Tropical Cyclones

Abstract

This paper reviews the history of tropical cyclone research from the late nineteenth century until the present with an emphasis on observational studies. The topics include tropical cyclone theory, climatology, structure, genesis indices and intraseasonal-to-centennial variability and trends. Possible future directions are also suggested.

RÉSUMÉ

[Traduit par la rédaction] Le présent article porte sur l’histoire de la recherche sur les cyclones tropicaux depuis la fin du XIX^e siècle jusqu’à aujourd’hui, en mettant l’accent sur les études d’observation. Les sujets abordés comprennent la théorie des cyclones tropicaux, la climatologie, la structure, les indices de genèse et la variabilité et les tendances intrasaisonnières à centennales. Des orientations futures possibles sont aussi suggérées.

KEYWORDS:

• tropical cyclone
• tropical cyclone theory
• tropical cyclone climatology
• tropical cyclone structure

1 Introduction

Tropical cyclones, also regionally called “hurricanes” in the western hemisphere, “typhoons” in the Western North Pacific, and “cyclones” in the South Pacific and Indian Ocean, are intense atmospheric vortices rotating around a low-pressure centre. Each year, there are 70–100 named tropical cyclones occurring around the world. Tropical cyclone intensity is primarily measured by its maximum sustained wind speed (Vmax), which is often divided into seven intensity categories including tropical depression (Vmax ≤ 38 mph), tropical storm (Vmax between 39–73 mph), and Category 1–5 hurricanes (Vmax ≥ 74 mph). The most intense tropical cyclone ever recorded using modern instrumentation is the 1961 Typhoon Nancy in the western North Pacific, which had a maximum wind speed of 213 mph. As measures of the size and impact area of tropical cyclones, the mean radius of maximum wind is about 65 km (Kimball & Mulekar, 2004), the mean radius of tropical-storm-scale winds (39 mph) is about 185 km, while the mean radius of appreciable wind (5.7 mph) is 1200 km (Knaff et al., 2014). The tropical cyclone’s eyewall is often tilted outward with height, and the eye size at upper levels is generally larger than that near the surface (Stern et al., 2014). For the 13348 tropical cyclones recorded in the International Best Track Archive for Climate Stewardship (IBTrACS) dataset from 1831 to 2019 (Knapp et al., 2010), the mean translation speed is 17.7 km h^–1. The mean lifetime of a tropical cyclone is slightly shorter than one week (6.2 days), with the longest lifetime of a tropical cyclone lasting more than one month (33 days). 31% of all tropical cyclones, 67% of hurricanes and 92% of major hurricanes experience rapid intensification during their lifetime, which is defined as an increase of maximum wind by at least 34.5 mph (30 kt) in 24 h.

There have been a series of review papers discussing the history of tropical cyclone research (e.g. Bergeron, 1954; Emanuel, 2003; Emanuel, 2018; Gray, 1998; Montgomery & Smith, 2017; Ooyama, 1982; Riehl, 1950), most of which have emphasized theoretical and modelling studies. The purpose of this paper is to provide a brief review of observational and theoretical studies of tropical cyclones with an emphasis on observational work. Tropical cyclones are among the deadliest and costliest weather-related disasters. The 1970 Bhola cyclone is the deadliest tropical cyclone on record, with ∼500,000 fatalities in East Pakistan and India (Fritz et al., 2009). Despite improved technology and advancements in warning systems, tropical cyclones continue to cause large number of fatalities, and increasing amounts of property damage. Cyclone Nargis in 2008 killed 138,000 people in Bangladesh (Fritz et al., 2009), while Hurricane Katrina (2005), Tropical Storm Washi (2011), Super Typhoon Haiyan (2013) and Hurricane Maria (2017) had death tolls of 1836, 2546, 6329, 3057, respectively (Fig. 1). In 2017, three major hurricanes hitting the United States (U.S.) led to $268 billion in damage (NOAA NCEI, 2018), which cancelled 60% of the U.S. annual GDP growth in that year. The continued large death tolls and high financial losses from tropical cyclones reflect continued long-term challenges in tropical cyclone prediction as well as growing population exposure along the coastline (Klotzbach et al., 2018).

Fig. 1 Global map of population density in 2015 (red shading over land) and tracks of all tropical cyclones from 1990 to 2019 (magenta lines). Green dots on tracks are locations of rapid intensification events. Black boxes highlight some of the deadliest tropical cyclones in 1990–2019.

Forecasting tropical cyclone intensity, especially rapid intensification, remains one of the most vexing challenges in atmospheric science (Braun et al., 2018; Brown, 2017; Courtney et al., 2019a, 2019b; DeMaria et al., 2014; Hendricks et al., 2019; Rappaport et al., 2012). Tropical cyclone track forecasts have significantly improved over the past three decades (Cangialosi, 2018), but intensity improvements have occurred at a slower rate. More importantly, predicting rapid intensification remains extremely challenging (Brown, 2017), with state-of-the-art tropical cyclone forecast models often failing to predict rapid intensification (Fig. 2).

Fig. 2 Current status of tropical cyclone intensity forecasts (data from NCAR Tropical Cyclone Guidance Project, 2018).

The history of tropical cyclone research is summarized in Fig. 3. The first tropical cyclone recorded in Chinese historical documents, and likely in historical documents around the world, is a Jufeng (typhoon) that struck the coastal city of Mizhou in northern China in 816 AD (Louie & Liu, 2003). Jufeng is the earliest terminology used in Chinese for tropical cyclone, and means convergence of winds. Historical documents provide valuable records of tropical cyclone events going back to the fifteenth century (Callaghan & Power, 2010; Chenoweth, 2006; Moreau de Jonnès, 1822; Poey, 1855), and are discussed in more detail later in this paper. On longer time-scales, paleoclimate proxies have been used to reconstruct tropical cyclone activity for the common era and for the entire Holocene Epoch (Donnelly, Bryant, et al., 2001; Donnelly, Roll, et al., 2001; Liu & Fearn, 1993, 2000; Mora et al., 2006; Scott et al., 2003).

Fig. 3 Timeline of tropical cyclone research.

Basic modern meteorological instrumentation, such as rain gauges, anemometers, thermometers and barometers, were all invented by 1850. In the nineteenth century and the early twentieth century, there were numerous observational studies of tropical cyclone track, surface winds, central pressure and surface precipitation (e.g. Bowie, 1921; Carless, 1849; Chevalier, 1893; Cline, 1915; Fassig, 1928; Garriott, 1898; KimBall, 1915; Mitchell, 1926; Reid, 1846, 1849; Weightman, 1919). Carless (1849) showed a track map of a hurricane occurring in April 1847, including a depiction of the surface wind structure (Fig. 4(a)). Chevalier (1893) presented maybe the first schematic of tropical cyclone structure (Fig. 4(b)), which is quite similar to present-day schematics (e.g. Emanuel, 2018, see Fig. 15).

Fig. 4 Tropical cyclone studies in the nineteenth century and early twentieth century. (a) Track of a hurricane in April 1847 (from Carless, 1849). (b) Schematic of tropical cyclone structure (from Chevalier, 1893).

Since then, observational tools for studying tropical cyclones have advanced to include upper air soundings, aircraft flight level instruments, satellite infrared and visible sensors, airborne radars, satellite microwave sensors and spaceborne radars, operational analysis, reanalysis, and paleoclimate proxies. Using these observational datasets, research has been conducted on tropical cyclone climatology, climate variability, surface structure, upper air structure, heat/moisture/angular momentum/vorticity budgets, and environmental forcing. Based on these observational studies, theories and models have been developed on tropical cyclone structure, maximum potential intensity, formation and intensification.

This paper will be organized as follows. Observational studies on tropical cyclone climatology and variability will be reviewed in Section 2. Studies on tropical cyclone structure will be reviewed in Section 3. Tropical cyclone theory will be reviewed in Section 4. A summary of current challenges and suggested future directions will be provided in Section 5.

2 Tropical cyclone climatology and variability

a Climatology and Empirical Genesis Indices

Before the satellite era, information on tropical cyclone track and intensity came from surface reports from land stations and ships. One of the earliest efforts to construct a global tropical cyclone climatology was Byers (1944). Aircraft reconnaissance started after 1943, which was limited to the western Atlantic and parts of the Northwest Pacific. The launch of weather satellites in the 1960s and 1970s provided for the first time global coverage of tropical cyclone activity (e.g. Dvorak, 1975; Sadler, 1964). Regional best track datasets have been developed such as the National Hurricane Center (NHC) North Atlantic hurricane database (HURDAT/HURDAT2; Jarvinen et al., 1984; Landsea & Franklin, 2013), the Joint Typhoon Warning Center (JTWC) database (Chu et al., 2002), and the Southwest Pacific Enhanced Archive of Tropical Cyclones (SPEArTC) database (Diamond et al., 2012). The global IBTrACS database integrates data from all available sources (Knapp et al., 2010).

Tropical cyclones are convectively-coupled vortices generated inside a large-scale convective rotating environment. Tropical cyclones generally form and propagate within monsoon troughs and tropical/sub-tropical convergence zones. These regions are generally associated with convective disturbances, warm sea surface temperatures (SST), a moist lower troposphere, surface wind convergence, and large lower-tropospheric vorticity. Based on observations and theoretical considerations, empirical genesis indices have been developed such as the Yearly Genesis Parameter (YGP; Gray, 1968, 1975, 1979), the Modified Yearly Convective Genesis Potential Index (CYGP; Royer et al., 1998), the Genesis Potential Index (GPI; Emanuel & Nolan, 2004), and the Tippett et al. (2011) index (TCS). Gray (1968) constructed a comprehensive global climatology of tropical cyclone genesis and associated large-scale ocean-atmosphere environment using all datasets available at that time, and developed the YGP index (see also Gray, 1975, 1979, 1998). He showed that tropical cyclone genesis was closely related to six parameters: (1) the Coriolis parameter, (2) low-level relative vorticity, (3) tropospheric vertical wind shear, (4) ocean thermal energy, measured as ocean temperatures greater than 26°C to 60 m depth, (5) the difference in equivalent potential temperature between the surface and 500 mb, and (6) relative humidity in the mid-troposphere. The first three parameters specify a dynamic potential, while the last three parameters yield a thermal potential. The CYGP (Royer et al., 1998) is a variant of the YGP, and replaces the thermal potential of the YGP with a convective potential which is determined by convective precipitation from model output or reanalysis. The GPI (Emanuel & Nolan, 2004) also adopted low-level vorticity, vertical wind shear and mid-troposphere relative humidity as predictors, but also used maximum potential intensity (Bister & Emanuel, 1998) as a convective predictor. The TCS (Tippett et al., 2011) index is a variant of the GPI, and replaced maximum potential intensity with an SST index. Overall, the physical processes considered in the four indices are similar, but the mathematical formulations are different.

