Question

1. Even in Tornado Alley, the chances of a tornado striking any particular location are pretty small. To illustrate this point, let’s estimate the risk in the state of Kansas which averages 80 tornadoes per year.
   1. Explain why we chose Kansas for this problem instead of Texas, given that Texas averages more tornadoes (140) per year. To frame your answer, note that the area of Kansas is approximately 211,800 mi²while the area of Texas is about 676,600 mi². You should include calculations in your answer.
   2. To make an estimate of this risk, we need to know the path length (length of the tornado’s track) and path width (width of the tornado) of an average tornado. Path length and width vary widely from tornado to tornado, but reasonable estimates are 100 meters for an average path width and 2 km for an average path length. Let’s say you stand at a randomly chosen point in Kansas for a year. Further assume that every point in Kansas has an equal likelihood of being hit by a tornado. Estimate the chance that you’ll be in the path of a tornado that year. Show your work.
   3. Express your answer in another form by answering the following question: What’s the average return time for a tornado in Kansas. In other words, what’s the average length of time you’d have to wait between tornado occurrences at the point where you’re standing?

Answer 1

The total area for Kansas is 211800mi² or 54855.95km², with an average width of 100m and an average length of 2km. Thus, total area hit by a tornado is 0.2km². There are a total of 80 tornadoes a year in Kansas, thus, total area hit per year in Kansas is 80x0.2 = 16km².

b) Thus, the probability for the tornado to hit any given area in Kansas per year is 16/54855.95 = 0.00029 or 0.029%.

Similarly, the total area for Texas is 676600mi² or 1752385.96km². The total area hit by a tornado per year is 0.2x140 = 28km².

Thus, the probability for a tornado hitting an given area in Texas per year is 28/1752385.96 = 0.000016 or 0.0016%.

a) Thus, even though Texas has a higher average number of tornadoes hitting per ear, the probability is lower due to the larger area. Kansas would serve as a better example since even though it is on the higher end of the spectrum, the chances are less than half a percent.

c) The return time or recurrence interval is simply the reciprocal of annual probability. Thus, the recurrence interval for Kansas is 1/0.00029 = 3448.27 years.