BOVE TUES 3PM VEN I.pdf

8/12/2019 BOVE TUES 3PM VEN I.pdf

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CAT MODELING 101:

HURRICANE & EARTHQUAKE

Mark Bove, CPCU, AReSenior Research Meteorolo istMunich Reinsurance America, Inc.

RAA Catastrophe Modeling Conference12 February 2013


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Agenda

Cat Modeling Basics

Model Components

Model Process

Event Set Creation

Intensit Calculation

Vulnerability

Earthquake Modeling Basics

Event Set Creation

Intensity Calculation


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Basic Building Blocks of Catastrophe Models


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There are four basic components to all catastrophe

models, regardless of the peril being modeled.

oc as c ven e

Dama e Estimation

Loss Evaluation


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Stochastic Event Set

A set of discrete events covering all the important combinations of location,, ,

the (annual) probability of each event.

Account for all locations that are

impacted by peril of interest.

Have a sufficient number of events to

A Stochastic Event Set

should:

cover all possible sizes and intensities

that are possible in a given location.

Consider the probability of a given event

occurring.

Have enough events to produce

statistically stable loss results.


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A set of rules to calculate the intensity of each event at every site of interestindividual location insurance ortfolio etc.

Be based on established physics of the

hazard being modeled.

Intensity Calculations

should:

Should be calculated at every location

of interest.

Should consider environmental

influences at or around site of interest.

To calculate event intensities at each location of interest, the model requires

Geocodin and the relevant Geos atial Hazard Databases for the eril bein

modeled. Both of these tools are included in the model.


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Geocoding

data (building number, street, city, state, and postal code) into coordinates(usually latitude and longitude) that the risk modeling software can process.

,

better.

555 College Road East

Princeton, NJ 08543

= 40.351 N, 74.593 W

Map: Munich Reinsurance America


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Geospatial Hazard Databases

a a ases con a n ng n orma on

on the local environmental and/or

physical factors that can influence

an even s n ens y a e s e.

The relevant information depends

on the eril; With res ect to tro ical

cyclones: topography and surface

roughness.

Source: USGS


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Damage Estimation

Computational models to estimate the damage level of each structure, givenits vulnerability to the particular peril and the events intensity at the site

Consider several types of construction and buildingoccupancy (primary modifiers).

Consider other construction techniques that either

Dama e Estimation

ncrease or ecrease vu nera ty to t e per n

question (i.e. secondary modifiers). Consider the initial quality of construction, including

the adoption and enforcement of building codes, aswell as the a e and the maintenance of the buildin .

should: Have different damage/vulnerability functions for

buildings (structural and nonstructural elements),

contents, and time element.

Use a consistent measure to correlate event intensity

.

Account for so-called secondary hazards, such as

storm surge and demand surge.


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Loss Evalution

Evaluate insured losses, given the damage level & values, as well as thea licable insurance and reinsurance structures, such as deductibles, limits,

Determine how building damage

translates into insurance loss.

attachment points, treaty cessions, etc.

Determine whether or how to account

for:

Demand surgeoss va ua on

should:

Inflated claims

Aggressive construction contractors

Questionable claims settlement


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Model Output

Losses can be produced for a variety of financial perspectives.

The output of the catastrophe model contains the losses by event by

financial perspective.

Ground Up Loss

(Loss before policy limits/deductibles)

(Loss after application of limits and deductibles)

Treaty Loss

(Loss to individual treaties)Financial perspectives

Net Loss

(Loss after limits, deductibles, and treaties)

Reinsurance loss

(Loss suffered by the reinsurer)


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Model Flowchart

Provided by user Part of model

Stochastic

Event SetGeocoding

Engine

Intensity

CalculationGeospatialxposure

Data

Damage

Estimation

Database

Insurance Lossruc ure Evaluation


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Detailed Model Flowchart

1. Stochastic Event Set 2. Intensity Calculation

Let x=1 & n = Number of Events in Set.

If Event x footprint impacts any

location of interest, go to step 2.tensityatSite

int

, .

Complete when all n events are

assessed. EventIn

Source-to-Site Distance

dist

3. Damage Estimation

r

4. Loss Evaluation

sity Deductible

DamageFac

t

mean DF

The standard deviation

is usually estimated as

a function of the mean

robabilityDe

n

Ground-Up Loss= DF x Repl. Value

Limit

Event Intensity at SiteGround-Up Loss

.


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Model Output

Loss evaluation Event loss tables ELT

Simulated losses are stored for each simulated event and location in an event loss

table (ELT) together with associated occurrence frequencies (probabilities)


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Model OutputCreating Event Loss Distributions

Combine covera es buildin contents time

element) to arrive at a site (account) loss

distribution for each event .

Involves evaluating

the sum of correlated

random variables and

each event.

Combine policies to produce a portfolio loss

deductibles and limits.

