1. Applying an outer-loop to the WRF-LETKF system for typhoon assimilation and prediction
Shu-Chih Yang1,Kuan-Jen Lin1,
Takemasa Miyoshi2 and Eugenia Kalnay2
1 Dept. of Atmospheric Sciences, National Central University, Taiwan;
2 Dept. of Atmospheric and Oceanic Science, Univ. of Maryland, USA

2. Motivation
The regional EnKF needs a spin-up period when cold-starting the ensemble with global analyses.
For typhoon prediction, the reliability of the mean state strongly affects the track prediction.
The quality of initial mean state determines the spin-up length.
During the spin-up, valuable observations (e.g. reconnaissance aircraft) can’t be effectively used.
The “Running In Place” method can serve as a generalized outer- loop for the EnKF framework to improve the nonlinear evolution of the ensemble (Kalnay and Yang, 2010, Yang et al. 2012).
The RIP method is designed to re-evolve the whole ensemble to catch up the true dynamics, represented by observations.
Both the accuracy of the mean state and structure of the ensemble-based covariance are improved.
As many of you have experience, for regional EnKF, we usually cold start the initial ensemble members with the global analysis and perturbations with 3D-Var covariance structure.
Niither the mean of the ensemble nor the esenmble perturbations are optimal for mesoscale-related features
To deal with the EnKF’s spin-up problem, Eugenia and I proposed the running in place method to re…
And in this work, we also proposed an simplified version of RIP (the quasi outer-loop)

3. Standard LETKF framework
Obs(ti-1)
LETKF (ti-1)
xa0 (ti-1)
Nonlinear model
M[xa(ti-1)]
Time
xb0 (ti)
Separate into two slide, add the arrow (RIP/QOL) in the second
Obs(ti)
LETKF (ti)
xa0 (ti)

4. Standard LETKF framework
Obs(ti-1)
LETKF (ti-1)
xa0 (ti-1)
Nonlinear model
M[xa(ti-1)]
Time
Adjust dynamical evolutions at an earlier time
xb0 (ti)
By using the information provided the observations
Obs(ti)
LETKF (ti)
xa0 (ti)

5. “Running in place” in the LETKF framework
Obs(ti-1)
LETKF (ti-1)
Random Pert. + 
Xa0 (ti-1)
Nonlinear model
M [xa(ti-1) ]
Time 
xbn (ti) 
no-cost
Smoother
Very nice
Obs(ti)
LETKF (ti) 
Threshold > ε
xa(ti) 
False
Re-evolve the whole ensemble to catch up the true dynamics, represented by Obs

6. Increase the influence of observations
☐“Hard way”:
Reduce the observation error and assimilate this observation once.
Compute the analysis increment at once
“soft way”
Use the original observation error and assimilate the same observation multiple times.
The total analysis increment is achieved as the sum of multiple smaller increments (advantageous with nonlinear cases).
with nonlinear => for

7. Increase the influence of observations
“soft way”: RIP/QOL are advantageous corrections with nonlinear cases
With a smaller ensemble spread, smaller corrections allow the increments to follow the nonlinear path toward the truth better than a single increment.
1. Is unclear
Is=>are advantageous
corrections

8. With RIP/QOL, filter divergence is avoided!!
Results from the Lorenz 3-variable model (Yang et al. 2012a)
4D-Var
LETKF
standard
+QOL
+RIP
linear window
0.31
0.30
0.27
nonlinear window
0.53
(window=75)
0.68
0.47
0.35
With RIP/QOL, the LETKF analysis with nonlinear window is much improved, even better than 4D-Var!
Assimilation with different obs. sets
RIP and QOL use the observations more efficiently for the under-observed cases. x y z xy xz yz
xyz
ETKF
2.9
1.67
7.16
1.01
1.53
0.78
0.68
QOL
1.98
1.23
5.94
0.82
1.16
0.60
0.47
RIP
1.57
0.97
3.81
0.56
0.66
0.40
0.35
With fewer observations (constraint), the model trajectory is strongly affected by the nonlinear evolution of the initial errors.
Performance: RIP > QOL > standard ETKF

9. With RIP/QOL, filter divergence is avoided!!
Results from the Lorenz 3-variable model (Yang et al. 2012a)
4D-Var
LETKF
standard
+QOL
+RIP
linear window
0.31
0.30
0.27
nonlinear window
0.53
(window=75)
0.68
0.47
0.35
With RIP/QOL, the LETKF analysis with nonlinear window is much improved, even better than 4D-Var!
Assimilation with different obs. sets
RIP and QOL use the observations more efficiently for the under-observed cases. x y z xy xz yz
xyz
ETKF
2.9
1.67
7.16
1.01
1.53
0.78
0.68
QOL
1.98
1.23
5.94
0.82
1.16
0.60
0.47
RIP
1.57
0.97
3.81
0.56
0.66
0.40
0.35
With fewer observations (constraint), the model trajectory is strongly affected by the nonlinear evolution of the initial errors.
Performance: RIP > QOL > standard ETKF
How about RIP for a dynamical complex model?

