Comments & Replies

Our paper entitled: "The increasing intensity of the strongest tropical cyclones" published last September in Nature (henceforth EKJ08) garnered considerable attention in the scientific community. Here are replies to some of the comments we received about this work.

Comment: "If the total number of storms has not changed, and the number of strong storms has increased from 13 to 17, then surely the number of weak storms must have decreased proportionately."
Reply: We used statistics rather than arithmetic. The rate of strong tropical cyclones is much smaller than the rate of weak tropical cyclones. As the ocean warms the stronger tropical cyclones can "borrow" a few cyclones from below the threshold intensity that will significantly increase the rate of the stronger tropical cyclones while not significantly reducing the rate of weaker cyclones.

Comment: "Intuitively the number of tropical cyclones exceeding the mean rate plus 2 times the standard deviation as was shown in previous studies (e.g., Kossin et al. 2007) should be equivalent to number of tropical cyclones exceeding some upper quantile level as shown in EKJ08."
Reply: The number of cyclones exceeding plus 2 times the standard deviation is positively correlated to the rate of cyclones. A basin with a lower rate of tropical cyclones will have fewer cyclones exceeding plus 2 times the standard deviation compared with a basin with a higher rate, while the number of cyclones exceeding the 90th percentile is independent of the rate. Thus it is not appropriate to compare the differences between Kossin et al. (2007) and EKJ08 using this approach.

Comment: "I've regressed the most intense TC per season on year and my results do not match those presented in EKJ08."
Reply: A regression of the most intense TC per season is not the same as quantile regression on year as was done in EKJ08 for the following reasons. a) Quantile regression minimizes a linear absolute deviation statistic rather than a quadratic statistic, and b) quantile regression treats each intensity value equally; no wind speed contributes more to the model fit.

Comment: "Your results are only marginally significant and there are many factors contributing to hurricane intensification."
Reply: That is correct, but all else being equal, a warming of the tropical oceans where tropical cyclones form should increase their intensity. Since the strongest tropical cyclones are, on average, closest to there theoretical maximum potential intensity it stands to reason that if there is a warming signal it should be most apparent in the tendency of the strongest cyclones. Moreover, statistical inference is concerned with drawing conclusions based on data together with prior assumptions. Arguments that include the basic physics of the role ocean heat plays in tropical cyclone intensity have more weight before the data are examined.

Comment: "The authors claim that the increasing trend is consistent with theory, yet numerical modeling studies suggest a different sensitivity of tropical cyclone intensity to warming."
Reply: Numerical models are not theory. They are based on theory, but require many ad hoc empirical arguments that put them into the realm of "scenario generators." The theory we have in mind is the 2nd law of thermodynamics.

Comment: "I'm surprised that the relationship between intensity and sea-surface temperature is not stronger."
Reply: The physics of cyclone intensification works against the correlative relationship. An active year of tropical cyclones will effectively remove warmth from the ocean so that a seasonal average temperature will not correlate as strongly with tropical cyclone activity as one might expect even though the physical causality is strong.

Comment: "Yet when you look at scatter plots of these SST series versus number of intense TC’s there is no relationship in the warmer SST, more intense TC’s direction."
Reply: We did not look at the number of TCs; we looked at the intensity. There is no theory for TC formation. However, given a TC, there is a nice theory for the efficiency of intensification. So, we focused on intensity rather than on frequency. Given a TC in a nearly optimal dynamic environment, we should expect to see it reach a higher intensity with warmer SST. If on average 10% of the storms get within 5% of their MPI and the MPI increases then we would see the strongest storms getting stronger, assuming all else stays the same.

Comment: "Here's a hypothetical, what if the predictor had been another quantity that also shows a significant trend over the period 1981-2006, I don't know...my weight, perhaps...would one be discussing what the physical meaning of a non-significant correlation between the two was?"
Reply: This example has little to do with the relationship of TCs to warming seas since in the latter there is a theory linking the two, whereas with your weight and TCs there is none. In science this makes a big difference.

Erratum

In our paper "The increasing intensity of the strongest tropical cyclones" Nature, v455, 92-95, Figure 2b is incorrect. The correct figure is given here. The quantile values are labeled correctly on the original figure and the corresponding trend values in Table 1 are correct.

Quantile regression and extreme hurricane winds

Coastal tropical cyclones (TCs) pose a serious threat to society and the economy. Strong winds, heavy rainfall, and storm surge kill people and destroy property. The destructive power of the most intense TCs can rival that of earthquakes. The rarity of intense TCs implies that empirical estimates of their return periods will be unreliable. Fortunately extreme value theory provides parametric models for rare events and a justification for extrapolating to intensity levels that are greater than what has been observed. We developed an extreme value model for US hurricane intensity based on the method of peaks over thresholds using data over the period 1899-2006 (Jagger and Elsner 2006) and showed how the models can be used to assess the probability of extremely intense hurricanes controlling for climate factors.

Quantile regression offers another way to model extreme TC events that has yet to be examined. Quantile regression, introduced by Koenker and Bassett (1978), extends the ordinary least squares regression model to conditional quantiles (e.g., 90th percentile) of the response variable. It can be considered a semi-parametric technique because it relies on non-parametric quantiles, but uses parameters to assess the relationship between the quantile and the covariates.

Ordinarily we think of parametric models as more informative, with nonparametric models useful for an initial look at the data. A parametric model involves more stringent assumptions, but it is usually a good idea to start with stronger assumptions and back off toward weaker assumptions when necessary. However, parametric models are generally more sensitive to outlying data points, which can be problematic for extreme value models. Also, with parametric models care must be given to the form of the distribution. A drawback of parametric models is that the parameters can be more difficult to interpret physically. It is this difficulty in interpreting the parameters of the extreme value models with respect to issues of climate's influence on TC activity that prompted the present work. It is our contention that extreme value models are valuable for quantifying the probability of high winds from TCs conditional on climate covariates, but that quantile regression can be quite useful as an exploratory tool.