.


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Model Output

Creating Annual Loss Distributions By evaluating the

Combine all event loss distributions toarrive at an annualized probability

pro a y a e oss

from any one (two, threeetc.) event(s) can exceed

any given threshold..


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Model Output

Losses can be anal zed and a re ated on a location, olic or ortfolio level for which different

Exceedance Probability (EP) / Probable Maximum Loss (PML) Curve

insurance and / or financial structures can be applied for an event or annual aggregate basis

ce

edanc

PML

bilityofE

AAL

ualProb

Loss ($)

An

N-yr Loss


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Hurricane Modeling Basics

Source: NOAA


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Perils included in U.S. Tropical Cyclone Models

Explicitly Modeled Perils (Perils included in Event Set/Intensity Calculation):

Direct Wind Damage

Wave action (Offshore Platform Only)

Implicitly Modeled Perils (Perils included via vulnerability curves):

Indirect wind damage (Falling trees & limbs, projectiles, etc.)

Thunderstorm-related perils (Lightning, Hail, Tornado)

Wave Action (Mainland US Only) Coastal Erosion

Non-Modeled Perils:

Winter Storm perils occurring in Transitioning Storms

Secondary events triggered by tropical cyclone, such as nuclear plant incidents orprolonged inland flooding.


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Tropical Cyclone Event Set Development

Primary Stochastic Event Set Methodologies

Event Tree

Modeling using every possible intensity at every desired location,

Landfall parameters for stochastic events are fixed for each U.S.

landfall

Basin Simulation

ttempt to mo e t e ent re t ant c as n to recreate rea st churricane event sets using hundreds of thousands of model

iterations (years)

Each stochastic events characteristics are allowed to evolve over

time based on model parameters


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Tropical Cyclone Event Set Development:

Event Tree Example

10 miles m es

Point 1

Intensity

55 mph 75mph 95 mph 115 mph 135 mph 155 mph

45 90 135 45 90 135 45 90 135 45 90 135 45 90 135 45 90 135

Landfall Angle

10m 20m 30m 10m 20m 30m 10m 20m 30m

Rmax

Six intensities * 3 landfall angles * 3 Rmax sizes = 54 Events at Point 1.

Procedure is then repeated at Point 2, Point 3, , Point N.


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Basin Simulation

Attempt to model the entire Atlantic Basin to recreate realistichurricane event sets using hundreds of thousands of modelera ons years

statistical data from the historical event database (HURDAT) tocreate realistic simulations of Atlantic activity

Number of overall events er ear & U.S. landfalls eryear

Genesis / Lysis locations

Maximum sustained winds

Central pressure

Radius of maximum winds


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Basin Simulation

ModelYear

# Events

hurricane activity for 10,000 years. Using the fitted distribution of Atlantic

1 10

2 17

3 8

activity (previous slide), we can use a

random number generator to determine4 11

5 13

year

Once we determine how man events

7 9

8 12

form in each year, the next question is:Where in the Atlantic did they form?

9 1210 7

11 18

10,000 14


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Basin Simulation


Model Year 1

Event 8

Event 7

Event 6Event 4

Event 2Event 10

Event 1Event 9

Event 5

s ng e a a ase, one can oca e e po n s o or g n o s or ca

storms in the Atlantic. One can then create a 2D genesis probabili ty field based

on these data, then randomly assign genesis locations based on the 2D field.


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Basin Simulation

Storm Movement

Using HURDAT data, one can

Map: NOAA Coastal Services Center

ca cu a e s a s cs on ra e o s orm

motion and storm direction Tropical cyclone speed and direction

,one cant use statistics from theentire basin to create one direction

and forward speed distribution for a

Divide Atlantic into uniform gridboxes and calculate statistics ineach box

Determine speed and directionstatistics from historical stormswithin a radius of the storm that

Model Year 1, Event 1

Origin location and historical storms

moves w e even


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Basin Simulation

Storm Movement

Based on random sampling, direction 10%an spee s e erm ne or o e

Year 1, Storm 1, and its location ismoved ahead 6 hours in time, thenprocess is repeated

45%

Direction and speed distributionsmay be altered based on type of

historical storm track

1%35%

Track calculations usually havememory of previous motion to avoidsharp turns or jumps in motion

1%1%5%

yDensity

Probabilit

Rate of Movement


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Basin Simulation

Storm Lysis

At each time step that storm is


modeled, there is a probability that

the storm dissipates Probability of Lysis is dependent on

lysis and other physical parameters,such as:

Storm latitude

Over land or water Event 1

Track Model Output

Once track model run for N years is completed (and properly calibrated),

you can discard tropical cyclone tracks that do not impact your locations ofinterest (i.e. storms that stay far out to sea)


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Basin Simulation

Track Calibration

Track model is calibrated so that storm counts in each grid box (or area of

region.

