# Carvill Hurricane Index

The Carvill hurricane index (CHI) is an index which describes the potential for damage from an Atlantic hurricane. The CHI is used as the basis for trading hurricane futures and options on the Chicago Mercantile Exchange (CME).

## Index calculation

The CHI takes as input two variables: the maximum sustained wind speed of a hurricane in miles per hour and the radius to hurricane force winds of a hurricane in miles (i.e. how far from the center of the hurricane winds of 74 mph or greater are experienced). If the maximum sustained wind speed is denoted by V and the radius to hurricane force winds is denoted by R then the CHI is calculated as follows:

$CHI = \left ( \frac{V}{V_0} \right )^3 + \frac{3}{2}\left ( \frac{R}{R_0} \right ) \left ( \frac{V}{V_0} \right )^2$

where the subscript 0 denotes reference values. For use on the CME, the reference values of 74 mph and 60 miles are used for the maximum sustained wind speed and radius of hurricane force winds respectively.

## Index history and data

The development of the CHI was based on work published by Lakshmi Kantha at the Department of Aerospace Studies at the University of Colorado in Boulder, Colorado. Kantha's paper[1] in Eos developed a number of indices based on various characteristics of hurricanes. The ReAdvisory team at the reinsurance broker RK Carvill[2] used the basics of the Kantha paper to develop an index which became the CHI.

The data for the CHI comes from the public advisories issued for named storms by the National Hurricane Center. Specifically, to determine the maximum sustained wind speed, the following verbiage is looked for:

MAXIMUM SUSTAINED WINDS ARE NEAR XX MPH

To determine the radius to hurricane force winds, the following phrase is looked for:

HURRICANE FORCE WINDS EXTEND OUTWARD UP TO XX MILES

For example, Advisory 23A[3] for Hurricane Katrina at 1pm Central daylight time on Sunday, August 28, 2005, gave the maximum sustained wind speed of 175 mph and the radius of hurricane force winds of 105 miles resulting in a CHI value of 27.9.

## Data

Public advisories from the National Hurricane Center are archived back to 1998. The table below lists the CHI values for all the landfalling hurricanes since 1998 based on the NHC Public Advisories.

Table 1: Historical storms and the CHI (1998 to 2005)
Name Year Landfall NHC advisory number V(mph) R(miles) Saffir–Simpson category CHI
Bonnie 1998 North Carolina 31B 115 115 3 10.7
Earl 1998 Florida 11 80 115 1 4.6
Georges 1998 Mississippi 51B 105 45 2 5.1
Bret 1999 Texas 17 140 40 4 10.4
Floyd 1999 North Carolina 34A 110 115 2 9.6
Irene 1999 Florida 9 75 30 1 1.8
Lili 2002 Louisiana 48A 100 60 2 5.2
Claudette 2003 Texas 27A 75 30 1 1.8
Isabel 2003 North Carolina 49A 100 115 2 7.7
Charley 2004 Florida 18 145 30 4 10.4
Frances 2004 Florida 44A 105 75 2 6.6
Ivan 2004 Alabama 55B 130 105 3 13.5
Jeanne 2004 Florida 49B 115 70 3 8.0
Dennis 2005 Florida 25B 120 40 3 6.9
Katrina 2005 Florida 9 75 15 1 1.4
Katrina 2005 Louisiana 26A 145 120 4 19.0
Rita 2005 Texas 26B 120 85 3 9.9
Wilma 2005 Florida 36 125 90 3 11.2

Prior to 1998, the data becomes sparse. However, using data from the HURSAT[4] database at NOAA it is possible to construct a set of CHI values for storms back to 1983.

Modeled data is available from a number of sources:

## Notes

1. ^ L. Kantha, "Time to Replace the Saffir-Simpson Hurricane Scale?", Eos, Vol. 87, No. 1, 3 January 2006
2. ^ RK Carvill website