Volume 125, Issue 6 e2019JD031515
Research Article
Free Access

The Stationary Banding Complex and Secondary Eyewall Formation in Tropical Cyclones

Anna Vaughan

Corresponding Author

Anna Vaughan

School of Earth Sciences, University of Melbourne, Melbourne, Victoria, Australia

Now at Department of Earth Sciences, University of Cambridge, Cambridge, UK

Correspondence to: A. Vaughan,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing

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Kevin J. E. Walsh

Kevin J. E. Walsh

School of Earth Sciences, University of Melbourne, Melbourne, Victoria, Australia

Contribution: Conceptualization, Methodology, Resources, Writing - review & editing, Supervision, Funding acquisition

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Jeffrey D. Kepert

Jeffrey D. Kepert

Bureau of Meteorology, Melbourne, Victoria, Australia

Contribution: Conceptualization, Methodology, Resources, Writing - review & editing, Supervision

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First published: 25 February 2020
Citations: 4

Abstract

89 GHz passive microwave satellite data are used to develop a five year climatology of the incidence and morphology of the stationary banding complex in tropical cyclones and quantify changes in convective morphology prior to secondary eyewall formation. The stationary banding complex is shown to be present in 39% of passive microwave overpasses. Morphology varies substantially between tropical cyclones, with crossing angles ranging from 0.19° to 61.78° and azimuthal extents from 0.29 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0001 to 4.02 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0002 radians. Variations in the incidence and geometry of the stationary banding complex are observed in different environmental conditions and geographic locations. For 84 secondary eyewall formation events included in the sample, a stationary banding complex is observed within 6 hr of the secondary eyewall developing in 79% of cases. Within 12 hr prior to secondary eyewall formation, the crossing angle is significantly lower than its sample median, while the azimuthal extent is higher than its sample median. These results demonstrate that secondary eyewall formation is (most) often preceded by the formation and axisymmetrization of a stationary banding complex.

Key Points

  • A stationary banding complex is observed in 39% of passive microwave images of tropical cyclones
  • A stationary banding complex is observed within 6 hr of secondary eyewall formation in 79% of events
  • Stationary banding complex crossing angle (azimuthal extent) is significantly lower (higher) within 12 hr of secondary eyewall formation

1 Introduction

Understanding the incidence and dynamics of variations in the convective structure of tropical cyclones (TCs) is vital for improving forecasting of intensity (Dvorak, 1975; Velden et al., 2006), size (Huang et al., 2012), storm surge (Irish et al., 2008), wind radii (Knaff et al., 2014), and surface wave height (Lazarus et al., 2013). Two frequently observed changes in convective morphology are Secondary Eyewall Formation (SEF; Willoughby et al., 1982) and the development of a stationary banding complex (SBC; Willoughby et al., 1984). SEF occurs when outer rainbands coalesce to form a new eyewall concentric to the existing inner eyewall, known as a secondary eyewall (SE). An SBC is a mesoscale Wave Number 1 convective asymmetry that remains quasi-stationary relative to the vortex. This asymmetry consists of one dominant rainband known as the principal rainband, which is separated from the inner core by a convection free moat. Smaller rainbands termed the secondary rainbands may be joined to the edges of the principal rainband. Schematics of these configurations are shown in Figure 1.

Details are in the caption following the image
Schematic diagrams of 89GHz brightness temperature illustrating different convective morphology in TCs, showing (a) spiral banding, (b) a stationary banding complex (SBC) and (c) concentric eyewalls.

During SEF, TCs often exhibit increases in size (Bell et al., 2012; Huang et al., 2012) and integrated kinetic energy (Maclay et al., 2008), and often changes in intensity also (Sitkowski et al., 2011; Willoughby & Black, 1996). Understanding this process is therefore vital from the perspective of operational forecasting, yet SEF remains difficult to predict (Kossin & Sitkowski, 2009, 2012; Kossin & DeMaria, 2016), and the dynamical processes responsible for the development of the SE are not well understood (Wu et al., 2016).

