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

2008 Typhoon Sinlaku

09/08 00Z-09/09 12Z Tropical depression09/12 18Z-09/11 00Z Typhoon09/11 06Z-09/12 18Z Super typhoon09/13 00Z-09/14 06Z Typhoon

Observations: Upper-air sounding, dropsonde, surface station

11 00Z★ ★★

Experiment settings for the real caseExperiment settings for the real case

2008/09/0800Z

09 00Z 10 00Z 12 00Z

Standard LETKF run

With RIP

With RIP turn-off RIP

★ ★ ★ ★ ★

★: Dropsondes (reconnaissance aircraft) are available

LETKF

LETKF-RIP

LETKF-RIPs

Two cases are evaluated:(1)Typhoon structure is well observed by the dropsondes(2)Typhoon is under-observed.

Dynamical adjustmentDynamical adjustment OBS (QuikSCAT)(Wind Speed)suf vs. w (LETKF-RIP)

(Wind Speed)suf vs. w (LETKF)

•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.

Difference (RIP − LETKF)

Time: 2008/09/09 12Z

Observation ImpactObservation Impact

The first aircraft data is available for the typhoon structure

LETKFLETKF-RIP

Observation impact is computed according to Li et al. (2010), Kalnay et al. (2012).

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

Anal time:2008/09/09 06Z

Impact on Typhoon track predictionImpact on Typhoon track prediction

C130 aircraft data

At early developing stage of the typhoon, the aircraft data can provide more useful information with RIP for improving track prediction.

4-Day track prediction initialized at 09/09 06Z

LETKFLETKF-RIP

Anal time:2008/09/09 06Z

Another case: the typhoon is under-observedAnother case: the typhoon is under-observed

No reconnaissance aircraft available near the typhoon

Analysis time: 09/10 12Z

For the under-observed case, the LETKF-RIP analysis still leads to a better track prediction.

LETKFLETKF-RIP

Impact on Typhoon track predictionImpact on Typhoon track predictionMean absolute track Error

Mean cross track Error Time LETKF LETKF-RIP09 06z 130 (N) 87(N)09 12z 87(N) 43(N)09 18z 77 21(N)10 00z 13 1110 06z 47 87(N)10 12z 47 3210 18z 60 0

Error of land fall location

•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).