This study uses ground-based dual-Doppler radar and surface observations to document the structural and surface features of the arc-shaped radar echoes (ASREs) evident along an outer rainband of Typhoon Longwang as it approached northern Taiwan on 1 October 2005. The particular aim of this study is to explore the possible distinction between the present case, previously documented tropical cyclone rainbands (TCRs), and squall lines. The dual-Doppler-derived fields show that the leading precipitation of the studied ASREs exhibited a convective nature with a sharp horizontal gradient of reflectivity and a significant vertical extent. The regions behind the leading convection were characterized by band-relative rear-to-front flow at low levels and were associated with a broader area of stratiform precipitation. The deep layer of front-to-rear flow extending from the surface to the upper troposphere was generally present ahead of the ASREs. This flow appears to be lifted upward at and immediately ahead of the leading edge of the low-level rear-to-front flow to form rearward-tilting updrafts. These airflow patterns are similar to those of the convective region of squall lines but differ fundamentally from those of previously documented TCRs that were located closer to the inner core of cyclones. The detailed analyses of surface fluctuations during the passage of one of the studied ASREs further show an abrupt pressure rise (2 mb), a temperature drop (4°C), and a pronounced deceleration of inflow air coincident with the leading heavy precipitation. The evaluation presented suggests that the convectively generated cold pool may be important in influencing the structures and propagation of the studied ASREs.
It has long been recognized that precipitation within tropical cyclones is not distributed uniformly throughout the storm; instead, it tends to be organized into elongated, banded features called “rainbands” or “spiral bands.” In addition to the eye and eyewall, the tropical cyclone rainbands (TCRs) are the most striking and persistent features of tropical cyclones seen from meteorological radar and satellite images (Wexler 1947; Senn and Hiser 1959; Willoughby et al. 1984; Cecil et al. 2002; Houze 2010). Improving our understanding of TCRs is important not only because they often contain regions of heavy rain and stronger wind speeds (Anthes 1982; Ryan et al. 1992; Samsury and Zipser 1995) but also because of their potential impact on the evolution and intensity of tropical cyclones (e.g., Willoughby et al. 1982; Shapiro and Willoughby 1982; Willoughby 1990; May and Holland 1999; Houze et al. 2006; Wang 2009).
In the past few decades, a large number of tropical cyclone studies have attempted to seek the possible origins of TCRs. Despite the diversity of these previous investigations, considering the appearance of TCRs as a manifestation of atmospheric wave activities initiated within tropical cyclones appears to be one of the most widely proposed concepts in both observational and theoretical perspectives (e.g., Diercks and Anthes 1976; Kurihara 1976; Willoughby 1977; Montgomery and Kallenbach 1997; Gall et al. 1998; Chen and Yau 2001; Corbosiero et al. 2006; Yu and Tsai 2010). Although the fundamentals of the aforementioned wave dynamics have been broadly established to explain the observational aspects of TCRs in terms of their spiral nature and propagation characteristics, little is known regarding the physical processes conducive to the triggering and maintenance of moist convection associated with TCRs.
With significant advances in aircraft instrumentation technology since the 1970s, the mesoscale structures of TCRs over the open ocean have been well explored (Barnes et al. 1983; Jorgensen 1984; Barnes and Stossmeister 1986; Powell 1990a,b; Ryan et al. 1992; Samsury and Zipser 1995; Hence and Houze 2008). Despite the variability in some details of TCR structures from case to case, the results from these aircraft investigations have revealed several common precipitation and airflow features, such as the dominance of low-level inflow in the vicinity of the rainband, overturning convective updrafts (i.e., directed away from the storm center at mid- to upper levels), and the radially outward tilt of rainband cells with prevalent convective (stratiform) precipitation on the inner (outer) side. It is thus reasonable to suspect that the moist convection associated with TCRs would most likely possess some unique convective structures tied to the vortex dynamics in a manner similar to the eyewall convection but in distinct contrast to ordinary convective systems such as squall lines (Marks and Houze 1987; Houze 2010). However, most of these rainband studies are actually dealing with the so-called principal band, a well-known rainband type that is clearly separated from the eyewall’s precipitation with stationary characteristics relative to the tropical cyclone center (Willoughby et al. 1984; Marks 2003). These previous investigations do not provide an adequate depiction of the entire spectrum of TCRs.
As proposed by previous theoretical and modeling studies of tropical cyclones, the behavior of TCRs would be ultimately determined by the degree to which they are influenced by the inner-core vortex dynamics of the cyclone (e.g., Diercks and Anthes 1976; Kurihara 1976; Willoughby 1977; Montgomery and Kallenbach 1997; Wang 2008). When TCRs are located or advanced over regions beyond the inner-core environment, which can be conceptually considered as the outer rainbands, their associated moist convection would be weakly constrained by the vortex dynamics (Wang 2008, 2009). Consistent with this speculation, a recent observational study by Yu and Chen (2011) investigated the statistical characteristics of TCRs from an extensive dataset of rainbands distributed over a wide range of radial distances from the tropical cyclone center (50–600 km). Their results show a clear dependence of TCR surface fluctuations on the radial distance, particularly with stronger convectively generated cold pools in the outer TCRs than in the inner TCRs. The importance of the cold pool to the initiation and maintenance of TCRs has also been emphasized by relatively fewer investigators of tropical cyclones (e.g., Yamasaki 1983, 2005; Sawada and Iwasaki 2010). Moreover, as noted in a recent review article of tropical cyclones by Houze (2010), the convective elements along the outer TCRs can sometimes develop arc-shaped radar echoes (ASREs), a signature suggesting the possible occurrence of an intense convectively generated outflow moving toward the rainband from the inner (i.e., rear) side. This observational evidence appears to support the hypothesis that under some circumstances, the outer TCRs may exhibit a convective behavior toward the squall-line-like precipitation system (e.g., Houze 1977; Zipser 1977). However, this scenario is more speculative than definitive at this stage and has not been verified because of the lack of detailed kinematic and thermodynamic information within these rainband features.
