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    Plan view of ELDORA reflectivity data at 2-km altitude observed on 21 Sep 2005. Boxes outline data sections used in the analysis. Leg 1 is from 1642 to 1657 UTC, leg 2 is from 1741 to 1755 UTC, and leg 3 is from 1831 to 1841 UTC. Flight tracks corresponding to each leg are drawn as dotted and/or dashed lines. Visible satellite imagery from the Geostationary Operational Environmental Satellite-East (GOES-E) is shown in the background.

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    CFADs of radar reflectivity (in 3-dB bins) for (a) leg 1, (b) leg 2, and (c) leg 3. Frequencies are normalized by total number of data points. The outermost contour corresponds to 1% frequency. Inner contours increase at an interval of 7%, and shaded regions correspond to frequencies greater than 36%.

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    CFADs of vertical velocity (in 1 m s−1 bins) for (a) leg 1, (b) leg 2, and (c) leg 3. Frequencies are normalized by total number of data points. The outermost contour corresponds to 1% frequency. Inner contours increase at an interval of 7%, and shaded regions correspond to frequencies greater than 36%.

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    Positive, negative, and net vertical mass transport profiles for (a) leg 1, (b) leg 2, and (c) leg 3. Profiles are normalized by the maximum area-weighted positive transport value from leg 1.

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    Profiles of average divergence for (a) leg 1, (b) leg 2, and (c) leg 3.

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    (a) Azimuthally averaged field of radial velocity from leg 1. Average reflectivity values are overlaid as black contours (dBZ). (b) As in (a), but for tangential velocity. Positive values are cyclonic. (c) As in (a), but for vertical velocity. (d) As in (a), but for divergence.

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    Conceptual model of a squall line with a trailing-stratiform area viewed in a vertical cross section oriented perpendicular to the convective line. In the trailing stratiform rain region, ascending front-to-rear flow occurs within the cloud and descending rear inflow occurs below the cloud base. Adapted from Houze et al. (1989, their Fig. 1).

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    (a) Idealized pattern of normalized diabatic heat sources in a purely stratiform rainband. Adapted from Moon and Nolan (2010, their Fig. 5b). (b) Kinematic response in a vortex circulation to the idealized stratiform heat sources in (a). Arrows show radial and vertical velocity components of the response. Contours show tangential velocity component of the response with an interval of 0.5 m s−1. Adapted from Moon and Nolan (2010, their Fig 14a).

  • View in gallery

    (a) Azimuthally averaged field of radial velocity from leg 2. Average reflectivity values are overlaid as black contours (dBZ). (b) As in (a), but for tangential velocity. (c) As in (a), but for vertical velocity.

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    As in Fig. 9, but for leg 3.

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    (a) Vertical profiles of tangential momentum tendency [Eq. (1)] averaged between 90- and 124.8-km radius from leg 2. Individual terms and total are shown. (b) As in (a), but for terms averaged between 125.4- and 160.2-km radius.

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    Plan view of reflectivity at 2-km altitude. Each black dot represents the averaged convergence maximum at 4-km altitude along each radial from legs 1 and 2. The blue stars show release locations of dropsondes A–F. The axis coordinates are horizontal distance (km), where the origin is the center of the storm. Legs 1–3 are outlined by the dotted boxes.

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    (a) Composite of radial velocity from radially aligned cross sections of leg 1. The centers of the individual cross sections (denoted by the origin of the x axis) are located on the black dots in Fig. 12. (b) As in (a), but for tangential velocity. (c) As in (a), but for vertical velocity. (d) As in (a), but for relative vertical vorticity.

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    As in Fig. 13, but for leg 2.

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    (a) Vertical profiles of tangential momentum tendency from the composite fields (Fig. 13) of leg 1. Terms are averaged between −4.2 and 4.2 km along the x axis. Individual terms and total are shown. (b) As in (a), but for leg 2 composites from Fig. 14.

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    Skew-T diagrams of temperature profiles measured by dropsondes A–F from Fig. 12. The black line is air temperature and the gray line is dewpoint temperature. Release times for the dropsondes are at the bottom of each diagram.

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    (a) Plan view schematic of an organized rainband complex in a mature tropical cyclone. Reflectivity contours (20 and 35 dBZ) show embedded convective cells that collapse (dashed contours) and form stratiform precipitation traveling around the storm. The arrows represent tangential jets associated with each precipitation feature, with VT indicating the jet within the stratiform sector. (b) Schematic of the dynamics within a stratiform rainband [see the straight gray line in (a)]. Reflectivity contours are drawn. The line arrows represent vortex-scale motions associated with the overall storm, and the broad arrows represent mesoscale motions associated with the stratiform rainband. The broad arrows of the descending inflow are driven by two regions of a radial buoyancy gradient (∂B/∂r). The plus signs indicate regions of increasing tangential velocity by the secondary circulation. The circled region indicates the tangential jet (VT). Latent cooling and latent heating occur in the indicated regions.

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Dynamics of the Stratiform Sector of a Tropical Cyclone Rainband

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Abstract

Airborne Doppler radar documented the stratiform sector of a rainband within the stationary rainband complex of Hurricane Rita. The stratiform rainband sector is a mesoscale feature consisting of nearly uniform precipitation and weak vertical velocities from collapsing convective cells. Upward transport and associated latent heating occur within the stratiform cloud layer in the form of rising radial outflow. Beneath, downward transport is organized into descending radial inflow in response to two regions of latent cooling. In the outer, upper regions of the rainband, sublimational cooling introduces horizontal buoyancy gradients, which produce horizontal vorticity and descending inflow similar to that of the trailing-stratiform region of a mesoscale convective system. Within the zone of heavier stratiform precipitation, melting cooling along the outer rainband edge creates a midlevel horizontal buoyancy gradient across the rainband that drives air farther inward beneath the brightband. The organization of this transport initially is robust but fades downwind as the convection dissipates.

The stratiform-induced secondary circulation results in convergence of angular momentum above the boundary layer and broadening of the storm's rotational wind field. At the radial location where inflow suddenly converges, a midlevel tangential jet develops and extends into the downwind end of the rainband complex. This circulation may contribute to ventilation of the eyewall as inflow of low-entropy air continues past the rainband in both the boundary layer and midlevels. Given the expanse of the stratiform rainband region, its thermodynamic and kinematic impacts likely help to modify the structure and intensity of the total vortex.

Corresponding author address: Anthony C. Didlake Jr., Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195. E-mail: didlake@washington.edu

Abstract

Airborne Doppler radar documented the stratiform sector of a rainband within the stationary rainband complex of Hurricane Rita. The stratiform rainband sector is a mesoscale feature consisting of nearly uniform precipitation and weak vertical velocities from collapsing convective cells. Upward transport and associated latent heating occur within the stratiform cloud layer in the form of rising radial outflow. Beneath, downward transport is organized into descending radial inflow in response to two regions of latent cooling. In the outer, upper regions of the rainband, sublimational cooling introduces horizontal buoyancy gradients, which produce horizontal vorticity and descending inflow similar to that of the trailing-stratiform region of a mesoscale convective system. Within the zone of heavier stratiform precipitation, melting cooling along the outer rainband edge creates a midlevel horizontal buoyancy gradient across the rainband that drives air farther inward beneath the brightband. The organization of this transport initially is robust but fades downwind as the convection dissipates.