It is well established that the SE forms from convection in preexisting spiral rainbands (e.g., Hawkins & Helveston, 2004). Numerical simulations suggest that SEF is initiated by projection of rainband diabatic heating onto the azimuthal mean (Rozoff et al., 2012), vorticity accumulation in the outer rainbands (Judt & Chen, 2010), or boundary layer feedbacks in response to rainband heating and vorticity anomalies (Huang et al., 2012; Kepert, 2013; Zhang et al., 2017). Case studies of SEF events in hurricanes Rita (2005) (Bell et al., 2012; Didlake & Houze, 2011, 2013; Houze et al., 2007) and Earl (2010) (Didlake et al., 2018) used high-resolution Doppler radar observations to demonstrate that, in both of these cases, an SE developed from the axisymmetrization of a preexisting SBC. For both of these events, a strong midlevel mesoscale inflow jet developed in the downshear left quadrant, descending into the boundary layer and creating a local vorticity maximum at the radius of the incipient SE. Didlake et al. (2018) suggested that this jet acts to accelerate the tangential circulation in the downshear left quadrant, after which SEF is triggered by axisymmetric processes. Qiu and Tan (2013) observed a similar inflow pattern in a numerical simulation, suggesting that this operates in conjunction with axisymmetric boundary layer mechanisms to trigger SEF by enhancing inflow on the opposite side of the TC. This pathway to SEF has been observed in other numerical simulations (Fang & Zhang, 2012; Zhang et al., 2017).

Together, this previous work strongly suggests a relationship between the SBC and SEF. Despite this, it remains unclear how rainband morphology varies prior to SEF climatologically. Quantifying this variation is difficult as no previous work has examined the climatological incidence or morphology of the SBC. It is well understood that the SBC is oriented relative to the direction of the deep-layer environmental shear, with convective cells developing in the downshear right quadrant, propagating down the band and dissipating in the downshear left quadrant (e.g., Barnes et al., 1983; Corbosiero & Molinari, 2003). SBC formation has been attributed to shear-induced asymmetries in potential temperature and vorticity induced by the vortex tilt (Riemer & Montgomery, 2011; Riemer, 2016; Willoughby et al., 1984). Understanding of the structure and morphology of individual bands is derived either from case studies (Barnes et al., 1983; Houze et al., 2006; Powell, 1990a, 1990b; Tang et al., 2018; Wang et al., 2018), or composite profiles of microphysical structure that do not capture the morphology of individual bands (Cecil & Zipser, 2002; Cecil et al., 2002). To date, studies of rainband geometry have been limited to case studies of individual rainbands using airborne Doppler radar (Barnes et al., 1983; Didlake et al., 2018; Hence & Houze, 2008; Powell, 1990a) or small samples of rainbands using land-based radar (Senn et al., 1957).

This study aims to clarify the role of the SBC in SEF by developing the first climatology of SBC formation and morphology. Specifically, we aim the following:
  1. Quantify the climatological incidence of SBC formation, and document how this varies geographically.
  2. Quantify variations in SBC morphology.
  3. Establish the incidence of the SBC and variations in morphology at different times prior to SEF.

Section 2 describes the data set used to identify SBCs and SEs and the analysis methodology. Section 3 presents a climatology of SBC incidence and formation, with morphology discussed in section 4. These results are used in section 5 to quantify changes in rainband morphology prior to SEF. Finally, a discussion and conclusions are presented in section 6. Methodology and results are based on those outlined by Vaughan (2018).

2 Data Set and Methodology

2.1 Data Set

2.1.1 Passive Microwave Data Set

A 5-year TC centered Passive Microwave (PMW) data set is used to identify SEs and SBCs. Raw 85–92 GHz data are taken from the NASA Precipitation Processing System STORM archive (National Aeronautics and Space Agency, 2018) using level 1C products for the Global Precipitation Mission Microwave Imager (GMI; Hou et al., 2014), Advanced Microwave Scanning Radiometer 2 (AMSR-2; Maeda et al., 2016), and the Special Sensor Microwave Imager/Sounder (SSMIS; Hollinger et al., 1990). Data of 85–92 GHz are suitable for viewing convective morphology as this frequency range is unaffected by the upper level cirrus canopy that obscures infrared observations (Spencer et al., 1989) and has been used to identify SEs in previous climatologies (Hawkins & Helveston, 2004; Kuo et al., 2009; Yang et al., 2013).