This study represents a continuous effort to fill the gaps in our general knowledge of TCRs by performing detailed analyses of an outer TCR associated with Typhoon Longwang (2005) as it approached Taiwan. The nature of propagation and some detailed surface characteristics for this particular rainband over the land of northern Taiwan have been described in a recent study by Yu and Tsai (2010). This outer band, labeled as “R2” in Fig. 4b of Yu and Tsai, was located at a radial distance of about 200 km and tended to propagate away from the cyclone center. One of the most important aspects of the outer rainband is that it developed ASREs well offshore east of northern Taiwan and then moved northwestward into dual-Doppler coverage by two operational Doppler radars located in northern Taiwan. Therefore, this rainband provides us a unique opportunity to retrieve three-dimensional wind fields within the arc-shaped segments of the outer TCR and to explore the possible similarities of their structures to squall-line convective systems. In addition, as mentioned earlier, our knowledge on the precipitation and airflow structures of TCRs has primarily been obtained from investigations of the principal band of tropical cyclones (e.g., Powell 1990a; Hence and Houze 2008). The principal band has a quasi-stationary nature with respect to the tropical cyclone center and has been hypothesized to be typically located near the boundary between the inner core and outer environment in tropical cyclones (Willoughby et al. 1984). According to Houze (2010), the principal band may be more appropriately considered as the inner TCRs because most of the band lies within the inner-core region except for a band segment near its upwind end. The degree of representation of the principal band to the outer TCRs in terms of their structures and dynamics remains poorly understood. One of the major objectives of this study is to provide clues for this unresolved issue.
2. Data and methodology
The primary datasets used to document the precipitation and airflow structures of the studied outer TCR were provided by the Central Weather Bureau of Taiwan’s operational S-band (10-cm) Weather Surveillance Radar-1988 Doppler (WSR-88D) on Wu-Fen-San (WFS) and by the Civil Aeronautics Administration (CAA) operational C-band (5 cm) Doppler radar located at Taoyuan International Airport. The locations of the two radar sites are indicated in Fig. 1. Both radars provide volumetric distributions of reflectivity and radial velocity with a temporal interval of 6 min (for the WFS radar) and 5–10 min (for the CAA radar) between each volume. Detailed characteristics of the WFS and CAA radars can be found in Yu and Cheng (2008). The WFS radar is located about 10 km inland from the northern coast and has a longer wavelength; thus, it can provide wider data coverage and less attenuation than the CAA radar. Isochrones of the 30-dBZ leading edge of the studied TCR observed from a sequence of the lowest plan position indicator (PPI) scans (0.4° elevation) of the WFS radar during the period of greatest interest is also indicated in Fig. 1. Two arc-shaped segments of radar echoes (A1 and A2 in Fig. 1) were evident along the rainband, and the appearance of A1 (A2) started at approximately 2114 (2143) UTC.
The dual-Doppler synthesis from the WFS and CAA radars derived from the multiple-view reflectivity and radial velocity data (Ray et al. 1980) is applied to retrieve the three-dimensional wind field associated with the studied ASREs as they moved northwestward into regions immediately off the northern coast of Taiwan (Fig. 1). The inset box in Fig. 1 marks the synthesis domain extending from the northern coast of Taiwan to about 60 km offshore. The cross-beam angles of the two radars within the synthesis domain were mostly between 40° and 90°, thus producing relatively smaller uncertainties and errors in the dual-Doppler-derived winds due to the inherent limitation of synthesized geometries (Doviak and Zrnić 1993).
The National Center for Atmospheric Research (NCAR) SOLO software (Nettleton et al. 1993) is used to unfold the radial velocities and to remove sea clutter and unreasonable (or incorrect) values of radar reflectivity and radial velocity data. The NCAR REORDER software (Oye et al. 1995) is used to interpolate reflectivities and radial velocities from raw PPI scans to Cartesian coordinates with a horizontal grid spacing of 1 km and a vertical grid spacing of 0.25 km over a volume of 90 × 60 km2 in the horizontal (box in Fig. 1) and 10 km in the vertical, with the lowest analysis level located at 0.25 km MSL. Owing to the propagating nature of the studied typhoon rainband, the advection adjustment due to the rainband’s movement was also considered for the interpolation procedure. The movement of the rainband for a given period of synthesis was obtained by tracking its leading edge using a sequence of the PPI scans of the WFS radar. The moving speed and direction of the rainband varied slightly during the different synthesis periods, and their mean values were calculated to be 27 m s−1 and 300°, respectively. At grid points where multiple reflectivity data are available, the maximum observed reflectivity value is retained to mitigate the effects of attenuation. Synthesis of the gridded radial velocities into horizontal wind fields is performed using the NCAR software program Cartesian Space Editing, Synthesis, and Display of Radar Fields under Interactive Control (CEDRIC; Mohr and Miller 1983). Vertical air motions are obtained through the variational adjustment of the anelastic continuity equation with boundary conditions of zero vertical motions at the surface and the echo’s top.
