The effects of climate change on temperature and sea-level are mostly well understood and readily quantified, albeit with uncertainty. The effects of climate change on other variables, however, are generally less well understood. In this article, we consider aspects of the possible effects of climate change on the frequency and intensity of tropical cyclones, with a particular focus on quantities that are directly of relevance to tropical cyclone risk and risk modelling. There are essentially three methodologies that one can use to investigate the question of how the frequency and intensity of tropical cyclones might change. One is theory. There is no complete theory of tropical cyclones that can give good explanations for all the aspects of tropical cyclone behavior that are seen in nature. However, for the intensity of tropical cyclones, there is a body of theory [1] that can be used to attempt to predict how tropical cyclones might change in the future: the implications of this theory are that the intensities of individual tropical cyclones may have already increased, and may continue to increase, all other things being equal [2]. The second methodology that one can use to understand the possible effects of climate change on tropical cyclones is dynamical modelling of the climate using climate models. In a recent survey of climate model results for tropical cyclones [3], different models were found to give somewhat different results, highlighting the uncertainty, but many models showed decreasing overall frequency of tropical cyclones, the highest resolution models suggested an increase in the frequency of very intense tropical cyclones (strength categories 4 and 5), and most models showed an increase in the proportion of tropical cyclones that reach very intense. The third methodology that one can use to understand how tropical cyclones may change under a changing climate is to look at the past, and use statistical analysis to assess whether it is already possible to see any changes in tropical cyclone behavior that could be due to climate change. This is difficult for three particular reasons: tropical cyclones, especially the most intense tropical cyclones, are rare; past measurements of tropical cyclone behavior are inhomogeneous in coverage and quality [4]; and tropical cyclone behavior is affected by climate variability on multiple time-scales, much of which is not fully understood, and which hinders the detection of long-term trends [5]. As a result, there is no clear consensus, at this point, as to whether the impacts of climate change can be said to have been clearly detected in the historical record for tropical cyclones, although some claims have been made with respect to the increasing intensity of the strongest storms [6,7].

In a recent paper, Kossin et al. [8] described an analysis based on the latest version of the ADT-HURSAT dataset [9,10] (where ADT stands for Advanced Dvorak Technique and HURSAT stands for HURricane SATellite), in which they showed that there is a statistically significant (outside a 2.5%–97.5% confidence interval—henceforth “significant”) increase in the ratio of the number of category 3, 4 and 5 (cat35) fixes to the number of category 1, 2, 3, 4 and 5 (cat15) fixes in that dataset, over the period 1979 to 2017. Kossin et al. [8] used ADT-HURSAT, which is an objectively processed satellite dataset of global tropical cyclone observations, as it provides a more homogeneous time-series of tropical cyclone observations than the International Best Track Archive [11], even though the latter dataset may be more accurate in some ways. The fixes that they considered are 6 hourly measurements, and there are typically multiple fixes for each tropical storm. In general, cat35 fixes are defined as those that record windspeeds of 96+ knots, and cat15 fixes are those that record windspeeds of 64+ knots. Since in the ADT-HURSAT data intensity is discretized into 5 knot bins, this corresponds to windspeeds of 100+ knots and 65+ knots, respectively, in this dataset.

Kossin et al. [8] used a number of different statistical methods for investigating possible changes in the ratio of cat35 (henceforth major hurricane (MH)) to cat15 fixes (henceforth just “the MH ratio”), including consideration of the differences in the ratio between block averages of early and later periods of the data, and a linear trend analysis of the MH ratio combined into three-year sub-periods. These two methods both show significant signals corresponding to an increase in the MH ratio. They noted that this increase is consistent with theoretical and dynamical modelling results, which suggests an increase in the proportion of major tropical cyclones due to climate change [3].

However, from the point of view of tropical cyclone risk and risk modelling, the implications of this increase are hard to understand. The ratio of cat35 to cat15 fixes is not something that is explicitly included in most tropical cyclone risk models. In this article, our goal is therefore to analyze the increase identified in Kossin et al. [8] and understand what changes within the dataset are driving it, in terms of quantities that are more closely aligned with risk modelling. In particular, we will attempt to answer the following questions:

These are arithmetical questions about the increase in the MH ratio, rather than being questions about the physical drivers or mechanisms behind the increase. Answers to these questions can help risk modelers decide how they could adjust risk models to reflect the increasing MH ratio, should they wish to.

In Section 2 below, we provide a brief review of the linear trend analysis that Kossin et al. [8] used to identify the increase. In Section 3, we provide a heuristic analysis to understand what might be driving the linear trend. In Section 4, we provide a quantitative analysis using decomposition of the trend slope to identify the statistical drivers behind the linear trend. In Section 5, we summarize and draw some conclusions.

In this section, we briefly review the increase in the ADT-HURSAT MH ratio that was identified in Kossin et al. [8]. The ADT-HURSAT data we use for our analysis are available on the internet as part of the supplementary information provided by Kossin et al. [8]. Figure 1a shows the annual numbers of category 1 and 2 (cat12), cat35, and cat15 fixes in the ADT-HURSAT dataset, for the period 1979 to 2017. In this and all the subsequent analysis, we omitted 1980 for reasons of incomplete data, following Kossin et al. [8]. In all the time series plots, linear interpolation was used between 1979 and 1981, although the calculation of trend-lines and significance levels all treat 1980 as a missing value. We see from Figure 1a that the three time series are correlated. That cat15 is correlated with both cat12 and cat35 is not surprising since the cat15 numbers are simply the sum of the cat12 and cat35 numbers. That cat12 and cat35 are correlated is also not surprising, since each storm that reaches cat35 must pass through cat12. We also see that the vertical distance between the cat12 and cat35 time series tends to decrease over time and is lower in the second half of the series than the first.