A limitation of PMW imagery is that no PMW instruments are in geostationary orbit, resulting in irregular spatial and temporal coverage. Together, the constellation of instruments used here gives a mean revisit time of 4.20 hr for this data set. Given that the structure of an SBC evolves on a timescale of at least 6 hr (Tang et al., 2018; Wang et al., 2018) and SEs on a timescale of at least 12 hr (Sitkowski et al., 2011), this temporal resolution is sufficient for this study. Swath widths for these six instruments range from 930–1,700 km, sufficient to cover the entire rainband field in a majority of cases.

For each swath in the raw data set, the International Best Tracks for Climate Stewardship (IBTrACS; Knapp et al., 2010) data set is used to identify any TCs with a center fix within the swath and intensity greater than 65 kts at the time of the satellite overpass. Both the horizontally and vertically polarized brightness temperature data for each TC contained within the swath are regridded to a 1,500 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0003 1,500 km Cartesian grid centered on the TC at 2 km resolution using bicubic spline interpolation. The choice of 2 km resolution is made to be consistent with other PMW image archives, which have a resolution of 1–2 km (Knapp, 2008; Turk et al., 1999). It is noted that all instruments are recalibrated to 89 GHz using histogram matching in the raw data set (Berg et al., 2016), eliminating uncertainty due to frequency differences (Yang et al., 2014).

False color composites are produced from the raw channels following a technique similar to that outlined by Lee et al. (2002). The red (R), blue (B), and green (G) channels of the 89 GHz satellite images are determined according to the following equations.
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0004
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0005
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0006
where urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0007 is the 89 GHz vertically polarized brightness temperature, urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0008 is the 89 GHz horizontally polarized brightness temperature channel, and urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0009 is the 89 GHz polarization corrected temperature (PCT), defined by (Spencer et al., 1989)
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0010
Identifying the extent of rainbands relies on determining which pixels in each image are classified as raining. As a urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0011 of less than 255 °K has been established a threshold for precipitation (Spencer et al., 1989), a further constraint is imposed that
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0012
Examples of the resulting PMW images are shown in Figure 2. In these images, red pixels indicate areas of rain, while green and blue indicate low-level warm clouds or the underlying surface. Prior to classification, each image is manually checked and rejected if the entire rainband field is not included in the swath or any part of the TC is over land.
Details are in the caption following the image
Examples of (a,b,c) SBCs and (d,e,f) SEs identified in 89GHz PMW imagery, for (a) TC Amanda at 01:29Z May 26. 2014, (b) TC Bruce at 23:34Z Dec. 21, 2013, (c) Typhoon Noul 22:15Z May 9, 2015, (d) Typhoon Kilo 7:21Z Sep. 5, 2015, (e) TC Atsani 7:45Z Aug. 18, 2015, (f) Typhoon Meranti 20:26Z Sep. 13, 2016. White dashed lines on images indicate the location of the SBC or SE.

2.1.2 Environmental Conditions

To quantify the large-scale environmental conditions at the time of each image, the current maximum intensity, maximum potential intensity, and deep-layer (850–200 hPa) shear magnitude are linearly interpolated to the time of each overpass. Maximum intensity data are taken from the IBTrACS data set (Knapp et al., 2010). Maximum potential intensity and deep-layer shear magnitude are taken from the Statistical Hurricane Intensity Prediction Scheme (SHIPS; DeMaria et al., 2005). Within this data set, maximum potential intensity is calculated following the definition in Emanuel (1986). Deep-layer shear magnitude is averaged over the TC from 200–800 km radius.

2.2 Methodology

The convective morphology of all images for TCs globally between 2012 and 2016 is analyzed, for a total for 3,881 individual classifications.These 5 years are chosen as they correspond to the launch of the AMSR-2 instrument in 2012 and the end of availability of SHIPS data in 2016. Each TC is classified manually using an objective classification scheme. A classification consists of three steps: SE identification, SBC identification, and rainband identification. This scheme is manually implemented using a matlab pipeline. The analyst is sequentially shown each image and prompted to classify it as SE/SBC based on the criteria outlined below. For SBC cases, the extent of the rainband is manually identified on the image to allow the geometry to be quantified.

