1. 1 Simulations of Rapid Intensification of Hurricane Guillermo with Data assimilation Using Ensemble Kalman Filter and Radar Data Jim Kao (X-2, LANL) Presentation at Navy/LANL Joint Workshop on Use of Lightning Data and Advanced Modeling March 25, 2009 Special thanks to M. Potocki, S. Guimond, and J. Reisner

2. 2 Presentation Layout Introduction Rapid Intensification, Guillermo IPO Data Assimilation Method and Procedure Ensemble Kalman Filter (EnKF), Sampling Method, Observational Errors HIGRAD Simulations A fully compressible hydrodynamic code with 300 x 300 x 71 cells to cover 1200 Km x 1200 Km x 15 Km with 12 prognostic variables Results of Assimilated Simulations Data of latent heat at 1900 UTC, Aug. 2, was assimilated into HIGRAD Concluding Remarks

3. 3 Rapid Intensification (RI) of Hurricanes are catastrophic with loss of human lives and property damage Wind Speeds Increase by 15 m/s (33.5 mph) in 24 hours Favorable environmental conditions (e.g., high SST, low-level moisture, weak shear, upper-level easterlies, etc.) are identified. Difficult to predict due to nonlinear dynamics between asymmetric features of convection and rotation. Observations by remote sensing platforms, e.g., Doppler radars and lightning measurement arrays, have generated extra data for a better understanding of RI. Current study concentrates on Guillermo’s intensive observation period from 1830 UTC, Aug. 2 to 0030 UTC Aug. 3, 1997, with duel Doppler radar measurements of latent heat and winds.

4. 4 Ensemble Kalman Filter (EnKF) Is Effective for Data Assimilation in 3-D Codes EnKF is a Monte-Carlo version of the extended Kalman filter (EKF). EKF analytically predicts the 1 st order time change of covariance matrices, but prohibitively expensive. EnKF instead collects statistics from an ensemble simulation. This class of techniques blends observations into a model’s predictions to provide an optimal estimate of the true state, i.e., maximum likelihood, based on the Bayse theory with the Gaussian assumption. The ensemble members are constructed by sampling the model’s parameter space using the Latin Hyper-Cube method (LHC). The optimal parameters are also estimated.

5. 5 Data Assimilation Procedure (Slides 5-7) 1.A HIGRAD dump (x 0 ) at Cycle 7200 (= 2 hours) was handed over by code developers. The vector x includes all the variables plus 2 parameters: qvsurf=0.95 and evaplimit=10.0, that were used in the simulation. 2.An ensemble of M members (M=20) were constructed using the LHC sampling over the 2 values of parameters above (see Slide 8). 3. A half-hour simulation was conducted for each member of the ensemble (X m, m= 1,20) and the reference case (x 0 ) to Cycle 9000. Representation of x 0 is shown in Slide 9. The ensemble spread is demonstrated in Slides 10-12.

6. 6 Data Assimilation Procedure (cont.) 4. A number of N data points (N is limited to 700 due to computer memories) were evenly selected from the gridded dataset (y o ) of latent heat (upper panels of Slide 13) of Guillermo near 1900UTC on Aug. 2, 1997, derived from the radar signals of hydrometeor intensities. 5.From x m for m=1,20 in Step 3, we collect “modeled” latent heat (e.g., lower panels of Slide 13 for m=1) according to the locations of y o and define them h m. 6. Using Steps 4 and 5 above, we establish a difference vector d m op for each member of the ensemble: d m op = y o – h m, (1), where “o” denotes observations and “p” denotes predictions.

7. 7 Data Assimilation Procedure (cont.) 7. The “assimilated” member (x m a ) (e.g., Slide 15) is obtained through the linear combination of “o” and “p” x m a = x m + K d m op (2) with K as the Kalman gain (or weighting) matrix expressed as: K = ______________________________ (3) + R where the over-bar denotes the ensemble mean and R is the covariance of the observational errors bounded by 15%. 8. Wind data can, in principle, be simultaneously assimilated. But, due to the distinctively different magnitudes between latent heat and winds, some sort of normalization is required. Here, we first demonstrate the latent heat assimilation.

