School of Meteorology (Defense)

DEVELOPEMNT OF ARPS-LETKF WITH 4D-EXTENSION AND INTER-COMPARISON WITH ARPS-ENSRF

Gang Zhao
OU School of Meteorology

25 November 2013, 8:00 AM

National Weather Center, Room 4140
120 David L. Boren Blvd.
University of Oklahoma
Norman, OK

The Local Ensemble Transform Kalman filter (LETKF) is developed with the Advanced Regional Prediction System (ARPS). This ARPS-LETKF system is tested by assimilating the simulated radar observations in a super-cell storm Observation System Simulation Experiment (OSSE). The results show that it could assimilate radar observations effectively and produce the analysis which fits the truth and observations well.
Then its performance was inter-compared with the existing ARPS-EnSRF system in the same OSSE with simulated radar observations. With their optimal localization radii, the performances from ARPS-EnSRF and ARPS-LETKF are close to each other when these DA systems reach the stable stage. In the beginning spin-up stage, if only radar radial wind observations are analyzed, the performances from LETKF and EnSRF are comparable. But when the radar reflectivity observations are assimilated, EnSRF outperforms LETKF with considerable differences during the spin-up stage. Further inspection indicates that the biased differences in performances are caused by the effect of nonlinear observation forward operator. The EnSRF and the LETKF choose the different places to make the implicit linearization for the nonlinear observation operator. This difference in linearization leads to the systematic differences in the analysis error performances from EnSRF and LETKF. This conclusion was further supported by the results from a few additional experiments.
And then this LETKF system was extended to its 4D version. With the 4D-LETKF algorithm, the high frequent observations (such as radar observations) distributed over a time window could be analyzed simultaneously without timing error. This 4D-LETKF system is assessed by analyzing the simulated radar observations in 2 OSSEs with a fast-moving and a slow-moving supercell storm respectively. And its performance was compared with regular 3D-LETKF with different length of time windows. The results indicated that, compared to the regular 3D-LETKF which takes the asynchronous data in a time window as observed at same analysis time, 4D-LETKF shows better performance mainly due to the timing error in the former method. And compared to the 3D-LETKF which utilizes the observations with very short time windows, 4D-LETKF could reach the same performance after a few DA cycles and save computational cost by fewer analysis cycles. The hierarchical filter (HF) was adopted as an adaptive localization scheme in this 4D-LETKF system for the sake of the flow-dependent covariance, esp. the temporal covariance. The results show that the hybrid localization of HF and regular non-adaptive localization could improve the performance of 4D-LETKF, esp. with the longer time window.
Furthermore, divergence equation and pressure tendency equation of ARPS model had been applied as 2 constraints into this ARPS-LETKF system for the purpose of balance in analysis. This constrained LETKF system was also tested with simulated radar data in the same OSSE as used in the experiments to compare EnSRF and LETKF.

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