10. Application of LETKF-RIP to typhoon assimilation/prediction
Experiment setup:
Regional Model: Weather Research and Forecasting model (WRF, 25km)
RIP is used as an generalized outer-loop to improve the ensemble evolution during the spin-up
Assimilation schemes: LETKF and LETKF-RIP with 36 ensemble members
LETKF-RIP setup
Computed the LETKF weights at analysis time (00,06,12,18Z)
Use these weight to reconstruct the ensemble (U, V) at (03,09,15,21Z)
perform the 3-hr ensemble forecasts
Re-do the LETKF analysis (only one iteration is tested) A B
time 00 03 06 09 12 15 18

11. Observations used in the OSSE experiments

12. Results from OSSE: Impact on analyses (Improving the TY’s inner core)
N-S vertical cross-section of wind speed
COV(Vc, U)LETKF vs. U error ★
TRUTH
LETKF
LETKF-RIP
Time
Rapid intensification in 12 hours
COV(Vc, U)RIP vs. U error ★
The covariance structure is strongly correlated to error pattern so that the observation information can be better spread out
The covariance structure is strongly correlated to error pattern.
RIP Effectively spins up the dynamical structure of the typhoon!
Yang et al. 2012b

13. Results from OSSE: Impact on typhoon prediction (Improving the TY’s environmental condition)
Capture the west-ward turning direction of the typhoon track 12 hour earlier!!
Truth
LETKF-RIP
LETKF
Φ300hPa (2-day forecast)
Yang et al. 2012b

14. Application to real observations
2008 Typhoon Sinlaku
Observations:
Upper-air sounding, dropsonde, surface station
09/08 00Z-09/09 12Z Tropical depression
09/12 18Z-09/11 00Z Typhoon
09/11 06Z-09/12 18Z Super typhoon
09/13 00Z-09/14 06Z Typhoon

15. Experiment settings for the real case
Standard LETKF run
LETKF
With RIP
LETKF-RIP
With RIP
turn-off RIP
LETKF-RIPs ★ ★ ★ ★
2008/09/08
00Z ★ ★ ★ ★
09 00Z
10 00Z
11 00Z
12 00Z
★: Dropsondes (reconnaissance aircraft) are available
Two cases are evaluated:
Typhoon structure is well observed by the dropsondes
Typhoon is under-observed.

16. (Wind Speed)suf vs. w (LETKF-RIP) (Wind Speed)suf vs. w (LETKF)
Dynamical adjustment
(Wind Speed)suf vs. w (LETKF-RIP)
OBS (QuikSCAT)
The RIP scheme enhances the cyclonic flow and the vertical motion near the eyewall.
The asymmetric structure with the strong winds is captured in the LETKF-RIP analysis.
(Wind Speed)suf vs. w (LETKF)
Difference (RIP − LETKF)
Let’s first look at an example of dynamical adjustment by RIP
Time: 2008/09/09 12Z

17. Reduce the 6-hr fcst error
Observation Impact
Observation impact is computed according to Li et al. (2010), Kalnay et al. (2012).
Anal time:2008/09/09 06Z
LETKF
LETKF-RIP
The first aircraft data is available for the typhoon structure
Wow!
Li et al.
The effectiveness of the dropsonde data is greatly improved by RIP and the negative impact shown in the control run can be alleviated.
Reduce the 6-hr fcst error

18. Impact on Typhoon track prediction
4-Day track prediction initialized at 09/09 06Z
Anal time:2008/09/09 06Z
C130 aircraft data
LETKF
LETKF-RIP
By improving the effectiveness of the observations, the track prediction is significantly improved.
At early developing stage of the typhoon, the aircraft data can provide more useful information with RIP for improving track prediction.

19. Another case: the typhoon is under-observed
Analysis time: 09/10 12Z
No reconnaissance aircraft available near the typhoon
For the under-observed case, the LETKF-RIP analysis still leads to a better track prediction.
LETKF
LETKF-RIP

20. Impact on Typhoon track prediction
Mean absolute track Error
With RIP, the track prediction is significantly improved during the LETKF’s spin-up period.
RIP is especially useful for improving forecasts beyond 36 hours and the typhoon landfall location is better predicted.
LETKF
LETKF-RIP
36hr
Error of land fall location
Time
LETKF
LETKF-RIP
09 06z
130 (N)
87(N)
09 12z
43(N)
09 18z 77
21(N)
10 00z 13 11
10 06z 47
10 12z 32
10 18z 60
Mean cross track Error
LETKF
LETKF-RIP
* N: not landfall at Taiwan
Averaged during the spin-up period (first two days)

21. LETKF-RIP vs. LETKF-RIPs (RIP is turned off after spin-up)
Averaged for the last two days
Init: 09/09 12Z
Cross-track error
LETKF
LETKF-RIP
LETKF-RIPs
LETKF-RIPs
LETKF
LETKF-RIP
Error of central Psfc
When RIP is always used, the TY after the LETKF spin-up is too intense and both the track and intensity prediction are degraded.
This means that after RIP is used, the nonlinear evolution of ensemble is improved! Witth this advantage, the following assimilation without RIP can still perform a better assimilation with a better ensemble space.
When RIP is turned off after the spin-up (2-day), the performance of the track/ intensity prediction is even better than the LETKF prediction.

22. Summary
RIP can be used as a generalized outer-loop to improve the nonlinear evolution of the ensemble during the spin-up.
The RIP scheme accelerates the spin-up of the WRF-LETKF system and provides further adjustments for improving typhoon assimilation and prediction.
The value of flight data during the developing stage of typhoon is effectively increased.
Even when the typhoon is under-observed, the RIP analysis can still provide an improved prediction.
The dynamical adjustments include both the inner core and environmental condition of the typhoon.
RIP can be turned off after the system has spun up (2 days).
an improved
After spin-up