Storm intensities observed from different meteorological agencies

For this study, TC is defined as a storm whose lifetime-maximum intensity (LMI) exceeds 34 kt, and the LMIs per TC over the past 30 years (1986–2015) are extracted from the two best-track data sets. JMA and JTWC best-track data record TC winds at 5-kt intervals, respectively as 10-min and 1-min average values. Only the reliability of the research findings could be enhanced by the observational consistency between the different observations. For this, the comparable intensities are sought from the two observations. It is somewhat common to match the LMI in JTWC with 1.2 times10 of that in JMA, but this does not work well across all intensity levels.5,6 Elsner et al.11 introduced a quantile approach to the analysis of LMI, and Kang and Elsner7 employed the same idea for matching the intensities between the two best-track data. The fundamental assumption is that an intensity event share the same probability level even in different observations though recorded as having different absolute magnitudes. In this study, the inverse empirical cumulative distribution function (ECDF) is employed to find the probability level of the quantile. Here, the probability level of an LMI is defined by the cumulative proportion inversely from the highest LMI (see Supplementary Fig. S1). Figure 1 shows the probability level of LMI at 10-kt intervals in JMA and JTWC. Each black dot represents the 30-yr (1986–2015) mean of annual cumulative proportions. Probability–Probability (P–P) plots are normally used to evaluate the skewness of a distribution. As 1-min average wind should allow larger spread than 10-min average wind, the range of JTWC is larger than that of JMA. This makes the dots digress from a diagonal line of the same probability level. Now that the probability level of storm intensity is identified, the warning categories in the TC classifications from the two best-track data sets can also be compared.

Fig. 1 Probability–Probability (P–P) plot of the LMIs at 10-kt intervals in JTWC and JMA best-track data. Each black dot represents the 30-yr (1986–2015) mean of annual probability levels. Probability level is calculated by the cumulative proportion inversely from the highest LMI. The dashed diagonal line draws the matching probability level of the TC intensities between JTWC and JMA Full size image

Overcoming climate change perspective

To see the response of the probability level of LMI to global warming, global mean SST (GMSST) can be used as a direct indicator of the warming environment.9,12 GMSST represents the annual variation of the global ocean warmth. As Bjerknes feedback works along,13 annual variation of GMSST shows a fluctuation similar to ENSO variation on relatively shorter timescale. At the same time, the forced increase is seemingly apparent on relatively longer timescales.12 Here, GMSST implies not merely a single physical parameter, but the indication of a synthetic environment where all environmental factors are constrained by the warmth level. The understanding of the environmental factors has been in progress, dealing with regional SST, vertical wind shear, vorticity, stability, and so forth.14,15 Figure 2 shows the correlation

Fig. 2 Correlation coefficients of the annual probability levels of LMI with time (linked black dots) and GMSST (linked orange dots). The annual probability level means the annual variation of the cumulative proportion at each threshold LMI. Observations come from a JMA and b JTWC, respectively. Ninety-five percent confidence intervals are shaded in gray and orange colors for time and GMSST, for each. The average of the annual probability levels is labeled on the right ordinate Full size image

coefficients of the annual cumulative proportions with time and GMSST, respectively. Positive sign indicates an increasing portion of TCs whose LMI exceeds the threshold value. Considering the fact that the correlation coefficient is the same as the regression coefficient when both the predictor and the predictand are standardized, the response to time (linked black dots) could be understood as the standardized amount of climate change. Each shaded area shows the 95% confidence interval and confirms that a statistically significant change is rarely captured even at the strongest LMI range. The response of the cumulative proportions to GMSST (linked orange dots), on the other hand, is found to be clearer than to time. In both best-track data sources, statistically significant correlation appears for the cumulative proportions around 40% and less, which means the stronger TCs are more responsive.11 As long as the 30-yr GMSST reflects the forced warming, the result implies that the simpler ‘‘climate change’’ approach to TC intensity using only time might weaken the global warming signal.

Quantified worsening of storm warning validity

Now, we examine and compare the influence of GMSST increase on the storm warning categories also shown using JTWC observation to further understand the validity of the storm warning categories. Firstly, the level of warning categories by 30-yr mean of the cumulative proportions at each threshold LMI, are compared among the three different sources. Warning categories of JMA, JTWC, and SS are divided into four, three and six intervals, respectively (Table 1). The cumulative proportion method reveals that ‘‘Super typhoon’’ is not the highest level of warning. ‘‘Violent typhoon’’ in JMA ranks at the highest warning category covering only 7% of the strongest storms. ‘‘Super typhoon’’ in JTWC and ‘‘Hurricane category 5’’ in SS, on the other hand, represent 18% and 12%, respectively. ‘‘Very strong typhoon’’ in JMA and ‘‘Hurricane category 4’’ in SS are comparable as covering each 31% and 29%.

Table 1 TC classifications for JMA, JTWC, and SS Full size table

Secondly, binomial logistic regression is employed to model the cumulative proportion of LMIs on GMSST. Since the probability level ranges from 0 to 1, the logit is used as the link function in the generalized linear model (GLM). For the cumulative proportion as the dependent variable, ‘‘success’’ is defined as the number of annual TCs over the threshold LMI inclusive, and ‘‘failure’’ is defined as all the rest. GLM assumes a linear relationship between the nonlinear link function and GMSST. In spite of the ‘‘global warming hiatus’’, meaning a pause between 1998 and 2013,16 the increase of GMSST is seen as ongoing.17 From a simple linear perspective, the increase of GMSST is significant as + 0.33 ± 0.041 (s.e.) °C/30 yr. Then the GMSST input as the single explanatory variable is produced by the prediction of linear model over the 30 years (1986–2015). On an assumption that the internal variation has no trend, the modeled GMSST implies the time series of GMSST where the internal variation is removed.

Based on this linear assumption of the global warming, modeled GMSST influence on the warning categories are shown in Fig. 3 (see Supplementary Fig. S2 for comparison with the prediction results by GLM on time). As the logistic regression works, the warning level for each category shows nonlinear change by GMSST change over the same period. All GLM results show significant responses to the increasing global ocean warmth at 95% confidence level, except for the thresholds of ‘‘Typhoon’’ in JTWC and ‘‘Hurricane category 1’’ in SS (see Supplementary Table S1). Modeled cumulative proportion of the beginning year (1986) is denoted in dark blue color at the left side of each column, and that of the ending year (2015) in orange color at the right. All values are rounded off to the nearest whole number. Warning categories in all TC classifications are experiencing the increasing proportion, which is most apparent in the set of strongest storms. ‘‘Violent typhoon’’ in JMA started from 4% and reached up to 12% over the 30 years. As the highest level among the warning categories, 12% could be considered as still being effective for rarely occurring extreme events. Nevertheless, the truth is that the warning for one per 25 storms in the past is not valid any longer. This is similar to the hurricane category 5 in SS, though the coverage is a bit larger than ‘‘Violent typhoon.’’ The validity of ‘‘Super typhoon’’ is seen to be more seriously affected by global warming. The earlier 13% is changed to 24% by the end of the period, which means one per 4.2 storms making the word ‘‘super’’ seem somewhat misleading. Other categories also show widening ranges, though the gap looks less than that of the strongest categories. ‘‘Very strong typhoon’’ and ‘‘Hurricane category 4’’ added 14% and 15% more storms, each reaching 38% and 37%. This implies that we see those warnings or more dire as often as one in every 2.6 and 2.7 storms. The larger proportion can be understood as representing the reality of the increasing threats, the frequency of warnings is, in practice, making the warning less effective. Overall, it seems clear that the validity of current warning categories are suffering from the warming environment.