At the coast, number of landfalls is usually calibrated by the historicallandfall rate in different coastline segments, or gates.

Gate landfall frequencies are smoothed using data from adjacent gates oroffshore data for regions that often see bypassing storms.

G

Landfall Rate at D = 0.3D + 0.2C +

0.2E + 0.12B + 0.12F +0.04A + 0.04G NC

CD

ESC

suranceAmeric

a

ABGA

Map:M

unichRei


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Intensity Calculation (Storm-Scale)

There are several factors that im act a tro icalcyclones intensity and overall wind field

Minimum central pressure

m en sea eve pressures surroun ng e rop ca cyc one

Local frictional effects

Photo: Munich Reinsurance America


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Central Pressure Calculation

A minimum central ressure is assi ned to storm at ori in, and isallowed to change with time, based on historical pressure change

distributions in the region.

Little pressure data in much of historical record, however

Pressure will typically decrease (storm becomes more intense) whenstorm is over warm water, regions of typically low wind shear, and is far

from any major land features Pressure will typically increase (storm becomes less intense) when

over cooler waters, in regions of high wind shear, over land, or nearrugged terrain

n mum pressures are usua y cappe ase on s or ca pressuresand physical limits occurring in nature

Based on central pressure and assumed pressure outside the storm,


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Initial Wind Field Calculation

There are several different equations or mathematical approximationsthat can be used to simulate a hurricane wind field

Gradient Wind Equation

Holland B Parameter

Etc.

These e uations t icall use central ressure, Rmax, and assumed

pressure outside of storms circulation envelope, along with an assumedwind decay rate (inside and outside the eyewall)

Hurricane winds are calculated on a rid and for each location of interest

for each time step of a stochastic event during landfall

T i l C l E t S t D l t


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Example Wind Field (Frictionless)

km/hr

insuranceAmer

ica

Image:

MunichRei


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Intensity Calculation (Local-Scale)

Location Wind Intensity

The wind experienced at a given site during a hurricane depends on several

source, pa an s e reg ona c arac er s cs

Source characteristics:

, ,

transition (if occurring)

Path characteristics:

Distance from eyewall, strong or weak side of storm

Site Characteristics:

Upwind locations land use and cover (fetch)

Elevation, topography, or building height

Models typically use peak highest gust at site of interest/grid box over life of

event to estimate damage; some consider both duration and intensity of highwinds


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Event Probabilities

Event Set Reduction (optional)

Similar storms in the overall stochastic event set can be removed if thean a ra es are e cons an .

Advantage: Smaller event set, model runs more quickly

Disadvantage: Loss of simulation year data in event set, makesassessing multiple events in a single year difficult.

Event B

Event A

ven a e:

0.00000978

Event B Rate:

Max. Winds:

0.00000978

Discard Event A; Event A rate

Event A: 75 mph

Event B: 78 mph

,becomes:

0.00001956



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Hurricane Damage Estimation

Vulnerability Curves

Covers dozens of types of structures and occupancies, as

well as default curves when this information is unknown

, ,

time element / business interruption

Modifiers for different qualities of construction

Sources of Structural Vulnerability Data

Claims data from historical events

Laboratory testing of structures and components

Computer simulations of structural response

Expert analysis and opinion


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Hurricane Damage Estimation

nceAmericaClaims Data Analysis

Amount of dama e re orted in claims for

r rt:MunichReinsur

each construction type or occupancy

compared to modeled wind speed at

location to develop vulnerability curves

ag

eFact

Cha

eanDam

Maximum Wind Gust (mph)

Earthquake


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Earthquake

Modeling Basics

Source: USGS


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Perils included in U.S. Earthquake Models

Explicitly Modeled Perils (Perils included in Event Set/Intensity Calculation):

Ground Shaking

Implicitly Modeled Perils (Perils included via factors and/or vulnerability curves):

Liquefaction

Landslides

Fire Following Earthquake

Earthquake Sprinkler Leakage

Non-Modeled Perils:

Tsunami

Secondary events triggered by earthquake, such as nuclear incidents.


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Peril Models: EarthquakeEarth uake Event Set Develo ment

Identify potential earthquake sources

Assign an appropriate magnitude-frequency relationship and a

corresponding recurrence interval distribution to each source

scre ze e magn u e sca e e ween e owes magn u e

of interest and the maximum magnitude for each source

Distribute events around the source


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Peril Models: EarthquakeEvent Set: Identif Potential Sources

USGS National Seismic Hazard Maps are basis for model EQ sources

Source: California Geological Survey


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Peril Models: EarthquakeEvent Set: Fre uenc / Severit Relationshi s

For each fault, both

historical seismicity

and paleoseismic

studies of sli rates

(where available) are

used to determine the

-

relationship.

