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

Limitations of a strictly actuarial approach

Total Number of United States Landfall Events, by Category,

U.S. Hurricane Damage, , Adjusted for Inflation, Wealth, and Population

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

Additional Problem: Nonstationarity of climate

Atlantic Sea Surface Temperatures and Storm Max Power Dissipation (Smoothed with a filter) Scaled Temperature Power Dissipation Index (PDI) Years included: Data Sources: NOAA/TPC, UKMO/HADSST1

Bringing Physics and Math to Bear

Physics of Mature Hurricanes

Energy Production

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

Annual Maximum Potential Intensity (m/s)

Numerical Simulation of Hurricanes

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

Typhoon Megi 10/17/ GMT

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

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

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

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

Multiply nested grids

Nested-grid domains

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

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

Model behavior: Maximum wind speed

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

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

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

Hindcast of Katrina

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

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

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

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

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.

Example:

The time series of other flow components: or where each F i 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.

Track: Empirically determined constants:

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

Comparison of Random Seeding Genesis Locations with Observations

Example: 50 Synthetic Tracks

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

Calibration Absolute genesis frequency calibrated to globe during the period Absolute genesis frequency calibrated to globe during the period

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

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

Seasonal Cycles Atlantic

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

3000 Tracks within 100 km of Miami 95% confidence bounds

Return Periods

Sample Storm Wind Swath

Simulated vs. Observed Power Dissipation Trends,

Last 20 years of 20 th century simulations 2. Years of IPCC Scenario A1b (CO 2 stabilized at 720 ppm) 1. Last 20 years of 20 th century simulations 2. Years of IPCC Scenario A1b (CO 2 stabilized at 720 ppm) Compare two simulations each from 7 IPCC models:

IPCC Emissions Scenarios This study

Basin-Wide Percentage Change in Power Dissipation

Basin-Wide Percentage Change in Storm Frequency

7 Model Consensus Change in Storm Frequency

Explicit (blue dots) and downscaled (red dots) genesis points for June- October for Control (top) and Global Warming (bottom) experiments using the 14-km resolution NICAM model. Collaborative work with K. Oouchi.

Coupling large hurricane event sets to surge models (with Ning Lin) Couple synthetic tropical cyclone events (Emanuel et al., BAMS, 2008) to surge models – SLOSH – ADCIRC (fine mesh) – ADCIRC (coarse mesh) Generate probability distributions of surge at desired locations

5000 synthetic storm tracks under current climate. (Red portion of each track is used in surge analysis.)

Tracks of 18 “most dangerous” storms for the Battery, under the current (left) and A1B (right) climate, respectively

SLOSH mesh for the New York area (Jelesnianski et al., 1992)

Surge Return Periods for The Battery, New York

Example: Intense event in future climate downscaled from CNRM model

ADCIRC Mesh

Peak Surge at each point along Florida west coast

Return levels for Tampa, including three cases : control (black), A1B (blue), A1B with 1.1ro and 1.21 rm (red)

Summary: History too short and inaccurate to deduce real risk from tropical cyclones History too short and inaccurate to deduce real risk from tropical cyclones Global (and most regional) models are far too coarse to simulate reasonably intense tropical cyclones Global (and most regional) models are far too coarse to simulate reasonably intense tropical cyclones Globally and regionally simulated tropical cyclones are not coupled to the ocean Globally and regionally simulated tropical cyclones are not coupled to the ocean

We have developed a technique for downscaling global models or reanalysis data sets, using a very high resolution, coupled TC model phrased in angular momentum coordinates We have developed a technique for downscaling global models or reanalysis data sets, using a very high resolution, coupled TC model phrased in angular momentum coordinates Model shows skill in capturing spatial and seasonal variability of TCs, has an excellent intensity spectrum, and captures well known climate phenomena such as ENSO and the effects of warming over the past few decades Model shows skill in capturing spatial and seasonal variability of TCs, has an excellent intensity spectrum, and captures well known climate phenomena such as ENSO and the effects of warming over the past few decades

Event Set for ASP Projects Must have and be able to use MATLAB Go to Download and read Readme_matlab_scripts.pdf Download the two zip files Current event set is for the Atlantic basin; by tomorrow morning I will post an event set for the U.S. east and Gulf coasts.

Ocean Component : ((Schade, L.R., 1997: A physical interpreatation of SST-feedback. Preprints of the 22 nd Conf. on Hurr. Trop. Meteor., Amer. Meteor. Soc., Boston, pgs ) Mixing by bulk-Richardson number closure Mixed-layer current driven by hurricane model surface wind

Couple to Storm Surge Model (SLOSH) Ning Lin Courtesy of Ning Lin

Surge map for single event

Histogram of the SLOSH-model simulated storm surge at the Battery for 7555 synthetic tracks that pass within 200 km of the Battery site.

Surge Return Periods, New York City

Genesis Distributions

Why does frequency decrease? Critical control parameter in CHIPS: Entropy difference between boundary layer and middle troposphere increases with temperature at constant relative humidity

Change in Frequency when T held constant in

Probability Density by Storm Lifetime Peak Wind Speed, Explicit and Downscaled Events

Change in Power Dissipation with Global Warming

Analysis of satellite-derived tropical cyclone lifetime-maximum wind speeds Box plots by year. Trend lines are shown for the median, 0.75 quantile, and 1.5 times the interquartile range Trends in global satellite-derived tropical cyclone maximum wind speeds by quantile, from 0.1 to 0.9 in increments of 0.1. Elsner, Kossin, and Jagger, Nature, 2008