Menkes et al. (2012) evaluated the performance of these four indices using reanalysis datasets and found that differences between indices are large and vary depending on the regions and on the timescales considered. Climatological mean genesis density for all indices exhibits large regional discrepancies, which can commonly reach up to ±50% (Fig. 5 upper panel). All indices except the TCS show an equatorward bias in climatological mean genesis, especially in the northern hemisphere where this bias can reach 5°. For seasonal timescales on which the indices are historically fitted, all indices reproduce the phase of the seasonal cycle adequately although with a bias in amplitude in some regions. The TCS is the best-fitted index overall. The most striking feature at interannual scales is the inability of all indices to reproduce the observed amplitude of interannual variability (Fig. 5 lower panel), although they can reproduce modulation linked to ENSO. In terms of genesis mechanisms inferred from the analysis of the contributing terms, the indices show a wide variation at seasonal timescales.

Fig. 5 (Upper) Climatological mean cyclogenesis numbers in (a) observations and predicted by genesis indices including the (b) YGP, (c) CYGP, (d) GPI and (e) TCS. (Lower) Standard deviation of interannual anomalies of cyclogenesis in observations and predicted by genesis indices (from Menkes et al., 2012).

Next, we review observational studies on the modulation of tropical cyclone activity by key global climate variability from intraseasonal time-scales to centennial time-scales. The dominant modes investigated herein are the Madden-Julian Oscillation (MJO), ENSO, the Atlantic Multi-decadal Oscillation (AMO), and global warming.

b MJO

The dominant tropical climate mode on intraseasonal time-scales is the MJO – the 30–90-day oscillation of tropical climate system (Lin et al., 2006; Madden & Julian, 1971). The MJO has been found to modulate tropical cyclone activity in different ocean basins including the western north Pacific (Kim et al., 2008; Li & Zhou, 2013; Liebmann et al., 1994), the northern Indian Ocean (Kikuchi & Wang, 2010; Krishnamohan et al., 2012; Liebmann et al., 1994), the northeast Pacific (Barrett & Leslie, 2009; Maloney & Hartmann, 2000a), north-central Pacific (Klotzbach & Blake, 2013), the North Atlantic (Aiyyer & Molinari, 2008; Barrett & Leslie, 2009; Klotzbach, 2010; Klotzbach, 2012; Klotzbach & Oliver, 2015; Maloney & Hartmann, 2000b; Ventrice et al., 2011), and the southern hemisphere (Bessafi & Wheeler, 2006; Chand & Walsh, 2010; Hall et al., 2001; Ho et al., 2006; Leroy & Wheeler, 2008; Ramsay et al., 2012). See Klotzbach (2014) for an extensive review of the MJO-TC relationship. Liebmann et al. (1994) first studied the relationship between tropical cyclones of the Indian and western Pacific oceans and the MJO. They found that tropical cyclones preferentially occur during the MJO’s convectively-enhanced phase and cluster around the MJO’s low-level cyclonic vorticity and convergence anomalies (Fig. 6(a)).

Fig. 6 Modulation of tropical cyclones by the MJO. (A) Composite positions of tropical cyclones (asterisks) relative to the MJO vorticity anomaly (from Liebmann et al., 1994). (B) (left) Statistically significant increases (green arrows) and statistically significant decreases (red arrows) in ACE from the phase 1–8 average by tropical cyclone basin. (right) Statistically significant differences in 200–850-mb vertical shear (westerly shear anomalies in red, easterly shear anomalies in blue) and 300-hPa omega (up arrows represent upward motion, down arrows represent downward motion) from the phase 1–8 average (from Klotzbach, 2014).

Camargo et al. (2009) analysed global genesis density anomalies associated with different phases of MJO and found that they were consistent with an empirical genesis potential index. Of the four environmental variables comprising the index, mid-level relative humidity was the largest MJO-driven contributor, with low-level vorticity having the second largest contribution. Vertical wind shear and potential intensity only had minor contributions. Klotzbach (2014) examined tropical cyclone genesis, rapid intensification, and basin-wide accumulated cyclone energy – an index accounting for frequency, intensity and duration of tropical cyclones – associated with the MJO lifecycle for all ocean basins, and found that the convectively-enhanced phases of the MJO and the phases immediately following them were typically associated with above-average tropical cyclone frequency for each of the global TC basins. The convectively suppressed phases of the MJO were typically associated with below-average tropical cyclone frequency (Fig. 6(b)). The number of rapid intensification periods was also shown to increase when the convectively-enhanced phase of the MJO was impacting a particular tropical cyclone basin.

c ENSO

The dominant global climate mode on interannual timescales is ENSO – the 3–7-year oscillation of tropical coupled ocean-atmosphere climate system (Bjerknes, 1969; Lin & Qian, 2019). In the Atlantic, in El Nino years, there is a tendency toward fewer tropical cyclones, while La Nina years increase Atlantic tropical cyclone activity (Gray, 1984; Gray et al., 1993; Gray & Sheaffer, 1991; Knaff, 1997; Patricola et al., 2015). ENSO also affects the number of landfalls in the United States, with fewer TCs experienced in El Niño years (Bove et al., 1998; Klotzbach et al., 2018; Pielke & Landsea, 1999). El Niño also tends to reduce Atlantic hurricane intensity (Landsea et al., 2004) and move tropical cyclone genesis locations outside of the tropics (Elsner & Kara, 1999). Factors that have been identified as responsible for these changes in tropical cyclone activity El Niño years are increases in vertical wind shear (Shapiro, 1987; Goldenberg & Shapiro, 1996; Patricola et al., 2015) and increases in upper-level temperatures, thereby stabilizing the atmosphere (Tang & Neelin, 2004).

The modulation of tropical cyclones by ENSO can be summarized by Fig. 7 (Camargo et al., 2007). In the western North Pacific, there is a southeastward (northwestward) shift of tropical cyclone activity in El Niño (La Niña) years (Chan, 1985; Chia & Ropelewski, 2002; Dong, 1988; Patricola et al., 2018; Wang & Chan, 2002). This southeastward shift in El Niño years has been attributed to the eastward extension of the monsoon trough and associated low-level westerlies in the western North Pacific (Lander, 1994, 1995) and reduction of vertical wind shear (Clark & Chu, 2002). In El Nino years typhoons also tend to last longer, become more intense, and have more recurving trajectories (Camargo et al., 2007; Camargo & Sobel, 2005; Wang & Chan, 2002), thereby also altering landfall probabilities for East Asian countries (Saunders et al., 2000; Elsner & Liu, 2003; Wu et al., 2004). Sobel and Camargo (2005) hypothesized that anomalous typhoon-induced near-equatorial westerly winds generated in El Niño years might even act to strengthen the warm event, resulting in a positive feedback between El Niño and tropical cyclones.

Fig. 7 Modulation of tropical cyclones by ENSO. Difference of the anomalies in El Nino and La Nina years for (a) ASO genesis density, (b) ASO track density, (c) JFM genesis density and (d) JFM track density (from Camargo et al., 2007).

More hurricanes tend to form in the central Pacific during El Niño events (Clark & Chu, 2002). More tropical cyclones occur near Hawaii (Murakami et al., 2015). This has been attributed to smaller vertical wind shear and greater low-level relative vorticity in that region (Chu, 2004; Chu & Wang, 1997; Clark & Chu, 2002; Wu & Lau, 1992).

Eastern North Pacific tropical cyclone activity tends to be enhanced when Atlantic tropical cyclone activity is suppressed and vice versa (Elsner & Kara, 1999). Although no ENSO influence has been found in tropical cyclone frequency in the eastern North Pacific (Whitney & Hobgood, 1997), the number of intense hurricanes tends to increase in El Nino years (Gray & Sheaffer, 1991) and tropical cyclone activity shifts westward during El Nino events (Irwin & Davis, 1999), with an increased likelihood that some of these hurricanes will propagate into the central North Pacific (Chu, 2004). This shift has been attributed to environ- mental parameters having different characteristics east and west of 116°W (Collins & Mason, 2000) in ENSO years, with both dynamic and thermodynamic conditions becoming much more conducive in the western portion of the eastern North Pacific in El Niño years (Collins et al., 2016).

There is a strong association between the variability of sea surface temperatures in the Indian and Pacific Oceans (Pan & Oort, 1983). The association of north Indian Ocean tropical cyclone frequency and ENSO is apparent during the months of May and November, with fewer intense tropical cyclones occur during El Nino events (Singh et al., 2000). Girishkumar and Ravichandran (2012) found that less accumulated cyclone energy was generated during October-December in the Bay of Bengal during El Niño years. They ascribed the decrease in El Niño years to anticyclonic vorticity anomalies, decreased convection and reduced upper ocean heat potential.