In addition to radar measurements, other data sources used in this study include surface and sounding observations at Pengjiayu (PJY) and Banciao (BC), as indicated in Fig. 1. In particular, the surface station at PJY, located about 60 km off the northern coast of Taiwan, experienced the passage of A2 and recorded high-resolution observations in time (1 min). The data provided from this offshore station allow us to investigate the finescale surface kinematic and thermodynamic fluctuations of the ASRE segment and to complement the inadequate sampling of Doppler observations near the surface levels.
3. Rainband environment
Because the rawinsonde site at BC was located adjacent to the southern edge of the synthesis domain (cf. Fig. 1), thermodynamic and kinematic profiles observed from the sounding were used to provide a basic context for the environmental conditions accompanying the studied TCR. The thermodynamic characteristics prior to the passage of the studied TCR, as revealed by the BC sounding taken at 1800 UTC 1 October, were characterized by a generally unsaturated condition throughout the troposphere (Fig. 2). Two shallow moist layers were present near 1 and 3 km MSL; their presence, however, would be contaminated by the influence of light precipitation occurring earlier over northern Taiwan. The level of free convection (LFC) and equilibrium level (EL) observed from the sounding were equal to about 800 m and 8.5 km MSL, respectively. Note that although the LFC was somewhat low and the convective inhibition (CIN) was only about 15 J kg−1, the excess air parcel temperature from its environment remained small until reaching about 3 km (MSL). This feature implies that a suitable convective forcing at low levels is still required for the triggering of deep moist convection. The convective available potential energy (CAPE) was calculated to be about 660 J kg−1, which is comparable to previously observed CAPE values of a tropical cyclone environment at a similar radial distance (i.e., ~200 km) from the typhoon center (Bogner et al. 2000). However, this CAPE value was much lower compared with the squall-line environment that has CAPE values usually greater than 1200–1500 J kg−1 (Bluestein and Jain 1985; Wyss and Emanuel 1988; Meng and Zhang 2012).
The corresponding vertical profile of equivalent potential temperature and environmental winds from the BC sounding are shown in Fig. 3. There was generally convective instability (i.e., a decrease in equivalent potential temperature with height) below about 4 km (Fig. 3a). Because the typhoon center was located near and off the eastern coast of central Taiwan during the study period (cf. Fig. 1), the prevailing winds over northern Taiwan were primarily from the east (Fig. 3b). The tropospheric winds generally veered with height, and the mean shear vector below about 5 km (MSL) was oriented toward the west-northwest, with a roughly reverse shear direction (i.e., toward the east-northeast) aloft. The mean shear vector, particularly in the lower troposphere, was primarily parallel to the orientation of the studied TCR (Fig. 1), indicating the presence of much stronger (weaker) along-band (cross-band) vertical shear. This feature is different from the tropical squall-line environment that typically exhibits a principal component of the shear perpendicular to the line’s orientation (Barnes and Sieckman 1984; Rotunno et al. 1988). The possible roles of the shear characteristics in the present case will be discussed in the following sections.
4. Dual-Doppler-derived structures
In this study, dual-Doppler synthesis was performed, during which A1 and A2 moved into the coverage of the synthesis domain (Fig. 1). A sequence of the larger-scale precipitation patterns of the studied TCR during these synthesis periods indicate that A1 arrived near the southeastern corner of the synthesis domain at 2200 UTC 1 October (Fig. 4a) and that A2 did not advance into the domain until about 2250 UTC (Fig. 4h). Note that only the western portion of A2 was captured by the dual-Doppler observations. Both A1 and A2 moved northward out of the synthesis domain after about 2300 UTC. Nine sets of dual-Doppler synthesized wind and precipitation were derived from the 1-h duration (i.e., 2200–2300 UTC). For a clear depiction of the rainband’s structures, we have adapted the terminology “front” and “rear” in a manner similar to that of squall lines. The studied rainband moved roughly northwest (cf. Fig. 1), so that front (rear) refers to the northern (southern) side of the band. Moreover, the rainband was oriented roughly parallel to the circle centered on the typhoon center, and the moving direction of the typhoon center was also approximately west–east (cf. Fig. 1), following the orientation of the rainband over the synthesis domain. For this particular case, the difference between the front-to-rear (rear-to-front) flow seen from the rainband’s coordinate system and the storm-scale inflow (outflow) defined with respect to the typhoon center is expected to be minor.
