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--> --> -->Soundings inside TC eyes indicate that an inversion (typically 850-500 hPa) separates warm and dry air aloft from moist air below (Willoughby, 1998), and the warm air within the eye thus contributes to the characteristic feature of a warm core (La Seur and Hawkins, 1963; Hawkins and Rubsam, 1968; Hawkins and Imbembo, 1976). (Durden, 2013) showed by analyzing a relatively small number of dropsonde eye profiles extending above 300 hPa that the maximum temperature anomaly can be observed at varying levels, ranging from 760 to 250 hPa. Correlations exist between the maximum temperature anomaly level and TC intensity, upper-level divergence, environmental instability, and storm size. (Durden, 2013) also found there are multiple maxima of temperature anomalies in some cases, and these maxima are located predominantly at middle and upper levels. (Stern and Zhang, 2016) used high-altitude dropsondes and a high-resolution numerical simulation to investigate the warm-core structure of Hurricane Earl, also indicative of two maxima of perturbation temperature at 4-6 and 9-12 km, respectively. They further pointed out that the intensity of these two maxima is sensitive to the choice of the reference state, as mentioned in (Durden, 2013). Different from the findings in (Durden, 2013) and (Gao et al., 2017), (Stern and Zhang, 2016) showed no systematic relationship between the warm-core level and either intensity or intensity change.
Another significant thermodynamic structure of the eye is high equivalent potential temperature harbored in the lowest few kilometers (Hawkins and Imbembo, 1976; Jorgensen, 1984b; Willoughby, 1998; Montgomery et al., 2006; Sitkowski and Barnes, 2009; Barnes and Fuentes, 2010; Dolling and Barnes, 2012). Such high-entropy air has been proposed in some studies to facilitate the boost of convection in the eyewall if mixed into the eyewall region (Braun, 2002; Persing and Montgomery, 2003; Montgomery et al., 2006; Cram et al., 2007; Barnes and Fuentes, 2010). (Persing and Montgomery, 2003) and (Montgomery et al., 2006) argued that it is possible for a storm to achieve superintensity, a circumstance where the maximum wind speed in the eyewall surpasses the estimated maximum potential intensity (Emanuel, 1986, 1988; Holland, 1997), under the condition that the transport of high-entropy air from the storm eye to the eyewall becomes abundant. However, (Bryan and Rotunno, 2009) and (Barnes and Fuentes, 2010) believed that the role of such entropy transport in maximum storm intensity is very limited because of the relatively small volume of eye excess energy.
Downdrafts are a representative dynamic feature of the TC eye, which have been demonstrated to predominantly contribute to the formation of the warm core (Shapiro and Willoughby, 1982; Schubert et al., 2007; Vigh and Schubert, 2009; Stern and Zhang, 2013a, 2013b). Mean sinking motion inside the eye is generally small. The region of maximum subsidence is radially broad in the beginning of rapid intensification, and later tends to be concentrated along the eye/eyewall interface, with the mean descent increasing up to 10-20 cm s-1 as the storm further intensifies (Liu et al., 1997; Stern and Zhang, 2013a, 2013b). Moreover, (Schubert et al., 2007) argued that subsidence just inward of the eyewall tends to become stronger in a TC with a larger eye or with higher inertial stability.
Apart from the dynamical and thermodynamic structures noted above, the geometric features of TC eyes have also attracted an increasing level of attention. Satellite and radar observations show that TC eyes are regularly characterized by rotating smooth shapes (e.g., circular and elliptical shapes; Mitsuta and Yoshizumi, 1973; Kuo et al., 1999; Reasor et al., 2000; Oda et al., 2005; Aberson et al., 2006; Barnes and Barnes, 2014), while polygonal eyes in the shapes of hexagons, pentagons, squares, and triangles are also observed (Lewis and Hawkins, 1982; Muramatsu, 1986; Hendricks et al., 2012). It has been indicated that the behavior of elliptical eyes is closely associated with wavenumber-2 vortex Rossby waves (Montgomery and Kallenbach, 1997) resulting from barotropic instability (Kuo et al., 1999; Kossin et al., 2000; Reasor et al., 2000; Wang, 2002; Oda et al., 2005). High-wavenumber vortex Rossby waves related to barotropic instability and the breakdown of the eyewall ring of elevated vorticity constitute the most likely driving mechanism for polygonal eyes (Schubert et al., 1999; Menelaou et al., 2013). The asymmetries associated with both elliptical and polygonal eyes have been shown to have an impact on TC structure and intensity. (Schubert et al., 1999) found in an unforced 2D framework that barotropic instability and the inward mixing of vorticity from the eyewall into the eye tend to decrease the maximum tangential wind. In contrast, (Menelaou et al., 2013) showed that the asymmetric structures regarding the polygonal eye act to lower the wind speed at the radius of the maximum wind, while they can accelerate the flow radially inside and outside of that location. (Kuo et al., 2016) examined the convective features associated with elliptical and polygonal eyes, showing that the shock-like boundary layer radial wind structure forces strong updrafts at the top of the boundary layer to produce deep convection at the edge of the major axis. In addition, eye size may give expression to some important structure and intensity change of TCs. After completing a concentric eyewall cycle, a TC often possesses larger eye size. Annular hurricanes (Knaff et al., 2003) have relatively bigger eyes (Wang, 2008), and sinking motion just inward of the eyewall is stronger in a larger eye such that a moat region generally occurs therein (Schubert et al., 2007). It has also been shown that a reduction in the eye area accompanies the intensification of TCs (Barnes and Barnes, 2014), and the rate of eyewall contraction is smaller in TCs with large eyes (Stern et al., 2015).