Figure 1b shows the MH ratio. When the MH ratio is created, much of the variability cancels out between the two datasets because of the correlation between the series. Kossin et al. [8] also argued that this cancellation includes some cancellation of observational errors. An example would be that if a cat35 storm is missed (e.g., due to satellite failure), it will be missed from both the cat35 and cat12 records and hence will have a minimal impact on the MH ratio. This cancellation of errors is one of the reasons why Kossin et al. [8] chose to focus on the ratio of cat35 to cat15 fixes, rather than the numbers of fixes themselves.

However, from the point of view of trying to inform tropical storm risk quantification, it is necessary to consider the data for the actual counts of fixes, not just the MH ratio, and that is what we will do below. Using counts means that our analysis is exposed to a greater extent to the impacts of observational errors and variability in the data, because we lose the advantage of the cancellation of errors mentioned above. This should be taken into account in the interpretation of the results below: the count data should not be used for quantifying subtle signals. However, the main drivers we identify in our analysis below will turn out to be large signals that are hopefully reasonably robust.

If we write $c_{12}$ as the number of cat12 fixes, $c_{35}$ as the number of cat35 fixes, and $c_{15}$ as the number of cat15 fixes then $c_{15}=$ $c_{12}+$ $c_{35}$ and the MH ratio $r$ is given by

That the cat12 and cat35 time series get closer together over time in Figure 1a implies that $c_{12}/c_{35}$ is reducing, which in turn implies that $r$ is increasing, which is what we see in Figure 1b.

One of the methods used by Kossin et al. [8] was to group the annual values of the MH ratio into triads (groups of three years), and consider statistical significance of a trend in the triad values, where the trend was fitted using Theil–Sen regression. As an alternative, and somewhat more simply, we fit a linear trend directly to the annual values shown in Figure 1b using ordinary least squares (OLS), with 1980 omitted. Using OLS facilitates the decomposition analysis we describe in Section 4 below. The OLS trend is also shown in Figure 1b. Above and below the OLS trend-line, we show two other lines which have the same mean as the OLS trend-line, but slopes which give the 95% confidence intervals around the trend slope. The OLS trend is positive and significant, with a p-value of p = 0.01.

Fitting a linear trend to these ratios is not strictly defensible, since the ratios are bounded between zero and one, while the trend line ultimately stretches from minus infinity to infinity. We tested the importance of avoiding this problem by transforming the ratios using a probit transform, to give them a possible range from minus infinity to plus infinity, before fitting the trend. This, however, made little difference to the results, since the range of the ratios is rather small, and the probit transform is close to linear over this range. For the remainder of our analysis, we proceed with the untransformed values for simplicity.

Based on Kossin et al.’s [8] analysis, and the linear trend analysis given above, there seems little doubt that the increase in the MH ratio is robust (i.e., is not an artefact of interannual variability in the dataset). However, from the point of view of fully understanding the implications of the increase for risk analysis, the question remains as to what is driving the increase.

In this section, we perform a heuristic investigation to try to understand what might be driving the trend in the MH ratio. We will then complement this with a quantitative analysis in Section 4.

We now describe an analysis in which we decompose the trend in the MH ratio into various component terms, in order to make the heuristic analysis of the previous section quantitative.

In a study based on the ADT-HURSAT database of global tropical cyclone observations, Kossin et al. [8] identified a statistically significant increasing trend in the ratio of the number of cat35 fixes to the number of cat15 fixes (the MH ratio). We have explored the origens of this trend in terms of trends in the underlying numbers of fixes by storm category and by region in order to inform decisions about how tropical cyclone risk models might be adjusted to reflect the trend, for risk modelers interested in making such an adjustment.

We find that the main driver of the trend in the MH ratio is a downward trend in the cat15 fixes, which itself is driven by a statistically significant downward trend in the number of cat12 fixes, which itself is mostly driven by a statistically significant downward trend in the number of cat1 fixes. That in turn is driven by a statistically significant downwards trend in the number of cat1 fixes outside the North Atlantic basin. The North Atlantic cat1 fixes show an increasing trend, unlike any other basin.

The downward trend in cat1 fixes has an implication for regions affected by tropical cyclones, which is that the number of cat1 fixes occurring today in all regions except the North Atlantic seems to be lower than in previous decades. Risk estimates outside the North Atlantic based on the average number of cat1 fixes over previous decades might be too high.

A secondary driver for the upward trend in the MH ratio is a weak and non-significant upward trend in the cat 35 fixes. This is driven by a strong and significant upward trend in the number of cat34 fixes in the North Atlantic, which counteracts a downward trend in the number of cat35 fixes on average over the other basins. The trend in the number of cat34 fixes also has implications for risk estimation. Risk estimates for the North Atlantic based on averages of numbers of cat34 fixes over previous decades might be too low.

All these results must be understood in the context of the uncertainties in the underlying data. For instance, as discussed in Kossin et al. [8], there are gaps in the data. While these gaps do not have a big impact on estimates of the MH ratio and the results presented in Kossin et al., they are likely to have a bigger impact on the estimates of trends in the numbers of fixes that we have presented here.

Based on the above results, there are various ways that risk modelers could make adjustments if they wished to incorporate the trend in the MH ratio into their models. One way would be to adjust the global numbers of cat35 and cat12 fixes uniformly across all basins, although this would ignore the strong regional signals described above. Another way would be to adjust the numbers of cat34 fixes in the Atlantic basin, and the numbers of cat1 fixes in other basins, since these are the regional signals that are the main drivers for the increase. Given the uncertainties, all such adjustments to risk models should perhaps be treated as exploratory sensitivity tests, to test the impact of different hypotheses, rather than as fully credible views of hurricane risk.