1. A New Scheme for Chaotic-Attractor-Theory Oriented Data Assimilation
Jincheng Wang and Jianping Li
LASG, IAP
University Allied Workshop, Japan, 2008

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

3. Introduction
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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

4. The new scheme 4DSVD for CDA
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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

5. Comparison of 4DSVD and 4DVAR Observation time interval
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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

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

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

8. Some OSSEs using WRF model
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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= 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

9. Some OSSEs using WRF model
Analysis Fields
OSSE-1
True State
OSSE-2
OSSE-3
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10. Some OSSEs using WRF model
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Analysis Error
OSSE_1
OSSE_2
把它换成彩色的，从新画，冷暖色调的
OSSE_3

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

12. Some OSSEs using WRF model
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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

13. Conclusions and Discussions
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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

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Thank you!