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

Contents Introduction A new scheme 4DSVD for CDA University Allied Workshop Introduction A new scheme 4DSVD for CDA Comparison of 4DSVD and 4DVAR Some OSSEs using WRF model Conclusions and Discussions

Introduction University Allied Workshop Disadvantages of the traditional data assimilation (DA) methods 4DVAR EnKF 1. Adjoint Model 1. Initial ensemble 2. Large computation time TEXT 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

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

Comparison of 4DSVD and 4DVAR Observation time interval University Allied Workshop 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: Exp. ExpG1 ExpG2 ExpG3 ExpG4 Observation time interval 0.1 0.2 0.5 1.0

Comparison of 4DSVD and 4DVAR University Allied Workshop Analysis errors of 4DSVD and 4DVAR 4DSVD 4DVAR 4DVAR -4DSVD

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

Some OSSEs using WRF model University Allied Workshop 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-1 OSSE-2 OSSE-3 图要从新画一下。顺序反了，并且标注OSSE-1等，从新画更换顺序 Exp. Observation Num. Observed Fields Analyzed Fields OSSE-1 2400 Surface Temp. OSSE-2 600 OSSE-3 150

Some OSSEs using WRF model Analysis Fields OSSE-1 True State OSSE-2 OSSE-3 University Allied Workshop

Some OSSEs using WRF model University Allied Workshop Analysis Error OSSE_1 OSSE_2 把它换成彩色的，从新画，冷暖色调的 OSSE_3

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

Some OSSEs using WRF model University Allied Workshop Table 1. The averaged errors in RMS sense of analysis state and the optimal truncation number of all OSSEs Experiment Optimal RMSE of analysis Optimal truncation number OSSE-1 1.01 137 OSSE-2 1.20 60 OSSE-3 1.58 20

Conclusions and Discussions University Allied Workshop 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

University Allied Workshop Thank you!