The stratiform-induced secondary circulation results in convergence of angular momentum above the boundary layer and broadening of the storm's rotational wind field. At the radial location where inflow suddenly converges, a midlevel tangential jet develops and extends into the downwind end of the rainband complex. This circulation may contribute to ventilation of the eyewall as inflow of low-entropy air continues past the rainband in both the boundary layer and midlevels. Given the expanse of the stratiform rainband region, its thermodynamic and kinematic impacts likely help to modify the structure and intensity of the total vortex.

Corresponding author address: Anthony C. Didlake Jr., Department of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195. E-mail: didlake@washington.edu

1. Introduction

Spiral rainbands populate the region outside of the eyewall in tropical cyclones. Rainband precipitation typically has discrete or connected convective cells on the upwind end and stratiform precipitation on the downwind end, thus displaying the life cycle of convection within each band (Atlas et al. 1963). In the presence of environmental wind shear, multiple rainbands tend to form an organized complex of rainband convection (Willoughby et al. 1984; Houze 2010) such that the upwind convective ends and downwind stratiform ends generally occur in predictable regions of the storm (Hence and Houze 2012b). Nascent and mature convective cells are most prominent in the downshear half of the storm and these features contain convective-scale structures that vary with radius (Corbosiero and Molinari 2002, 2003; Didlake and Houze 2013). As slowly falling ice particles from convective cells travel downwind, the rainbands dissolve into a broad, relatively invariant swath of stratiform precipitation in the left-of-shear half of the storm (Hence and Houze 2012b). This downwind stratiform precipitation sector is distinct from the stratiform portions of more active rainbands that contain embedded convective cells (Powell 1990a; May 1996). While upwind convective cells comprise more vigorous vertical exchanges, the downwind stratiform portion of the rainband may have a more direct impact on the overall storm dynamics owing to its more areally extensive mesoscale nature and closer proximity to the eyewall. The current study explores the dynamics of the stratiform rainband zone, as a better understanding of this feature of the storm may lead to improved forecasts of intensity and structural changes in tropical cyclones.

Past observations (May and Holland 1999; Hence and Houze 2008) show that downwind stratiform portions of rainbands exhibit weak vertical velocities that are organized into net upward transport in mid- and upper levels and net downward transport in lower levels. The heating profile associated with this vertical transport leads to potential vorticity (PV) generation in the midlevels (Raymond and Jiang 1990). These stratiform rainbands may contain midlevel tangential jets, which can be attributed to the aforementioned PV source (May et al. 1994; Samsury and Zipser 1995; May and Holland 1999; Franklin et al. 2006). Condensational latent heating associated with net upward transport may also drive a pronounced overturning circulation that enhances the secondary circulation of the storm vortex (Eliassen 1951). These processes suggest that despite the weakened vertical velocities associated with stratiform precipitation, the stratiform ends of rainbands continue as a dynamically active feature that begs for more detailed observations and a more complete understanding.

In this study, we analyze high-resolution aircraft observations of a mesoscale stratiform rainband from Hurricane Rita collected during the 2005 Hurricane Rainband and Intensity Change Experiment (RAINEX; Houze et al. 2006, 2007). The dataset obtained in RAINEX by the National Center for Atmospheric Research (NCAR) Electra Doppler Radar (ELDORA) allows for a dual-Doppler analysis that retrieves the full three-dimensional reflectivity and kinematic fields in exceptional detail. The objectives of this study are to use these data to characterize the structure and evolution of the stratiform sector of a well-documented rainband and to infer the roles of the observed features in the overall storm dynamics. Given the organized transition from convective to stratiform precipitation in tropical cyclone rainbands, these features are often compared to squall lines with trailing stratiform precipitation. We will show that the along-band structure of an organized rainband complex is not dynamically similar to a squall line; rather, the cross-band structure of the purely stratiform end is organized by the vortex tangential circulation to resemble a squall-line structure, albeit to a limited extent. This study will corroborate certain aspects of previous studies of stratiform rainbands, but it will also provide new insight on how overturning can be locally enhanced within the stratiform rainband despite the decay of its cellular structure. We begin in section 2 by describing the data and methods of analysis. Section 3 presents general statistics of the stratiform rainband. Sections 4 and 5 examine the kinematics, thermodynamics, and evolution of the stratiform rainband. Section 6 discusses the implications that the results have on the overall storm structure and intensity. Finally, section 7 presents the conclusions of the study. The reader can use the conceptual model in this final section as a reference for the rainband features discussed throughout the paper.

2. Data and methodology

On 21 September 2005, the Naval Research Laboratory (NRL) P3 aircraft and the National Oceanic and Atmospheric Administration (NOAA) 43 P3 (N43) aircraft were deployed as part of RAINEX to investigate the rainbands of Hurricane Rita. During this mission, the NRL P3 employed curved flight tracks, running parallel to the rainbands rather than straight flight-leg segments crossing the eyewall, to provide an extensive and continuous view of the rainband processes. The NRL P3 was equipped with the NCAR ELDORA instrument, which is noted for its high sampling resolution (Hildebrand et al. 1996). The current study focuses on ELDORA data collected during three time segments: 1642–1657 (leg 1), 1741–1755 (leg 2), and 1831–1841 UTC (leg 3). During this time, Rita was intensifying rapidly and reached maximum sustained winds of 75 m s−1 and central pressure of 920 hPa at 1800 UTC [for more on Rita, see Beven et al. (2008)]. ELDORA is an X-band dual-Doppler radar that operates with two beams pointing approximately 16° fore and aft. As the aircraft flies along a track, the beams intersect at 400-m intervals, providing two components of the wind vector everywhere within range of the radar.

The radar data were first corrected for navigation and instrumental errors (Testud et al. 1995; Bosart et al. 2002) and manually edited using the NCAR Solo II software (Oye et al. 1995) to remove noise and radar artifacts. The reflectivity and velocity data were then interpolated to a Cartesian grid with a resolution of 600 m in the horizontal and 400 m in the vertical. The lowest vertical level of data that we used was 800 m, as sea spray can contaminate radar observations below this level. The three-dimensional wind field was retrieved using a variational technique that minimizes the differences between radar-measured and retrieved velocity components [a complete description is given in Reasor et al. (2009)]. The storm translation was assumed to be constant and was removed from the wind field. A two-step three-dimensional Leise filter (Leise 1982) was then applied, yielding a minimum resolvable wavelength of approximately 5 km. After the wind field was retrieved, the data were initially examined using the NCAR Zebra analysis and visualization software [originally designed by Corbet et al. (1994), later modified by James et al. (2000), and presently maintained at the University of Washington], which interactively plots overlays of multiple parameters from horizontal and vertical cross sections of the dataset. The data were then interpolated to a cylindrical coordinate system with radial resolution of 600 m and azimuthal resolution of 0.375°.

During the time of study, the N43 aircraft flew parallel track to the NRL aircraft and observed the same rainband. The N43 aircraft was equipped with an X-band dual-Doppler tail radar that scans vertically and a C-band lower fuselage (LF) radar that scans horizontally. A dual-Doppler analysis of the N43 tail radar agreed well with the ELDORA analysis, verifying the features that are presented in the following sections. Vortex centers were determined by a simplex algorithm (Neldar and Mead 1965) that maximizes the LF radar reflectivity within a 5-km-wide annulus centered on the radius of maximum reflectivity. Griffin et al. (1992) showed that using the LF radar to track the vortex center can be effective, although their exact technique was different from the one presently used. The results shown in this paper are not sensitive to small variations in the analyzed circulation centers. Dropsondes were continually released from both N43 and NRL aircraft, providing measurements of the pressure, temperature, and humidity. These data were quality controlled with either the NCAR Aspen or NOAA Hurricane Research Division (HRD) Editsonde software.