Figure 5 shows the precipitation and band-relative horizontal winds at 1 km (MSL) from four consecutive synthesis periods (2212, 2218, 2230, and 2235 UTC) when the A1 entity was best depicted by dual-Doppler observations. The precipitation of A1 exhibited a narrow-banded feature of high reflectivity with maximum values greater than 45 dBZ. The location of A1 coincided with the flow boundary between the southerlies/southeasterlies to the south of the rainband and the northerlies/northeasterlies to its north. For A1 and the rainband segment east of A1, the low-level southerly flow component (i.e., the rear-to-front flow) was generally present (cf. Fig. 5c). In contrast to an obvious confluent zone of airflow coincident with the studied rainband, the low-level northerly inflow tended to pass through the regions of relatively less organized precipitation located ahead (north) of the rainband.
A smaller-scale (~15 km in diameter) cyclonic (anticyclonic) vortex was also evident on the western (eastern) end of A1 at earlier time periods (Figs. 5a,b), a signature similar to the so-called bookend vortices or line-end vortices that are produced behind the ends of the convective line (e.g., Weisman 1993; Weisman and Davis 1998). The vertical extent of the vortices was confined to the lower troposphere below 3–4 km MSL (not shown). During the synthesis periods, the observed vortices weakened rapidly and disappeared at 2230 UTC, along with the weakening of the rear-to-front flow (from about 9 m s−1 at 2212 UTC to 3 m s−1 at and after 2230 UTC) associated with A1. Note that the horizontal scale of the observed rear-to-front flow was obviously larger than that of the vortices (cf. Figs. 5b,c), implying that the occurrence of the rear-to-front flow is not exclusively related to or caused by the observed counterrotating circulations. However, the development of the vortices along the rainband would reinforce the rear-to-front flow locally (Weisman 1993), which is consistent with a local maximum of rear-to-front flow found between the observed vortices (cf. Figs. 5a,b). Owing to the time constraint of dual-Doppler observations (only ~1 h), the formative time and actual duration of the observed vortices and their possible causal relationship with the rear-to-front flow are uncertain. A sequence of lowest PPI scans of the WFS radar available prior to the dual-Doppler synthesis period revealed that a notable decrease in the approaching radial velocity (i.e., the flow became more perpendicular to the rainband) started to occur in conjunction with the initial appearance of A1 and A2 (not shown), which suggests the close proximity of the strengthening of the low-level rear-to-front flow along the rainband to the development of A1 and A2.
Two vertical sections perpendicular to the approximately west–east-oriented rainband at 2218 and 2230 UTC are chosen to illustrate the primary characteristics of the cross-band circulations for A1 (Fig. 6). A1’s precipitation exhibited a significant vertical extent (the 40-dBZ contour exceeding 4 km MSL) and pronounced horizontal gradients of reflectivity particularly near the leading edge of the rainband, indicating the convective nature of the precipitation. A deep layer of northerly inflow extending from the lowest analysis level to the upper troposphere was observed. In particular, the inflow appears to be lifted upward at and immediately ahead of the leading edge of the low-level rear-to-front flow. A narrow zone of the low-level heaviest precipitation (>40 dBZ) coincided with strong updrafts (maximum derived vertical velocity of 3–5 m s−1) and convergence between the two opposite flows. The intensity of the Doppler-derived convective updrafts was weaker compared with previous dual-Doppler studies of squall lines that have a maximum magnitude of vertical velocity on the order of 10 m s−1 in the convective region (e.g., Roux 1988; Jorgensen et al. 1997). The relatively weak upward motions for the present case are consistent with the lower CAPE characterizing the rainband’s environment. There were some spatial and temporal variations for the vertical extent of the rear-to-front flow, but the typical depth was observed to be about 2–4 km (cf. Fig. 6). Except for a lack of signature of the vortices evident from A1, similar horizontal and vertical patterns of airflow and precipitation were also documented for A2 (Figs. 7a,b) as its western segment moved into the northeastern region of the synthesis domain.
A relatively wide area of stratiform precipitation was present behind the leading heavy precipitation of A1 and A2 (cf. Figs. 6, 7b). Over most of these regions, relatively weak downward motions (~1 m s−1) were generally present in the lower troposphere, which suggests that the low-level rear-to-front flow was characterized by the negative-buoyancy air. Given the rearward tilt of the leading updraft and the dominance of band-relative front-to-rear flow in the mid- to upper troposphere, the backward transport of upper-level ice particles generated in the convective region may contribute to the occurrence of the stratiform precipitation. This argument is supported by the presence of the brightband signature observed in some local regions at the height of 4–5 km MSL near the melting level (e.g., Y = 10 km in Fig. 7b). However, examination of a sequence of larger-scale PPI scans of reflectivity from the WFS radar during the formation of the stratiform precipitation also suggests that the remnant of backward moving, decaying convective elements along the rainband is probably an additional contributor.