In El Nino years, an increase in the formation of tropical cyclones occurs in the South Pacific near the date line simultaneously with a decrease near Australia (Basher & Zeng, 1995; Evans & Allan, 1992; Hastings, 1990; Revell & Goulter, 1986). In La Nina years, an enhanced risk of landfall occurs in Australia with more tropical cyclones tracking close to the Queensland coast, while in El Nino years the tracks are more zonal west of the date line (Dong, 1988; Nicholls, 1979, 1985; Nicholls et al., 1998). This shift is related to the extension of the monsoon trough and equatorial westerlies in El Nino years in the South Pacific, favouring the formation of twin tropical cyclones (Ferreira et al., 1996), tropical cyclogenesis late in the season and east of 160°W in the South Pacific (Chu, 2004). Chand et al. (2013) and Magee et al. (2017) showed that tropical cyclone activity shifts northeastward during El Niño years in the South Pacific, leading to increased likelihood of impacts for French Polynesia, while TC activity is favoured in the Coral Sea region during La Niña events (Terry, 2007).

d Global Warming and AMO

There have been numerous observational studies on trends of tropical cyclone activity associated with global warming (e.g. Bhatia et al., 2019; Elsner et al., 2008; Emanuel, 2005; Klotzbach & Landsea, 2015; Knapp et al., 2007; Kossin, 2018; Kossin et al., 2013, 2014; Kossin & Vimont, 2007; Landsea, 2007; Landsea et al., 2006; Mei & Xie, 2016; Pielke et al., 2005; Schreck et al., 2014; Sobel et al., 2016; Studholme & Gulev, 2018; Webster et al., 2005; Weinkle et al., 2012). See Knutson et al. (2010), Klotzbach and Landsea (2015) and Walsh et al. (2016) for reviews of related studies and Knutson et al. (2019, 2020) for a detection and attribution assessment and a recent update on climate model response to anthropogenic warming, respectively. Webster et al. (2005) documented a large and significant increase in both the number as well as the percentage of category 4 and 5 hurricanes for all global basins from 1970 to 2004, which was supported by Emanuel (2005) with estimates of accumulated cyclone energy for the North Atlantic and western North Pacific basins. However, these results were questioned by several studies which pointed out the large uncertainty and short length of the datasets (e.g. Landsea et al., 2006; Pielke et al., 2005). Ten years later, with longer and better calibrated datasets, Klotzbach and Landsea (2015) found that the global frequency of category 4 and 5 hurricanes has shown a small, insignificant downward trend while the percentage of category 4 and 5 hurricanes has shown a small, insignificant upward trend between 1990 and 2014. Accumulated cyclone energy globally had experienced a large and significant downward trend during the same period. The primary reason for the increase in category 4 and 5 hurricanes noted in observational datasets from 1970 to 2004 by Webster et al. (2005) was concluded to be primarily due to observational improvements at the various global tropical cyclone warning centres, mostly in the period from 1970 to 1989. Bhatia et al. (2019) used observations and a model experiment to study the intensification rates of tropical cyclones. Their results suggested a detectable increase of Atlantic intensification rates and reveal a need for more reliable data before detecting a robust trend at the global scale.

One limitation of modern tropical cyclone datasets is their short length. Historical documents provide important records of tropical cyclone occurrence and tracks for the time before modern observations began (Chenoweth, 2006; Garcia-Herrera et al., 2018; Scheitlin et al., 2010). The research on historical documents for the North Atlantic basin was started by Moreau de Jonnès (1822) who used almanacs and written histories of the Caribbean colonies to document observed hurricanes in the West Indies back to the year 1495 (Fig. 8(a)). Meanwhile, Southey (1827) created a chronology using information from British newspapers, and Reid (1838, 1849), Redfield (1831, 1854), and Piddington (1848) uncovered additional cyclones using ship's log books, weather diaries, and other newspapers. Poey (1855) summarized these studies together with his own research. Ludlum (1963) and Millas (1968) consulted the Poey list, and others built after that time and using it. More cyclones have been uncovered in subsequent studies (Fernandez-Partagas & Diaz, 1996; Mock, 2004). Chenoweth (2006) conducted a reanalysis of the 1700–1855 portion of Poey's original published list using historical newspaper accounts, weather diaries, and ships’ logbooks. Of the 348 separate entries in Poey's original list, 149 were rejected and 198 were accepted. Due to errors in dating and location, and the linking of separate entries as parts of the same storm, only 170 of the 198 accepted entries were unique storms. Thirteen undated storms of the remaining 170 were dated. The authorities cited by Poey vary in their reliability. Of those cited 10 or more times, there was an average of one incorrect citation for every 3.1 correct citations. The most and least reliable authorities used by Poey were identified. An updated corrected chronology from all published sources was presented, which included 383 unique storms through 1855. The historical Atlantic basin chronology is still being updated (Chenoweth & Divine, 2008, 2012; Garcia-Herrera et al., 2005).

Fig. 8 (a) Major contributors leading to the Chenoweth archive (from Scheitlin et al., 2010). (b) The number of hurricanes passing through 10–20°N, 61.5°W from 1690 to 2007. The red line is the 21-year moving mean (from Chenoweth & Divine, 2008). (c) The number of cyclones in the Bay of Bengal. The red line is the 5-year running mean. (d) The number of landfalling tropical cyclones in the Philippines (from Kubota & Chan, 2009). (e) The number of landfalling tropical cyclones in eastern Australia. The linear trend of −0.0021 TCs year^–1 is also shown (from Callaghan & Power, 2010).

In addition to the Atlantic, historical reconstructions of tropical cyclone activity have also occurred in other basins. Many tropical cyclone events were recorded in China’s official historical documents and have been compiled together by Zhang (2013). Historical time series have also been reconstructed for the entire western North Pacific (Chan & Shi, 2000; Chen et al., 2019; Kubota & Chan, 2009; Liu et al., 2001; Zhang, 2013), the Northern Indian Ocean (Singh et al., 2000) and Australia (Callaghan & Power, 2010). On longer time-scales, tropical cyclone activity has been derived from paleoclimate proxies such as lake sediment cores, stalagmites, corals and marine sediment cores (Chen et al., 2012; Denommee et al., 2014; Donnelly, Bryant, et al., 2001; Donnelly, Roll, et al., 2001, 2015; Donnelly & Woodruff, 2007; Haig et al., 2014; Liu & Fearn, 1993, 2000; Mora et al., 2006; Nyberg et al., 2007; Scott et al., 2003; Toomey et al., 2013, 2016; van Hengstum et al., 2013; Zhou et al., 2019).

Fig. 8 shows the historical records of tropical cyclones in (b) the North Atlantic (Chenoweth, 2006), (c) the Indian Ocean, (d) the northwestern Pacific (Kubota & Chan, 2009), and (e) Australia (Callaghan & Power, 2010). None of the records show an increasing trend of tropical cyclone activity. In fact, both the Indian Ocean record and the Australian record show a decreasing trend. Since it is more difficult to uncover tropical cyclones occurring earlier in the record, these historical records generally tend to underestimate the tropical cyclone numbers in the early parts of the records. These basins require additional research and study before any definitive conclusion on trends can be made.

Fig. 9 shows tropical cyclone activity in the Common Era reconstructed from paleoclimate records in the (a) North Atlantic (Donnelly et al., 2015), (b) the northwestern Pacific (Zhou et al., 2019), and (c) Australia (Haig et al., 2014). Similar to the historical records, the paleoclimate records do not show increasing trends in tropical cyclone activity. Therefore, modern instrument records, historical records and paleoclimate records consistently suggest that overall tropical cyclone activity does not increase (and may actually decrease) with ongoing global warming, similar to what has been found in recent climate model analysis with anthropogenic warming forcing by Knutson et al. (2020).

Fig. 9 (a) Hurricane activity index (red) and number of hurricane events per century (black) for Salt Pond, MA (from Donnelly et al., 2015). (b) Tropical cyclone activity index for the northwestern Pacific (from Zhou et al., 2019). (c) Tropical cyclone activity index for Western Australia (from Haig et al., 2014).

One of the primary drivers of the global climate on multi-decadal timescales is the AMO. Many studies have analysed the modern instrumental record and found that the AMO strongly modulates tropical cyclone activity in the Atlantic basin (Bell & Chelliah, 2006; Caron et al., 2015; Goldenberg et al., 2001; Klotzbach, 2011; Klotzbach & Gray, 2008; Knight et al., 2006; Zhang et al., 2018; Zhang & Delworth, 2006), with more Atlantic hurricane activity occurring when the AMO is positive. Positive phases of the AMO are associated with a warmer tropical North Atlantic, reduced vertical wind shear and increased instability, favouring increases in Atlantic hurricane activity and US landfalling hurricane activity (Klotzbach et al., 2018). There are many proposed mechanisms of AMO, such as the North Atlantic Oscillation (NAO) coupled oscillator (Delworth et al., 2017; Sutton et al., 2018; Timmermann et al., 1998), cloud-radiation feedback (e.g. Clement et al., 2015), and external volcano forcing (e.g. Birkel et al., 2018; Knudsen et al., 2014; Mann et al., 2020, 2021).

Fig. 10(a) illustrates the maximum entropy spectrum of the AMO index from ERSST for 147 years (1880–2016) and LMR2.0 reanalysis for the past 2000 years. They both show strong spectral peaks at the multi-decadal timescale between 40–90 years. Fig. 10(b) demonstrates the maximum entropy spectrum of tropical cyclone activity index for North Atlantic and Northwestern Pacific. They also show strong peaks at the multi-decadal timescale between 40 and 90 years. Spectral peaks in the same frequency band are not necessarily correlated with each other. To test the correlation, Fig. 10(c) illustrates the lag-correlation of global LMR SST anomalies with tropical cyclone activity index for the two ocean basins. Black stars denote the grids with correlation coefficient above the 95% confidence level. For North Atlantic, tropical cyclone activity is significantly correlated with global SST anomalies and the pattern is similar to the AMO SST pattern. For Northwestern Pacific, tropical cyclone activity is also significantly correlated with global SST anomalies and the pattern is similar to the ENSO SST pattern. Therefore, paleoclimate datasets confirm that the AMO significantly modulates tropical cyclone activity in North Atlantic for the past 2000 years.