3. General statistics and stratiform characterization

The term “stratiform precipitation” denotes the precipitation process in which upward motion of saturated air induces the growth of ice particles but the ascent remains weak enough on average to allow the ice particles to drift downward and fall out (Houze 1993, 197–200, 1997). When viewed on radar, stratiform rain produces echoes with relatively weak horizontal gradients and often a brightband of enhanced reflectivity just below the 0°C level. Atmospheric convection, which refers to the overturning of the atmosphere to neutralize buoyant instability, is a dynamic regime in which stratiform precipitation can develop. Following rapid, vigorous overturning during the convective stage of convection, the older, collapsed convection then exhibits the microphysical processes that define stratiform precipitation. Barring any large-scale influences, this particular type of stratiform precipitation, which we will refer to as convection-generated stratiform precipitation, tends to develop a specific set of dynamical features. Vertical velocities become weak (generally less than 2 m s−1) as they are the remnants of decayed vigorous overturning. These vertical velocities become organized into upward net transport within the cloud layer at mid- and upper levels, while in the levels below, latent cooling leads to downward net transport of air. As required by mass continuity, net horizontal convergence arises in the layer between the ascending and descending air masses. In this section, we examine reflectivity and kinematic statistics of Rita's rainband with the notion of convection-generated stratiform precipitation in mind.

The reflectivity field in Fig. 1 shows a spiral band of precipitation extending around half of the storm. The NRL aircraft observed this feature by flying along the rainband in a spiral fashion, mostly through the center of the precipitation swath. Continuous aircraft radar observations showed that this rainband was a singular, slowly varying band that remained approximately stationary with respect to the storm center during the time span of the observations. An examination of rainband convection around the storm indicates that this mesoscale swath of precipitation represents the downwind stratiform end of Rita's stationary band complex (Willoughby et al. 1984); the opposite side of the storm contained heterogeneous convective precipitation (Didlake and Houze 2013). Thus, we assume that the dataset obtained on the three flight legs indicated in Fig. 1 captures the stratiform rainband at three distinct stages of the rainband's evolution as the convection spirals around the storm.

Fig. 1.
Fig. 1.

Plan view of ELDORA reflectivity data at 2-km altitude observed on 21 Sep 2005. Boxes outline data sections used in the analysis. Leg 1 is from 1642 to 1657 UTC, leg 2 is from 1741 to 1755 UTC, and leg 3 is from 1831 to 1841 UTC. Flight tracks corresponding to each leg are drawn as dotted and/or dashed lines. Visible satellite imagery from the Geostationary Operational Environmental Satellite-East (GOES-E) is shown in the background.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

When displayed on a contoured frequency by altitude diagram (CFAD; Yuter and Houze 1995), stratiform rain echoes produce a sharply peaked distribution appearing as a narrow zone of maximum frequency of occurrence, with a bump in frequencies toward higher reflectivity at the brightband level (e.g., Yuter and Houze 1995, their Fig. 8a). The CFADs of legs 1–3 (Fig. 2) have characteristics that agree with those produced by stratiform precipitation in non–tropical cyclone convective systems. All CFADs have a relatively narrow distribution from approximately 5 km to the top of the domain. Below 5 km, the contours remain tightly packed for the higher reflectivities while the contour distribution widens slightly for lower reflectivities, which is indicative of the relatively precipitation-free areas on either side of the rainband. The high-frequency contours are centered on about 30 dBZ. Leg 2 contains outlier and high-frequency echoes that are slightly higher than the other legs. Near 5 km, the frequency contours for all legs exhibit a bump toward higher reflectivities indicating brightband echoes. These characteristics are also generally consistent with stratiform precipitation in rainbands from a single case study (Didlake and Houze 2009, their Fig. 5b) and in the climatology of storm echoes compiled by Hence and Houze (2012b, downshear-left quadrant in their Fig. 8). The similarity in distributions between the three legs is consistent with strong tangential advection of slowly falling ice particles above the melting layer.

Fig. 2.
Fig. 2.

CFADs of radar reflectivity (in 3-dB bins) for (a) leg 1, (b) leg 2, and (c) leg 3. Frequencies are normalized by total number of data points. The outermost contour corresponds to 1% frequency. Inner contours increase at an interval of 7%, and shaded regions correspond to frequencies greater than 36%.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Figure 3 shows CFADs of the vertical velocities in the stratiform rainband. These velocities are consistent with the typical vertical velocities of convection-generated stratiform precipitation. In legs 1 and 2, the majority of vertical motions have a magnitude less than 1 m s−1 and outliers throughout the low to midlevels reach 4 m s−1. The distribution of leg 3 is noticeably narrower, containing a sharper peak in the 0 m s−1 frequencies and few outliers beyond 3 m s−1 in magnitude. As the last stage of the convection life cycle, vertical velocities are very weak here in the most downwind portion of the rainband. Returning to Fig. 1, legs 1 and 2 contain streaks of enhanced reflectivity reminiscent of embedded convective elements. Yet, the vertical velocity CFADs suggest that vigorous convective motions are virtually absent in the rainband. Upward velocities in excess of 4 m s−1 are infrequent, indicating a lack of deep buoyant updrafts. These nonconvective streaks of enhanced reflectivity will be discussed further in section 5.

Fig. 3.
Fig. 3.

CFADs of vertical velocity (in 1 m s−1 bins) for (a) leg 1, (b) leg 2, and (c) leg 3. Frequencies are normalized by total number of data points. The outermost contour corresponds to 1% frequency. Inner contours increase at an interval of 7%, and shaded regions correspond to frequencies greater than 36%.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Figure 4 presents vertical mass transport profiles, calculated using air densities from the Jordan (1958) standard tropical Atlantic profile. Leg 1 has the mass transport profile that convection-generated stratiform precipitation tends to produce in mesoscale convective systems not associated with tropical cyclones (Houze 2004). Upward net transport occurs above the 4-km level with downward net transport below. Leg 2 exhibits similar upward net transport above 6-km altitude and negligible downward net transport in low levels. Between 4 and 5 km, upward transport is slightly greater than that of leg 1. Leg 3 contains the smallest upward and downward transport, and the net transport profile is reversed from leg 1; it contains positive transport in low levels and negative transport aloft. Thus, this profile differs distinctly from that expected of collapsing convection alone.

Fig. 4.
Fig. 4.

Positive, negative, and net vertical mass transport profiles for (a) leg 1, (b) leg 2, and (c) leg 3. Profiles are normalized by the maximum area-weighted positive transport value from leg 1.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

The vertical profiles of average divergence in Fig. 5 generally follow the vertical mass transport profiles, as required by mass continuity. Again, leg 1 has a profile that is most representative of convection-generated stratiform precipitation, consisting of convergence in the low to midlevels and divergence aloft and near the surface. These statistics indicate that the rainband evolves from a structure with characteristics typical of convection-generated stratiform rain to a band with equally strong precipitation but much different kinematics. We emphasize, moreover, that the strengthened reflectivities and upward transport in the leg 2 zone are enhancements of a stratiform nature and not a formation of new convection in the stratiform zone. This fact will become clearer in the subsequent sections of this paper in which we examine more closely the kinematics and precipitation of the three flight-leg regions.

