Hurricane forecasting

March 15, 2006 6:40 PM

National Hurricane Center and the Likelihood of Hurricanes. In December 2003 the NHC predicted a 68% chance of a major (Category 3-4-5) hurricane hitting the US, in fact there were three major hits on the US (Charlie, Ivan, and Jeanne). In December 2004 the NHC predicted a 69% chance of a major hurricane, in fact there were four major hists (Dennis, Katrina, Rita, and Wilma). The odds of that happening are about 0.9% (see link for math), or "statistically very significant evidence" the NHC predictions are understated. Forecast for 2006: 81% chance of a major hurricane.
posted by stbalbach (34 comments total)

I didn't want to editorialize on why the NHC forecasts are understated, but perhaps their models are not taking into account some fundamental change in the climate that has thus far never been seen before. The margin of error is incredibly large (statistically very significant) two years in a row.
posted by stbalbach at 6:43 PM on March 15, 2006

I can't help but think that the "once bitten twice shy" rule might be one of the reasons why they're boosting it up to 81% this year. No real risk of crying wolf since everyone's awareness is pretty high, and covers their ass nicely. The environment factor (the fact that they had a record number of hurricanes last year and how this fits into the global warming model) is likely another reason why.
posted by furtive at 6:49 PM on March 15, 2006

"If we make one additional assumption - that the probability of any subsequent major landfalling storms is independent of the first and each other, then we can compute the probability of the observed outcomes given the forecast."
posted by prak at 6:50 PM on March 15, 2006

... and a 30% chance of rain this Saturday.
Weathermen! What do they know!
posted by mischief at 6:58 PM on March 15, 2006

aftermath.
posted by longsleeves at 7:05 PM on March 15, 2006

It's as if there were some unknown meterological force...making the...globe....get....warmer...
posted by stenseng at 7:06 PM on March 15, 2006

Let me just say the math used in first link is very, very dubious to me at first glance. If the probability of a given event is p then the probability for n independent events is p^n is it not? For instance the probability of rolling three 3's in a row is (1/6)^n, but if you just came up to me and wanted to know the odds that the next throw would be three the correct answer would be (1/6) becuase it is independent. I would say the odds of four major hurricanes hitting the US in 2005 should be (0.69)^4 ~ 24%. What are they doing that I am not seeing?
posted by ozomatli at 7:11 PM on March 15, 2006

some unknown meterological force

Duh, it was the meteorite.
posted by dhruva at 7:12 PM on March 15, 2006

doesn't it also have to do with el nino/la nina? i remember hearing somewhere that one of them causes more active hurricane seasons, and then when you factor in the warming and currents and ocean temps....

and aren't we all thrilled with such competent leadership in charge ready, willing, and able to help Americans, given these forecasts--not. /disgusted
posted by amberglow at 7:15 PM on March 15, 2006

The math is indeed wonky.

Let p be the probability that one event will occur, and P be the probability that at least one will occur (assuming independence).

The site is correct when it claims that the probability of two events occurring is p², three events p³ and so on (as ozomatli says). Where they go wrong is in claiming that the aggregate probability P is the sum of all of these.

You can easily see that this is bogus, because for any p over 0.5, the series p + p² + p³ + ... does not converge to a result less than 1, which it would have to do to be a valid probability.

The right way to calculate the probability of one or more events, given the probability of exactly one, is to compound the probabilities that the events will not occur, then subtract the result from 1 (certainty). So we get

(1 - P) = (1 - p) * (1 - p²) * (1 - p³) * ...

This is the basis for the birthday paradox.
posted by flabdablet at 7:25 PM on March 15, 2006

You can easily see that this is bogus, because for any p over 0.5, the series p + p2 + p3 + ... does not converge to a result less than 1, which it would have to do to be a valid probability.

Actually, for any p the series p + p^1 + p^2 + ... is greater than one.
posted by ozomatli at 7:36 PM on March 15, 2006

what if p = 0.00001?
posted by delmoi at 7:38 PM on March 15, 2006

Anyway yes, global warming.
posted by delmoi at 7:38 PM on March 15, 2006

"It's as if there were some unknown meterological force...making the...globe....get....warmer..."