Fig. 10 (a) Maximum entropy spectrum of the AMO index from ERSST and LMR2.0 reanalysis. (b) Maximum entropy spectrum of tropical cyclone activity index for North Atlantic (NATL; Donnelly et al., 2015) and Northwestern Pacific (NWP; Zhou et al., 2019). (c) Lag-correlation of LMR SST anomalies with tropical cyclone activity index for the NATL and NWP. Black stars denote the grids with correlation coefficient above the 95% confidence level.

3 Tropical cyclone structure

In this section, we review the observational studies on tropical structure following approximately the timeline in history and from lager spatial scales to smaller spatial scales. The observations of tropical structure began at the surface, and then advanced to the upper levels. Since the spatial resolution of tropical cyclone observational datasets has been increasing with time, observational studies advanced from lager spatial scales to smaller spatial scales, i.e, from the external large-scale environment to the internal cyclone-scale structure, and then to the inner core, the eyewall and the central eye. Therefore, we will review first the observational studies of the surface and boundary layer structure of tropical cyclones, and then the horizontal structure from the large-scale environment into the central eye, followed by the vertical structure from the large-scale environment into the central eye.

a Surface and Boundary Layer Structure

The surface boundary layer structure of tropical cyclones and associated physical processes have been studied using radar, aircraft flight-level and dropwindsonde data (Barnes & Powell, 1995; Black et al., 2007; Black & Holland, 1995; Blackwell, 2000; Cione et al., 2020; Drennan et al., 2007; Franklin et al., 2003; French et al., 2007; Giammanco et al., 2012; Hock & Franklin, 1999; Huang, Wu, et al., 2018; Kepert, 2006a, 2006b; Knupp et al., 2006; Lee & Chen, 2012; Molinari et al., 2013; Moss, 1978; Moss & Merceret, 1976, 1977; Powell, 1982, 1990a, 1990b; Powell et al., 2003; Schneider & Barnes, 2005; Schwendike & Kepert, 2008; Sparks et al., 2019; Tang et al., 2018; Vickery et al., 2009; Wroe & Barnes, 2003; Zhang, Black, et al., 2008; Zhang et al., 2009; Zhang, Marks, et al., 2011; Zhang, Rogers, et al., 2011, 2013; Zhang & Drennan, 2012; Zhang & Uhlhorn, 2012). The implementation of the Global Positioning System dropwindsonde (GPS sonde) provided a wealth of high resolution wind profiles within tropical cyclones (Hock & Franklin, 1999). GPS sonde composite wind profiles contained a jet-like structure with a logarithmic increase in wind speed from the surface often to the height of the maximum wind speed, followed by a gradual decrease in wind speed above the height of the maximum wind speed (e.g. Franklin et al., 2003; Powell et al., 2003; Vickery et al., 2009).

Zhang et al. (2013) constructed a composite boundary layer structure using 1878 GPS dropsondes in 19 hurricanes (Fig. 11(a)). The kinematic boundary layer height (the frictional inflow layer height) is almost double the thermodynamic boundary layer height (the well-mixed layer height). The height of the maximum tangential wind was located between the kinematic and thermodynamic boundary layer heights. All three boundary layer heights decrease inward towards the centre of the tropical cyclone. The frictional inflow layer height is higher in the downshear quadrants, with the downshear-right quadrant being the highest. The well-mixed layer height and the height of maximum tangential wind speed are very similar at the eyewall, but are higher outside in the left quadrants. Estimates of vertical eddy diffusivity (Km) from observations in the eyewall boundary layer are difficult to obtain. There are only a few observations in the North Atlantic (Zhang, Marks, et al., 2011), the western North Pacific (Sparks et al., 2019), and over land (Tang et al., 2018). Zhang, Marks, et al. (2011) found that the turbulence parameters estimated underneath the eyewall are nearly an order of magnitude larger than those outside of the eyewall. In the intense eyewall region, the horizontal length scale of the dominant turbulent eddies is between 500 and 3000 m, and the corresponding vertical length scale is approximately 100 m. Sparks et al. (2019) found a superlinear relationship between diffusivity and wind speed in the eyewall region in western North Pacific typhoons, which is different from the more linear relationship in Atlantic hurricanes. Tang et al. (2018) studied three landfalling tropical cyclones and found that the estimated Km was significantly larger than the oceanic values, suggesting that models should use different parameterizations of Km over land versus over ocean.

Fig. 11 Boundary layer processes. (a) Schematic diagram of the characteristic height scales in the tropical cyclone boundary layer for the four quadrants relative to the shear direction (from Zhang et al., 2013). (b) The drag coefficient Cd as a function of 10 m wind speed from various studies (from Hsu et al., 2017). (c) MSLP vs best-track maximum surface winds (Vmax) interpolated to the time of the observations and the associated best-fit relationships to these data for 1974–87 (from Knaff & Zehr, 2007).

Boundary layer rolls have been observed in tropical cyclones, and their impacts on eddy flux transport are still under investigation (Lorsolo et al., 2008; Morrison et al., 2005; Wurman & Winslow, 1998; Zhang, Katsaros, et al., 2008; Huang, Li, et al., 2018). Boundary layer rolls generally have a wavelength of 200–1600 m. Using National Weather Service WSR-88D Doppler radars, Morrison et al. (2005) found that rolls occurred in 35–69% of radar volumes of tropical cyclones. Zhang, Katsaros et al. (2008) analysed aircraft data and suggested that roll vortices may be a significant factor modulating air–sea momentum exchange. Spaceborne synthetic aperture radar provides a unique capability to image the sea surface imprints of quasi-linear streaks induced by these rolls. Huang, Li et al. (2018) analysed synthetic aperture radar images and found rolls underneath the eye, eyewall and rainbands. The roll wavelengths were longest just outside of the RMW, and decrease both inward and outward. The spatial distribution of these roll wavelengths was asymmetrical.

An important boundary layer process related to tropical cyclone intensity change is the levelling off, or limiting value, of the marine drag coefficient in high winds (Bell et al., 2012; Black et al., 2007; Chen et al., 2013; Donelan et al., 2004; Holthuijsen et al., 2012; Hsu et al., 2017; Jarosz et al., 2007; Powell et al., 2003; Sanford et al., 2011; Vickery et al., 2009; Fig. 11(b)). Moreover, the drag coefficient, given similar wind speeds, is smaller for smaller-radii storms (Vickery et al., 2009). Enhanced sea spray by short or breaking waves is speculated as a cause for this observed relationship.

The relationship between maximum surface wind speed and minimum sea level pressure is important for tropical cyclone monitoring and forecasting. Tropical cyclones are well approximated by gradient wind balance, which determines the wind-pressure relationship (Chavas et al., 2017; Willoughby, 1990; Willoughby & Rahn, 2004). Because the actual relationship is a function of several factors related to the tropical cyclone environment and structure which vary from case to case, there is considerable scatter about any given wind-pressure relationship (Atkinson & Holliday, 1977; Courtney & Knaff, 2009; Dvorak, 1975; Harper, 2002; Koba et al., 1990; Knaff & Zehr, 2007; Kossin, 2015; Love & Murphy, 1985). Knaff and Zehr (2007) compared the various wind-pressure relationships used in different basins (Fig. 11(c)). They found that latitude, size, and environmental pressure, which all can be quantified in an operational and post-analysis setting, are related to predictable changes in the wind-pressure relationships. These factors can be combined into equations that estimate winds given pressure and estimate pressure given winds with greater accuracy. Kossin (2015) studied the changes of wind-pressure relationships in eyewall replacement cycles that have been observed in North Atlantic hurricanes. He found that the wind-pressure relationship can vary substantially during an eyewall replacement cycle depending on the intensity at the start of the cycle, and these relationships may be considerably different than the typical Dvorak wind-pressure relationship used in that basin.

b Horizontal Structure from the Large-Scale Environment to the Central Eye

Observational studies have found many large-scale environmental conditions favouring tropical cyclone formation, such as monsoon shearlines, low-level wind surges, nearby previously developed tropical cyclone, interaction of binary vortices, and upper-troposphere synoptic-scale environment. Tropical cyclones tend to form on monsoon shearlines in the western North Pacific and Australian region (Chen et al., 2004; Harr et al., 1996; Holland, 1995; Lander, 1994; McBride & Keenan, 1982; Ramage, 1974b; Ritchie & Holland, 1999; Wu et al., 2013; Zong & Wu, 2015a, 2015b), and inside the troughs of easterly waves in the North Atlantic and Eastern North Pacific basins (Avila, 1991; Avila & Pasch, 1992; Dunkerton et al., 2009; Dunn, 1940; Hankes et al., 2015; Hopsch et al., 2010; Landsea, 1993; Leppert et al., 2013a, 2013b; Molinari et al., 1997; Palmer, 1952; Thorncroft & Hodges, 2001; Wang, 2018; Wang & Hankes, 2014; Zawislak & Zipser, 2014). In the western North Pacific and Australian region, the monsoon shearlines are associated with strong low-level vorticity, convergence and convection, all favouring development of tropical cyclones (Fig. 12(a); Holland, 1995). McBride and Keenan (1982) studied 20 years of tropical cyclone genesis in the Australian region, and found that 97% of pre-cyclone cloud clusters are on the monsoon shearline at the point of development. Zong and Wu (2015b) analysed 11 years of tropical cyclone genesis in the western North Pacific, and found that nearly all of the genesis events occurred on the monsoon shearline. For the North Atlantic and the eastern North Pacific, tropical cyclone genesis is often associated with easterly waves. Theoretically, when waves propagate in shear flow and arrive at the critical layer where mean flow and wave speed are equal, parcels experience irreversible displacements and trapping in the location of “cat’s eye”, which was named after the shape of the flow pattern (Andrews & McIntyre, 1978). Dunkerton et al. (2009) studied 61 named storms from 1998 to 2001, and found that 88% of them were clearly generated by easterly waves. In the remaining seven cases, either a multiple-wave interaction was involved, or easterly waves were not well-defined. They suggested that the cat's eye in the critical layer provided anomalous cyclonic low-level vorticity, enhanced moisture, increased convection, and mesoscale vortex aggregation, that all feedback on the parent wave, favouring tropical cyclone formation. Wang (2018) analysed 150 Atlantic named storms and found that they generally formed near the centre of the cat’s eye in easterly waves. Leppert et al. (2013a) examined 10 years of easterly waves in the Atlantic and eastern North Pacific, and found that waves that developed into tropical cyclones have larger fractional coverage of deep convection than non-developing cases.