Fig. 5.
Fig. 5.

Profiles of average divergence for (a) leg 1, (b) leg 2, and (c) leg 3.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

4. Rainband structure in the upwind region

We first use azimuthal averages to examine the dynamics of leg 1. Figure 6 presents the azimuthal average of radial velocity, tangential velocity, vertical velocity, and divergence, with contours of the average reflectivity values overlaid. The secondary circulation is dominated by two distinct regimes: rising outflow and sinking inflow. A third regime exhibits sinking outflow at 2-km altitude in the outer regions of the rainband. In the absence of convective-scale overturning, this outflow, as explained by Kepert (2001) and Kepert and Wang (2001), is a steady-state supergradient response to the maximum tangential winds located within and just above the boundary layer. In this paper, we define the top of the tropical cyclone boundary layer as the altitude of the maximum axisymmetric tangential wind. In the lowest levels, frictional inflow occurs as part of the larger vortex circulation; this radial inflow, as confirmed by dropsondes, extends down to the surface below the lowest level of available radar data. The mesoscale rising outflow forms when dying upward convective motions from upwind collect and flow outward along lines of constant angular momentum. The sinking inflow appears to be separated into three inflow bursts, located outside the heaviest precipitation between 5- and 9-km altitude, beneath the brightband at 4-km altitude, and in the boundary layer on the inner side of the rainband. This disjointed pattern suggests that separate dynamics are governing each inflow burst. The divergence field, which is dominated by its radial component, contains convergence maxima that correspond clearly to the deceleration of the upper two inflow bursts. Enhanced divergence above enhanced convergence occurs at 130-km radius near the brightband level, which is a pattern that Kim et al. (2009) also observed in a stratiform rainband of Tropical Storm Gabrielle using a single-Doppler radar and wind profiler.

Fig. 6.
Fig. 6.

(a) Azimuthally averaged field of radial velocity from leg 1. Average reflectivity values are overlaid as black contours (dBZ). (b) As in (a), but for tangential velocity. Positive values are cyclonic. (c) As in (a), but for vertical velocity. (d) As in (a), but for divergence.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

The secondary circulation above the boundary layer has features reminiscent of squall-line dynamics (Fig. 7), in which the trailing stratiform precipitation region contains descending rear inflow (e.g., Zipser 1969; Smull and Houze 1987; Houze et al. 1989; Houze 1993, 348–394, 2004). Previous studies have suggested that the cross-band airflow in a tropical cyclone rainband has some similarity to leading-line/trailing-stratiform mesoscale convective systems (MCSs) (e.g., Barnes et al. 1983; Barnes and Stossmeister 1986; Powell 1990a,b; May et al. 1994). In an MCS, sloping updrafts advect lighter precipitation particles upward and away from the leading convective line in a broad anvil cloud, below which latent cooling induces negative buoyancy and mesoscale downward motion (Biggerstaff and Houze 1991). As proposed by Smull and Houze (1987), shown by thermodynamic Doppler retrieval by Braun and Houze (1995), and simulated by Yang and Houze (1995), the mesoscale vertical motions near the convection source introduce a mesolow and corresponding pressure gradient that pulls air inward from the environment. This cool mesoscale downdraft air entering from the environment at midlevels joins with convective-scale downdraft air in the convective region and converges with the sloping front-to-rear flow of the squall line. In this way the mesoscale downdraft cooperates to maintain the mesoscale lifting of the MCS. A dynamic view of the midlevel inflow and mesoscale downdraft is that with an anvil cloud base sloping upward and rearward; condensational heating above and latent cooling below the sloping boundary comprise a horizontal buoyancy gradient, which generates horizontal vorticity and thus drives the rear inflow in a subsiding jet (Braun and Houze 1997).

Fig. 7.
Fig. 7.

Conceptual model of a squall line with a trailing-stratiform area viewed in a vertical cross section oriented perpendicular to the convective line. In the trailing stratiform rain region, ascending front-to-rear flow occurs within the cloud and descending rear inflow occurs below the cloud base. Adapted from Houze et al. (1989, their Fig. 1).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

In the tropical cyclone rainband considered here, the rising outflow in a radial cross section (Figs. 6a,c) looks somewhat like the squall-line model, but it results from different dynamics. The convection source does not occur on the inner side of the band; rather, it is located in the upwind portion of the rainband. Therefore, the descending inflow seen in the radial sections of the stratiform rainband considered in this paper is not essential for sustaining the mesoscale uplift as in the MCS. Instead, weakly rising air in the upper portions of the rainband travels radially outward to conserve its angular momentum, and this flow of air outlines condensational heating in this region of the storm. Similar to an MCS, the rising radial outflow sorts hydrometeors according to their fall speeds and source altitudes (Biggerstaff and Houze 1991); consequently, some falling ice particles become concentrated to produce the brightband region, while other ice particles are lofted far outward into the upward-sloping anvil cloud. Downward motion within the heaviest precipitation of the stratiform sector of the rainband (Fig. 6c) occurs at and below the brightband, which circumstantiates cooling from melting and evaporation. Radially inward, upward motion and condensational heating continue and extend downward to the boundary layer. We suggest that this greater depth of heating is due to decreased latent cooling because fewer ice particles are melting on this side of the rainband and high-humidity air from the storm core reduces evaporation. Somewhere between 120- and 140-km radius in Fig. 6, a radial gradient of buoyancy (∂B/∂r) exists as condensational heating transitions to latent cooling. This transition should be steepest at 4–5-km altitude where the melting layer comprises a region of concentrated latent cooling. The result is a local minimum of ∂B/∂r, which generates a local maximum of horizontal (tangential) vorticity near 4.5-km altitude (not shown). This tangentially oriented horizontal vorticity maximum is manifested mostly as the midlevel inflow burst beneath the brightband and increased outflow just above.

Radially outward, the rising motion in Fig. 6c (indicating the cloud layer) slopes upward with increasing radius. Sublimational cooling, and resulting negative buoyancy, likely drives the downward motion above 5-km altitude as falling ice particles exit the cloud layer. Consequently, regions of negative ∂B/∂r, and therefore tangential vorticity generation, occur along the sloping cloud base, which results in the observed outer inflow burst (Fig. 6a). Braun and Houze (1997) also determined that sublimational cooling generated a separate inflow burst in the rear of an MCS. While both the midlevel and outer inflow bursts can be explained by regions of negative ∂B/∂r, they are induced by different cooling events that occur in different locations within the rainband, resulting in separate inflow bursts. We note that a heat source alone would create a horizontal buoyancy gradient; however, the onset of cooling regions locally amplifies the horizontal buoyancy gradient and concentrates the observed inflow circulations.

Moon and Nolan (2010) examined the dynamic response of the hurricane wind field to idealized heating patterns of a stratiform rainband (Fig. 8a). They demonstrated that midlevel inflow is indeed a dynamic response to the heating within a stratiform rainband (Fig. 8b); furthermore, their inflow was part of a midlevel overturning circulation that resembles the inflow–outflow dipole centered on the brightband in Fig. 6a. In the current observations, some of the midlevel inflow descends and continues as boundary layer inflow, which is a feature that is captured by the response circulation of Moon and Nolan (2010).