2.2.1 Eyewall Classification

The TC is classified as either containing an SE or not containing a secondary eyewall (NSE). An SE is defined as a quasi-circular ring of convection with urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0013 K around the inner eyewall that is at least 2/3 complete with a clear moat. Although these thresholds are somewhat arbitrary, this definition is similar to that used in previous PMW climatologies of SEF (Hawkins & Helveston, 2004, 2008; Kossin & Sitkowski, 2009; Kuo et al., 2009; Sitkowski et al., 2011). Examples of images classified as SE are shown in Figures 2d–2f. Although recent work has used fully automated techniques to identify SEs (Yang et al., 2013), extensive testing demonstrated that brightness temperature averaging missed large numbers of SEs in smaller and asymmetric systems and was therefore deemed unsuitable for this study.

2.2.2 SBC Classification

Each image is classified as either containing an SBC (SBC) or not containing an SBC (NoSBC). The seminal work of Willoughby et al. (1984) defined an SBC as “a group prominent spiral rainbands that maintains a fixed position relative to the vortex, usually on the east side.” As part of this study, multiple classification techniques were trialed using computer vision methods to identify the SBC; however, these proved unsuitable given the wide range of TC sizes, SBC presentations, and interactions with other elements of the convective structure. A series of criteria are therefore chosen to objectively identify regions of convection corresponding to an SBC as defined by Willoughby et al. (1984).

For the purposes of this study, an SBC is defined as a Wave Number 1 convective asymmetry with urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0014 K that satisfies the following four criteria:
  1. The SBC has a length to width ratio greater than 2:1 and spiral geometry. Here the width of a rainband is defined as the distance across the widest point of the principal band and the length the distance from the upwind to downwind end of the band.
  2. The SBC is separated from the inner core by a clear moat along at least 2/3 of the band length.
  3. The structure of the SBC consists of one principal band, which all other bands are attached to.
  4. The SBC is either attached to the inner core convection surrounding the eyewall or separated by a narrow convection free moat.

Criteria 1 and 2 exclude cases where asymmetric convection is observed that does not have a clear spiral structure and is not separated from the inner core. Criterion 3 is necessary to exclude groups of rainbands without a dominant principal band. Finally, Criterion 4 excludes prominent outer convective complexes, which may meet the asymmetry and size criteria but are distinct from the SBCs documented in previous observational work (Didlake & Houze, 2013; Tang et al., 2014; Willoughby et al., 1984).

Examples of images classified as SBC are shown in Figures 2a–2c.

2.2.3 Geometry Classification

For those TCs classified as containing an SBC, the innermost edge of the SBC that is clearly separated from the eyewall is manually identified using a command line tool implemented in MATLAB. Examples of SBCs identified in the PMW data set are indicated by white dashed lines in Figures 2a–2c. The geometry of the band is then quantified by fitting a logarithmic spiral to the manually identified points using nonlinear least squares minimization.

A logarithmic spiral is described by the equation
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0015
where urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0016 and urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0017 are real constants. Although more sophisticated models have been developed to describe TC rainband geometry (Anthes, 1972; Yurchak, 2007), a logarithmic spiral provides the best fit to the widest variety of rainband types (Senn et al., 1957) and has been used to model rainbands in recent work (Kepert, 2018).
From the logarithmic spiral fit, two parameters are used to characterize each band: the azimuthal extent ( urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0018) and crossing angle ( urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0019). The azimuthal extent is defined by
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0020
with the sign reversed for Southern Hemisphere TCs, where urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0021 and urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0022 are the start and finish coordinates of the rainband and urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0023 is the number of complete revolutions of the band around the TC. The crossing angle is defined by
urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0024
with the sign reversed for Southern Hemisphere TCs. This provides a measure of the circularity of the band, where 0° is circular and 90° is a radial straight line. In the context of SEF, these parameters capture the extent to which vorticity and diabatic heating project onto the azimuthal mean and the degree to which the band has axisymmetrized as it evolves into an SE. These parameters are preferred over using the absolute length of the band as they are independent of the absolute vortex size.

2.2.4 Kernel Density Estimation

Kernel density estimation (KDE) is used to compare the joint distributions of rainband crossing angle and azimuthal extent for TCs in different basins and at different stages prior to SEF. This method provides an estimate of the probability distribution of a random variable (Silverman, 2018) and is here used with a Gaussian kernel and implemented using the python seaborn library.