Fig. 12 Horizontal structure. (a) Schematic of the interacting mechanisms leading to enhanced potential for tropical cyclone formation in the monsoon confluence zone (from Holland, 1995). (b) Horizontal plot on the 200 mb surface for the favourable superposition of an upper-level trough composite with wind vectors and Ertel PV (shaded). The increment in longitude and latitude is 10 degrees (from Hanley et al., 2001). (c) Schematic representation of the horizontal structure of radar reflectivity and the atmospheric flow in which it is imbedded (from Willoughby et al., 1984). (d) Schematic illustration of shear-induced convective asymmetry based upon observations of Jimena and Olivia (from Black et al., 2002). (e) Horizontal structure of a tropical cyclone with concentric eyewalls. The dashed arrow represents environmental shear (from Hence & Houze, 2012). (f) Location of convective bursts in intensifying tropical cyclones. Radial coordinates are normalized by RMW. Black arrow represents environmental shear (from Rogers et al., 2013).

Low-level wind surges sometimes serve as triggers for tropical cyclogenesis (Briegel & Frank, 1997; Fujita et al., 1969; Gray, 1998; Lee et al., 1989; Li, 1936; Love, 1985a, 1985b; Yokoi & Takayabu, 2010; Zehr, 1992). Fujita et al. (1969) presented a case study showing that large-scale cross-equatorial wind surges from the winter hemisphere to the summer hemisphere can generate anticyclones in the summer hemisphere, which interact with the subtropical high and aid in tropical cyclone formation. This was confirmed to be a fairly common scenario by the composite study of Love (1985b). In other cases, low-level wind surges may come from the subtropics. Yokoi and Takayabu (2010) found that the formation of cyclone Nargis was triggered by a low-level easterly surge blowing towards the genesis point from the subtropics. Horizontal convergence at the head of the surge associated with active convection induced externally forced convergence that triggered cyclogenesis. In addition, the active convection seemed to contribute to the preconditioning of mid-tropospheric humidity. The easterly surge was associated with a cold surge in the eastern coastal portion of the Eurasian continent, which is a typical feature of cold surges in April.

Tropical cyclone formation and track can be strongly affected by the presence of a nearby previously developed tropical cyclone, and the interaction of these binary vortices has been a frequent topic of study (Brand, 1970; Carr et al., 1997; Carr & Elsberry, 1998; Dong & Neuman, 1983; Haurwitz, 1951; Hoover, 1961; Jang & Chun, 2015; Lander, 1995; Lander & Holland, 1993; Qian et al., 2016; Wu et al., 2003; Yang et al., 2008). Dong and Neuman (1983) studied 36 years of data and found that the annual average number of binary cyclone events is 1.5 in the western North Pacific and 0.33 in the North Atlantic. Lander and Holland (1993) analysed 43 years of binary cyclone events and found a variety of interactions including capturing, stable cyclonic orbiting, cyclone merging, and cyclone escaping. Jang and Chun (2015) studied binary cyclone events in western north Pacific for 62 years (1951–2012). A total of 98 binary TCs occurred with an annual average of 1.58. The occurrence frequency of binary TCs shows significant year-to-year variations and there are two peaks in the mid-1960s and early 1990s. Three-fourths (76.3%) of the binary TCs occurred between July and September, which is consistent with the high activity season of TCs in general. They identified six representative trajectories strongly related to the environmental flow and the location of the subtropical high.

The upper-troposphere synoptic-scale environment associated with tropical cyclones is often characterized by anticyclonically curved flow as part of a large-scale ridge, and a poleward/eastward outflow jet linking the tropical cyclone with midlatitude westerlies (e.g. Black & Anthes, 1971; Chen et al., 2015; Colon & Nightingale, 1963; Fett, 1966; Fischer et al., 2019; Hanley et al., 2001; Merrill, 1988a, 1988b; Molinari et al., 1995, 1998; Ramage, 1974a; Riehl, 1948; Sadler, 1976, 1978; Shieh et al., 2013). Hanley et al. (2001) constructed composites for six types of upper-tropospheric flow associated with tropical cyclones, all of which contained a large-scale ridge with four possessing an outflow jet. An example is shown in Fig. 12(b). The poleward/eastward outflow jet tends to generate an eddy flux convergence of angular momentum (DeMaria et al., 1993; Fischer et al., 2019; Molinari & Vollaro, 1989; Peirano et al., 2016; Wu & Cheng, 1999), but there is debate on whether the eddy flux convergence of angular momentum is connected to rapid intensification. Potential vorticity associated with the trough can advect inward and may enhance inner-core potential vorticity and thereby strengthen the tropical cyclone (Leroux et al., 2013). Vorticity advection generates a quasi-geostrophic forcing of upward motion and enhances genesis (Bracken & Bosart, 2000; Fischer et al., 2017). Equatorward intrusion of an upper-tropospheric trough may also enhance the outflow jet and favour intensification, as long as it does not generate overly strong shear (Hanley et al., 2001). These interactions are also sensitive to the details of the ridge-trough configuration (Chen et al., 2015; Fischer et al., 2019; Hanley et al., 2001; Peirano et al., 2016).

The internal structure of tropical cyclones has been studied using weather radar, especially Doppler radar, aided by aircraft flight-level data and dropsondes (e.g. Black & Hallett, 1999; Black et al., 2002; Bluestein & Marks, 1987; Bundgaard, 1958; Dodge et al., 1999; Fletcher et al., 1961; Gamache et al., 1993; Guimond et al., 2010, 2016; Halverson et al., 2006; Heymsfield et al., 2010; Houze et al., 1992; 2007, 2009; Jordan, 1959; Jorgensen, 1984a, 1984b; Lussier et al., 2014; Marks, 1985; Marks & Houze, 1984, 1987; Marks et al., 1992; Montgomery et al., 2014; Nguyen et al., 2017; Raymond & Lopez Carillo, 2011; Rogers et al., 2012, 2013, 2015, 2016; Sanger et al., 2014; Simpson & Starrett, 1955; Wadler, Rogers, et al., 2018; Wadler, Zhang, et al., 2018; Wexler, 1947; Willoughby et al., 1982, 1984; Zawislak et al., 2016). Willoughby et al. (1984) constructed a composite horizontal structure of the full tropical cyclone using airborne radar reflectivity and in situ dynamic and thermodynamic data (Fig. 12(c)). They found that the hurricane vortex may be divided into an inner gyre with closed air trajectories moving with the vortex, and an outer envelope with open environmental air trajectories passing through the vortex and around the core. Spiral rainbands form near the boundary between the core and the envelope where the Rossby number is of order unity. Spiral rainbands differ dynamically both from convective rings due to its asymmetric nature and from propagating gravity-wave bands because its Doppler-shifted frequency is below the local inertia frequency. In more intense systems with stronger convective instability, spiral rainbands may evolve into a convective ring and move into the vortex core. Outward propagating gravity-wave bands have also been observed, which are often associated with track oscillations as the storm makes landfall or recurves. The eyewall and spiral rainbands are generated along the cyclonic uplifting atmospheric inflow into the centre of tropical cyclone.

The internal structure of a tropical cyclone, especially its asymmetric structure, is significantly affected by environmental wind shear, as revealed by both aircraft reconnaissance data (e.g. Black et al., 2002; DeHart et al., 2014; Miller, 1964; Simpson & Riehl, 1958; Wadler, Rogers, et al., 2018) and satellite measurements (Alvey et al., 2015; Chen et al., 2006; Tao & Jiang, 2015; Tao et al., 2017; Zagrodnik & Jiang, 2014). Black et al. (2002) analysed the effects of shear on the horizontal structure of two hurricanes (Fig. 12(d)). Convective updrafts formed in the downshear side of the eyewall and advected around the eye and ascended to the tropopause when reaching the upshear side of the eyewall, while precipitation-driven downdrafts started at the upshear side and predominated below 6 km. Wadler, Rogers, et al. (2018) constructed composites using aircraft passes over a 13-year period. They found that the downshear-right region had the lowest and weakest updrafts, while the upshear-left region had the highest and strongest updrafts, which confirmed the results from the case study of Black et al. (2002). They further discovered that, comparing with steady-state storms, intensifying storms have higher and stronger updrafts advected into the upshear-left region, as well as stronger and deeper updrafts inside the RMW. Chen et al. (2006) examined TRMM satellite-measured surface rainfall in both the northern hemisphere (NH) and southern hemisphere (SH). They discovered that shear enhanced the rainfall asymmetry, and the maximum rainfall is located in the downshear-left quadrant in the NH, which rotates more to the upshear-left quadrant when intensity increases. The surface rainfall maximum is consistent with the highest and strongest updrafts observed by aircraft reconnaissance. For the SH, the maximum rainfall is in the downshear-right quadrant, suggesting that, similar to the NH, convective updrafts gradually grow higher and stronger following the rotating wind around the eyewall. A stronger eyewall vortex advects the convective updrafts further downstream.