Since the geometric traits of eyes are important elements of the inner core of TCs, as documented above, and precisely reflect some essential aspects of TC structure and intensity change, which are critical to forecasts and numerical simulations of TCs, we investigate in the current study the geometric characteristics of eyes before TC landfall in South China. The TCs making landfall in south China are nearly those progressing in the South China Sea where 3.3 TCs formed per year on average (Chen et al., 2015). TCs forming in or moving into the South China Sea may experience intensity change before making landfall in South China during a very short period, due to the small basin size, thus compounding the difficulty of TC forecasting.
Figure1. TC tracks analyzed in this study, with different colors indicating the minimum sea level pressure. Red dots denote the locations of the ground-based radars at Yangjiang (YJ), Haikou (HK), and Guangzhou (GZ).Since the focus of this study is the use of radar reflectivity data to determine the geometric characteristics of TC eyes, we need to establish whether or not an eye is present. Following (Weatherford and Gray, 1988) and (Vigh et al., 2012), the presence of an eye is only validated if a circular, precipitating, inner-cloud feature (namely, an eyewall) subtends at least half of the candidate eye region. If the eyewall completely surrounds the eye region, a closed eye is reported. If the eyewall encircles at least half the eye region without breaks, an open eye is recognized. If the eyewall does not subtend at least half the eye, no eye is present. Although as mentioned above TC eyes may possess polygonal shapes, the eyes in the current samples are dominated by quasi-elliptical shapes. To discuss the geometric features of the eyes, we first need to fit the elliptical shapes of the eyes. Since a large reflectivity gradient exists near the interface of the eye and the eyewall (Liu et al., 1997), we can separate them from each other based on reflectivity values. Note that different reflectivity thresholds have been employed to determine the boundary between the eye and the eyewall, such as 10 (Jorgensen, 1984a; Corbosiero et al., 2005), 20 (Hazelton and Hart, 2013), and 25 dBZ (Barnes and Barnes, 2014). In this study, 20 dBZ is used as the outer edge of the eyes. A least-squares method is used to fit the elliptical shape of the eyes based on 20-dBZ reflectivity contours. This fitting can not only illustrate the shape of a closed eye, but also facilitate the approximation of the shape of an open eye. Figure 2 shows examples of the fitted eye shapes of Typhoons Chanthu (2010) and Rammasun (2014). At 0230 UTC 22 July 2010, Chanthu had an oval eye at z=5 km, with its maximum diameter oriented northwest-southeast (Fig. 2a). At 0500 UTC 18 July 2014, Rammasun also showed an elliptical eye at z=4 km, but with the maximum diameter oriented northeast-southwest (Fig. 2b). Among the 133 samples, no TCs were undergoing concentric eyewall replacement. The geometric features of eyes including size, the maximum and minimum diameter, and roundness, are examined in this study. The eye roundness can be measured by the eye roundness value (ERV; Barnes and Barnes, 2014), which is calculated as \begin{equation} {\rm ERV}=\sqrt{1-\left(\dfrac{b}{a}\right)^2} , \ \ (1)\end{equation} where a and b are the semimajor and semiminor axes of the fitted ellipse, respectively. Lower ERVs correspond to more circular eyes. As shown in Figs. 2a and b, the ERVs of Typhoons Chanthu (2010) and Rammasun (2014) are 0.74 and 0.53, respectively, suggesting the eye of Rammasun (2014) is more circular than that of Chanthu (2010).
