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We define ‘grey swan’ tropical cyclones as high-impact storms that would not be predicted based on history but may be foreseeable using physical knowledge together with historical data. Here we apply a climatological–hydrodynamic method to estimate grey swan tropical cyclone storm surge threat for three highly vulnerable coastal regions. We identify a potentially large risk in the Persian Gulf, where tropical cyclones have never been recorded, and larger-than-expected threats in Cairns, Australia, and Tampa, Florida. Grey swan tropical cyclones striking Tampa, Cairns and Dubai can generate storm surges of about 6 m, 5.7 m and 4 m, respectively, with estimated annual exceedance probabilities of about 1/10,000. With climate change, these probabilities can increase significantly over the twenty-first century (to 1/3,100–1/1,100 in the middle and 1/2,500–1/700 towards the end of the century for Tampa). Worse grey swan tropical cyclones, inducing surges exceeding 11 m in Tampa and 7 m in Dubai, are also revealed with non-negligible probabilities, especially towards the end of the century.

The term ‘black swan’^{1, 2} is a metaphor for a high-consequence event that comes as a surprise. Some high-consequence events that are unobserved and unanticipated may nevertheless be predictable (although perhaps with large uncertainty); such events may be referred to as ‘grey swans’^{3, 4} (or, sometimes, ‘perfect storms’⁵). Unlike truly unpredicted and unavoidable black swans, which can be dealt with only by fast reaction and recovery, grey swans—although also novel and outside experience—can be better foreseen and systematically prepared for^{4, 5}.

Tropical cyclones (TCs) often produce extreme wind, rainfall and storm surges in coastal areas. Storm surges are especially complex functions of TC characteristics (track, intensity and size) and coastal features (geometry and bathymetry), and they are also the most fatal and destructive aspect of TCs (see ref. 6 for a comprehensive review of global TC surge observations and impacts). Hence, storm surge is an appropriate and practical metric for identifying grey swan TCs. The most infamous TC disasters early this century were attributable to storm surges, but they should not be considered grey swans, as they had been or could have been anticipated based on historical observations and/or experience. Hurricane Katrina (2005), the costliest US natural disaster, generated the highest US recorded surge flooding (~10 m; ref. 7), but its impact on New Orleans, due largely to the levee failure, had been anticipated by various studies⁸. Cyclone Nargis (2008), the worst natural disaster in Myanmar’s history and one of the deadliest TCs worldwide, struck Myanmar’s Ayeyarwady River Delta at an unusually low latitude (near 16° N) and induced extreme surges (over 5 m); however, the catastrophic fatalities in the hardest-hit areas were largely due to the lack of evacuation plans and cyclone awareness⁹, although intense tropical cyclones had been active in the Bay of Bengal and made landfall in Myanmar (for example, in 2006). Hurricane Sandy, which devastated the US Northeast coast in 2012, set the record-high storm tide (3.4 m) at the Battery in New York City (NYC); however, its storm surge (2.8 m) at the Battery was much lower than those of the 1821 NY hurricane (4.0 m; refs 10, 11) and more severe grey swan TCs (4.5–5 m) that had been simulated for the region^{12, 13}. Typhoon Haiyan (2013), the deadliest TC in Philippine history, and probably the most powerful TC to make landfall worldwide, generated extreme water levels up to 8 m near the most-affected Tacloban area¹⁴, but the water level was comparable to those induced by earlier storms, including a severe typhoon that struck the area in 1897 (7.3 m; refs 6, 15).

Prediction of a grey swan TC is meaningful and practically useful only when associated with some likelihood/probabilistic statement; for example, the probability of exceeding the storm surge level induced by the TC in a year is 10⁻³. The Monte Carlo (MC) method, based on numerous synthetic simulations, is an important way to assess the probability of grey swan TCs. Most current MC methods^{16, 17, 18} simulate synthetic TCs using (fairly limited) historical TC statistics. In contrast, a statistical–deterministic model¹⁹, which is independent of the TC record, simulates TC environments statistically and generates TCs in the simulated environments deterministically. This statistical–deterministic approach may sometimes be more reliable, as observations of the large-scale TC environment are often better constrained than those of TC characteristics in areas with very limited TC history. It is also more likely to generate unexpected but realistic grey swan TCs, because, rather than extrapolating historical TCs, it applies physical knowledge of TCs and ample observations of the large-scale environment. Moreover, as the synthetic TC environments can be generated for any given climate state, this model can simulate grey swan TCs not only in the current and past climates but also in projected future climates²⁰. As TC activity may vary with changing climate^{21, 22, 23, 24}, the model enables quantitative projection of how grey swan TCs will evolve in the future. This statistical–deterministic TC model has been integrated with hydrodynamic surge models²⁵ into a climatological–hydrodynamic method¹³, which has been shown to generate extreme storm surges that are far beyond historical records but are compatible with geologic evidence²⁶. The method has been used to study storm surge risk and mitigation strategies for NYC (refs 27, 28), and it is applicable to any coastal city. Here we apply the method to another three highly vulnerable regions: Tampa in Florida, Cairns in Australia, and the Persian Gulf; we identify their grey swan TCs as the synthetic TCs that are associated with extremely low annual exceedance probabilities (large mean return periods) of the induced storm surges (see Methods).