The airflow and precipitation structures of A1 and A2 presented above exhibit several fundamental aspects that differ from those of previously documented TCRs and/or principal bands (e.g., Barnes et al. 1983; Powell 1990a; Hence and Houze 2008). The cross-band circulations within the principal band were usually dominated by low-level inflow from the outer to the inner side of the band, and the inflow was lifted upward near the inner side to produce radially outward-leaning convective motions (i.e., overturning updraft). In contrast, the strong convective updrafts of A1 and A2, generally with a radially inward (i.e., rearward) tilt, were closely related to the flow convergence produced as the low-level inflow ahead of the rainband encountered the rear-to-front flow behind (i.e., the flow from the inner to the outer side of the rainband). As described in section 3, there was no obvious positive buoyancy of the lifted air parcel in the lowest 3 km MSL (cf. Fig. 2). The convective forcing associated with the low-level rear-to-front flow may play a crucial role in the triggering or maintenance of intense convection along the rainband. Moreover, the region of stratiform precipitation associated with A1 and A2 was observed on the inner side of the rainband, which is to some degree consistent with the presence of upper-level front-to-rear flow in the convective regions, as described earlier. Such a configuration of precipitation distribution is also different from that of the principal band, whose stratiform precipitation was preferably located on the outer side of the band.
In contrast, the cross-band airflow structures of A1 and A2 appear quite similar to those of squall lines. As revealed by a large number of previous observational studies, the most typical kinematic signatures characterizing the convective region of a mature squall line include the low-level rear-to-front flow behind the leading edge of convection, a deep layer of inflow feeding convection from the front, and a rearward-sloping updraft presumably as the starting point of the so-called ascending front-to-rear flow evident in the mid- to upper troposphere over the trailing stratiform region (e.g., Roux et al. 1984; Smull and Houze 1985; Houze et al. 1989; Wang et al. 1990; Jorgensen et al. 1997; Houze 2004). The origin of the low-level rear-to-front flow is somewhat ambiguous in the literature, but it has been commonly related to the convectively generated outflow from the existing convective cells and evaporative cooling of precipitation behind the line. Theoretical and observational investigations have also shown that the persistent lifting of the warm and moist inflow by the cold rear-to-front flow is a primary forcing mechanism contributing to the maintenance of leading convection for squall-line systems (e.g., Rotunno et al. 1988; Roux 1988). The airflow patterns described above could be clearly observed from the dual-Doppler-derived winds for A1 and A2. It is thus reasonable to suspect that the convective behavior and/or processes of the studied ASREs may take on some sort of squall-line-like dynamics. The issue concerning the degree of similarity between the studied ASREs and squall lines will be further elaborated through the close examination of surface kinematic and thermodynamic fluctuations, as discussed in the next section.
5. Surface fluctuations
Figure 8 summarizes the variations of various surface meteorological quantities [temperature T, dewpoint temperature Td, perturbation pressure p′, equivalent potential temperature θe, cross-band (Vc) and along-band (Va) wind components, and rainfall rate (RR)] observed from the time series of the surface measurements as A2 passed over the PJY station. To minimize the influence of the storm-scale typhoon depression on the observed pressure values, p′ was calculated by subtracting the 1-h running mean of surface pressure from the pressure values recorded at a given time (e.g., Yu and Tsai 2010). However, the perturbation pressure obtained via the procedure above and the absolute pressure were found to have nearly the same fluctuations in terms of their magnitude and temporal trend. The time–height cross section of radar reflectivity at the PJY surface station observed by the WFS radar is also shown in Fig. 8 to provide a basic context for the precipitation characteristics associated with A2. The propagating direction and speed of A2 during its passage at the station was estimated to be 312° and 26 m s−1, respectively, corresponding to a cross-band (along band) propagating speed of 17.6 (19.4) m s−1. Because of the considerable propagation, the distortion of vertical precipitation structures due to the time lag of radar scanning between the low and high elevations of the PPI may be significant. To mitigate this effect, the specific measuring time of each radar beam was also considered when interpolating radar observations into the time–height cross section shown in Fig. 8.
A generally rearward-sloping leading edge was evident, being featured with an intense horizontal gradient in radar reflectivity and a sharp increase in surface rainfall rates (from 0 to 63 mm h−1). It seems that the leading edge also exhibited a frontward tilt in the lowest 2.5 km MSL. However, this feature was not obvious from the vertical cross sections of dual-Doppler observations at different synthesis periods (cf. Figs. 6, 7b), and thus it may be not a robust characteristic of the leading edge. The primary pressure fluctuations were characterized by an abrupt increase (~2 mb within a horizontal distance of only ~3 km from X = 15 to 18 km) coincident with the leading edge followed by a gradually decreasing trend. The most pronounced decrease in temperature (4°C), dewpoint temperature (3.5°C), and equivalent potential temperature (16 K) also occurred across the leading edge, with a relatively minor decrease (variation) ahead of the A2 and behind the leading heaviest precipitation. The magnitudes of these thermodynamic fluctuations are smaller than the mean fluctuation values of pressure and temperature (3.6 mb and 8.9 K, respectively) observed within midlatitude mesoscale convective systems (Engerer et al. 2008), but they are obviously larger than the typical values of surface fluctuations associated with TCRs (Yu and Chen 2011).
