## PDI: Elsner

Willis writes:
Well, looking at these studies is giving me a headache. My latest one is High frequency variability in hurricane power dissipation and its relationship to global temperature, James B. Elsner et al.

I went to look for some of Elsner’s work because of Steve Bloom’s comment, viz:

Good news for bender: Elsner’s a *serious* statistics wonk.

Not.

They smooth the September PDI and the September ACR SST, as they describe here:

In order to investigate the high frequency relationship between PDI and Atlantic SST we first fit
a nonlinear trend to each of the signals by applying a regression smoother (Chambers and Hastie
1991) with a span of 44 years. A smoothed value at a given year is obtained by fitting a weighted
regression to the neighboring values within a chosen time span of the year, where the weights are a
decreasing function of time from the given year. Figure 2 shows the raw and smoothed time series
of annual hurricane PDI values. The coefficient of determination $(R^2)$ between the smoothed PDI
and smoothed SST series is 84% indicating a strong relationship. Results are in agreement with
those in Emanuel (2005) showing the unprecedented upswing in hurricane destructiveness related
to rising Atlantic SST.

Well, a couple of problems with that. First is that their dataset is 59 years long (1947-2004), and their filter is 44 years wide …

Second, I haven’t a clue what they’ve done with their PDI data. They say they got it from HURDAT, but it looks nothing like my calculation of the PDI from HURDAT. It also looks nothing like Emanual’s PDI, or Landsea’s PDI. Elsner says:

We adjust the pre-1973 wind speeds to remove biases using the same procedure as described in Emanuel (2005) ,,,

but this is not the case. Here’s the difference:

The effect of this change is to make the fit with the SST much better than that of the Emanuel data.

Third, they use, not the PDI as claimed in the quote above, but the cube root of the PDI, $\sqrt[3]{PDI}$, for their calculations … kinda defeats the purpose of a PDI, since it no longer measures power dissipation, but that’s OK. However, their claim in the abstract and in the quote above about "hurricane destructiveness" is not shown by a correlation with $\sqrt[3]{PDI}$, as that does not measure "destructiveness".

Finally, they make no attempt to correct for autocorrelation, it doesn’t even get a mention. When you smooth two series and calculate their $R^2$ value, you also need to calculate the significance of that value. This is done by calculating an effective "N" for the series, and using the effective N to calculate the significance of the $R^2$ value. When you do this with a smoothed series, it rapidly loses significance as the smoothing increases.

For example, with an equivalent smoothing to the one they use, the R^2 between global temperature and $\sqrt[3]{PDI}$ (which they discuss at length) is 0.68, which is pretty impressive. Unfortunately, the significance is p = 0.08, not statistically significant …

w.

1. Paul Penrose
Posted Oct 10, 2006 at 7:30 AM | Permalink

I’m not even sure that global temperature is a meaningful metric for these kind of analyses anyway. Wouldn’t make more sense to use the regional temperature instead? In this case, say the Atlantic basin maybe? Everybody seems to be hung up on global temperature these days.

2. Judith Curry
Posted Oct 10, 2006 at 7:45 AM | Permalink

Willis thank you for this analysis. My own concerns about the paper are as follows. Elsner uses a Granger Causality test to determine whether Atlantic SSTs are driven by global changes. Elsner shows is that: there is a strong linear correlation between global air temperatures and Atlantic SSTs, and the global temperatures lead the Atlantic SSTs. He then concludes that Atlantic SSTs arise largely from global changes.
First, the fact that Atlantic SSTs do not directly effect global surface air temperature is not news; there is good previous evidence (which elsner does not ciete) that AMO does not influence global temperature. The issue of main concern is that there is no physical mechanism that i can think of that would cause the Atlantic SSTs to follow global air temperature (especially since atlantic air temperature shave been included in the global average). I concluded that the result was essentially a statistical artifact, of statistical interest but without a credible physical mechanism. Now I see that there may be some problems with the statistical analysis. This example reinforces the need for both a physical and statistical explanation of the data..

3. Tim Ball
Posted Oct 10, 2006 at 7:55 AM | Permalink

“When you do this with a smoothed series, it rapidly loses significance as the smoothing increases.” Maybe someone should consider that dictum and revisit the ice core record which is smoothed more than any other record I know.

4. Jeff Weffer
Posted Oct 10, 2006 at 6:48 PM | Permalink

One thing the data shows is that a long time series is required.

Pick 1983 to 2005, for example, and you get nothing but a straight line going up (ie. data selection). Pick 1950 to 1970 and you get a straight line going down.

I prefer the data series that goes back to 1850 so we get a better picture of what is really happening.

5. Willis Eschenbach
Posted Oct 11, 2006 at 2:31 AM | Permalink

Judith, I find that Elsner’s right about the Atlantic SST, the global SAT, and the lag. The correlation is larger (0.96) with a one month lag than a direct correlation. (0.76).

The fly in the ointment, as always, is the autocorrelation. Because of the autocorrelation, none of the lag correlations are statistically significant (for a 0 to six month lag or lead, the p values vary from 0.15 to 0.96).

Plus, as you point out, correlation is not causation …

w.

6. Ken Fritsch
Posted Oct 11, 2006 at 9:29 AM | Permalink

I am attempting to digest the review of Elsner and summarize what it means — at least to me.

1. Reviewers here indicate that the physical and statistical evidence for the correlation of SST to global SAT is lacking.

2. Review here finds Elsner’s statistical analyses for the low frequency correlation of PDI versus SST as weak as those found here previously in the Emanuel 2005 review.

3. Elsner is evidently making the case that global SAT strongly effects SST which it turn has a strong influence on PDI on a low frequency (decadal) time scale. He refers to this SAT effect on PDI as being indirect.

4. Elsner then proceeds to show/conclude that the direct effect of global SAT on NATL PDI is negative.

5. Elsner’s reasoning for separating the global SAT into indirect and direct effects on PDI appears to me to be related to his attempt, in the end, to “lend support to the offset hypothesis (Shen et al. 2000) that increased hurricane intensity due to higher SST is partially compensated by decreased intensity to greater atmospheric stability resulting from tropospheric temperatures that are warm relative to SST.”

Given that hypothesis and the fact that I thought it goes against current observations, but not climate computer model predictions, I ask is Elsner (and Shen 2000 ??) shying away from looking directly at SST and ocean tropospheric data for evidence because of the model/observation discrepancies and/or because of a lack of data over a sufficiently long time period for it to be used to show statistical significance?