Tampa, located on the central west Florida coast, is highly susceptible to storm surges. Although many fewer storms have made landfall in this area than in regions farther north and west on the Gulf Coast or further south on the Florida Coast, Tampa Bay is surrounded by shallow water and low-lying lands; a 6-m rise of water can inundate much of the Bay’s surroundings²⁹. Two significant historical events have affected Tampa. The Tampa Bay hurricane of 1848 produced the highest storm tide ever experienced in the Bay, about 4.6 m, destroying many of the few human works and habitations then in the area. The Tampa Bay hurricane of 1921 produced an estimated storm tide of 3–3.5 m, inducing severe damage (10 million in 1921 USD).

To investigate the current TC threat for Tampa we simulate 7,800 Tampa Bay synthetic TC surge events in the observed climate of 1980–2005 (late twentieth century) as estimated from the NCEP/NCAR reanalysis³⁰. To study how the threat will evolve from the current to future climates, we apply each of six climate models to simulate 2,100 surge events for the climate of 1980–2005 (control) and 3,100 surge events for each of the three climates–2006–2036 (early twenty-first century), 2037–2067 (middle), and 2068–2098 (late)–under the IPCC AR5 RCP8.5 emission scenario. The six climate models, selected as in ref. 24 from Coupled Model Intercomparison Project Phase 5 (CMIP5), are CCMS4 (denoted as CCMS; NCAR), GFDL-CM3 (GFDL; NOAA), HADGEM2-ES (HADGEM; UK Met Office Hadley Centre), MPI-ESM-MR (MPI; Max Planck Institution), MIROC5 (MIROC; CCSR/NIES/FRCGC, Japan), and MRI-CGCM3 (MRI; Meteorological Research Institute, Japan).

The large synthetic surge database includes many extreme events affecting Tampa. As a comparison, the 1921 Tampa surge event is also simulated (Fig. 1a). The 1921 Tampa hurricane had a track similar to that of the 1848 Tampa hurricane³¹, travelling northwestwards over the Gulf of Mexico and making landfall north of Tampa Bay. The ‘worst’ synthetic case (among 7,800 events) in the reanalysis climate of 1980–2005 has a similar track (Fig. 1b). However, this grey swan TC is more intense (upper Category 3, compared to the lower Category 2 1921 storm), inducing a higher surge at Tampa of over 5.9 m (compared to 4.0 m simulated for the 1921 storm). We have also identified grey swan TCs affecting Tampa that have very different tracks, especially those moving northwards parallel to the west Florida coast before making landfall. For example, Fig. 1c shows an extremely intense storm (104 m s⁻¹; ‘worst’ case generated under the late twenty-first-century climate projected by HADGEM) that moves northwards parallel to the coast and turns sharply towards Tampa Bay, inducing a storm surge of 11.1 m in Tampa. In such cases, the storm surges are probably amplified by coastally trapped Kelvin Waves. These waves form when the storm travels along the west Florida coast and propagate northwards along the Florida shelf, enhancing the coastal surges, especially when the storm moves parallel to the shelf and at comparable speed to the wave phase speed³². This geophysical feature makes Tampa Bay even more susceptible to storm surge.

a, The 1921 Tampa hurricane simulated based on observed storm characteristics, including 1-min wind intensity (at 10 m) V_m = 43.1 m s⁻¹, minimum sea-level pressure P_c = 967.8 mb and radius of maximum wind R_m = 36.0 km (when the storm is at its nearest approach point to the site). Simulated surge at Tampa is 4.0 m. b, The ‘worst’ surge (5.9 m) event for Tampa in the NCEP/NCAR reanalysis climate of 1980–2005, with V_m = 54.7 m s⁻¹, P_c = 953.4 mb and R_m = 39.7 km. c, The ‘worst’ surge (11.1 m) event for Tampa in the 2068–2098 climate projected by HADGEM for the IPCC AR5 RCP8.5 emission scenario, with V_m = 104.3 m s⁻¹, P_c = 829.6 mb and R_m = 17.0 km. The shaded contours represent the simulated surge height (m; above MSL) and the black curve shows the storm track.

The TC threat to Cairns, in the far north of Queensland, may not be well recognized. The city is located about 300 km south of Bathurst Bay, which was hit in 1899 by Cyclone Mahina (the most intense TC in the Southern Hemisphere, inducing what may have been the highest surge flooding (13 m) in the historical record³⁷). According to the Australian Bureau of Meteorology, at least 53 cyclones have affected Cairns since it was founded in 1876, and several high-intensity storms (for example, Cyclones Larry in 2006 and Yasi in 2011) were near misses. Recent events include Cyclones Justin in 1997, Rona in 1999, and Steve in 2000, all making landfall north of Cairns; although these storms ( m, they induced major flooding (due also to tide and waves) and significant damage ($100–190 million) in the area. (Simulations of these historical cyclones, in comparison with observations, are shown in Supplementary Fig. 4.)