3 Climatology of SBC Formation

To avoid uncertainty in the timing of stationary banding complex formation (SBCF) events due to the irregular temporal resolution of the PMW data set, an SBCF event is defined as a sequence of two PMW images within 6 hr where the first is classified as NoSBC and the second as SBC. The second image in the sequence, that is, the first image classified as SBCF, is then classified as an SBCF data point. Similarly, a NoSBCF event is defined as a sequence of two PMW images within 6 hr where neither image is classified as containing an SBC. Here the NoSBCF event point is taken as the second image. Using these definitions, a total of 318 SBCF and 1,730 NoSBCF events are included in the data set.

Geographic locations of SBCF events are shown in Figure 3a. A total of 1,506 PMW images contain an SBC, comprising 39% of all PMW overpasses. In this analysis, differences in morphology are considered by basin for the North Atlantic, Eastern Pacific, Western Pacific, South Indian Ocean, and South Pacific. As only 93 PMW overpasses are included in the North Indian Ocean, this basin is not included. Percentages of passes with an SBC and total sample numbers for each basin are summarized in Table 1. The overall incidence of passes with an SBC does not vary significantly between basins, ranging from 42% in the Western Pacific basin to 35% in the Southern Indian Ocean. There is a small but significant difference in event latitudes, with a median of 18.17° for SBCF and 19.58° for NoSBCF, although the physical reasons for this difference is not known.

Details are in the caption following the image
Geographic distributions of events included in the sample for (top) SBCF events and (bottom) SEF events.
Table 1. SBC Statistics by Basin, Where urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0025 Is the Crossing Angle and urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0026 is the Azimuthal Extent
Basin Total images %SBC Median urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0027 Median urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0028
Western Pacific 1,554 42% 10.42° 1.48 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0029 rad
Eastern Pacific 897 37% 12.24° 1.29 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0030 rad
South Indian Ocean 492 35% 12.19° 1.31 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0031 rad
South Pacific 355 39% 13.88° 1.26 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0032 rad
North Atlantic 490 36% 12.98° 1.21 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0033 rad
Total sample 3,881 39% 11.54° 1.37 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0034 rad

In order to assess the role of the large-scale environmental conditions in SBCF, the intensity, maximum potential intensity, and deep-layer shear distributions are compared for the SBCF and NoSBCF events. Differences between the two groups are significant at the 95% level for all parameters using a two-sample Kolmogorov-Smirnov (KS) test (Figure 4). SBCF events occur in an environment with higher median intensity (85 kts compared with 81.82 kts), higher median maximum potential intensity (133.65 kts compared to 124.99 kts), and lower median deep-layer shear (11.17 kts compared to 12.72 kts).

Details are in the caption following the image
Cumulative distributions comparing environmental conditions for the SBCF and NoSBCF groups, maximum intensity (top), deep-layer shear (middle), and maximum potential intensity (bottom) .

4 Geometry of SBCs

SBC geometry is analyzed with respect to the crossing angle and azimuthal extent parameters. Figure 5 shows the distribution of crossing angles for all SBCs in the sample. Crossing angles range from a minimum of 0.19° to a maximum of 61.78°, with a median of 11.54°. Examples of the extremes of the distribution are shown in Figures 5b and 5c.

Details are in the caption following the image
Crossing angle variation between SBCs, showing (a) crossing angle distribution for all bands in the sample, (b) example of an SBC with crossing angle of 0.89° in TC Funso at 05:43Z 26 January 2012. (c) Example of an SBC with crossing angle of 61.78° in Hurricane Ingrid at 07:59Z 15 September 2013.

Figure 6 shows the variation in crossing angle and azimuthal extent for PMW overpasses in different basins. TCs in the Western Pacific basin are significantly more likely to have lower crossing angle, with a median crossing angle of 10.42° compared to 12.24°, 13.88°, 12.19°, and 12.98° for the Eastern Pacific, South Pacific, South Indian Ocean, and North Atlantic basins, respectively. The crossing angle of an SBC varies depending on the current intensity, maximum potential intensity, and deep-layer shear magnitude. Differences in crossing angle for SBCs in different environmental conditions are analyzed by comparing geometry of rainbands in the first and fourth quartiles for each of these three parameters (Figure 8). Differences in crossing angle are significant at the 99% level for maximum intensity and deep-layer shear magnitude using a two-sample KS test. Higher maximum intensity occurs with lower crossing angle, with a median of 13.61° (10.28°) for values in the first (fourth) quartile. Lower crossing angle is also associated with lower shear, with a median of 10.40° (13.08°) for values in the first (fourth) quartile, respectively.

