A New Scheme for Chaotic-Attractor-Theory Oriented Data Assimilation

1. A New Scheme for Chaotic-Attractor-Theory Oriented Data Assimilation Jincheng Wang and Jianping Li LASG, IAP Email: wjch@mail.iap.ac.cn University Allied Workshop, Japan, 2008

2. Contents • Introduction • A new scheme 4DSVD for CDA • Comparison of 4DSVD and 4DVAR • Some OSSEs using WRF model • Conclusions and Discussions

3. Introduction • Disadvantages of the traditional data assimilation (DA) methods 4DVAR EnKF 1. Adjoint Model 1. Initial ensemble TEXT 2. Large computation time 2. Difficult to match 4DVAR performance 3. Background error covariance matrix • Chaotic-Attractor Oriented DA (CDA) theory(Qiu and Chou, 2006) • To reduce the dimension of the DA problem • Consider the Characteristics of the Atmospheric model • The chaotic attractor of the atmospheric model exists • Its dimension is much smaller than the degree of the model space • The attractor could be embedded into space R2S+1 • DA problem can be solved in the attractor phase space

4. The new scheme 4DSVD for CDA 1. Generate samples 2. Generate expanded simulated observations 3. Get the coupled base vectorsthrough SVD 4. Obtain the analysis state by mapping the observations on the phase space of the model attractor

5. Comparison of 4DSVD and 4DVAR • Experiments setup Model: Lorenz 28-variable model True state: Integrated the model from an artificial initial condition Observation: Observed by adding Gaussian random noise Sample strategy: Selected from the model outputs Sample size: 100 Number of experiments: 30 Time window: [0, 1.0] Experiments:

6. Comparison of 4DSVD and 4DVAR Analysis errors of 4DSVD and 4DVAR 4DSVD 4DVAR 4DVAR -4DSVD

7. ExpG1 ExpG3 ExpG2 ExpG4 Comparison of 4DSVD and 4DVAR Averaged analysis errors of all the experiments of the groups in assimilation time window. (a) 4DSVD (b) 4DVAR 16 times

8. Some OSSEs using WRF model OSSE-1 • Experiments design Model: Advanced Research WRF (ARW) modeling system True state: Run the model for 24 hours started at 0600 UTC 11 May 2002, IC and BC generated from FNL Observation: Observed by adding Gaussian random noise Analysis variable: Surface temp. (at Eta=0.9965 level) Sample strategy: Selected from the forecast history Sample size: 150 Time window: [1200 UTC, 2400 UTC] ,12 May 2002 Experiments: OSSE-2 OSSE-3

9. Some OSSEs using WRF model Analysis Fields OSSE-1 True State OSSE-2 OSSE-3

10. Some OSSEs using WRF model Analysis Error OSSE_1 OSSE_2 OSSE_3

11. Some OSSEs using WRF model Domain-averaged RMSE of analyses as a function of base vector number.

12. Some OSSEs using WRF model Table 1. The averaged errors in RMS sense of analysis state and the optimal truncation number of all OSSEs

13. Conclusions and Discussions Conclusions: • 4DSVD is an effective and efficient DA scheme for CDA method in simple and more real model situations even if the observations are incomplete. • The optimal truncation number is not only related with the dimension of the chaotic-attractor number but also with number of the observations Discussions: • Need more experiments to evaluate its performance in real observation and real model situation • How to determine the optimal basis vector number

14. Thank you!