To study the TC threat for Cairns, we simulate 2,400 synthetic Cairns TC surge events in the NCEP/NCAR reanalysis climate of 1980–2010. The ‘worst’ surge for Cairns is about 5.7 m, induced by an intense storm (80 m s⁻¹) travelling perpendicularly to the coast and making landfall just north of Cairns (Fig. 4a). This grey swan TC is much stronger than Cyclones Justin, Rona and Steve, and makes landfall much closer to Cairns. It resembles a hypothetical Cyclone Yasi that is moderately intensified (by about 10 m s⁻¹) and shifted northwards by about 160 km.

The associated annual frequency for the synthetic events is 0.16. a, The ‘worst’ surge (5.7 m) event for Cairns, with V_m = 79.3 m s⁻¹, P_c = 901.1 mb and R_m = 22.3 km. The shaded contours show the simulated surge height (m; above MSL) and the black curve shows the storm track. b, Estimated storm surge level as a function of return period for Cairns. The red dots show the synthetic data, and the dash curves show the 90% statistical confidence interval. Orange dots show the tidal-gauge-observed Cairns storm surges (six in total) between 1980 and 2010; green dots show the modelled surges for these historical TCs (the annual frequency of the historical storms is 0.19).

The Persian Gulf is a mediterranean sea of the Indian Ocean, connected to the Arabian Sea through the Strait of Hormuz and Gulf of Oman. The Persian Gulf is comprised of hot, shallow, and highly saline water, which can support the development of intense TCs and storm surges. However, no TC has been observed in the Persian Gulf, and TC development in the Arabian Sea is limited by the region’s typically low humidity and high wind shear⁴¹. Cyclone Gonu (2007), the strongest historical TC in the Arabian Sea (Category 3; 78 fatalities and 4.4 billion in damage), came close to entering the Persian Gulf, making landfall at the mouth of the Gulf on the easternmost tip of Oman and then in southern Iran. It is scientifically interesting and socially important to ask if such a strong TC can travel into the Persian Gulf.

To answer this question, we assess the TC threat for three major cities bordering the Persian Gulf: Dubai, Abu Dhabi and Doha. For each of these cities, we simulate 3,100 synthetic TC surge events in the NCEP/NCAR reanalysis climate of 1980–2010. As the maximum width of the Persian Gulf is only about 340 km, it may be poorly resolved by the NCAR/NCEP reanalysis resolution of 2.5 degrees (about 250 km); thus we also apply a higher-resolution reanalysis data set, the NASA Modern-Era Retrospective Analysis⁴² (MERRA; with a resolution of 0.67° × 0.5°), to simulate the TC surge events for Dubai. The obtained surge levels and probabilities, however, are very similar for the two data sets. We here present the result for Dubai from the MERRA reanalysis (whereas the results for Dubai, Abu Dhabi and Doha from the NCEP/NCAR reanalysis are shown in the Supplementary Information). In these simulations, some of the synthetic storms originate in the Arabian Sea and move into the Persian Gulf, but the majority originate, surprisingly, within the Gulf. Moreover, the most extreme surges are all induced by intense storms that originate within the Gulf.

Figure 5a shows the ‘worst’ surge (among 3,100 events in the climate of 1980–2010) for Dubai. This grey swan TC originates in the northwest region of the Persian Gulf, moves southeastwards in the Gulf, and makes landfall north of Dubai with extremely high intensity (115 m s⁻¹), generating a storm surge of 7.4 m in Dubai. The intensity of this grey swan TC is far beyond the highest observed TC intensity worldwide (Typhoon Haiyan of 87 m s⁻¹). This extremely high wind intensity is due to very large potential intensities (PIs), made possible by the area’s high sea surface temperature (SST; with summertime peak values in the range of 32–35 °C (ref. 43)) and the deep dry adiabatic temperature profiles characteristic of desert regions. Indeed, the PI calculated (with the method of ref. 44) using the Dammam (Saudi Arabia) atmospheric sounding and an SST of 32–35 °C is between 109 m s⁻¹ and 132 m s⁻¹. (The daily PI calculated using the sounding and the Hadley Centre observed SST, shown in Supplementary Fig. 5, confirms this result.) Furthermore, surface cooling from deep-water upwelling is nearly impossible in this highly saline and mixed body of shallow water (with a mean depth of about 36 m and a maximum depth of 90 m), and when, occasionally, the wind shear is small, the storm can fully achieve its potential intensity. (We note, however, that the estimated pressure intensity has not been similarly evaluated, which will be done in the future, but the storm surge is less sensitive to the pressure than to the wind intensity.)

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