Details are in the caption following the image
KDE plots showing variations in SBC geometry by basin. (a) Total sample (ALL), (b) Eastern Pacific (EPAC), (c) Western Pacific (WPAC), (d) North Atlantic (NATL), (e) South Indian Ocean (SIO), and (f) South Pacific (SPAC).

The azimuthal extent distribution for all SBCs in the sample is shown in Figure 7. Values range from 0.29 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0037 to 4.02 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0038 radians, with a median of 1.37 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0039 radians. Examples of the extremes of the distribution are shown in Figures 7b and 7c). As for the crossing angle, differences in azimuthal extent are apparent between basins and in different large-scale environmental conditions. Azimuthal extents are significantly higher in the Western Pacific with a median of 1.48 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0040 radians compared to 1.29 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0041, 1.26 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0042, 1.31 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0043, and 1.21 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0044 radians for the Eastern Pacific, South Pacific, South Indian Ocean, and North Atlantic basins, respectively (Figure 6).

Details are in the caption following the image
Azimuthal extent variation between SBCs, showing (a) azimuthal extent distribution for all bands in the sample and (b) example of an SBC with azimuthal extent of 0.62 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0035 radians in TC Giovanna at 04:08Z 11 February 2012. (c) Example of an SBC with azimuthal extent of 4.02 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0036 radians in Typhoon Nangka at 03:27Z 9 July 2015.

Analyzing the differences between environmental conditions in the same manner as the crossing angle, significant differences in azimuthal extent are observed for SBCs in the first compared to fourth quartile of each of the three parameters (Figure 8). Higher maximum intensity and maximum potential intensity occur with significantly higher azimuthal extent, with first (fourth) quartile median values of 1.17 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0045 radians (1.60 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0046 radians) and 1.22 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0047 radians (1.38 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0048 radians) for maximum intensity and maximum potential intensity, respectively. Lower magnitude of deep-layer shear is associated with higher azimuthal extent, with median values of 1.50 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0049 radians (1.21 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0050 radians) for SBCs in the first (fourth) quartile. Note that higher intensity is associated with lower crossing angle, as expected, but this relationship is opposite for VMPI. We speculate that this is because most TCs do not reach their VMPI, due to factors such as wind shear that are not included in the formulation of potential intensity. For dynamical reasons, crossing angle should be more physically related to actual rather than potential intensity.

Details are in the caption following the image
KDE plots demonstrating variations in SBC geometry in different environmental conditions. First quartile of intensity (VMAX 1), fourth quartile of intensity (VMAX 4), first quartile of deep-layer shear (SHRD 1), fourth quartile of deep-layer shear (SHRD 4), first quartile of maximum potential intensity (VMPI 1), and fourth quartile of maximum potential intensity (VMPI 4).

5 Morphology Prior to SEF

A total of 147 unique SEF events are observed in the sample. As for SBCF events, to ensure that the time of SEF is accurate to within 6 hr, an SEF event is defined as a sequence of two PMW overpasses within 6 hr of each other classified as NSE and SE, respectively. For comparison, a NoSEF event is defined as a PMW image where no subsequent image contains an SE within 24 hr. Applying this criterion, 84 SEF events and 3,078 NoSEF events are included in the data set. Locations of the SEF events are shown in Figure 3b.

Given the discontinuous nature of the 89 GHz PMW coverage, it is challenging to track the evolution of rainbands leading up to SEF with the current data set. Images are therefore binned in different time periods prior to SEF to investigate the average structure of the TC at intervals prior to SEF. PMW overpasses within 24 hr of the SEF events described above are divided into four groups: 0–6, 6–12, 12–18, and 18–24 hr prior to SEF. Statistics of sample size and morphology for images in each of these four time periods are shown in Table 2. SBCs are observed in 79%, 55%, 60%, and 72% of events in 0–6, 6–12, 12–18, and 18–24 hr, respectively, compared to 35% in the No SEF group. In the 24 hr prior to SEF, a TC is therefore substantially more likely to be classified as SBC. The increase in percentage of events with an SBC at 18–24 hr is partially explained by TCs in the sample with multiple SEF events where data points are counted in both the 0–6 and 18–24 hr groups.