Given an unsaturated condition for the subcloud regions (i.e., T > Td), the decreasing trend of temperature as A2 passed by was consistent with the evaporative influence of precipitation particles. Note that the horizontal advection should not be favorable for the temperature drop across the rainband because surface winds were characterized by airflow from the warm (front) to cold (rear) side of the band (i.e., negative values of the cross-band wind component). However, a notable decrease in the absolute moisture amount (i.e., lower dewpoint temperature) near and behind the leading edge cannot be reasonably attributed to the evaporative processes that are expected to increase moisture. The downward transport of drier air originating from higher altitudes by convectively induced downdrafts may be an additional process contributing to the observed thermodynamic feature (e.g., Barnes et al. 1983; Skwira et al. 2005). Further support of this possibility is that, as revealed by the BC sounding in Fig. 3a, the ambient θe values exhibited two elevated minima, 334 and 331 K, located at 1.5 and 4.5 km (MSL), respectively. The minimum θe value (~340 K) shown in Fig. 8 was close to the elevated θe values. In addition, dual-Doppler observations also suggest the occurrence of some significant convective downdrafts associated with the leading convection, as evident in the vertical cross sections of the studied ASREs (e.g., near Y = 22 km in Fig. 6a). A combination of evaporative cooling and the downward transport of low-θe air aloft has also been shown to contribute to the development of a boundary layer cold pool with negative perturbations of both temperature and water vapor fields for tropical deep convection (Tompkins 2001).
The surface level was dominated by the front-to-rear flow, and an obvious deceleration of inflowing air (from −12 m s−1 at X = 15 km to −6 m s−1 at X = 21 km) and a relatively minor fluctuation of the along-band flow were observed across the leading edge. In contrast to nearly uniform winds over regions of light, shallow precipitation prior to the passage of the leading edge, the intensities of cross-band and along-band flow were generally more variable over the rear portions of A2, where enhanced stratiform precipitation was present and the modification of surface airflow by heavy rainfall could probably be significant. It appears that the low-level rear-to-front flow evident behind the leading edge of A2 as observed from the dual-Doppler-derived winds did not extend downward to the surface. The presence of the dominant front-to-rear flow is consistent with a more direct and significant influence of surface friction near the ground that would favor the intensification of inflow, particularly under strong ambient wind conditions associated with tropical cyclones, such as the present case.
The characteristics of a rapid rise (drop) in pressure (temperature) shown in Fig. 8 were similar to those documented during the passage of gust fronts and the leading edge of squall lines (e.g., Wakimoto 1982; Roux et al. 1984). Because the pressure jump observed at the leading edge for the present case coincided with a rapid decrease in temperature and a sharp increase in rainfall rates, it is possible that water loading and a convectively generated cold pool contributed to the observed signature of pressure fluctuations. To provide some physical insight into the possible cause of the surface pressure jump at the leading edge, the surface perturbation pressure resulting from the hydrostatic effects within cloud and precipitation systems can be evaluated by a diagnostic equation derived from the integration of the vertical momentum equation with the assumption of the inertial (acceleration) term equal to zero. The equation can be expressed as
where is the surface perturbation pressure caused by the convective effects; ρ0 and Tυ0 are the reference air density and virtual temperature (only a function of height and obtained from surface observations and BC sounding), respectively; is the perturbation virtual temperature; g is the gravity acceleration; qr is the rainwater mixing ratio; ZT is the height of echo top; and ZLCL is the height of the lifting condensation level (LCL). The terms on the right-hand side of (1) represent various hydrostatic effects contributing to the surface pressure perturbations, including subcloud warming/cooling (A), in-cloud warming/cooling due to convective motions and diabatic effects (B), and water loading (C). For term A, was calculated as the difference between the surface-observed virtual temperature and the mean virtual temperature averaged over regions ahead of the leading edge. The height of the LCL was estimated from surface-observed temperature and dewpoint temperature using the procedures described in Wilde et al. (1985). The vertical profile of precipitation observed by the WFS radar as shown in the top panel of Fig. 8 was utilized to calculate term C. In this calculation, the empirical formula between the reflectivity factor and the rainwater mixing ratio (qr = 0.001 73Z0.613/ρ) for tropical convection derived by Hauser and Amayenc (1986) was used. Because the region of the leading heaviest precipitation for the studied ASREs was primarily characterized by the organized convective updrafts (i.e., the dominance of in-cloud warming due to latent heat release, cf. Figs. 6, 7), term B should have a generally negative effect on the pressure rise across the leading edge and was thus initially ignored in our evaluation.