Figure2. Radar reflectivity (dBZ) of (a) Typhoon Chanthu (2010) at z=5 km at 1830 UTC 21 July 2010 and (b) Typhoon Rammasun (2014) at z=4 km at 2100 UTC 17 July 2014. The right-hand panels show blow-ups of the eye region reflectivity of the two TCs, with a red ellipse indicating the fitted eye. Lines a and b represent the semimajor and semiminor axes, respectively. See text for details.The intensity and locations of tropical cyclones at 0000, 0600, 1200 and 1800 UTC are derived from the China Meteorological Administration best-track dataset (Ying et al., 2014). If the radar detection is not at these standard synoptic times, a linear interpolation of best-track intensity is used to estimate the corresponding TC intensity. To represent the environments associated with the TCs, the Remote Sensing Systems optimally interpolated SST data are employed to describe the SST averaged inside the 200-km radius from the storm center; and the NCEP final reanalysis is used to calculate the 200-850-hPa vertical wind shear (VWS), which is averaged over the area between 200 and 800 km from the TC center, and to compute the mid-tropospheric relative humidity averaged between 700 and 500 hPa for an annulus similar to that used for VWS.
3.1. TC intensity, intensity change, translation, and environments
Figure 3 depicts the characteristics of intensity, intensity change, and movement of the 133 samples. The intensity of the majority of the samples ranges from 950 to 990 hPa (Fig. 3a), consistent with the finding in (Vigh et al., 2012), which shows that most Atlantic TC eyes form at minimum central pressure between 997 and 987 hPa. Nearly half of the samples show little intensity change (Fig. 3b), and 16 and 22 samples are undergoing rapid intensification (6-h pressure tendency <-11 hPa) and weakening (6-h pressure tendency >11 hPa), respectively. More than 60 samples move at a translation speed of 4-6 m s-1, and more than 30 samples have relatively slower translation speeds of smaller than 2 m s-1 (Fig. 3c). This is also accordant with the result in (Vigh et al., 2012), suggesting that eyes form over a wide band of TC movement speeds with a typical range of 2.5-5.8 m s-1. The selected TCs are generally steered by the easterly flow of the subtropical high (not shown), thereby progressing northwestward (Fig. 3d).
Figure3. Frequency distributions of (a) minimum surface level pressure (units: hPa), (b) 6-h pressure tendency (units: hPa), (c) translational speed (units: m s-1), and (d) direction of the TCs.
Figure4. Frequency distributions of (a) SST (units: °C), (b) 700-500-hPa relative humidity (units: %), (c) 850-200-hPa vertical wind shear magnitude (units: m s-1) and (d) direction.Most of the SSTs in the vicinity of the storm's circulation exceed 29°C, with a mean value of 29.6°C (Fig. 4a), agreeing with the mean SST for eye formation indicated in (Vigh et al., 2012). Because of moist flow with respect to the South China Sea monsoon in summer, the highest frequency of TCs occurs in an environment with a 700-500-hPa relative humidity between 75% and 85%, with a mean value of 78% (Fig. 4b). The magnitude of 850-200-hPa VWS associated with the TCs is concentrated between 4 and 12 m s-1, with a mean value of 7.9 m s-1 (Fig. 4c), indicative of moderate-to-strong VWS. Figure 4d further shows the nature of a typical VWS in the South China Sea during summer——that is, northeasterly shear prevailing due to the southwesterly monsoon flow in lower layers.
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3.2. Geometric characteristics of TC eyes
As noted in prior studies, eye size and its change are important structural features of TCs, and are therefore discussed here first. As a TC intensifies, enhanced eyewall convection drives compensating downdrafts and hence increase the warming in the eye (Zhang et al., 2002; Stern and Zhang, 2013a, 2013b), which in turn leads to the central pressure dropping (Willoughby, 1998). As a result, tightening of the pressure gradient across the wind maximum makes the wind increase at, and inward from, the radius of maximum wind, such that the eyewall and eye contract (Willoughby, 1998). Figure 5 shows boxplots of eye areas at z=2, 4 and 6 km, categorized according to the TC framework set out by the China Meteorological Administration TC category. The median and mean eye area reduce with TC intensity, except for STY storms. This seems to agree with conventional wisdom that eyewalls generally shrink during intensification. However, the median and mean eye size increase form TY to STY storms. Similar eye size distributions also appear in (Kimball and Mulekar, 2004), who showed that the eye radius median of category-2 hurricanes was much larger than that of category-5 hurricanes, while the median increased from category 3 to category 4. In fact, as pointed out in (Stern and Nolan, 2009), a relationship between eye size and TC intensity would only be expected for a given TC. A study of diverse TC samples by (Hazelton and Hart, 2013) hence suggests almost no relationship between the eye size and the storm intensity.
