Applying an outer-loop to the WRF-LETKF system for typhoon assimilation and prediction Shu-Chih Yang 1 ,Kuan-Jen Lin 1 , Takemasa Miyoshi 2 and Eugenia Kalnay 2 1 Dept. of Atmospheric Sciences, National Central University, Taiwan; 2 Dept. of Atmospheric and Oceanic Science, Univ. of Maryland, USA
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Applying an outer-loop to the WRF-LETKF system for typhoon assimilation and prediction
Applying an outer-loop to the WRF-LETKF system for typhoon assimilation and prediction. Shu-Chih Yang 1 ,Kuan-Jen Lin 1 , Takemasa Miyoshi 2 and Eugenia Kalnay 2 1 Dept. of Atmospheric Sciences, National Central University, Taiwan; - PowerPoint PPT Presentation
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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
MotivationMotivation• 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.
Standard LETKF frameworkStandard LETKF framework
LETKF (ti-1)LETKF (ti-1)
xa0 (ti-1)
xa0 (ti)
LETKF (ti)LETKF (ti)
Nonlinear modelM[xa(ti-1)]
Nonlinear modelM[xa(ti-1)]
xb0 (ti)
Obs(ti)
Obs(ti-1)
Tim
e
Standard LETKF frameworkStandard LETKF framework
LETKF (ti-1)LETKF (ti-1)
xa0 (ti-1)
xa0 (ti)
LETKF (ti)LETKF (ti)
Nonlinear modelM[xa(ti-1)]
Nonlinear modelM[xa(ti-1)]
xb0 (ti)
Obs(ti)
Adjust dynamical evolutions at an earlier time
Obs(ti-1)
Tim
e
“Running in place” in the LETKF framework“Running in place” in the LETKF framework
Xa0 (ti-1)
LETKF (ti-1)LETKF (ti-1)
xa(ti) False
xbn (ti)
Random Pert.+
Obs(ti)
Tim
e
Obs(ti-1)
Nonlinear modelM [xa(ti-1) ]
Nonlinear modelM [xa(ti-1) ]
LETKF (ti)LETKF (ti) Threshold > ε
no-cost Smoother
€
˜ x an (ti−1)
Re-evolve the whole ensemble to catch up the true dynamics, represented by Obs
Increase the influence of observationsIncrease 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).
Increase the influence of observationsIncrease 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.
With RIP/QOL, filter divergence is avoided!! With RIP/QOL, filter divergence is avoided!!
x y z xy xz yz xyzETKF 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 RIP/QOL, the LETKF analysis with nonlinear window is much improved, even better than 4D-Var!
•RIP and QOL use the observations more efficiently for the under-observed cases.
Performance: RIP > QOL > standard ETKF
4D-VarLETKF
standard +QOL +RIP
linear window 0.31 0.30 0.27 0.27
nonlinear window
0.53(window=75) 0.68 0.47 0.35
Assimilation with different obs. sets
Results from the Lorenz 3-variable model (Yang et al. 2012a)
With RIP/QOL, filter divergence is avoided!! With RIP/QOL, filter divergence is avoided!!
x y z xy xz yz xyzETKF 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 RIP/QOL, the LETKF analysis with nonlinear window is much improved, even better than 4D-Var!
•RIP and QOL use the observations more efficiently for the under-observed cases.
Performance: RIP > QOL > standard ETKF
4D-VarLETKF
standard +QOL +RIP
linear window 0.31 0.30 0.27 0.27
nonlinear window
0.53(window=75) 0.68 0.47 0.35
Assimilation with different obs. sets
Results from the Lorenz 3-variable model (Yang et al. 2012a)
How about RIP for a dynamical complex model?
Application of LETKF-RIP to typhoon assimilation/prediction
Application of LETKF-RIP to typhoon assimilation/prediction
06 09 1200 03 15 18
time
AB
LETKF-RIP setup1)Computed the LETKF weights at analysis time (00,06,12,18Z)
2)Use these weight to reconstruct the ensemble (U, V) at (03,09,15,21Z)
3)perform the 3-hr ensemble forecasts4)Re-do the LETKF analysis (only one iteration is tested)
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
Observations used in the OSSE experimentsObservations used in the OSSE experiments
TRUTH LETKF LETKF-RIP
Time
Rapid intensification in 12 hoursRapid intensification in 12 hours
Results from OSSE: Impact on analyses(Improving the TY’s inner core)
Results from OSSE: Impact on analyses(Improving the TY’s inner core)
N-S vertical cross-section of wind speedCOV(Vc, U)LETKF vs. U error
★
COV(Vc, U)RIP vs. U error
★
The covariance structure is strongly correlated to error pattern.RIP Effectively spins up the dynamical structure
of the typhoon!
Yang et al. 2012b
Results from OSSE: Impact on typhoon prediction (Improving the TY’s environmental condition)
Results from OSSE: Impact on typhoon prediction (Improving the TY’s environmental condition)
TruthLETKF-RIPLETKF
TruthLETKF-RIPLETKF
Capture the west-ward turning direction of the typhoon track 12 hour earlier!!
Yang et al. 2012b
Φ300hPa (2-day forecast)
Application to real observationsApplication to real observations
•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.
* N: not landfall at Taiwan
LETKFLETKF-RIP
LETKFLETKF-RIP
Averaged during the spin-up period (first two days)
36hr
LETKF-RIP vs. LETKF-RIPs (RIP is turned off after spin-up)
LETKF-RIP vs. LETKF-RIPs (RIP is turned off after spin-up)
LETKF-RIPs
LETKF
LETKF-RIP
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.
LETKFLETKF-RIPLETKF-RIPs
Error of central Psfc
Averaged for the last two days
Cross-track errorInit: 09/09 12Z
SummarySummary
• 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).