Regarding the eyewall, tropical cyclones occasionally have concentric eyewalls and go through eyewall replacement cycles (ERCs) with the old eyewall contracting and gradually being replaced by a growing outer new eyewall (e.g. Bell et al., 2012; Black & Willoughby, 1992; Blackwell, 2000; Didlake et al., 2017, 2018; Didlake & Houze, 2011, 2013a, 2013b; Dodge et al., 1999; Dougherty et al., 2018; Fischer et al., 2020; Fortner, 1958; Hence & Houze, 2012; Holliday, 1977; Hoose & Colon, 1970; Houze et al., 2007; Jordan, 1966; Jordan & Schatzle, 1961; Kossin & Sitkowski, 2009; Kuo et al., 2009; Molinari et al., 2019; Samsury & Zipser, 1995; Sitkowski et al., 2011, 2012; Willoughby et al., 1982; Wu et al., 2012; Yang et al., 2013, 2014; Zhu & Yu, 2020). Occasionally triple eyewalls are also observed (McNoldy, 2004; Zhao et al., 2016). Concentric eyewalls occur primarily in major hurricanes (Hawkins et al., 2006; Kossin & Sitkowski, 2009; Kuo et al., 2009). 55% of major hurricanes in the western North Pacific, 70% in the Atlantic, and 35% in the eastern North Pacific have concentric eyewalls at least once in their lifetime. For major hurricanes reaching an intensity of 138 mph (above category 4), the percentages are 80% for the western North Pacific, 70% for the Atlantic, 50% for the eastern North Pacific, and 40% for the SH. Over the western North Pacific, 27% of all tropical storms and 40% of hurricanes have concentric eyewalls at some point during their lifetime.

Sitkowski et al. (2011) studied the lifecycle of ERC using 31 years of flight level data from 79 Atlantic hurricanes. They identified three phases of ERCs: intensification, weakening, and reintensification. The entire ERC lasts 36 h on average. All times and intensities listed in the discussion that follows are composite averages. The first phase lasts for ∼9 h and often exhibits rapid intensification with the inner wind maximum intensifying by 7 m s^–1 (41 mph day^–1), while the outer wind maximum intensifies by 5 m s^–1 (29 mph day^–1). The second phase lasts for ∼16 h with the inner wind maximum weakening by −10 m s^–1 (−33 mph day^–1), while the outer wind maximum intensifies by 9 m s (30 mph day^–1). The third phase lasts for ∼11 h with the inner wind maximum weakening by −7 m s^–1 (−34 mph day^–1), while the outer wind maximum intensifies by 4 m s^–1 (19 mph day^–1).

Hence and Houze (2012) analysed the horizontal structure of concentric eyewalls using 10 years of TRMM satellite radar data (Fig. 12(e)). They found that, similar to the single eyewall, the convective cells begin their development in the downshear-right quadrant, grow and intensify in the downshear-left quadrant, and become weaker in the upshear-left quadrant, before dissipating entirely in the upshear-right quadrant. The bulking of the precipitation in the downshear-left quadrant of the primary eyewall results in a narrowing of the moat in that quadrant, whereas the moat in the upshear-right quadrant is wider and clearer. Recently, Zhu and Yu (2020) analysed environmental influences on tropical cyclone concentric eyewalls, and found that concentric eyewalls occurred in a relatively quiescent environment with weaker inflows, weaker low-level troughs, and weaker sub-tropical highs.

Regarding the central eye, a long-term misconception is that the tropical cyclone eye is a region free of deep convection. Rogers et al. (2013) analysed airborne Doppler radar observations from 93 eyewall passes, and found cases with a large number of convective bursts inside the eye, especially during rapid intensification events (Fig. 12(f)). Wadler, Rogers, et al. (2018) compared the hot towers between rapid intensification events and steady-state events and found that the intensifying events have stronger and deeper updrafts inside the RMW. Zagrodnik and Jiang (2014) constructed composite convection and latent heating structure using 14 years of TRMM precipitation radar data, and found that strong convection and latent heating occurred in the innermost 50 km region, especially for altitudes above 10 km. They also found that rapid intensification was associated with enhancement of moderate-to-deep convection in the innermost 50 km region. Alvey et al. (2015) constructed composites using 15 years of satellite passive microwave measurements and obtained similar results. Ground and satellite observations of lightning distribution in tropical cyclones also show strong convection inside the eye (Cecil & Zipser, 1999; DeMaria et al., 2012; Jiang & Ramirez, 2013; Molinari et al., 1994, 1999; Stevenson et al., 2014, 2016, 2018; Xu et al., 2017).

c Vertical Structure from the Large-Scale Environment to the Central Eye

Our knowledge of a tropical cyclone’s vertical structure has advanced significantly from the large-scale environment to the central eye through analysis of upper air soundings, airborne Doppler radar and flight level data. The evolution of summary schematics clearly shows the progress of our knowledge of a tropical cyclone’s vertical structure (Fig. 13).

Fig. 13 Vertical structure. (a) Vertical cross-section of potential temperature (solid) and temperature (dashed) of a hurricane (from Palmen, 1948). (b) Schematic view of convection and the secondary circulation a typical tropical cyclone (from Frank, 1977a). (c) Convective and mesoscale updrafts and downdrafts in the inner core (from Marks & Houze, 1987). (d) Precipitation processes, cloud distribution and charge separation in tropical cyclones (from Black & Hallett, 1999). (e) Vertical structure of a sheared tropical cyclone (Cristobal 2014) (from Nguyen et al., 2017). (f) Vertical structure of a hurricane undergoing eyewall replacement (from Houze et al., 2007). (g) Composite vertical cross-section of latent heating (from Zagrodnik & Jiang, 2014). (h) Composite vertical cross-section of convective bursts in the eyewall (from Wadler, Rogers, et al., 2018).

The earliest upper air observations in the 1930s and 1940s provided the first view of the vertical structure of tropical cyclones and associated large-scale environment (Haurwitz, 1935; Palmen, 1948; Simpson, 1947; Wexler, 1945). It has long been speculated that the low central pressure of a tropical cyclone is associated with high temperatures in the eye. Based on the application of the hydrostatic equation to temperature measurements in typhoon eyes as they passed over high mountains, Haurwitz (1935) correctly inferred the tropospheric warm core in tropical cyclones and the vertical tilt of eyewall. By piecing together the earliest aircraft flights into hurricanes, Wexler (1945) presented a schematic of the vertical structure of a tropical cyclone showing tilted deep eyewall convection and a secondary circulation. Simpson (1947) constructed vertical cross-sections of temperature and relative humidity. Using upper-air radiosonde data, Palmen (1948) presented a vertical cross-section of temperature and potential temperature for the whole tropical cyclone (Fig. 13(a)). He stated: “This picture of the hurricane shows us a vortex of a warm core consisting of ascending moist air and inside it another still warmer, but much drier air originally produced by strong subsidence”. The tropospheric warm core has since been confirmed by many studies (Hawkins & Imbembo, 1976; Hawkins & Rubsam, 1968; Jordan, 1961; LaSeur & Hawkins, 1963).

After accumulation of sounding data for several decades, it was possible to construct composites of tropical cyclone’s internal structure, especially the wind flow as well as heat, moisture, angular momentum and vorticity budgets (Frank, 1977a, 1977b; Holland & Merrill, 1984; Lee, 1989a, 1989b; McBride, 1981; McBride & Zehr, 1981; Merrill, 1984, 1988a, 1988b). The schematic by Frank (1977a) added convective heating associated with the eyewall and spiral rainbands, as well as the secondary circulation (Fig. 13(b)). There is an inflow convergence layer from the surface to 800 mb, and an outflow divergence layer at 400 mb and above with a peak around 150 mb. There is strong large-scale ascent in the inner-core region and much weaker descent in the outer region. The vertical profile of tangential wind is bottom-heavy and peaks around 850 mb. Relative humidity increases inward and reaches 90% in the inner-core region.

Airborne radar measurements beginning in the late 1970s made it possible to study the vertical structure of tropical cyclone’s eyewall and central eye. Using aircraft precipitation radar and flight level data, Jorgensen (1984b) examined the 3D precipitation structure of a typical eyewall. He found that the inner edge of the eyewall slopes substantially outward with height, and radar reflectivity decreases fairly rapidly with height above the 0°C level. The radial convergence and updraft are radially inward of the maximum wind and rainfall. Using airborne Doppler radar measurements, Marks and Houze (1987) constructed the 3D wind field of the inner core of a tropical cyclone (Fig. 13(c)). They found that the secondary circulation is characterized by a deep layer of radial inflow in the lower troposphere and a layer of intense outflow above 10 km. The rising branch of the secondary circulation was located at the inner edge of the eyewall and sloped radially outward, with discrete convective-scale bubbles of more intense upward motion superimposing on this mean rising current. Convective-scale downdrafts were located throughout and below the core of the maximum precipitation in the eyewall. Outside the eyewall, the precipitation was predominantly stratiform, with a radar bright band at the melting level, a mesoscale updraft above, and a mesoscale downdraft below. The structure is quite similar to a typical squall line with trailing stratiform precipitation (Zipser, 1977; Houze, 1982).

Using aircraft flight-level microphysics measurements, Black and Hallett (1999) analysed the detailed structure of precipitation processes, cloud distribution and charge separation (Fig. 13(d)). Ocean surface temperatures were typically near 28°C, and cloud-base temperatures were near 22°C. In mature hurricanes, typical vertical velocities near the 0°C level are 5–8 m s^–1, with convection extending to well beyond the −40°C isotherm – the temperature for homogeneous ice nucleation. Charge separation occurs in the mixed phase region around the melting level where multiple types of hydrometeors exist, limited in altitude by the lack of supercooled water above −5°C. White dots above the melting level indicate where small ice particles, frozen drops, and graupel exist, while black drops below the melting level indicate rain. Vertical motion in the tropical cyclone leads to redistribution of hydrometeors. The tangential circulation changes from cyclonic flow to anticyclonic outflow near the top of the storm, and ice is primarily redistributed at mid-levels in the atmosphere.