Fig. 8.
Fig. 8.

(a) Idealized pattern of normalized diabatic heat sources in a purely stratiform rainband. Adapted from Moon and Nolan (2010, their Fig. 5b). (b) Kinematic response in a vortex circulation to the idealized stratiform heat sources in (a). Arrows show radial and vertical velocity components of the response. Contours show tangential velocity component of the response with an interval of 0.5 m s−1. Adapted from Moon and Nolan (2010, their Fig 14a).

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Some other aspects of the Moon and Nolan (2010) circulation are not consistent with the observed stratiform rainband, such as maximum radial flow occurring at the 0°C level (4-km altitude) and enhanced midlevel outflow along the inner side of the rainband. These inconsistencies are a result of their idealized heating pattern, which depicted identical structures of heating and cooling within the rainband. Instead, the current observations (Fig. 6c) indicate that heating extends radially inward of the cooling region and below the melting level, while radially outward, heating continues in an upward-sloping structure.

5. Downwind development of the stratiform rainband

The overall statistics from section 3 showed that the rainband in Hurricane Rita became decreasingly like convection-generated stratiform precipitation with increasing proximity to its downwind end. In this section, we use different analysis methods to examine how this situation developed.

a. Azimuthal averages

Figures 9 and 10 show the azimuthally averaged fields of radial, tangential, and vertical velocity from legs 2 and 3. Compared to leg 1, the radial inflow in leg 2 is stronger, deeper, and more continuous. The display of continuous inflow rather than separate inflow bursts could indicate more overlap of melting and sublimation regions, stronger overall cooling, or both. The inflow continues radially inward of the rainband but bending upward. This ascending inflow in leg 2 and the descending inflow in leg 1 are the two paths that Moon and Nolan (2010) found for radial inflow crossing their idealized stratiform rainband (cf. Fig. 8b). Consistent with the vertical mass transport profile (Fig. 4b), sinking motion (Fig. 9c) driven by latent cooling is still apparent but not as widespread in the low levels. The tangential winds in leg 2 are expected to be stronger as the rainband spirals inward from leg 1 to a smaller radius. Yet, comparing the velocities of Figs. 6b and 9b at the same radii, we see that the wind field in leg 2 has strengthened, which is likely a result of the midlevel inflow.

Fig. 9.
Fig. 9.

(a) Azimuthally averaged field of radial velocity from leg 2. Average reflectivity values are overlaid as black contours (dBZ). (b) As in (a), but for tangential velocity. (c) As in (a), but for vertical velocity.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Fig. 10.
Fig. 10.

As in Fig. 9, but for leg 3.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

To examine these changes in the tangential wind field, we calculate the tangential momentum tendency terms. The tangential momentum equation in cylindrical coordinates (r, θ, z) is given by
e1
where
e2
In these equations, u, υ, and w are the radial, tangential, and vertical velocities; p is pressure; ρ is density; f is the Coriolis parameter; and η is the combined vertical vorticity resulting from radial shear of the tangential wind, curvature of the tangential wind, and the Coriolis effect. The right-hand-side terms of Eq. (1) represent radial flux of vertical vorticity, azimuthal advection, vertical advection, pressure gradient acceleration, and frictional dissipation. Calculations of azimuthal advection yield large negative values at all altitudes that represent a downwind shift of accelerated tangential velocities. This downwind shift is similar for all three flight legs analyzed in this study and the shift does not significantly affect the shape of the acceleration vertical profile. We therefore ignore the azimuthal advection term in our calculations. We also ignore the pressure gradient term since our analyses involve averages over significant azimuthal segments. Last, frictional dissipation cannot be calculated with the current dataset, but we expect for this term to have a negligible impact on our overall conclusions.

Figure 11 gives the vertical profiles of momentum tendency terms averaged over two radial ranges spanning the descending inflow. In the inner region (Fig. 11a), the radial flux of vorticity peaks between 3 and 4 km, while vertical advection contributes comparably to the total ∂υ/∂t between 6 and 10 km. These results show that the inflow and ascent portions of the mesoscale stratiform circulation are equally important in strengthening the wind field between 2 and 8 km. In the outer region (Fig. 11b), vertical advection is less important to the total ∂υ/∂t as the radial flux of vorticity accelerates the tangential winds between 2 and 9 km. A detailed analysis of the radial flux of vorticity term () indicates that its curvature component (/r), which results from angular momentum conservation, is largely responsible for the shape of the vertical profile. Although supergradient outflow and sinking motion yield a negative ∂υ/∂t below 2 km, the stratiform precipitation dynamics increase the tangential circulation throughout a significant depth of the storm.

Fig. 11.
Fig. 11.

(a) Vertical profiles of tangential momentum tendency [Eq. (1)] averaged between 90- and 124.8-km radius from leg 2. Individual terms and total are shown. (b) As in (a), but for terms averaged between 125.4- and 160.2-km radius.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Leg 3 exhibits a markedly different radial wind field (Fig. 10a) containing nearly homogeneous radial outflow with the exception of pronounced inflow near 13-km altitude.1 The faint diagonal pattern of decreased radial velocities is likely composed of remnants of descending radial inflow found upwind. The absence of clear midlevel inflow here in leg 3 is not surprising since the vertical velocities were shown to be weak and unorganized (cf. Figs. 3c and 4c). Figure 10c reiterates the insignificance of the vertical velocities in leg 3. Legs 2 and 3 both exhibit descending inflow at higher altitudes, appearing to be disconnected from the rainband circulation.

The most notable feature exhibited in leg 3 of the rainband is a pronounced midlevel tangential jet near 3–4-km altitude (Fig. 10b). Past studies document observations of such a midlevel jet in stratiform rainbands and explain its development through potential vorticity generation associated with the latent heating profile (May et al. 1994; May and Holland 1999). Moon and Nolan (2010) showed in their idealized simulations that this jet is a vortex response to the heating. While their idealized jet occurs throughout the rainband, the current observations and the full-physics simulation of Franklin et al. (2006) both indicate that the jet occurs only in mature or decaying regions of the stratiform rainband. Tangential advection must play a significant role in forming the jet here since the local vertical velocity field is not sufficiently strong and organized to generate potential vorticity at the altitude of the tangential jet. Midlevel jets are also found within or near rainband stratiform precipitation that contains embedded convective cells (Barnes et al. 1983; Powell 1990a; May 1996; Hence and Houze 2008) and it seems reasonable to suggest that some association between the jets exists. But the current observations indicate that the mature stratiform midlevel jet and the active-convection midlevel jet occur on different sides of the storm and are not connected. Consequently, we suggest that the two jets are inherently different. Tangential jets in the vicinity of active convection are convective-scale features that are immediately spurred by convective-scale vertical motions and are often not at midlevel altitudes (Didlake and Houze 2013). In contrast, the tangential jet in mature stratiform precipitation is a mesoscale feature connected with a mesoscale secondary circulation and consistently remains in the midlevels.

b. Convergence maximum composites

Taking the azimuthal average of a spiral rainband can smear possibly important details in its structure. Therefore, we use an analysis method that follows approximately the spiral shape of the rainband to highlight any further structural or dynamical details. We have seen that legs 1 and 2 exhibit midlevel radial inflow that abruptly decelerates within the stratiform rainband, producing a local maximum in convergence near the 4-km level (Fig. 6d). We use this convergence maximum as an anchor for cross-section composites. The exact procedure is as follows. Along each radial, a running average of the 4-km-level radial convergence is calculated over a 4-km radial distance and the location of the maximum averaged convergence is identified. This location becomes the fixed center of a radial cross section spanning 90 km. The composite center locations from legs 1 and 2 are shown in Fig. 12. The line of maximum convergence is robust and continuous everywhere except for the downwind end of leg 1 and the upwind end of leg 2. We examined composites that excluded these varying locations of maximum convergence and found that they have little influence on the total composited fields. In leg 3, the signal of strong convergence becomes less apparent as the midlevel inflow weakens. Nonetheless, the composite technique becomes less potent in this leg since the rainband is much more circular, making the azimuthal average effective for a rainband-following analysis.

