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

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)

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)

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)

“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

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

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

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

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?

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

Observations used in the OSSE experiments

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

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

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

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.

(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

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

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.

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

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)

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.

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