8. 8 Parameter distributions using LHC sampling over the reference values (0.95, 10). The green star represents the converged values after the assimilation

9. 9 Modeled surface pressure, wind speeds, vertical motion and latent heat from the reference run at Cycle 9000, which serve as a foundation for the future assimilation and will be used to contrast assimilated fields

10. 10 Differences of surface pressures at Cycle 9000 before data assimilation for selected ensemble members (1,2,5 and 20) are detectable

11. 11 Similarly, differences of low-level winds at Cycle 9000 before data assimilation for selected ensemble members (1,2,5 and 20) are detectable

12. 12 Patterns and magnitudes of mid-level latent heat at Cycle 9000 before data assimilation for selected ensemble members (1,2,5 and 20) are more alike than pressure and winds

13. 13 Observed (upper panels) vs. simulated (lower panels) latent heat show significant differences both in patterns and magnitudes.

14. 14 Observed (upper panels) vs. simulated (lower panels) wind speeds show significant differences both in patterns and magnitudes.

15. 15 Differences of surface pressures at Cycle 9000 after data assimilation for selected ensemble members (1,2,5 and 20) are less detectable (c.f., Slide 10)

16. 16 The effects from assimilation of latent heat support a more rigorous convective storm 1. We have assimilated the latent heat data at 1900 UTC, Aug.2, into the HIGRAD simulations at Cycle 9000 for an ensemble of 20 runs. 2.The overall effects of this assimilation in comparison with the reference run are: low-level cooling (Slide 17)  deepened surface pressure (Slide 15)  stronger low-level winds (Slide 18)  stronger vertical motion (Slide 19) and surface evaporation (Slide 20). 3.The above effects suggest a more rigorous convective situation in line with the converged parameter values shown in Slide 8 ( * ). 4. We then allow Member #1 to continue another 7200 cycles (2 hours) to see the evolution out of the above effects (Slides 21-25).

17. 17 Potential temperatures before (upper panels) vs. after (lower panels) assimilation; cooling effect is seen for low-levels

18. 18 Wind speeds before (upper panels) vs. after assimilation; stronger winds are seen for low-levels

19. 19 Vertical motions before (upper panels) vs. after assimilation; stronger vertical winds are seen for low-levels

20. 20 Water vapor before (upper panels) vs. after assimilation; more abundant moisture is seen for low-levels

21. 21 Surface pressure evolution at Cycle 10800 and 14400 for simulations with (upper panels) and without (lower panel) latent heat assimilation. Much lower center pressures are seen for the case with assimilation.

22. 22 Low-level wind evolution at Cycle 10800 and 14400 for simulations with (upper panels) and without the latent heat assimilation. Much stronger winds are produced in the case with assimilation.

23. 23 Mid-level vertical motion evolution at Cycle 10800 and 14400 for simulations with (upper panels) and without assimilation. Vertical motions are not only stronger also laterally expanded in the assimilated case.

24. 24 Mid-level rain evolution at Cycle 10800 and 14400 for simulations with (upper panels) and without assimilation. Again, rain is not only stronger also laterally expanded in the assimilated case.

25. 25 Mid-level eye-wall latent heat evolution at Cycle 10800 and 14400 for simulations with (upper panels) and without assimilation. More spotty hot-tower like distribution is seen for the assimilated case.

26. 26 Concluding Remarks Our methodology of assimilating radar latent heat data of Guillermo into the HIGRAD hurricane code with the ensemble Kalman filter (EnKF) has been shown to capture the features of rapid intensification. Simulations with a single-time data assimilation are able to produce rapid intensification (RI) within two hours of simulation time. The cost of EnKF is reasonable for “now-casting” purposes. It is suspected, however, that the simulated RI is the result of the intrinsic difference between the modeled and observed latent heat both in magnitudes and altitudes. The refinement of the HIGRAD code based on the IPO datasets is recommended.