Figure5. Boxplots of the eye area at z=2, 4, and 6 km, categorized according to the framework of the China Meteorological Administration. The mean and median are given by the dot and the horizontal line within the box, respectively, and the top and bottom edges of the box indicate the 25th and 75th percentiles, respectively. STS, TY, STY, and Super TY indicate severe tropical storm, typhoon, severe typhoon, and super typhoon, respectively. See text for further details of the TC categories.Figures 6a and b depict the vertical distributions of eye areas and the major axis normalized by corresponding values at z=2 km, respectively, mostly indicative of the vertical change in eye size. The most visible characteristic seen in Fig. 6 is the eye size increasing with height. For example, the mean eye area increases from 2116 km2 at z=2 km to 2652 km2 at z=7 km, and the maximum eye area increases from 4485 km2 at z=2 km to 6487 km2 at z=7 km (not shown). This relationship of eye size at an upper level being larger than at a lower level is significant at the 95% confidence interval, except for the two levels at 4 and 5 km (not shown). Figure 6 also shows that the increasing rate of the mean eye area and major axis is relatively greater in upper layers (e.g., from 5 to 7 km). This vertical change in eye size qualitatively agrees with the outward slope of the eyewall, which has been long realized in many studies (Malkus, 1958; Shea and Gray, 1973; Stern and Nolan, 2009, 2011; Rogers et al., 2012; Hazelton and Hart, 2013; Stern et al., 2014; Hazelton et al., 2015). (Stern and Nolan, 2009) argued that the radius of maximum winds should be approximately an absolute angular momentum M surface, and the eyewall slope will increase with radius if such a slope is measured by the radius of maximum winds. The slope varies along any given M surface. As we move upward along an M surface, we are also moving outward (namely, the radius of maximum winds is increasing) due to the M surface flaring outward, and the eyewall slope will thus be increasing. As a result, the increasing slope of the eyewall in upper layers leads to a more significant increasing rate of eye size therein, as indicated in Fig. 6. In contrast, vertical M advection is mainly offset by the radial advection of M in the mid-tropospheric eyewall (Li et al., 2014, 2015), such that M does not change much and the M surface tends to be upright. Therefore, the eyewall slope and the eye size increase with height in the mid-troposphere is not significant, as noted above.
(Emanuel, 1986) and (Stern and Nolan, 2009) theorized that there is no relationship between eyewall slope and TC intensity, which was observationally evidenced in (Stern and Nolan, 2009) and (Stern et al., 2014). In contrast, observations in (Hazelton and Hart, 2013) showed a statistically significant relationship between the eyewall slope measured by the 20-dBZ contour and TC intensity, suggesting that the eyewall was more upright as the storm was more intense. Given that the vertical change in eye size is a qualitative indication of eyewall slope, the relationship between that vertical change and TC intensity is shown in Fig. 7. Figure 7a portrays the ratio of the eye area at z=7 km to that at z=2 km, which is indicative of the eye size change in the vertical direction. It is shown that the ratio does not correlate with TC intensity, which agrees with the findings in (Stern and Nolan, 2009) and (Stern et al., 2014). However, it is surprising that there is a weak relationship (correlation coefficient r=-0.25; p<0.05) between the ratio and vertical wind shear associated with the TCs (Fig. 7a). On closer inspection, that weak correlation appears to result from the notable outliers in particular combinations of small shear and large ratios. As indicated in Fig. 4c, the vertical shear of most of the TC samples is greater than 4 m s-1, demonstrating the typical environment of monsoon flow. If those outliers with shear less than 4 m s-1 are removed, no relationship between the vertical change in eye size and vertical wind shear is observed in typical monsoon environments (Fig. 7b).
Figure6. Boxplots of (a) the eye area and (b) the major axis normalized by the value at z=2 km. The mean is given by the horizontal line within the box, and the top and bottom edges of the box indicate the 25th and 75th percentiles, respectively.(Stern and Nolan, 2009) also pointed out that there should exist a linear dependence of eyewall slope on the radius. It is thus supposed that the increasing ratio of eye size in the vertical direction will linearly increase with radius. However, Fig. 8a shows no relationship between the vertical change in eye size and the eye size at z=2 km. This likely implies that the vertical change in eye size may be fundamentally different in some ways from other measurements of eyewall slope, such as the slope of the radius of maximum wind (Stern and Nolan, 2009; Stern et al., 2014). Figure 8b shows scatterplots of the vertical change in eye size versus the 6-h change in minimum central pressure. Clearly, there is no relationship between the vertical change in eye size and the intensity tendency. Nevertheless, the vertical change in eye size for those rapidly intensifying samples is on average smaller than those for rapidly weakening samples (Fig. 8b), which appears to provide support to the idea that convection in regions of increased inertial stability is favorable to the intensification of TCs (Hack and Schubert, 1986; Rogers et al., 2013, 2015; Hendricks et al., 2014).
