Hail and thunderstorm-related hazards play a large role in annual weather-related property losses in North America. The goal of Project APOTH (Atmospheric Perils Other Than Hurricane) at Guy Carpenter is to develop the capability to credibly estimate probabilistic losses from the thunderstorm perils of hail, tornado and straight-line winds (non-tornado high wind gusts). The company has developed this methodology and is now testing its use in the US.

Our goal is to develop models that fill in where third party catastrophe vendors leave off. The perils covered by APOTH will eventually span hail, tornado, thunderstorm, wind and winter storm. Currently, we have the ability to run hail and tornado for homeowners' risks in the US. The application has been designed to be exportable to other countries. It also can be utilized to handle exposures in other lines of business, including the seasonality associated with crop-hail. While a few modelers have the capability to handle hail and tornado, we believe the new methodology involving the application of fractal theory greatly expands the accuracy of the results. The model has been created internally at Guy Carpenter. The key developers have been John Mangano, our staff meteorologist and John Major and Yakov Lantsman, both statisticians. The primary source of information was the National Weather Service (NWS) Severe Storms Laboratory database and the Guy Carpenter Catastrophe Index.

APOTH synthetic climatology

One of APOTH's main tasks was to characterize the climatology of hail, wind, and tornadoes; that is, where and when they occur, how intense and how often. This was done using the most recent years of the NWS database. The period 1982-1998 was assumed as a fairly complete baseline to estimate the average annual occurrence rates, with 1982 to 1992 requiring adjustments due to reporting bias.

The APOTH simulated hail and tornado climatology is a 1000-year sequence of calendar days built up from sequences of days selected out of the 1982-1998 Storm Data record. This is not to say that each time a particular historical date is used, the exact locations and intensities of severe weather are repeated just as they occurred. Instead, the historical date's reported severe weather is grouped into general regions of “activity”. The character of the severe weather within a given active region is analyzed and used as a basis for simulating completely new occurrences of severe weather within the general active area. Thus, while a simulated “synthetic” day's severe weather resembles that of its analogue historic day, it is a completely new “re-creation” based on that day.

One specific item derived in the course of developing the APOTH models is the 1000-year “synthetic” hail and tornado climatology. This information can readily be used to generate regional hazard maps pertaining to these perils. This article presents maps generated from the APOTH climatology which show the geographical pattern of average annual homeowners loss costs for the hail and tornado hazards in Texas. Comparisons made with information from other studies indicate the patterns developed in these APOTH-generated maps appear quite reasonable.

Hazard level of resolution

Hailstreaks drop a non-uniform amount of hailstones that must be modeled in order to evaluate the damage associated with exposures in an area impacted by a streak. The images on these pages illustrate the variability associated with hail intensity within a streak and how APOTH simulates this effect.

Exhibit 1a is a hailstreak pattern from the literature for a given event. You can see the volume of hailstones can vary significantly. In the red contour, there are over 4000 stones in a square meter of surface. Exhibit 1b illustrates a simulated streak pattern similar in size and intensity to this actual event.

When simulating hailstreaks, APOTH estimates the number and size of hailstones deposited in a square kilometer of surface. In Exhibit 1b, a one square kilometer scale is indicated. This level of hazard simulation appears to be adequate for hail modeling.

When a tornado takes place, we typically hear a report of its intensity based on the Fujita scale, ranging from “F0” for weak tornadoes through “F5” for catastrophic events. During the life cycle of a tornado, the intensity starts low and reaches a maximum before dying off. This maximum is what is typically reported. APOTH considers this variability when simulating tornadoes. Exhibit 2a illustrates the footprint of an F3 tornado that passed through Texas. As can be seen, the event can be depicted in intensity contours where the red area is when the tornado was at its strongest. In Exhibit 2b, a similar F3 tornado is simulated. The tornado path is overlaid onto a one square kilometer grid, and the affected area of each impacted kilometer is determined. APOTH estimates not only the percentage of the grid cell that the tornado hit but also by what distribution of Fujita scale.

Hazard simulation process

The basic process begins by simulating a day in a hypothetical 1000-year period. The model selects a historical “analogue” day, which occurred in a 30-day period around the date to be simulated. APOTH analyzes any severe weather that may have occurred on that historical day, and uses that as a basis for simulating hypothetical thunderstorm activity in the general region where the actual activity occurred. This analysis includes the intensity of the event, the volume of stones deposited and the orientation of the event. A random fractal field is developed from this historical event. This allows for the historical event to be perturbed in the area that the event took place. This fractal is condensed down to specific kilometer grids within the streaks. A client's exposure is assigned to a specific kilometer grid cells during the geocoding process, which allows the model to evaluate the extent of damage associated with the event.

This daily simulation process was intentionally designed into APOTH to allow for the expansion of simulating the effect of loss for crop-hail. Seasonality is key for determining the vulnerability of crops to damage when exposed to hail.

Homeowners vulnerability functions

In order to estimate losses given a simulated hail event, some form of vulnerability function is required. Vulnerability functions relate the loss associated with the amount of hazard severity being imposed on the property. The wind vulnerability of single family dwellings has been researched for some time, and is readily available in some form or another in engineering and insurance literature.

Hail vulnerability information is not so prevalent. The APOTH project developed a homeowners hail vulnerability function using the aggregated claims experience from the Guy Carpenter Catastrophe Index (GCCI) member companies. This large database includes daily homeowners claim counts, loss amount, and “cause of loss” by location (ZIP codes or ZIP groupings). For a given day, claim and loss rates were computed at each location for losses coded as hail. These were matched to storm data reports of hailsize occurring in the immediate vicinity on the date of loss. Analysis of this paired hail and loss data allowed the development of a credible homeowners hail vulnerability function.

The second difference between the hail and tornado loss costs is in their magnitude.

The tornado loss costs tend to be quite a bit lower than those for hail. This may seem surprising at first, since the general impression is that tornadoes have a much higher damage rate than hailstorms. While this is generally true, damaging tornadoes (greater than F0) are much less frequent than damaging hailstorms (over 1” diameter). Further, the ground area affected by tornadoes is very much smaller than for hailstreaks.

To illustrate this point, a query of the Storm Data database was made for all tornado and hail reports from 1992-1998. The query limited the cases to those falling in a box covering the northern two-thirds of Texas.

The tables to the right compare the frequency and land areas affected by hail and tornadoes.

The actual area affected by each tornado was available in the Storm Data database, and these were summed by Fujita Intensity (F-class). However, hailstreak dimensions are not part of the database, and the median hailstreak area of 6 square miles was used.

A more detailed comparison can be made, assigning a damage index to each tornado and hail size category and applying that to the land areas affected. Such an analysis does indicate a substantially larger hail hazard compared with that of tornado.


We are excited about this new application which will bring value to clients in analyzing and managing their hail and tornado risks. The data requirements for using this model are quite simple: either ZIP code aggregates of risk counts and coverages, or latitude/longitude can be used to input individual risks with their coverages.

The APOTH project presently has models that can realistically simulate both the geographical and seasonal characteristics of hailstorm and tornado occurrences, as well as model their small-scale ground damage patterns.

We now have the capability to estimate probabilistic losses for hail and tornado for the entire continental

US homeowners' book of business. The model should be easily extended to include other territories, once we know there is sufficient demand and have access to data at the required level of accuracy to ensure credible results.

John Tedeschi is senior vice president of Guy Carpenter Instrat.