Fig. 12.
Fig. 12.

Plan view of reflectivity at 2-km altitude. Each black dot represents the averaged convergence maximum at 4-km altitude along each radial from legs 1 and 2. The blue stars show release locations of dropsondes A–F. The axis coordinates are horizontal distance (km), where the origin is the center of the storm. Legs 1–3 are outlined by the dotted boxes.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Figures 13 and 14 present the composite fields of the three velocity components and relative vertical vorticity for legs 1 and 2. The radial wind composite for leg 1 (Fig. 13a) showcases the midlevel inflow burst, which connects to the outer inflow burst in an upward bend and reduction of magnitude near the outer edge of the brightband (~30-km distance). The vertical velocities (Fig. 13c) near the brightband display a more horizontal division between upward motion and downward motion than in the azimuthal average (cf. Fig. 6c), indicating a nearly horizontal cloud base. In this region, downward motion is greater at the brightband level than below, which is consistent with significant negative buoyancy introduced by melting cooling, corroborating the discussion in section 4. As midlevel inflow approaches the composite center, the flow of air splits into a distinct updraft and downdraft. Following the updraft, the flow of air rushes outward near 6.5-km altitude. This flow pattern completes an overturning circulation very similar to the simulations of Moon and Nolan (2010). The midlevel updraft is also collocated with a column of enhanced reflectivity. Although not deep or intense like that seen in typical convective precipitation, the updraft appears to enhance the local precipitation. This updraft explains the narrow line of increased reflectivity in the plan view of the stratiform rainband (legs 1 and 2 of Fig. 1) without having to invoke the presence of embedded convective elements. This line of enhanced reflectivity is thus seen to be a mesoscale feature produced within the stratiform zone without the aid of deep convection. This feature of the rainband seen by the ELDORA has been a lingering mystery since the field phase of RAINEX; it was known from the aircraft observations that convective elements were not present along this line. The downdraft branch of this circulation is also located within the enhanced reflectivity column and it has a weaker magnitude than the corresponding updraft. The downward airflow continues as accelerated inflow within the boundary layer.

Fig. 13.
Fig. 13.

(a) Composite of radial velocity from radially aligned cross sections of leg 1. The centers of the individual cross sections (denoted by the origin of the x axis) are located on the black dots in Fig. 12. (b) As in (a), but for tangential velocity. (c) As in (a), but for vertical velocity. (d) As in (a), but for relative vertical vorticity.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Fig. 14.
Fig. 14.

As in Fig. 13, but for leg 2.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

The composite secondary circulation and reflectivity fields from leg 2 (Figs. 14a,c) also exhibit features consistent with the previous analyses, but more sharply defined. As in the azimuthal average, leg 2 contains stronger radial inflow that is more tilted and more continuous than the flow pattern from upwind. The reduction in magnitude and upward bend in the radial inflow from leg 1 has nearly vanished. The outer edge of the brightband occurs farther inward at a distance of 25 km from the midlevel convergence maximum. The composite again contains a robust updraft and downdraft embedded in a column of enhanced reflectivity like that seen in leg 1.

The tangential wind composite from leg 1 (Fig. 13b) contains increased low-level winds associated with the boundary layer inflow burst, which is consistent with the azimuthal average. At the composite center, a tongue of higher wind speeds extends from low levels to 6 km. To examine how the secondary circulation shapes this feature, we calculate the tangential momentum tendency terms near the composite center and examine their vertical profile. Figure 15a shows that vertical advection has the largest value between 5 and 6 km, acting to form the collocated tangential wind feature. Radial flux of vorticity is negative in the 2–8-km layer because radial outflow is strongly present above and inward of the reflectivity column. Corresponding to the accelerated tangential winds, a vorticity couplet (Fig. 13d) lies at the composite center in the midlevels. From a vorticity-budget framework, the composite fields indicate the occurrence of tilting and stretching at the composite center, which produces the observed vorticity couplet. This couplet and its likely formation mechanism are consistent with the simulated stratiform rainband of Franklin et al. (2006).

Fig. 15.
Fig. 15.

(a) Vertical profiles of tangential momentum tendency from the composite fields (Fig. 13) of leg 1. Terms are averaged between −4.2 and 4.2 km along the x axis. Individual terms and total are shown. (b) As in (a), but for leg 2 composites from Fig. 14.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Traveling downwind, the tongue of elevated tangential winds (Fig. 14b) persists, while a clear midlevel jet has not yet appeared, consistent with the azimuthal average. The associated vorticity maximum (Fig. 14d), formerly part of a pronounced couplet, has grown, extending downward. Figure 15b shows that radial flux of vorticity has an increased role in building the tangential winds at the composite center. This term has become positive in leg 2 because radial inflow is stronger and continues on the inner side of the composite center. The radial flux of vorticity term creates a maximum of total ∂υ/∂t just above 3 km, which is exactly the altitude of the midlevel jet observed downwind in leg 3. This composite analysis illustrates that the mesoscale circulation associated with the stratiform rainband generates a descending midlevel vorticity maximum, which eventually actualizes the observed tangential jet in the downwind end.

c. Thermodynamic evolution

We now examine the thermodynamic profiles attained from dropsondes that sampled both sides of the midlevel convergence maximum and spanned a significant portion of the stratiform rainband. Figure 12 contains the release locations of six dropsondes and Fig. 16 presents their skew-T diagrams. These profiles are representative of other dropsonde measurements nearby.

Fig. 16.
Fig. 16.

Skew-T diagrams of temperature profiles measured by dropsondes A–F from Fig. 12. The black line is air temperature and the gray line is dewpoint temperature. Release times for the dropsondes are at the bottom of each diagram.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Profiles radially inside of the convergence line (dropsondes A–C) show that the air is saturated or nearly saturated with little variation among the three locations. Vertical motions at these locations are weak and unorganized, which allow for the generally moist air of the storm's inner core to remain unperturbed as indicated by the profiles. Outside of the convergence line, the profiles (dropsondes D–F) have a much different character, where each exhibits a sudden separation of the dewpoint and air temperatures, indicating dryer and warmer air aloft. This profile type signifies an unsaturated mesoscale downdraft (Zipser 1977), which is consistent with the observed vertical motions at these locations. The coinciding radial inflow, thus, is advecting unsaturated air in the direction of the storm core. Dropsonde B, which is located about 15 km inward of the convergence line, contains dry slots of air near 1.5-km altitude and at the surface. While the rainband appears to have been a boundary between the moist inner core and the drier surrounding environment, the profile of dropsonde B suggests that some of the inflowing dry air penetrated the rainband. It is well known that influxes of dry air into tropical cyclones (e.g., the Saharan air layer that affects Atlantic storms) are detrimental to storm genesis and intensification. Little has yet been discovered about the mechanism by which the dry air enters the storm. The descending mesoscale flow into stratiform rainband zone identified here appears to be one such mechanism.

