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.
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 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, , 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 , 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 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 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 (which they discuss at length) is 0.68, which is pretty impressive. Unfortunately, the significance is p = 0.08, not statistically significant …