## Probability and Risk

### Probability

Probability and risk concepts are used to quantify a homeowner or community's hurricane hazard. The likelihood of being exposed to a hazard of some given level or higher is known as the "exceedance probability." The exceedance probability is defined as a percent or fraction. For example, a 1% (or 0.01) annual flood exceedance probability means there is 1% change in any given year that the flood elevation will be at that level or higher.

Another popular probability term is "return period." Return period is defined as the inverse of the exceedance probability, expressed in years. In our example, a 1% flood exceedance probability has a return period of 100 years (1/0.01). The return period represents the average number of years between events of that magnitude or higher. The return period does not represent the actual number of years between such events. More specifically, it is plausible that an area can experience the 100-yr event two years in a row, or even twice in one year.

**Example of storm surge versus annual exceedance probability (left) and return period (right).**

### What is the 100-Year Floodplain?

The 100-year floodplain is a geographic region in which all locations have an annual flood exceedance probability of 1% or higher (or return period of 100 yrs or less). Here, the exceedance flood value is at least the ground elevation. Because probabilities vary by location, many locations within the floodplain have greater than a 1% chance of flooding to at least ground elevation.

A line on a map typically marks floodplains, where homes on one side of the line are in the floodplain and homes on the other are not. Yet, there is large uncertainty in estimating flood probabilities. So, it is likely that homes on either side of the floodplain line have very similar flood exposure.

**Flood return periods included in the 100-year floodplain.**

### What is My Flood Exposure if I Live in the 100-Year Floodplain?

In the U.S., a typical home mortgage is for 30 years. Suppose a family decides to purchase a home in the 100-year flood plain and plans to live in their home for 30 years. While the family's annual exceedance probability is at least 1% (100-yr return period), the likelihood that their home will flood in 30 years is at least 26% (more than 1 in 4). In other words, the chance of flooding in 30 years is 20 times more likely than winning $2 from one $1 Megamillions ticket (1 in 75).

**Likelihood of flooding in a 30 year period, by return period.**

### Risk

Risk has many definitions. Here, we will define actual risk as Probability times "Consequence". Consequence also has many definitions. For example, the number of deaths is a consequence, as is economic damage or impacts to the environment. Consider the case of economic damage by storm surge. As storm surge increases, economic damage increases. Yet, as storm surge increases, its probability decreases. So, extremely large storm surges are not typically associated with the largest risk (a number close to zero multiplied by a very large number). Small storm surges likewise are not typically associated with the largest risk (a number close to one multiplied by a very small number).

To illustrate risk, consider Hurricanes Rita (2005) and Ike (2008). Both storms were of similar size and intensity (central pressure) when they made landfall. Both generated similar storm surges. Yet, if both hurricanes made landfall today (2013), Hurricane Ike would cause nearly twice as much damage as Hurricane Rita (ICAT Damage Estimator)^{[1]}. The reason for this dramatic difference in damage is that Hurricane Rita made landfall along the relatively unpopulated coast at the Texas/Louisiana border, while Hurricane Ike made landfall in the densely populated the Houston/Galveston, TX region. So, while both of these surge events likely have a similar probability, their consequences are very different.

See the iCat Damage Estimator.

### Reference

[1] Pielke, Jr., R. A., Gratz, J., Landsea, C. W., Collins, D., Saunders, M., and Musulin, R., 2008. Normalized Hurricane Damages in the United States: 1900-2005. Natural Hazards Review, Volume 9, Issue 1, pp. 29-42.