The signature for subsidence in the outer dropsonde profiles varies in altitude along the rainband. Dropsonde D indicates dry air extending down to 0.75-km altitude, which coincides with the boundary layer inflow. Traveling downwind, the lowest extent of warm, dry air increases in altitude and surpasses the 2-km level in the profile most downwind. This evolution suggests a weakening of the mesoscale downdraft traveling along the rainband, which is consistent with the kinematic observations.

6. Some implications

a. Eyewall ventilation

Low-entropy environmental air that mixes into the eyewall region can dilute the heat content of the eyewall and thereby weaken the storm intensity (Simpson and Riehl 1958; Riehl and Malkus 1961). From the viewpoint of a Carnot heat engine, this entrainment process known as ventilation reduces the thermodynamic efficiency and work performed by the storm that is necessary to combat frictional dissipation (Emanuel 1986). Important as ventilation is, the exact mechanism by which it occurs has not heretofore been clearly identified. We do know from prior studies that ventilation of the eyewall occurs on the vortex scale along two possible pathways. The low-level pathway involves downdrafts that flush midlevel air into the inflow layer feeding the inner core; the midlevel pathway involves eddy fluxes of midlevel air directly into the eyewall (Powell 1990b; Cram et al. 2007; Tang and Emanuel 2010). The current observations indicate more specifically how the stratiform rainband is a possible agent for both forms of ventilation.

Cram et al. (2007) examined the trajectories of air parcels that ventilated the eyewall in Braun et al.'s (2006) simulation of Hurricane Bonnie (1998). During the simulation, Bonnie experienced moderate environmental wind shear. Air parcels ventilating the eyewall at midlevels (categorized as “class IV” in their paper) mostly traveled along a descending trajectory that originated from the left-of-shear half of the storm (Cram et al. 2007, their Fig. 16). This region of the storm persistently exhibited broad stratiform precipitation (Braun et al. 2006). These trajectories are consistent with the wind patterns and the azimuthal orientation of the observed stratiform rainband, which exhibited descending inflow to the left of the westerly shear vector.2 Other studies show that broad areas of precipitation prevail in the left-of-shear half of tropical cyclones (Franklin et al. 1993; Frank and Ritchie 1999, 2001; Chen et al. 2006), and this precipitation is predominantly stratiform in nature (Willoughby et al. 1984; Hence and Houze 2012b). By connecting the current study with previous studies, we suggest that environmental wind shear encourages midlevel ventilation of the eyewall by organizing rainband convection such that broad stratiform precipitation proliferates left of the shear vector and induces midlevel inflow of low-entropy air. The bulk of this circulation may not directly infiltrate the eyewall since the inflow rapidly decelerates within the rainband; however, the midlevel inflow can provide low-entropy air that eddy fluxes can mix into the eyewall at the downstream end of the rainband, where it becomes tangent to the eyewall.

In a series of idealized model simulations, Riemer et al. (2010) found downward fluxes of low–equivalent potential temperature (θe) air into the boundary layer extending over a large region that was tied to a wavenumber-1 convective feature outside of the eyewall. They suggested that this dilution of the boundary layer air followed the low-level pathway of ventilation and culminated in a weakening of the storm. The associated convective asymmetry was linked to the environmental wind shear in a similar fashion as the stratiform rainband sector in the current study. Trajectories from Cram et al. (2007) corresponding to the low-level pathway (“class II”) show that air parcels enter the eyewall on all sides of the storm. These findings are consistent with downdrafts that occur not only within convective rainbands (Powell 1990b) but also in stratiform rainband downdrafts such as seen along the stratiform region convergence line in the case analyzed here.

b. Tangential wind spinup and secondary eyewall formation

Smith et al. (2009) and Bui et al. (2009) describe two mechanisms for the spinup of a storm's tangential circulation in an axisymmetric framework. The first mechanism entails deep, balanced radial inflow above the boundary layer that results in convergence of angular momentum and expansion of the vortex circulation. The second mechanism entails unbalanced radial inflow within the boundary layer that advects angular momentum inward faster than friction can dissipate it, resulting in a strengthened eyewall circulation. Abundant rainband convection serves as a catalyst for the first spinup mechanism as such asymmetric entities of diabatic heating can produce an axisymmetric balanced response that strengthens the local tangential winds (Nolan and Grasso 2003; Hill and Lackmann 2009). Correspondingly, the circulation associated with the stratiform rainband examined here strengthened the local tangential winds (Fig. 11) and likely contributed to the expansion of Rita's axisymmetric wind field (Bell et al. 2012) via the first spinup mechanism.

Given the scale and organization of the observed features, we suggest that the downwind stratiform portions of rainbands of tropical cyclones are the primary features that broaden the tangential wind field. Nolan and Grasso (2003) and Nolan et al. (2007) demonstrate that the axisymmetric response of the vortex circulation is largely determined by the axisymmetric component of the asymmetric heat sources. From this perspective, the stratiform end of an organized rainband complex would be more efficient than the convective end in increasing the tangential circulation. The stratiform portion is a larger, mesoscale feature that has a somewhat more circular orientation and is located near the eyewall, while convective rainband regions are narrower, more sparsely populated, and cut across the radial rings at a more acute angle. This interpretation is consistent with the modeling study of Fudeyasu and Wang (2011), who also found that stratiform anvil clouds produced by rainbands led to inward transport of angular momentum and expansion of the tangential wind field.

Observations and modeling studies show that a secondary eyewall (Houze et al. 2007; Didlake and Houze 2011; Hence and Houze 2012a) often forms following a significant expansion of the tangential wind field (Qiu et al. 2010; Huang et al. 2012; Bell et al. 2012). Secondary eyewall formation begins an eyewall replacement cycle in which the new eyewall replaces the old eyewall, causing the storm to stagnate its intensification or weaken temporarily (Willoughby et al. 1982; Sitkowski et al. 2011). The initial formation mechanism remains unclear, but several theories for secondary eyewall formation have been proposed and the current observations suggest that stratiform rainband dynamics may play an important role in certain proposed formation processes. As the stratiform rainband expands the tangential wind field, it increases the extent of the “vortex beta skirt”3 and strengthens inertial stability such that convective-scale vorticity perturbations and their associated heating can more efficiently cascade upscale and axisymmetrize (Terwey and Montgomery 2008; Rozoff et al. 2012). If the broadened wind field exhibits a relaxed radial gradient of tangential wind, then this region contains a decreased filamentation time that allows for a sufficient number of convective elements to grow around the storm without being sheared apart by the primary circulation (Rozoff et al. 2006; Fang and Zhang 2012). Last, an expanded wind field increases the extent of the critical zone for secondary eyewall formation where growing convective elements will consistently contain low-level supergradient flow that encourages further convergence and eventual axisymmetrization of the convective elements (Didlake and Houze 2013).

The contribution of the stratiform rainband to the second spinup mechanism is less clear. As observed in legs 1 and 2, a portion of the midlevel inflow sinks within the reflectivity maximum and continues as locally enhanced inflow within the boundary layer. The impact that this locally enhanced inflow has on the eyewall circulation is a subject for future study.

