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1784572429[/url]']
Claude had a field day with the hyperbole (my word) and projections from the article, especially as ocean temps in the Pacific have only been reliably monitored for 50 to 75 years. Tough to project a 1 in 4000 year event with such little base data.

If one of the assumptions is that it double or quadruples the chance of a catastrophic CA flood holds, the state is well overdue for one.  

Without getting political, I don't think the state is prepared for one. A while back, I had an interesting conversation with one of the lead experts at Contra Costa Flood Control. Basically when it hits, we are in deep trouble, as much of the county was under water then, and it wasn't as bad as what happened to the Central Valley and the LA Basin. . ..

Actually, it is not tough at all.  If you measure the temperature every year for 50 years, you will get a sample mean and standard deviation.  If you then get a single measurement, you can calculate quite easily how many standard deviations you are from the mean (that’s the z-score).   A measurement 3.5 standard deviations above the mean corresponds to the 99.977th percentile, so you would expect only 0.023% of measurements to be as extreme or more extreme.  That is roughly 1 in 4,300 which is where you get the estimate.

Now, that doesn’t mean there aren’t some potential problems:
1) The most obvious is the assumption that temperature distributions are Normally distributed.  Reasonable assumption, but there might also reasonably be fat tails.  A 50 year history probably doesn’t let you test for deviations from Normality.

2) The estimates of the mean and standard deviation are that, estimates.  At a sample size of 50, the standard deviation estimate is generally (95% of the time) within about 20% of the true standard deviation.  That means that the estimated z-score could be too high if the estimated standard deviation was too low (you happened to be in a period of less variability than the underlying average).  If it turned out that we underestimated the variability by 20%, then it turns out that the “real” z-score (but bear in mind, unknowable, as we can’t measure the underlying distribution) could be inflated by 1/0.8, and would be about 2.8 if recalculated, which translates to a percentile of 99.75% or an approximate frequency of 1 in 400.

3) The mean is also an estimate (though estimating the mean tends to be more accurate than estimating the standard deviation), but 95% of the sample means are within 0.278 standard deviations of the true mean.

4) We are assuming that we are sampling from a single population of temperature measurements, but none of this is true if the mean temperature or variability in temperature is changing over time.

I think it is very reasonable to take the estimate of a 1 in 4000 El Niño with a grain of salt, but also it is not worth quibbling with whether this is a 1 in 4000 event, a 1 in 400 event, or a 1 in 40,000 event.  It is a massive anomaly compared to the historical record; a magnitude this large has not been seen before, so the effects are very unpredictable.

BC

[BostonCard]

1784572429[/url]']
Claude had a field day with the hyperbole (my word) and projections from the article, especially as ocean temps in the Pacific have only been reliably monitored for 50 to 75 years. Tough to project a 1 in 4000 year event with such little base data.

If one of the assumptions is that it double or quadruples the chance of a catastrophic CA flood holds, the state is well overdue for one.  

Without getting political, I don't think the state is prepared for one. A while back, I had an interesting conversation with one of the lead experts at Contra Costa Flood Control. Basically when it hits, we are in deep trouble, as much of the county was under water then, and it wasn't as bad as what happened to the Central Valley and the LA Basin. . ..

Actually, it is not tough at all.  If you measure the temperature every year for 50 years, you will get a sample mean and standard deviation.  If you then get a single measurement, you can calculate quite easily how many standard deviations you are from the mean (that’s the z-score).   A measurement 3.5 standard deviations above the mean corresponds to the 99.977th percentile, so you would expect only 0.023% of measurements to be as extreme or more extreme.  That is roughly 1 in 4,300 which is where you get the estimate.

Now, that doesn’t mean there aren’t some potential problems:
1) The most obvious is the assumption that temperature distributions are Normally distributed.  Reasonable assumption, but there might also reasonably be fat tails.  A 50 year history probably doesn’t let you test for deviations from Normality.

2) The estimates of the mean and standard deviation are that, estimates.  At a sample size of 50, the standard deviation estimate is generally (95% of the time) within about 20% of the true standard deviation.  That means that the estimated z-score could be too high if the estimated standard deviation was too low (you happened to be in a period of less variability than the underlying average).  If it turned out that we underestimated the variability by 20%, then it turns out that the “real” z-score (but bear in mind, unknowable, as we can’t measure the underlying distribution) could be inflated by 1/0.8, and would be about 2.8 if recalculated, which translates to a percentile of 99.75% or an approximate frequency of 1 in 400.

3) The mean is also an estimate (though estimating the mean tends to be more accurate than estimating the standard deviation), but 95% of the sample means are within 0.278 standard deviations of the true mean.

4) We are assuming that we are sampling from a single population of temperature measurements, but none of this is true if the mean temperature or variability in temperature is changing over time.

I think it is very reasonable to take the estimate of a 1 in 4000 El Niño with a grain of salt, but also it is not worth quibbling with whether this is a 1 in 4000 event, a 1 in 400 event, or a 1 in 40,000 event.  It is a massive anomaly compared to the historical record; a magnitude this large has not been seen before, so the effects are very unpredictable.

BC