Source: California Geological Survey


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Peril Models: EarthquakeEvent Set: Recurrence Interval Distribution

Recurrence Interval Distribution for California (No Subduction Zone EQs)

Magnitude Annual Rate Return Period

5.0 6 2 Months

.

6.0 1 1 Year

6.5 0.8 1.25 Years

7.0 0.1 10 Years

7.5 0.02 50 Years

8.0 0.005 200 Years

For source areas (modeled as pseudofaults), maximum magnitudes will not

e as g as t ose a ong nown au ts.

P il M d l E th k


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Peril Models: EarthquakeEvent Set: Event Rates

For each fault or area source, the frequency-severity relationship is combined

with a probability distribution to get event rates over a given time period (typically

1 year).

Poisson Model

Time Dependent Model

Stress Transfer Model

Only well-researched faults have time-dependent or stress transfer models

associated with them, all other models use Poisson modeling.

P il M d l E th k


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Peril Models: EarthquakeEvent Set: Discretizin

Length of fault determines maximum potential rupture length and magnitude,

and the potential magnitude of a quake along a fault can be any magnitude up

to its maximum.

There is a lot of uncertainty in earthquake magnitudes and the ground shaking

.

same fault or fault segment redundant. For example. the difference in impacts

between a M6.9 versus M6.8 earthquake on same fault segment are within the

hazard modeling uncertainty, so no need to model both magnitudes.

Thus, events are discretized, which means the models have gaps between

, .

This also lowers size of event set.

Usually done in set magnitude increments, fault-dependent

Models only need to consider damaging earthquakes, so a minimum strength

level can also be set in the model

Peril Models: Earthquake


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Event Set: Distributing Events on a Source

Fault X

M7.0

M6.0 (1)

M6.0 (2)

M6.5 (1)

M6.5 (2)



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Event Set: Individual Event Rates

Modeled Event Rates for different magnitude events along a given fault are

Magnitude Rate # Modeled Events Rate Per Event

M5.0 0.1 20 0.005M5.5 0.05 20 0.0025

M6.0 0.01 15 0.0007

. . .

M7.0 0.001 5 0.0002

M7.5 0.0005 2 0.00025

Chart: Munich Reinsurance America



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Peril Models: EarthquakeIntensit Calculation

The spread of the energy released by an earthquake is described by

attenuation equations.

For the United States, a set of attenuation equations are provided bythe U.S. Geological Survey as part of their National Seismic Hazard

,

in their models.

Earthquake Magnitude & Depth

Distance from source

equations, and is dependent on:

Duration of ground motion

Geological conditions along the

wave path

Local Soil Conditions



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Peril Models: EarthquakeIntensit Calculation: Ma nitude

Ma nitude 6.0 Ma nitude 6.9 Ma nitude 7.9

Source: USGS



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Peril Models: EarthquakeIntensit Calculation: De th

Northridge: Magnitude 6.7

Thrust Mechanism, 18 km depth

Nisqually: Magnitude 6.8

Normal Mechanism, 52 km depth

Source: USGS



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Peril Models: EarthquakeIntensit Calculation: Bedrock T e

Source: USGS



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Peril Models: EarthquakeIntensit Calculation: Site Characteristics

Recorded

Time Histories

Recording StationsSan Francisco

Oakland

Distance: 80 km / 50 miles

Yerba Buena Island (Rock)

Treasure Island (Landfill)

Calculated

Response Spectra

San Jose

Epicenter

Map: Munich Re America



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Peril Models: EarthquakeIntensit Calculation

There are two main methods of calculating an earthquakes intensity at a given

location of interest in catastrophe models:

Peak Ground Acceleration A measurement of the maximum pulse of ground

shaking at a location. Describes as a percentage of the acceleration due to

Spectral Acceleration An instrumental calculation combining ground motion,

site response, and building response.

Considers duration, frequency, and type of construction

Vulnerability curves will be calibrated to whatever intensity metric is used.

Earthquake Damage Estimation


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Vulnerability Curves

Covers dozens of types of structures and occupancies, as

well as default curves when this information is unknown

, ,

time element / business interruption

Modifiers for different qualities of construction

Sources of Structural Vulnerability Data

Claims data from historical events

Laboratory testing of structures and components

Computer simulations of structural response

Expert analysis and opinion


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THANK YOU! ANY QUESTIONS?

Mark Bove [email protected]


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Copyright 2013 Munich Reinsurance America, Inc. All rights reserved. "Munich Re" and the Munich Re logo are

internationall rotected re istered trademarks. The material in this resentation is rovided for our information onl , and

is not permitted to be further distributed without the express written permission of Munich Reinsurance America, Inc. or

Munich Re. This material is not intended to be legal, underwriting, financial, or any other type of professional advice.

Examples given are for illustrative purposes only. Each reader should consult an attorney and other appropriate advisors

to determine the applicability of any particular contract language to the reader's specific circumstances.

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