7. Conclusions

The NCAR ELDORA system captured high-resolution reflectivity and velocity observations of the stratiform sector of the stationary rainband complex in Hurricane Rita (2005). Our analysis of these observations is summarized in the conceptual model shown in Fig. 17. The plan view (Fig. 17a) shows the stratiform rainband sector as a mesoscale feature that forms in the downwind portion of the rainband complex that spirals around the eyewall. In the upwind portion of the rainband complex, growing convective cells exhibit vigorous vertical motions and convective-scale tangential jets indicated by individual arrows in the conceptual model. The circulations associated with these convective cells have a radial variability described by Didlake and Houze (2013). Traveling downwind, mature cells eventually collapse (indicated by the dashed outlines) as their associated vertical motions weaken. Lighter ice particles are advected farther downwind and form the nearly uniform band of stratiform precipitation. The upwind segment of the stratiform rainband sector exhibits kinematic statistics that are consistent with stratiform precipitation formed by convection in non–tropical cyclone contexts. Weak remnant convective vertical velocities are organized into upward net transport in the upper levels and downward net transport in the lower levels. A line of enhanced reflectivity develops within the stratiform sector. Convective updrafts do not produce this enhancement; rather, it is a result of motions that develop in response to the heating and cooling pattern associated with the stratiform cloud and precipitation in the stratiform zone of the rainband. Toward the end of the rainband complex, the vertical velocities, organized vertical transport, and enhanced reflectivity line fade, while a midlevel tangential jet, denoted by VT, develops.

Fig. 17.
Fig. 17.

(a) Plan view schematic of an organized rainband complex in a mature tropical cyclone. Reflectivity contours (20 and 35 dBZ) show embedded convective cells that collapse (dashed contours) and form stratiform precipitation traveling around the storm. The arrows represent tangential jets associated with each precipitation feature, with VT indicating the jet within the stratiform sector. (b) Schematic of the dynamics within a stratiform rainband [see the straight gray line in (a)]. Reflectivity contours are drawn. The line arrows represent vortex-scale motions associated with the overall storm, and the broad arrows represent mesoscale motions associated with the stratiform rainband. The broad arrows of the descending inflow are driven by two regions of a radial buoyancy gradient (∂B/∂r). The plus signs indicate regions of increasing tangential velocity by the secondary circulation. The circled region indicates the tangential jet (VT). Latent cooling and latent heating occur in the indicated regions.

Citation: Journal of the Atmospheric Sciences 70, 7; 10.1175/JAS-D-12-0245.1

Figure 17b shows a cross-sectional view taken across the stratiform zone of the rainband (gray line in Fig. 17a). The cross section cuts across the line of enhanced reflectivity in the stratiform region. Within the region enclosed by the 20-dBZ contour in Fig. 17b is a vertical column of enhanced reflectivity corresponding to the line of enhanced reflectivity shown in the plan view. This region also contains a brightband signature near 5-km altitude that indicates the melting layer. In the lowest levels, boundary layer inflow and supergradient outflow occur as part of the vortex-scale circulation (Kepert 2001; Kepert and Wang 2001). Weaker reflectivities aloft signify broadly distributed ice particles. Latent heating in these upper levels is maintained by a mesoscale updraft that travels radially outward along lines of constant angular momentum. As this rising outflow extends into the upper, outer portion of the band, an anvil cloud with a sloping base forms, and sublimation (and its associated latent cooling) occurs below the cloud base. Similar to the trailing anvil seen in squall lines (Braun and Houze 1997), this region exhibits a horizontal gradient of buoyancy (∂B/∂r < 0), which generates horizontal vorticity and drives mesoscale-descending inflow into the stratiform precipitation zone. A horizontal buoyancy gradient also exists in the midlevels radially inward of the brightband where condensational heating transitions to melting cooling. The horizontal vorticity that is generated results in further inflow of air beneath the brightband. As the rainband decays, the anvil region of the rainband extends radially inward and the two regions where ∂B/∂r < 0 become less distinct from one another.

The convergence region associated with the inward reach of the descending inflow concentrates at a certain radial location within the rainband, where the inflow then branches into different directions. Some of the flow turns upward, which locally enhances the precipitation and creates the collocated reflectivity column. Some of the flow continues downward into the boundary layer, which locally enhances the frictional inflow. The remaining flow continues inward along midlevel altitudes but at weaker velocities.

The current observations suggest that the secondary circulation of the stratiform rainband has opposing effects on the overall vortex. On one hand, the stratiform circulation can weaken the storm through ventilation of the eyewall. That conclusion builds upon the studies by Cram et al. (2007) and Tang and Emanuel (2010) by identifying the stratiform rainband as a possible agent for the eyewall ventilation mechanisms. The midlevel inflow consists of low-entropy air that may continue inward of the rainband in either the midlevels or the boundary layer. If this low-entropy air mixes into the eyewall, it will dilute the heat content of the eyewall and weaken the storm intensity. On the other hand, the stratiform-sector secondary circulation increases the tangential winds over a broad region (as indicated by plus signs in Fig. 17b) in the manner of Smith et al.'s (2009) first spinup mechanism (i.e., the mesoscale inflow results in convergence of angular momentum and broadening of the zone of strong tangential wind). This flow also develops the mesoscale midlevel jet, which was observed in other stratiform rainbands and explained in a potential vorticity framework (May and Holland 1999; Franklin et al. 2006).

Given the mesoscale nature of the downwind stratiform rainband, we suggest that this asymmetric feature is primarily responsible for the commonly observed axisymmetric broadening of the zone of strong tangential winds, which is consistent with the modeling study of Fudeyasu and Wang (2011). Furthermore, the stratiform rainband may be linked to storm intensity changes associated with eyewall replacement cycles since a broadening zone of strong tangential wind is often a precursor to secondary eyewall development. These hypotheses need to be tested using idealized simulations and realistic full-physics models to improve understanding of the impact that rainbands have on the storm intensity as well as the storm structure outside the eyewall region. Finally, more observations of storms with different structures and intensities are needed to determine the generality of the results presented herein.

Acknowledgments

We are thankful for the help and comments from Stacy Brodzik, Deanna Hence, Wen-Chau Lee, Angeline Pendergrass, and Michael Bell. Dr. Bell provided valuable guidance with radar data processing and interpretation. Beth Tully assisted with graphics and editing. This research was supported by the National Science Foundation under Grants ATM-0432623 and ATM-0743180 and the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program.

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1

We caution the reader against overvaluing the breadth of radial outflow in Fig. 10a as there is possibly a small error in the vortex center used for leg 3. During this time frame, Rita's eyewall exhibited convection spiraling into the eye, making the exact circulation center difficult to ascertain from radar reflectivity. Wind center fixes and Doppler radar data spanning the eyewall were also briefly unavailable at this time.

2

At the time of the observations, the 850–200-hPa wind shear vector was pointing east (89.5°) with a magnitude of 10 m s−1. Following the method of Hence and Houze (2011, 2012a,b), the shear was calculated from the National Centers for Environmental Prediction (NCEP) reanalysis winds in a radial ring of 500–750 km from the storm center.

3

As described in Terwey and Montgomery (2008), the vortex beta skirt is the region outside the primary eyewall where the azimuthal mean vertical vorticity extends outward with a persistently negative radial gradient in the lower troposphere.

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