Environmental vertical wind shear typically forces an asymmetric precipitation distribution in tropical cyclones, but the magnitude of this asymmetry can exhibit considerable variability even for similar shear magnitudes. Nguyen et al. (2017) examined the thermodynamic and kinematic influences on precipitation symmetry in two such cases: Bertha and Cristobal (2014). They found that consistent with the impact of shear, both cases exhibited a tilted vortex as well as a pronounced azimuthal asymmetry, with the maximum precipitation occurring in the downshear-left quadrant. However, Bertha was characterized by more symmetrically distributed precipitation and relatively modest vertical motion, while Cristobal was characterized by more azimuthally confined precipitation and much more vigorous vertical motion (Fig. 13(e)). Cristobal showed three potential enhancements to asymmetric precipitation: (i) convective downdrafts that transported low entropy air downward into the boundary layer, cooling and stabilizing the lower troposphere downstream in the left-of-shear and upshear quadrants; (ii) subsidence in the upshear quadrants, which acted to increase the temperature and decrease the relative humidity of the mid-troposphere, resulting in capping of the boundary layer; and (iii) lateral advection of mid-tropospheric dry air from the environment, which dries the TC's upshear quadrants.

Fig. 13(f) shows the vertical structure of concentric eyewalls in an eyewall replacement cycle (Hence & Houze, 2012; Houze et al., 2007). The vertical structure of the secondary (outer) eyewall is different from the primary (inner) eyewall and also different from the eyewall of single eyewall storms. The upper-tropospheric portions of the outer eyewalls are like the rainbands from which they evolve. Their lower-tropospheric portions are more intense and more uniform than rainbands of single eyewall storms, suggesting that these secondary eyewalls are forming from rainbands undergoing axisymmetrization and building from below. The inner concentric eyewalls are more strongly affected by shear than are the eyewalls of single eyewall storms, while the outer eyewalls are relatively unaffected by shear, which suggests the outer eyewall is amplifying the shear-induced asymmetry of the inner eyewall. Samsury and Zipser (1995) and Didlake et al. (2017) suggested that the final decay of the inner eyewall is largely due to the outer eyewall obstructing low-level moist radial inflow from reaching the inner eyewall and thus reducing its tangential wind acceleration and convection, which is in contrast to other weakening effects that counteract the inner eyewall transverse circulation at higher altitudes (Willoughby et al., 1982).

Convective vorticity transport, with the convective updrafts transporting higher vorticity boundary layer air into the upper level lower vorticity environment, occurs in the eyewall and central eye and is important for the tropical cyclone vorticity budget. The rotating updrafts are called “vortical hot towers” (Hendricks et al., 2004). With high resolution Doppler radar data, vorticity can be directly calculated (Guimond et al., 2016; Houze et al., 2009; Lussier et al., 2014; Raymond & Lopez Carillo, 2011; Rogers et al., 2012, 2015; Sanger et al., 2014). Houze et al. (2009) presented evidence of vortical hot towers in a tropical depression that later intensified into a hurricane. Rogers et al. (2015) found convective features with high vertical vorticity at 8 km altitude, which were likely vortical hot towers. These convective features were found inside the eye during the rapid intensification of a tropical storm into a hurricane.

It is interesting to compare the vertical distribution of latent heating and convective updrafts. Zagrodnik and Jiang (2014) constructed composite latent heating structure using 14 years of TRMM data (Fig. 13(g)). The latent heating profile in the eyewall is bottom-heavy and peaks at 5–6 km, which is consistent with the fact that condensation in convective updrafts mainly occurs in the lower and middle troposphere. Therefore, latent heating mainly warms up the lower and middle troposphere. On the other hand, convective updrafts and downdrafts have been analysed using aircraft flight level and Doppler radar data (Black et al., 1996; Jorgensen et al., 1985; Wadler, Rogers, et al., 2018). Wadler, Rogers, et al. (2018) constructed composite vertical cross-sections of convective bursts in the eyewall using 13 years of airborne Doppler radar data (Fig. 13(h)). The strongest convective updrafts and downdrafts occurred in the upper troposphere and peaked around 12 km. The convective updrafts in the upper troposphere were associated with very weak latent heating (Fig. 13(g)). Therefore, the upper-level warm core in tropical cyclones is likely heated up by upper-level downdrafts.

For over 100 years, it has been assumed that the tropical cyclone’s eye is dominated by sinking motion, which warms up the eye and enhances tropical cyclone intensity (Fig. 14(a)). However, few direct observations were available on vertical motion inside the tropical cyclone eye. Indirect observations from ozone measurements showed inconsistent results (Baray et al., 1999; Carsey & Willoughby, 2005; Collimore, 2018; Joiner et al., 2006; Newell et al., 1996; Penn, 1965, 1966; Rodgers et al., 1990; Stout & Rodgers, 1992; Zou & Wu, 2005). Using the global high-resolution ERA5 reanalysis collocated with satellite cloud and precipitation datasets, we found that tropical cyclone eyes with RMW > 50 km are in fact dominated by rising motion rather than sinking motion (Fig. 15(a and b)). The mean rising motion cools down the eye and could not explain the observed upper-level warm core. However, strong eddy updrafts and downdrafts exist inside the eye (Fig. 15(c)), which become stronger when the eyewall clouds grow in vertical extent. The stratospheric eddy downdrafts transport high enthalpy stratospheric air into the eye. Thermodynamic calculations show that a 4% intrusion of stratospheric hot air in the eye could explain the observed upper-level warm core. The stratospheric eddy downdrafts are not driven by convective hot towers penetrating into the stratosphere, but likely by divergence at the top of the eye. The observed tropical cyclone eye structure is summarized schematically in Fig. 14(b).

Fig. 14 Schematic depiction of tropical cyclone structure from (a) Emanuel (2018), and (b) This study.

Fig. 15 (a) Composite mean vertical pressure velocity ω at 400 mb for northern hemisphere tropical cyclones with RMW > 50 km categorized by intensity: tropical depressions, tropical storms, category 1–2 hurricanes, and major (category 3–5) hurricanes. (b) Profiles of mean vertical velocity in tropical cyclone eyes. (c) Profiles of maximum updrafts and downdrafts in tropical cyclone eyes. Data are from ERA5 reanalysis for 1979–2015.

4 Tropical cyclone theories

Next, we review briefly tropical cyclone theories. Although there were many speculations in the seventeenth to nineteenth centuries on the physical mechanisms of tropical cyclones, such as the hypothesis that tropical cyclones are driven by chemical reactions in the ocean (Ellis, 1791), the schematic presented by Chevalier (1893) may be considered the first descriptive model of a tropical cyclone (Fig. 4(b)). Amazingly, the Chevalier schematic is quite similar to today’s schematics with the surface low pressure and winds, tilted eyewall clouds, and sinking motion in the eye. Then in the early twentieth century, dry barotropic vortex models were developed for tropical cyclones (Fujiwhara, 1921; Rossby, 1948), which were used later in studying the tracks of tropical cyclones and interactions between binary cyclones (Holland & Dietachmayer, 1993; Kuo et al., 2008; Prieto et al., 2003; Ritchie & Holland, 1993).

Beginning in the 1950s, numerous tropical cyclone theories have been developed, which could be divided into seven groups, listed in the order from the spiral rainbands into the inner core and central eye: (1) wave/instability theories of the spiral rainbands, (2) theories of eyewall replacement cycles, (3) environmental forcing by upper-level troughs, (4) environmental forcing by wind shear, (5) balanced vortex theory of the inner core, (6) theories of maximum potential intensity, and (7) feedbacks between the moist convective vortex and the large-scale environment.

In the wave/instability theories of the spiral rainbands, atmospheric waves are used to explain the full structure of the tropical cyclone, including (1) inertia-gravity waves for the outer spiral rainbands, which could be forced from either inside or outside (Abdullah, 1966; Arakawa & Manabe, 1963; Kurihara, 1976; Lord Kelvin, 1887; Tepper, 1958; Willoughby, 1977, 1978a, 1978b, 1979); (2) Rossby waves for the eye region (Charney & Stern, 1962; Fjrtoft, 1950; Franklin et al., 2006; Guinn & Schubert, 1993; McDonald, 1968; Montgomery & Kallenbach, 1997; Schade, 1994), and (3) mixed Rossby-gravity waves for the eyewall region (Zhong et al., 2009). In the tropical atmosphere, convective coupling significantly reduces the equivalent depth and consequently slows down the phase speed of the waves (Lin et al., 2006; Wheeler & Kiladis, 1999). Other theories have attempted to explain spiral rainbands using Ekman layer instability (Faller, 1963; Fung, 1977; Lilly, 1966) or simply as a long-lived squall line (Robe & Emanuel, 2001; Rotunno et al., 1988).

Eyewall replacement cycles have been examined in numerous modelling studies, and many mechanisms have been proposed: (1) Montgomery and Kallenbach (1997) proposed that outward propagating vortex Rossby waves, which converge at a stagnation radius, induce a secondary tangential wind maximum through wave-mean-flow interactions. However, Judt and Chen (2010) presented a simulation of Hurricane Rita (2005) and showed that the presence of a moat region prevented the outward propagation of vortex Rossby waves. (2) Terwey and Montgomery (2008) proposed that axisymmeterization and an upscale cascade of vorticity from rainband convection within a region associated with a weak radial gradient of vorticity, referred to as a “beta skirt”, could generate the second eyewall. (3) Fang and Zhang (2012) proposed that stratiform downdrafts in the downwind direction create a lower-tropospheric frontal zone between the eyewall and rainband region, which facilitates the development of deep convection and a second eyewall. (4) Huang et al. (2012) and Abarca and Montgomery (2013) proposed that unbalanced dynamics leads to supergradient flow and ascent out of the boundary layer within a thermodynamically favourable location for convection. However, Kepert (2013) concluded that supergradient flow is a byproduct of frictional convergence and a broad expansion of the tangential wind field does not necessarily cause a local frictional updraft. (5) Kepert (2013) and Kepert and Nolan (2014) proposed that feedback between the boundary layer response to a perturbation in the radial gradient of the gradient wind vorticity could generate the second eyewall. (6) External forcings are also suggested as drivers of the second eyewall, such as upper-level troughs (Dai et al., 2017; Molinari & Vollaro, 1990; Nong & Emanuel, 2003) and vertical wind shear (Dougherty et al., 2018; Zhang et al., 2017).

