SSTHurricane Number Relationship

Having predicted SST using one of the four methods described above, the second part of the development of our SST-based hurricane number predictions is to model the relationship between SST and hurricane numbers. To do this, we consider only data from 1950 to the present, because of the data quality issues discussed in section 2. Using the framework of the Poisson Generalized Linear Model, SST was found to be a significant predictor for the number of hurricanes in the Atlantic basin. The relationship between SST and landfalling hurricane numbers, however, is only marginally significant. Why is there apparently such a large difference between the behaviour of basin and landfalling numbers? Is it that SST really doesn't affect landfalling hurricane numbers, or is the disappearance of the relationship at landfall just a statistical effect, similar to the disappearance of change-points when going from basin to landfall that was discussed in section 4? We considered this question in detail in Laepple et al., 2007, in which we showed that we would expect the correlation between SST and landfalling numbers to disappear, purely on statistical grounds. The argument is indeed very similar to the argument for why change-points disappear in the landfalling series: the signal-to-noise ratio decreases by a factor of two, which is just enough to hide the signal we might want to detect.

Based on this result, we believe that it is very possible that there is a dependency between the SST time-series and landfalling hurricane numbers, and that it makes sense to develop prediction models based on this assumption. We then have the possibility of using a direct prediction method (relate observed landfalling hurri cane numbers directly to SSTs) or an indirect prediction method (relate observed basin hurricane numbers to SSTs, and then predict landfalling hurricane numbers from basin hurricane numbers). Which is likely to be better? We investigated this question in some detail in Nzerem et al., 2007, and concluded that the indirect method is possibly slightly better, but that the two methods are likely to be very close (in terms of accuracy), so it is worth considering both.

The next question to address is which link function should we use to model the effects of SSTs on hurricane numbers. In the academic literature, it is common to use a log link i.e. to consider hurricane numbers as an exponentially increasing function of SST (see for example Elsner and Schmertmann, 1993 and Solow and Moore, 2000). This is mainly because it is common statistical practice to use a log link function when doing poisson regression, rather than for any more fundamental reason to do with hurricanes and SST. Fitting an exponential curve to the SST-hurricane number relation, is, however, rather dangerous, especially if we predict future SSTs to be as high, or higher, than have ever occurred in the past. This could potentially lead to predictions of very large numbers of hurricanes. We performed a laboriously detailed analysis of the observed relationships between SST and hurricane numbers (Binter et al., 2007a, b) and concluded that it is just as reasonable to model the SST hurricane number relationship using a piecewise linear function that is a straight line fit in the region of interest. This relationship is shown in Fig. 5.

In 2006, our SSTmodel range included three types of SST predictions; flat, linear and damped, direct and indirect predictions, and linear and log links for estimating the SST-hurricane number relationship. Combinations of these prediction types give a total of 12 SST-based predictions for landfalling hurricane numbers. These predictions are given in rows 9 to 20 of the summary Tables 2 and 3.

In 2007, we omitted the models based on the log link between hurricane number and SSTs partly because we ourselves felt this had little physical justification and partly because the 2006 experts indicated that they thought there was little physical justification for it (in the 2006 elicitation, these models were not given any weight by any of the experts). The damped predictions were also eliminated in the 2007 model suite because they are weighted combinations of the flat and linear predictions. Instead of an explicit damped model, the experts determined the damping for themselves by weighting the flat and linear models directly. The flat, linear, direct and indirect SST predictions for 2008-2012 are shown in rows 6-9 of Table 4 and similar predictions using the NH temperature are found in rows 10-13.

Predictions of landfalling numbers from the IPCC model predictions of SST, using both one and two-step methods, and direct or indirect predictions, are given in rows 14-17 of summary Table 4.

Since the climate shift predictions will vary depending on the probabilities that are given by the experts during the elicitation process, we do not show the actual predictions but we instead show the lowest and highest predictions of landfalling numbers that these models produce. These numbers are shown in rows 19a, b and 20a, b in summary Table 4.

Fig. 5 Correlation between Numbers of (a) Basin Hurricanes, (b) Landfalling Hurricanes and the SSTs in the MDR region to o

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