Table 2. SEF Statistics by Time Period
Time period Total SEF events Total images % events SBC Median urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0051 (°) Median urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0052 (rad)
0–6 hr 84 205 79% 9.72 1.68 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0053
6–12 hr 55 102 55% 11.18 1.79 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0054
12–18 hr 62 105 60% 10.33 1.45 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0055
18–24 hr 60 120 72% 12.37 1.40 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0056
No SEF 3,078 35% 12.14 1.30 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0057

The geometry of SBCs varies significantly from the sample median prior to SEF. KDE plots of band geometry at 0–12 hr, 12–24 hr, and cases where no SEF event occurs within 24 hr are shown in Figure 9. Differences between all distributions are significant at the 99% level using a 2-D KS test. SBCs observed within 12 hr of SEF have significantly higher azimuthal extent and lower crossing angle than those with no SEF within 24 hr, with median values of 9.89° and 1.69 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0058 radians, respectively. This compares to azimuthal extents and crossing angle medians of 11.67 and 4.5 for the 12–24 hr group, and 12.14° and 1.30 urn:x-wiley:jgrd:media:jgrd56090:jgrd56090-math-0059 radians for the noSEF group. The distribution at 12–24 hr is bimodal, suggesting that some TCs may maintain a coherent SBC configuration with high azimuthal extent and low crossing angle for longer than others prior to SEF.

Details are in the caption following the image
KDE plots of variation in SBC geometry at different time periods prior to SEF, from left to right: 0–12 hr prior to SEF, 12–24 hr prior to SEF, and cases with no SEF within 24 hr.

An observation from Figure 9 is that the NoSEF group contains cases that have high azimuthal extent and low crossing angle but do not go on to form SEs. In the context of previously proposed hypotheses that SEF is triggered when rainband heating and vorticity project substantially onto the azimuthal mean (Judt & Chen, 2010; Rozoff et al., 2012), it would be expected that these rainbands would develop into SEs. To assess why SEF does not eventuate in these cases, the maximum intensity, potential intensity, and deep-layer shear magnitude are compared for images in the 0–6 hr group, regardless of SBC morphology, and those in the NoSEF group with crossing angle (azimuthal extent) less than (greater than) the 50th percentile of values in the 0–6 hr group. Histograms of the distributions for the two groups for intensity, maximum potential intensity, and deep-layer shear are shown in Figure 10. Differences between distributions are modest but are significant at the 90% level using a two-sample KS test for all three parameters. Cases with no SEF have lower median shear and intensity and higher maximum potential intensity.

Details are in the caption following the image
Cumulative distributions comparing environmental conditions for the TCs with an SBC within 6 hours of SEF occurring and those with azimuthal extent greater than the 50th percentile of 0-6hr sample azimuthal extents and crossing angle less than the 50th percentile osf 0-6hr sample crossing angles, (top) intensity, (middle) deep-layer shear and (bottom) maximum potential intensity.

6 Discussion and Conclusion

Using 89 GHz PMW data, we compiled the first climatology of the formation and geometry of the SBC and used this to quantify changes in convective morphology prior to SEF. Specifically, we have demonstrated that 79% of SEF events followed the same pathway to SEF, with three stages consisting of the following:
  1. Formation of an SBC.
  2. Evolution of the SBC geometry to a configuration with high azimuthal extent and low crossing angle as compared to sample medians.
  3. Axisymmetrization of the SBC into an SE.

Results presented in sections 3-5 provided insight into the climatological characteristics of each stage of this process.