The magnitudes of terms A and C, their summation (A + C), and the observed surface perturbation pressure along the section corresponding to Fig. 8 are shown in Fig. 9. The hydrostatic pressure contributed by the subcloud evaporative cooling (a maximum of about 0.7 mb) appears to be more significant than the water-loading effect. The water-loading-induced pressure was generally small and had a maximum (~0.3 mb) at X = 19 km, coincident with the region of the leading heaviest precipitation. Particularly, the combination of terms A and C (a maximum of about 1 mb) explains only approximately 50% of the pressure rise observed at the leading edge. This result suggests that the nonhydrostatic effects may also be a potential contributor. As shown in Figs. 6–8, the dynamic forcings in association with a significant deceleration of the surface inflow air and the acceleration of vertical motions at the leading edge may possibly generate some nonhydrostatic pressure. To evaluate this possibility, the dynamic pressure due to the acceleration/deceleration of airflow (e.g., Yu et al. 2001) may be expressed as
where x, y, and z are the cross-band, along-band, and vertical directions, respectively. The expression of (2) can be derived by taking the differential operator (∇·) in the three-dimensional momentum equation and applying the anelastic approximation (e.g., Rotunno and Klemp 1982). The term on the right-hand side of (2) is proportional to the Laplace of the kinetic energy, and under a steady-state assumption it can be physically considered the Bernoulli effect (Yau 1979). Assuming the spatial variations of are most significant in the cross-band direction, (2) becomes
With the approximation of the derivatives by finite difference quotients, (3) can be written as
where h is the grid spacing valid for the estimate of the field derivatives; and ΔVc, ΔVa, and Δw are the differences in the cross-band wind component, the along-band wind component, and the vertical velocity over h. In addition, the subscripts (i.e., n) on indicate the grid notation. It is practical to consider that the velocity gradient is mainly confined to the interval of h centered at the middle grid location, with a relatively minor variation outside h. The velocity-gradient-induced pressure perturbations on both ends of the evaluated space can thus be assumed to be negligible [i.e., ], and (4) can be further expressed as
It is evident from (5) that the magnitude of dynamic pressure is proportional to the square of the velocity gradient in three respective directions. The expression of (5) is similar to the simplified Bernoulli equation at the stagnation point of a streamline when considering that the flow is steady and incompressible (Newton 1963; Wakimoto 1982). Based on Figs. 6–8, ΔVc and Δw at the leading edge can be roughly estimated to be 6 and 5 m s−1, respectively, and the average air density near the surface is approximately 1.15 kg m−3. These values yield a dynamic pressure of about 0.35 mb, a magnitude slightly larger than the maximum value contributed by water loading (cf. Fig. 9). Note that consideration of the velocity gradient in the along-band direction, if any, may further increase this estimated magnitude of the dynamic pressure. It is clear from the above evaluation that, in addition to the evaporative cooling and water-loading effects, the nonhydrostatic pressure generated by the dynamic forcings may also be important for the present case, which can help explain the significant pressure jump across the leading heaviest precipitation.
a. Cold pool dynamics
Although a squall-line-like airflow pattern and surface fluctuation was documented for the studied ASREs, it is uncertain whether the cold pool dynamics play a significant role in influencing or determining their convective behavior in terms of structure and propagation. To provide a plausible answer to this question, an evaluation based on radar and surface observations is presented in this section.
As described in section 4, a persistent structural characteristic of the studied ASREs is the rearward tilt of the leading updraft. According to the squall-line theory proposed by Rotunno et al. (1988), the relative strength of horizontal vorticity generated by the buoyancy gradient across the leading edge of the cold pool and the environmental vertical shear determines the tilting feature of the leading updraft. Following Rotunno et al. (1988), the buoyancy-generated vorticity C may be represented by
where θ0 is the base-state potential temperature, Δθmin is the surface cold pool temperature deficit relative to ambient conditions, and H is the cold pool depth. The environmental shear-induced vorticity Δu can be represented by the vertical shear over H. Rotunno et al. (1988) indicate that, when C = Δu, the convective motions at the leading edge of the cold pool are upright and most intense (i.e., the so-called optimal condition). In contrast, for situations in which C > Δu, the leading updraft is relatively weak and tends to slope rearward (i.e., upshear side) and vice versa.
For the present case, the Δθmin for the cold pool estimated from the surface observations shown in Fig. 8 is equal to 3.8 K, and θ0 is approximated by the mean potential temperature (299.5 K) averaged over regions ahead of the leading edge in Fig. 8. Because the low-level rear-to-front flow evident behind the leading edge would be characterized by negative-buoyancy air as described in section 4, its vertical extent (~3 km, cf. Figs. 6, 7) is assumed to be the maximum possible depth of the cold pool. For comparison, the C values are also calculated when considering the lower depth of the cold pool equal to 1 and 2 km. With these magnitudes, a range of values from 11 to 19 m s−1 is obtained for C. The magnitude of Δu may be readily obtained from the dual-Doppler-derived winds over regions ahead of the studied ASREs. This gives a mean Δu ranging from −0.6 to 2.3 m s−1 in the lowest 1–3 km MSL.
The calculations above indicate that the ambient vertical shear in the cross-band direction was generally weak and belonged to the so-called suboptimal (i.e., C > Δu) state. In this condition, the convective updrafts at the leading edge should be less intense and should exhibit a rearward tilt. This theoretical prediction appears to be consistent with the dual-Doppler observations showing a moderate-to-weak intensity of the leading updrafts (~3–5 m s−1) sloping over the cold air. A suboptimal condition has been similarly observed for some squall lines preceding landfalling tropical cyclones and the lifetime of these lines was found to be generally short (4 h on average) (Meng and Zhang 2012). The suboptimal state predicted herein seems inconsistent with the long-lasting nature of moist convection along the studied TCR. One should note that the present ASREs (i.e., A1 and A2) were actually embedded within the larger-scale rainband feature (cf. Fig. 1), and as indicated by Yu and Tsai (2010), the outer rainband was characterized by some wavelike signatures and the wave-induced motions may play a role in the development of its associated moist convection. Therefore, it is likely that the maintenance of the rainband’s convection may be governed by some kind of interactions between the localized, convectively generated cold pool and the wave dynamics.
