Using Physics to Help Assess Hurricane Risk

1. Using Physics to Help Assess Hurricane Risk Kerry Emanuel Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology

2. Limitations of a strictly actuarial approach

3. Total Number of United States Landfall Events, by Category, 1870-2004

4. U.S. Hurricane Damage, 1900-2004, Adjusted for Inflation, Wealth, and Population

5. Summary of U.S. Hurricane Damage Statistics: • >50% of all normalized damage caused by top 8 events, all category 3, 4 and 5 • >90% of all damage caused by storms of category 3 and greater • Category 3,4 and 5 events are only 13% of total landfalling events; only 30 since 1870 • Landfalling storm statistics are inadequate for assessing hurricane risk

6. Additional Problem:Nonstationarity of climate

7. Atlantic Sea Surface Temperatures and Storm Max Power Dissipation (Smoothed with a 1-3-4-3-1 filter) Years included: 1870-2006 Power Dissipation Index (PDI) Scaled Temperature Data Sources: NOAA/TPC, UKMO/HADSST1

8. Bringing Physics and Math to Bear

9. Physics of Mature Hurricanes

10. Energy Production

11. Theoretical Upper Bound on Hurricane Maximum Wind Speed:POTENTIAL INTENSITY Surface temperature Ratio of exchange coefficients of enthalpy and momentum Outflow temperature Air-sea enthalpy disequilibrium

12. Annual Maximum Potential Intensity (m/s)

14. Numerical Simulation of Hurricanes

15. The Problem • The hurricane eyewall is a region of strong frontogenesis, attaining scales of ~ 1 km or less • At the same time, the storm’s circulation extends to ~1000 km and is embedded in much larger scale flows

16. Typhoon Megi 10/17/10 0457 GMT

17. Eyewall Undergoes Frontal Collapse • Will always challenge spatial resolution of numerical models • High resolution required for numerical convergence • Proper formulation of 3-D turbulence critical for adequate simulation of eyewall

18. Global Models do not simulate the storms that cause destruction! Modeled Histograms of Tropical Cyclone Intensity as Simulated by a Global Model with 50 km grid point spacing. (Courtesy Isaac Held, GFDL) Observed Category 3

19. Numerical convergence in an axisymmetric, nonhydrostatic model (Rotunno and Emanuel, 1987)

20. How to deal with this? • Option 1: Brute force and obstinacy

21. Multiply nested grids

22. Nested-grid domains

23. How to deal with this? • Option 1: Brute force and obstinacy • Option 2: Applied math and modest resources

24. Time-dependent, axisymmetric model phrased in R space • Hydrostatic and gradient balance above PBL • Moist adiabatic lapse rates on M surfaces above PBL • Boundary layer quasi-equilibrium convection • Deformation-based radial diffusion

25. Model behavior: Maximum wind speed

27. Application to Real-Time Hurricane Intensity Forecasting • Must add ocean model • Must account for atmospheric wind shear

28. Ocean columns integrated only Along predicted storm track. Predicted storm center SST anomaly used for input to ALL atmospheric points.

29. Comparing Fixed to Interactive SST: Model with Fixed Ocean Temperature Model including Ocean Interaction

30. Hindcast of Katrina

32. How Can We Use This Model to Help Assess Hurricane Risk in Current and Future Climates?

33. Risk Assessment Approach: Step 1: Seed each ocean basin with a very large number of weak, randomly located cyclones Step 2: Cyclones are assumed to move with the large scale atmospheric flow in which they are embedded, plus a correction for beta drift Step 3: Run the CHIPS model for each cyclone, and note how many achieve at least tropical storm strength Step 4: Using the small fraction of surviving events, determine storm statistics. Details: Emanuel et al., Bull. Amer. Meteor. Soc, 2008

34. Synthetic Track Generation:Generation of Synthetic Wind Time Series • Postulate that TCs move with vertically averaged environmental flow plus a “beta drift” correction • Approximate “vertically averaged” by weighted mean of 850 and 250 hPa flow

35. Synthetic wind time series • Monthly mean, variances and co-variances from re-analysis or global climate model data • Synthetic time series constrained to have the correct monthly mean, variance, co-variances and an power series

36. 250 hPa zonal wind modeled as Fourier series in time with random phase: where T is a time scale corresponding to the period of the lowest frequency wave in the series, N is the total number of waves retained, and is, for each n, a random number between 0 and 1.

37. Example:

38. The time series of other flow components: or where each Fi has a different random phase, and A satisfies where COV is the symmetric matrix containing the variances and covariances of the flow components.Solved by Cholesky decomposition.

39. Track: Empirically determined constants:

40. Risk Assessment Approach: Step 1: Seed each ocean basin with a very large number of weak, randomly located cyclones Step 2: Cyclones are assumed to move with the large scale atmospheric flow in which they are embedded, plus a correction for beta drift Step 3: Run the CHIPS model for each cyclone, and note how many achieve at least tropical storm strength Step 4: Using the small fraction of surviving events, determine storm statistics. Details: Emanuel et al., Bull. Amer. Meteor. Soc, 2008

41. Comparison of Random Seeding Genesis Locations with Observations

42. Example: 50 Synthetic Tracks

43. 6-hour zonal displacements in region bounded by 10o and 30o N latitude, and 80o and 30o W longitude, using only post-1970 hurricane data

44. Calibration Absolute genesis frequency calibrated to globe during the period 1980-2005

45. Genesis rates Western North Pacific Southern Hemisphere Eastern North Pacific Atlantic North Indian Ocean

46. Captures effects of regional climate phenomena (e.g. ENSO, AMM)

47. Seasonal Cycles Atlantic

48. Cumulative Distribution of Storm Lifetime Peak Wind Speed, with Sample of 1755Synthetic Tracks 95% confidence bounds

49. 3000 Tracks within 100 km of Miami 95% confidence bounds

50. Return Periods