You win the thread, stenseng.
posted by poorlydrawnplato at 7:38 PM on March 15, 2006

The math does not look wonky to me. But I'm tired and these things are more subtle that most people give them credit for.

ozomatli, you're misunderstanding the basis. P = .69 is the chance of the US getting hit by one hurricane, bot NOT exactly one hurricane. Your reasoning only works if it were the probability of exactly one: it also rolls into the number the probability of getting 2, 3, 4, etc...

At least, that's their claim, but I'm not in the mood to really work it out, so I don't really know if they are making sense, but I strongly suspect they are.
posted by teece at 7:46 PM on March 15, 2006

What are they doing that I am not seeing?

It's stochastic analysis, not straight probability. Not that I remember the mathematics of it anymore, but in an ever-changing system, which a meteorological one is, the probability of an event is more difficult to determine than straight probability. It's a matrix of the interreaction of multiple probability equations as well as unknown variables. The computational power needed to run the regressions they used is fairly significant I would say.
posted by mrmojoflying at 7:51 PM on March 15, 2006

ozomatli: p + p² + p³ + ... is <= 1 for p <= 0.5; in fact it's exactly 1 when p = 0.5. Or did you actually mean to slip that p¹ term in there?

You're probably thinking of 1 + 1/2 + 1/3 + 1/4 + ... which is, indeed, nonconvergent.

teece: trust me, it's wonky.
posted by flabdablet at 8:00 PM on March 15, 2006

what if p = 0.00001?
posted by delmoi at 9:38 PM CST on March 15 [!]

SUM[n=1,inf] p^n = 1/(1-n),

so if 1/(1-n) < 1 then 1> n-1 --> n < 0, but we are not using negative probabilities so we have a contradiction. em>ozomatli, you're misunderstanding the basis. P = .69 is the chance of the US getting hit by one hurricane, bot NOT exactly one hurricane. Your reasoning only works if it were the probability of exactly one: it also rolls into the number the probability of getting 2, 3, 4, etc...

Here's the sticky point for me:

"If we make one additional assumption - that the probability of any subsequent major landfalling storms is independent of the first and each other, then we can compute the probability of the observed outcomes given the forecast."

So what exactly is the 69% then? The probability of being hit by at least one hurricane? If so how is that diffent from saying the probability of rolling at least one 3 is (1/6)? If the the next roll is independent then the probability of rolling at least two 3's in a row is (1/6)^2. I am not 100% sure that I am not missing something obvious.
posted by ozomatli at 8:06 PM on March 15, 2006

ozomatli: p + p2 + p3 + ... is < 1 for p =0.5; in fact it's exactly 1 when p=0.5. or did you actually mean to slip that p1 term in there?/em>

Goddamn it I do it every time:

Sum[n=0,inf] = 1/(1-n), but
Sum[n=1,inf] = n/(1-n)

I am officially retarded, don't listen to a word I say anymore.

*hangs head in shame*
posted by ozomatli at 8:19 PM on March 15, 2006

posted by ozomatli at 8:19 PM on March 15, 2006

teece: trust me, it's wonky.

Rereading your post, and looking at their math, I see what you are saying now. They've fouled up. But my mind is not working very well this evening: I need more drugs or something. Or sleep.
posted by teece at 8:30 PM on March 15, 2006

Duh, it was the meteorite.

I thought you were talking about this, at first. Man, I watch too much SciFi Channel.
posted by brundlefly at 8:32 PM on March 15, 2006

So the hurricane strike prediction numbers are indeed "wonky".

Here are some numbers that may be more concrete.

Notice the population projections for the peninsular state. The one that is experiencing a massive real estate price boom, and record housing starts. The one I live in.

The only state that really is just "asking for it".

Population growth in the coastal southeastern United States will mean more catastrophic loss should Atlantic storms become more numerous in frequency and of greater strength.

Most indicators lead to just such an assesment.
posted by PROD_TPSL at 8:47 PM on March 15, 2006

Some of you are probably wondering exactly where (mathematically) the article made it's mistake. Probability and Statistics was never my strongest subject, but IIRC it's because he forgot about inclusion-exclusion principle.