Environmental forcing by upper-level troughs has been assessed in many modelling studies (e.g. Challa et al., 1998; Challa & Pfeffer, 1980; Holland & Merrill, 1984; Komaromi & Doyle, 2018; Leroux et al., 2013, 2016; Molinari & Vollaro, 1990; Montgomery & Farrell, 1993; Nong & Emanuel, 2003; Pfeffer & Challa, 1981; Shi et al., 1997). The proposed physical mechanisms include an enhanced secondary circulation and convection by (1) eddy angular momentum flux, (2) quasi-geostrophic forcing, (3) potential vorticity forcing, and (4) jet-related upper-level divergence.

Environmental forcing by vertical wind shear has also been examined. The proposed physical mechanisms include (1) ventilation of environmental low-entropy air from the mid-level or boundary layer into the inner core (Cram et al., 2007; Riemer et al., 2010; Simpson & Riehl, 1958; Tang & Emanuel, 2010); (2) ventilation of upper-level high-entropy high-vorticity air out of the eye (Frank & Ritchie, 2001; Wong & Chan, 2004); (3) increasing the static stability of the inner core by an adiabatic midlevel warming response to vortex tilting (DeMaria, 1996; Wong & Chan, 2004); (4) eddy momentum fluxes opposing the symmetric overturning circulation (Wu & Braun, 2004); (5) increases of sensitivity to other environmental conditions such as mid-tropospheric humidity (Emanuel et al., 2004). The effects are also dependent on the height and depth of shear (Elsberry & Jeffries, 1996; Finocchio et al., 2016).

In the balanced vortex theories of the inner core, Eliassen (1951) first demonstrated that for a balanced vortex driven by momentum and thermodynamic forcings, a compensating secondary circulation is needed to restore thermal wind balance. Balanced vortex dynamics has been used to model the secondary circulation in the inner core (Hack & Schubert, 1986; Navarro et al., 2017; Pendergrass & Willoughby, 2009; Schubert et al., 2007; Schubert & Hack, 1983; Shapiro & Willoughby, 1982; Smith et al., 2018; Smith & Wang, 2018; Sundqvist, 1970; Vigh & Schubert, 2009; Wang et al., 2020; Willoughby, 1988, 2009). The vertical structure of the heating plays a central role in these models. There was not observed heating profile for tropical cyclone eyewall at the time of Sundqvist (1970) and the profile used was unrealistically top-heavy. Pendergrass and Willoughby (2009) used a realistic heating structure based on observations. They found that the efficiency with which imposed heating intensifies the vortex is most sensitive to the intensity itself and the vortex size rather than the vortex shape or the forcing tilt.

The maximum potential intensity of tropical cyclones has been estimated by several studies from the available thermodynamic energy in the environment assuming that the detailed cyclone dynamics and internal processes provide no constraint on the maximum achievable intensity. The estimates are based on (1) parameterization of eye-region subsidence (Holland, 1997; Miller, 1958); (2) calculation of the available energy to balance surface momentum losses (Malkus & Riehl, 1960); and (3) assumption that a tropical cyclone acts as a classic Carnot heat engine (Bister & Emanuel, 1998; Emanuel, 1987, 1991; Emanuel et al., 2013; Kleinschmidt, 1951; Kowaleski & Evans, 2016; Smith et al., 2008).

Feedbacks between the moist convective vortex and the large-scale environment play a key role in tropical cyclone intensity change. In the earliest models, there was no convective parameterization and the vortex was amplified by large-scale condensation (Haque, 1952; Kasahara, 1961; Kuo, 1961; Lilly, 1960; Rosenthal, 1964; Syono, 1953; Yanai, 1961). Unrealistic grid-scale convection was often generated in those models, showing the need for a convection scheme (see review by Kuo, 1965). The first generation of convective parameterization emphasized moisture convergence, and the feedback mechanism was often called convective instability of the second kind (CISK; Charney & Eliassen, 1964; Kuo, 1965; Ooyama, 1964; Smith, 1997; Yamasaki, 1968). The second generation of convective parameterization added surface heat fluxes, and the feedback mechanism was often called wind-induced surface heat exchange (WISHE; Emanuel, 1986; Emanuel, 1995; Emanuel et al., 1994; Montgomery et al., 2009; Ooyama, 1969; Rosenthal, 1971; Rotunno & Emanuel, 1987). Later, effects of convective vorticity transport were also introduced (Hendricks et al., 2004; Montgomery et al., 2006; Nguyen et al., 2008; Smith et al., 2009).

Tropical cyclones also have an internal feedback with the stratosphere. A stronger tropical cyclone causes stronger cloud top outflow, and stronger cloud top outflow will drive stronger stratospheric downdrafts from above, which penetrate into the eye, increasing the eye temperature and causing intensification. These form a positive feedback loop for rapid intensification. Based on the physical thinking and observational evidence presented above, Lin and Qian developed a toy model with two components: a moist updraft to predict the cloud top of moist convection in the eyewall, and a dry downdraft to predict downward intrusion of stratospheric or tropospheric air in the eye. For both the updraft and downdraft, entrainment is considered with a simple fixed entrainment rate. The starting level of the dry downdraft is determined by the cloud top of the moist updraft, with a parameterization of suction layer depth and intrusion depth based on observations. A tropical cyclone’s central pressure is calculated from the resulting temperature profile in eye. The tendency of the maximum wind is then calculated from the pressure gradient force and the frictional force, with a parametrization of dependence of eye size on maximum wind (Holland et al., 2010; Knaff & Zehr, 2007; Kossin, 2015).

Intensification of the tropical cyclone is driven by warm stratospheric downdrafts forced by deep eyewall convection, and enhanced by positive feedbacks when the starting altitude and penetration depth of the warm stratospheric downdraft both increase with stronger intensity, while size of the eye shrinks with stronger intensity. Tests using a fixed eye size give similar results. Decay of tropical cyclones is caused by three physical mechanisms: suppression of eyewall deep convection by upper troposphere warming, vertical wind shear, and surface friction. The environmental temperature profile for the moist updraft is assumed to be the temperature profile in the eye. Therefore, warming of the upper troposphere by the warm stratospheric downdraft suppresses the cloud top height of the moist updraft at the next time step, leading to a negative feedback. Vertical wind shear is assumed to linearly decrease relative to the cloud top height of the moist updraft. Surface friction is parameterized following the observed dependence of the drag coefficient on tropical cyclone intensity, and tests using fixed drag coefficient give similar results. Our new tropical cyclone intensity model is tested with forecast experiments for 2877 tropical cyclones from 1979 to 2015 (Fig. 16(a)). Our model can predict well rapid intensification of extreme tropical cyclones, and can be compared with existing tropical cyclone forecast models (Fig. 2). Examples of forecast for individual events are shown for some of the deadliest and costliest tropical cyclones, such as Cyclone Nargis, Cyclone 02B, Super Typhoon Haiyan, Hurricane Mitch, Hurricane Katrina, and Hurricane Sandy (Fig. 16(b)).

Fig. 16 (A) Forecast skill of the Lin-Qian tropical cyclone intensity model for 2877 tropical cyclones from 1979 to 2015. (B) Examples of forecasts from the Lin-Qian tropical cyclone intensity model.

5 Summary and future directions

This paper reviews the history of tropical cyclone research from the late nineteenth century until the present day with an emphasis on observational studies. We reviewed research on tropical cyclone climatology, genesis indices, intraseasonal-to-centennial variability and trends, tropical cyclone structure, and tropical cyclone theory.

We would like to suggest the following future directions for research:

1. Study of extremely deadly cyclones in North Indian Ocean. The deadliest tropical cyclones of the past 40 years, Cyclone 02B and Cyclone Nargis, both resulting in ∼130,000 fatalities, happened in the North Indian Ocean. Unfortunately, research on cyclones in this region is very limited. There is an urgent need for in-depth research to help save lives in this highly-populated region.

2. Storm-scale high-resolution reanalysis. The latest ERA5 reanalysis has a 0.25° horizontal resolution and can resolve, for the first time, the eyes of tropical cyclones. A higher resolution reanalysis incorporating all aircraft reconnaissance data and other datasets would significantly improve our knowledge and understanding of tropical cyclone eye dynamics, and the physical mechanisms of rapid intensification.

3. Paleo-cyclone data for the past 2000 years. These data are important for an improved understanding of tropical cyclone variability associated with global climate change as well as decadal and multi-decadal variability. We suggest that an international project be developed to promote and integrate all of the research efforts currently being undertaken in different countries. The goal of this project would be the release of a high-quality inter-calibrated paleo-cyclone dataset.

4. New physics for genesis indices and maximum potential intensity models. As reviewed in Section 2.a, current indices exhibit large regional discrepancies, which can commonly reach up to ±50%. These indices also show an equatorward bias. New physical understanding is needed to improve genesis indices and maximum potential intensity models. These models are important for short-term and long-term forecasts of tropical cyclone activity.

5. Vortex-stratosphere feedback in tropical cyclone forecast models. Tropical cyclone intensity forecasts still lag behind tropical cyclone track forecasts in terms of forecast skills, which strongly affects decision making for evacuations and thus life and property losses. We believe that it is important to test the effects of vortex-stratosphere feedback on tropical cyclone intensity forecasts using operational forecasting models. Currently, the stratosphere is often coarsely treated in models. Improving the stratosphere in models may induce a more realistic vortex-stratosphere feedback, and better tropical cyclone intensity forecasts.

Tropical cyclones are one of the deadliest and costliest natural disasters on Earth. Right now, most of the Regional Specialized Meteorological Centers lack support for model development. It is important that government fundings are provided to support a limited number of highly qualified researchers, who could focus on model development and improving real-time forecast capability. Improved forecast skills will lead to reduction in fatality and property damage.

Acknowledgements

Part of this work was done by TQ when working in the Department of Geography, The Ohio State University. P. Klotzbach would like to acknowledge support from the G. Unger Vetlesen Foundation. We would like to thank Mike Chenoweth and Scott Power for sharing their reconstructed tropical cyclone activity datasets.

Disclosure statement

No potential conflict of interest was reported by the author(s).