SBC formation is demonstrated to be largely independent of basin, unlike SEF, which is considerably more common in the Western Pacific than other basins (e.g., Hawkins & Helveston, 2004). SBC formation is more likely in TCs with higher intensity and potential intensity and lower deep-layer shear. The limited previous work that has investigated SBCF has suggested that the SBC forms as a result of the asymmetric vortex response to deep-layer shear (Willoughby et al., 1984; Riemer & Montgomery, 2011; Riemer, 2016). From this perspective, it would be expected that SBCF is more likely in an environment with stronger VWS. Although storm motion is also a contributing factor to convective asymmetry, this is second order to the effect of vertical shear (Corbosiero & Molinari, 2003; Thomsen et al., 2015) and is unlikely to play a role in the formation of the SBC (Riemer, 2016). This behavior is not observed in this study. Deep-layer shear values are significantly lower for cases in the SBCF group; however, SBCF is demonstrated to occur in a wide range of shear magnitudes (Figure 4, bottom). This suggests that further investigation of SBC formation mechanisms is required using high-resolution data sets or numerical simulations.

Considerable variation is observed in the geometry of SBCs. SBCs in TCs with higher intensity in an environment with lower deep-layer shear and higher potential intensity have significantly lower crossing angle and higher azimuthal extent. The dynamical reasons for these variations in azimuthal extent can be understood in terms of vortex tilt. A vortex in deep-layer shear tilts downshear, inducing a positive low-level potential temperature and vorticity anomaly downshear and negative anomalies upshear (Riemer, 2016). Higher maximum potential intensity is associated with more favorable storm averaged conditions for deep convection, enhancing the likelihood of convective development on the drier upshear side of the vortex. A vortex in a lower shear environment has reduced tilt, again reducing the dry anomaly upshear and allowing for the SBC to wrap further around the TC. The role of environmental conditions in determining the crossing angle is not immediately clear. The crossing angle of the SBC is likely related to the topology of the low-level flow controlling where developing convection is advected within the vortex (Chen et al., 2018).

Our statistical results strongly support the hypothesis that SEF is influenced by the development and morphology of an SBC. This is the first time that a preferred convective pathway to SEF has been documented. It is instructive to consider these results in the context of previously proposed hypotheses of the dynamics of SEF. The formation of an SBC within 6 hr of SEF in 79% of cases strongly suggests that asymmetric processes are important in SEF, for instance stratiform processes (Didlake et al., 2018) and asymmetric boundary layer inflow forcing (Qiu & Tan, 2013). The preference for higher azimuthal extent in the 6 hr prior to SEF provides observational evidence that the projection vorticity accumulation and diabatic heating within the rainbands onto the azimuthal mean may contribute to the development of the SE, as previously observed in numerical simulations (Judt & Chen, 2010; Rozoff et al., 2012). It is noted, however, that further work is required to explain why many SBCs with high circularity and azimuthal extent do not ultimately evolve into SEs. These results strongly suggest that symmetric processes such as VRWs (Montgomery & Kallenbach, 1997) and beta skirt axisymmetrization (Terwey & Montgomery, 2008) alone are insufficient to explain SEF in these cases, though it is possible that they operate in cases where no SBC is observed or in conjunction with other asymmetric mechanisms. It is important to note that given the nature of this statistical analysis, it is only possible to state that there is a correlation between the SBC and SEF. Further work using numerical simulations would be required to establish whether the SBC causes SEF.

Future work is required to explore changes in morphology in cases where an SBC is not present prior to SEF and to extend the results presented in this study to a larger data set. Additional years of data are needed to strengthen the conclusion of this paper and to ensure that the statistical distributions shown here reach full statistical stationarity. A fully automated rainband classification algorithm capable of fitting log spirals to all rainbands as opposed to only SBCs has been developed using a combination of a convolutional neural network and unsupervised clustering (Vaughan, 2018). Though this algorithm currently has low accuracy, it is anticipated that future versions will be applied to further explore morphological evolution prior to SEF. In addition, composites of high-resolution Doppler radar data will be used to improve understanding of dynamical processes at each stage of SEF.

Acknowledgments

This research was partially supported through the funding from the Earth System and Climate Change Hub of the Australian Government's National Environmental Science Programme. The analyses were partly performed on the National Computational Infrastructure system, supported by the Australian Government. The authors would also like to thank the Australian Research Council Centre of Excellence for Climate System Science for funding to support this research. Data sets and software used in this research are available from https://doi.org/10.26188/5e668067dc607.