For example, let's suppose we have the following events:

A: probability of exactly one MLH.
B: probability of exactly two MLH.
C: probability of exactly three MLH.
... so on and so forth.

The number that he is given (he calls it P but I want to call it π) is:

π = P(A or B or C ...) = 68%

where P() is the probability function (so he's looking for p = P(A)). He says that:

π = P(A) + P(B) + P(C) + ...

But that ignores inclusion-exclusion principle. He is over counting! The correct way to expand this probability is:

π = P(A) + P(B) + P(C) + ...
- P(A and B) - P(B and C) - P(A and C) - ...
+ P(A and B and C) + ...
...

So on and so forth. You can't calculate this (easily?), so mathematicians do what flabdablet suggests.
posted by sbutler at 9:09 PM on March 15, 2006

flabdablet: Let p be the probability that one event will occur, and P be the probability that at least one will occur (assuming independence).

...If we make one additional assumption - that the probability of any subsequent major landfalling storms is independent of the first and each other, then we can compute the probability of the observed outcomes given the forecast.

Sorry, I can't grok the math. Help me understand your point.

What do you mean, assuming independence? Hurricanes are not independent, equally likely events. All the hurricanes in a season are influenced by the same set of underlying conditions, i.e. global warming.

Right?
posted by ottereroticist at 12:05 AM on March 16, 2006

Math is hard
posted by PenDevil at 1:21 AM on March 16, 2006

Corrected link to birthday paradox.
posted by Civil_Disobedient at 4:40 AM on March 16, 2006

I'm just glad I am no loner near the coast. Any coast.
posted by Astro Zombie at 7:14 AM on March 16, 2006

Longer. I am a loner.
posted by Astro Zombie at 7:15 AM on March 16, 2006

This thread makes my head hurt. Where's Supes when you need him?
posted by NationalKato at 7:23 AM on March 16, 2006

ottereroticist: Global warming (or the fact that hurricane strength is cyclic) is an initial condition or parameter. It doesn't go towards the correlation between MLH events.

To put this another way, think about an answer to this question: "Is there any significance to the fact that hurricane X is the 2nd hurricane of the season? The 3rd? The 20th?" Each hurricane occurs independently of each other. At least, that's the assumption.

What would be a counter example? Suppose the first MLH causes damage to the coast that makes it easier for the second hurricane to become a MLH. And then suppose that second hurricane causes more damage, which makes it easier for the third MLH. Then you could not say that each hurricane is an independent event: clearly the preceding ones changed the conditions to make it easier for the subsequent ones.

None of this matters though because of what I said above. Expansion based on inclusion-exclusion principle doesn't care whether the events are independent, and that's what he screwed up.
posted by sbutler at 7:45 AM on March 16, 2006

What do you mean, assuming independence?

If you don't assume independence, you can't do the problem in any simple way. You'd have to figure out how the occurrence of one hurricane effects the chances for other hurricanes, and that would be something that only a meteorologist could make an informed guess about, and even then it'd be very wish-washy, I suspect.

It's likely that hurricanes are not independent, but that their interdependence is not all that likely to be big enough to seriously destroy this math. That is, hurricane A doesn't make it 20 times more likely or a hundred times less likely to get hurricane B. The effects, whatever they are, are hopefully fairly small.

But without that assumption, all you can do is shrug and say "who knows."
posted by teece at 8:07 AM on March 16, 2006

Hurricanes are very dependent. Because they depend on the heat energy contained in warm oceans and because a major hurricane sucks up that energy and turns it into overturned and flooded Volvos.
posted by Mitheral at 11:51 AM on March 16, 2006

They're dependent. From the little I've read, their not terribly dependent, though. Especially not for the first couple or few MLHs. The season is long enough that that dependence intra-season is probably not huge. Back-to-back Cat. 5s in the same spot would have a major dependence problem -- general MLHs across the entire coast line and season, probably not quite so much.

It's certainly there, but this non-meteoroligist bets it makes only a minor difference in the kind of back-of-the-envelope calculation The Oil Drum was trying to perform.
posted by teece at 4:39 PM on March 16, 2006