Figure7. (a) Ratio of eye area at z=7 km to that at z=2 km versus the environmental vertical wind shear. (b) As in (a) except for samples with vertical wind shear less than 4 m s-1 excluded. The black solid lines show the best fit to the data, and colors indicate minimum sea level pressure ranges.
Figure8. Ratio of the eye area at z=7 km to that at z=2 km versus (a) the eye area at z=2 km, and (b) TC intensity change. The black lines indicate the best fit to the data.Figure 9 depicts the frequency distribution of the ERV. The ERV is characterized by a quasi-Gaussian distribution, except at z=2 km, with values of 0.5-0.7 dominating. The mean ERVs for 2-7-km layers are 0.56, 0.55, 0.55, 0.55, 0.56 and 0.54, respectively. Furthermore, a weak but still identifiable relationship between the ERV and the minimum sea level pressure is found (Fig. 10a), showing that more intense storms tend to be provided with rounder eyes. Such a relationship appears from lower to upper levels. As mentioned in previous literature, the appearance of an elliptical eyewall is hypothesized to be in association with unstable vortex Rossby waves within the eyewall (Kuo et al., 1999; Kossin et al., 2000; Reasor et al., 2000; Kossin and Schubert, 2001; Wang, 2002; Oda et al., 2005). The relationship between the eye circularity and the storm intensity discussed here seems to indicate that the magnitude of wavenumber-2 vortex Rossby waves in the eyewall region decreases with TC intensity, which is worth investigating in depth using other observations and numerical simulations. A weak and positive relationship between the circularity and the maximum eye diameter is also seen. Figure 10b shows that the ERV tends to increase with the maximum eye diameter (namely, the major axis of the fitted elliptical eye), indicating that the smaller the maximum eye diameter, the rounder the eye. However, no relationship exists between the ERV and the eye size (not shown).
Many previous studies have pointed out that the behavior of elliptical eyes is governed by wavenumber-2 vortex Rossby waves in the eyewall (Kuo et al., 1999; Kossin et al., 2000; Reasor et al., 2000; Wang, 2002; Oda et al., 2005). This is indirectly corroborated by the rotational distribution of the major axis of the fitted elliptical eye, as shown in Fig. 11. The almost even occurrence of the major axis orientation in the azimuth reflects the eye rotation associated with the azimuthal propagation of wavenumber-2 vortex Rossby waves in the eyewall.
Figure9. Frequency distributions for eye circularity in six layers.
Figure10. Circularity versus the (a) minimum sea level pressure and (b) major axis length of the fitted eye at z=2, 4, and 6 km. The solid lines indicate the best fit to the data.
Figure11. Frequency distributions for the eye major axis orientation.It is found that the median and mean eye area decrease with TC intensity, except for STY storms. This result resembles the eye size distributions found in (Kimball and Mulekar, 2004), which showed that the eye radius median of category-2 hurricanes was much larger than that of category-5 hurricanes, while the median increased from category 3 to category 4. As also noted in prior studies, the eye size increases with height. The increasing rate of eye size is relatively greater in upper layers, qualitatively agreeing with the increasing slope of the eyewall in the upper troposphere. The ratio of eye size change in the vertical direction is shown to not correlate with TC intensity, somehow evidencing no relationship between eyewall slope and storm intensity. Correspondingly, no relationship is seen between the ratio of eye size change in the vertical direction and the vertical wind shear, as the outliers of very small shear are excluded. Unlike results in previous studies, there is no relationship between the vertical change in eye size and the eye size. This likely signifies that the vertical change in eye size may be fundamentally different in some ways from other measurements of eyewall slope, such as the slope of the radius of maximum wind. There also exists no relationship between the vertical change in eye size and the intensity tendency. In addition, ERVs of 0.5-0.7 are most frequently observed. More intense TCs generally have more circular eyes.
There are some caveats to this study that are important to note. Radar calibration errors will influence the determination of eye area and roundness. The offset in time between the radar observations and the analysis variables from the best-track data or the NCEP final reanalysis could introduce errors. Although the eye geometric characteristics of TCs embedded in monsoon-associated vertical shear are preliminarily discussed in the current study, how the change in vertical wind shear impacts upon eye geometry needs further investigation. In the future, we intend to study the eye geometric features associated with vertical wind shear with different profiles using high-resolution numerical simulations.
