Surface after 80 min assimilation

Truth EXP1

HR-EnKF

EXP2

LR-EnKF

EXP3

DR-EnKF

W at 6 km AGL after 80 min assimilation

Truth

EXP2

LR-EnKF

EXP1

HR-EnKF

EXP3

DR-EnKF

2-h Forecasts of ’, Z and Vh at surface

Truth

EXP2

LR

EXP1

HR

EXP3

DR

2-h Forecasts of w at 6 km AGL

Truth

EXP2

LR

EXP1

HR

EXP3

DR

Summary and Discussion• A new efficient dual-resolution (DR) approach for

EnKF is proposed and tested with simulated radar data for a supercell storm.

• It is shown that the EnKF analysis using DR is almost as good as the HR analysis, but is much better than the LR analysis.

• For this case, we save CPU 3-4 times. However, depending on the resolution one choose, the method have the potential to save CPU 10-50 times more than Original EnKF methods.

Summary and Discussion

• My new experiments: using Dx =Dy= 4km with model EnKF run, to provide error structure for Dx =Dy= 1km, single model run. The result is also very positive.