# Tag Archives: lightning

## the conditional probability of being struck by lightning (Part 4)

The National Weather Service released a report on being struck by lightning [Story here] that may be of interest to those of you read my previous posts on lightning (see below). The study confirms that men account for 82% of those struck by lightning, which I’ve blogged about before. More people are struck by lightning in July than in any other month.

Lightning fatalities by month

NOAA states that June, July and August have the most lightning in addition to having the most lightning fatalities, In fact, I was caught in a severe storm that rolled in quickly when I was running in a forest preserve in June. I suspect that the conditional probability of being struck by lightning doesn’t depend on seasonality as much as the picture above suggests, but I don’t have any proof.

The Washington Post Magazine ran a nice story about the ‘Spark Ranger’ Roy Sullivan who was struck by lightning seven times [Link]. A man who worked outside, Roy Sullivan was at an increased risk of getting struck by lightning. I’m not sure how that happened seven times.

## what is the conditional probability of being struck by lightning? Part 3

This is my third post on the conditional probability of being struck by lightning in response so an NPR article (HT to Tim Hopper). The National Weather Service tweeted:

More than 80% of lightning victims are male. Be a force of nature by knowing your risk, taking action and being an example #ImAForce

This suggests that the conditional probability of being struck by lightning depends on your gender. You might think that the conditional probability of being struck by lightning for a man is four times higher than four a woman. Not so fast.

In the NPR article, Susan Buchanan, a spokeswoman from the National Oceanic and Atmospheric Administration offered four explanations for why. They are quoted below with some minor changes from me. The first two explanations would affect the prior probability of being exposed to a thunderstorm:

1.  Men are more likely to be outside.

2.  More are more likely to have jobs that require them to work outside.

The second two would affect the conditional probability of being struck by lightning given one’s gender and that he/she is in a thunderstorm.

3. Men take more risks than women. “If you look at the percentage of men who take part in high risk sports that might give you an idea,” said Buchanan. Therefore, a man would be less likely to go inside during a thunderstorm.

4.  Men don’t want to be seen as “wimps.” This theory, she said, was backed up by talking to the Boy Scouts who said no one wants to be the one to say it’s time to go inside.

Putting this together:

1 < [Conditional probability of being struck by lightning given that one is a man and is in a thunderstorm] / [Conditional probability of being struck by lightning given that one is a women and is in a thunderstorm] < 4.

## what is the conditional probability of being struck by lightning? Part 2

My brother-in-law is a meteorologist and was happy to chat with me about the conditional probability of being struck by lightning (see my previous post here):

However, I can say right off the bat that there isn’t going to be one right answer.  There is substantial variation in both the microphysics and dynamics of moist convective systems.  As a result, there is wide variation in the lightning frequency from different storms.  Take, for example, so-called MCS’s (Mesoscale Convective Systems) that originate on the Front Range of the Rockies and propagate eastward in the nighttime hours, eventually affecting places like MSP, MSN, or ORD in the morning hours.  These are profligate lightning generators, often producing essentially continuous lightning.  Meanwhile, a completely different animal from MCS’s are baroclinic frontal convective systems.  Often these will pass through with only occasional lightning (occasional lightning is officially defined by the weather service as no more than once every 2 minutes).  Then, perhaps most interesting of all, there are some storms that generate copious cloud-to-cloud or cloud-to-air lightning but very little cloud-to-ground lightning.  The specific reasons for the wide variation in lightning frequency and type are still the subject of research (we have generally poor observations of microphysical processes, especially those processes in violent convective storms).

So, the type of storm will affect your conditional probability of being struck by lightning.

My brother-in-law also helped me to compute the probability of being struck by lightning conditioned on whether there is a storm.

P(L|S) = P(S|L) P(L) / P(S)
where
L = event of getting struck by lightning
S = event that there is a storm
We need to estimate values for P(S|L), P(L), and P(S).
P(S|L) is easy; It’s 1 (you can’t have lightning without a storm).
Estimates for P(L) and P(S) can be obtained from the public sphere.
A little searching reveals that ~ 400 people per year are struck by lightning.  If we assume the strike incidents are independent and uniformly distributed across the 365 days of the year, then the number of people struck on any given day is roughly 400/365. An estimate for P(L) for any given day is then the number of people struck on any given day divided by the total US population.  Using 310 million as the US population we get P(L) for any given day is (400/365) / (310×10^6) = ~ 3.5 x 10^(-9).

An estimate of P(S) can be obtained from the so-called “thunderstorm-day” statistic, which is the number of days in some prescribed time interval in which thunder is heard at a given location (and hence a storm must have been within striking distance of that location).  A little searching reveals that the thunderstorm-days per year of Washington D.C. is 32.8, based upon the last 30 years of data.  If we assume the stormy days are independent and uniformly distributed across the 365 days of the year, then P(S) for any given day is 32.8 / 365 = ~.09.  However, this is not a reasonable assumption: the estimate of P(S) for Washington, D.C., for a given day in July is ~.25

Given the above:

P(L|S) = 1 * 3.5×10^(-9) / .09 = 3.9×10^(-8)

I tried to extend this analysis to compute the conditional probability of interest:

P(L | O, S)

where O = event that you are outside. When applying Bayes Rule and rearranging the probabilities, I eventually get to expressions that depend on P(L), such as this one:

P(L | O, S) = P(S | L, O) P(O | L) P(L) / (P(A | S) P(S) ) = P(L) / (P(A | S) P(S) )

(assuming that P(S | L, O) = P(O | L) = 1 for our purposes). However, this is problematic, since estimates for P(L) (like the one that my brother-in-law reports above) implicitly capture the likelihood that people are outside, P(L | O, S). This is circular reasoning.