The importance of the cold pool dynamics for the studied ASREs may also be assessed by whether they propagate at a speed similar to the laboratory density current (Simpson 1969). A large number of previous observational studies have shown that some atmospheric disturbances, such as cold fronts, thunderstorm outflow, and squall lines, can sometimes bear high resemblance to the density current in terms of their associated airflow patterns and propagation speed (e.g., Miller and Betts 1977; Carbone 1982; Wakimoto 1982; Shapiro 1984; Roux et al. 1993; Yu and Smull 2000). However, little is known about the degree of propagation similarity between the TCRs and the density current.
When considering the influence of ambient winds on the propagation speed of a density current, the velocity of an atmospheric cold pool Vcp can be approximated by the expression (Simpson and Britter 1980)
where H is the depth of the cold air; ρe and ρc are the environmental and cold pool densities, respectively; V0 is the ambient cross-band wind component ahead of the cold pool (negative for a wind toward the cold air and vice versa); and k and b are empirical constants. Based on Simpson and Britter (1980), the best fit of (7) to atmospheric observations gives the constant k and b equal to 0.9 and 0.6, respectively. It is clear from (7) that the cold pool propagation is mainly driven by the pressure gradient force induced by the difference of air density across the leading edge of the cold pool. For the present case, H is again assumed to range from 1 to 3 km. The ρe (ρc) value is approximated by the mean density averaged over regions ahead of (behind) the leading edge (cf. Fig. 8), which is calculated to be 1.146 (1.165) kg m−3. Mean magnitudes of V0 (ahead of A2) averaged below 1–3 km (MSL), which are estimated from the dual-Doppler synthesis winds valid at a time (2250 UTC) closest to the surface observations shown in Fig. 8, are between 4.3 and 4.9 m s−1. These values yield a Vcp between 14.0 and 22.7 m s−1. This theoretical prediction appears to provide a reasonable range of magnitudes for the observed cross-band propagating speed (17.6 m s−1, as described in section 5) of A2.
It should be noted that the density current dynamics is commonly treated as a two-dimensional problem (i.e., considering the plane of the vertical and the propagation direction). Because the studied ASREs exhibited a pronounced propagating motion not only in the cross-band direction but also the along-band direction (19.4 m s−1), their propagating nature may be more complex than what we have discussed above. The studied typhoon rainband was aligned mainly parallel to the large-scale cyclonic typhoon circulation (cf. Fig. 1), so A1 (A2) was actually embedded within an environmental condition with strong along-band winds. From the “density current” viewpoint, the ambient flow (shear) and rotating environment have been recognized as important factors influencing the density current propagation (e.g., Liu and Moncrieff 1996; Dalu and Baldi 2010). As calculated from the dual-Doppler observations, the mean value of the along-band wind component averaged below 3 km (MSL) is found to be approximately 25 m s−1. It is possible that such intense ambient flow also has a substantial impact on the propagation of the studied ASREs. The three-dimensional structures and behavior of the density current within the tropical cyclone environment, as well as the possible similarity of propagation between the TCRs and the density current, deserve future observational and theoretical investigation, particularly in the presence of a stronger convectively generated cold pool such as the present case.
b. Origin of the vortices
An interesting horizontal airflow feature associated with A1, as observed from the earlier period of dual-Doppler synthesis winds, is the two counterrotating line-end vortices (cf. Figs. 5a,b). Unfortunately, our dual-Doppler observations captured the line-end vortices during their dissipating stage, which cannot support the detailed analysis of vorticity budget to investigate their formative processes. The line-end vortex signature has been frequently documented along the leading convection within both tropical and midlatitude mesoscale convective systems (e.g., Jorgensen and Smull 1993; Scott and Rutledge 1995; Jorgensen et al. 1997), but not within tropical cyclones, although the mesovortices emerging from the deep convective areas of tropical cyclones have been occasionally documented (e.g., Hendricks and Montgomery 2006). As described in section 4, the appearance of the line-end vortices would probably be favorable for the local intensification of low-level rear-to-front flow and the subsequent development of arc-shaped radar signatures along the studied TCR, although these evolving aspects are more speculative than conclusive due to the lack of adequate verification from available observations. Note that there was no evidence of the line-end vortices for A2 and that its airflow patterns were also similar to A1, as described in section 4. Hence, the presence of the line-end vortices may increase the along-band variability of airflow and precipitation but may not alter the overall structural characteristics of the studied ASREs.
A number of previous modeling studies have shown that the formative processes of the line-end vortices within convective lines are essentially related to the tilting of the horizontal vorticity associated with either environmental vertical shear or convectively generated shear (e.g., Weisman 1993; Trier et al. 1997; Weisman and Davis 1998). As described in section 3, the ambient vertical shear for the studied TCR was aligned mostly along the rainband, which suggests a horizontal vorticity vector primarily in the cross-band (i.e., south–north) direction. It is generally difficult to explain the counterrotating vortices arranged in the west–east direction, as in the present case, by the tilting of this ambient horizontal vorticity when subjected to the cross-band variations of vertical velocity (cf. Fig. 5b).
However, as shown in the previous section, the presence of a near-surface cold pool was clearly evident in the present case, and the horizontal vorticity generated by the cold pool–updraft interface is expected to be significant. It is possible that the convectively generated shear may be a more important vorticity source than the ambient shear in producing the observed vortex pair when considering the tilting as a primary mechanism for the vortex initiation.
For example, given a roughly east–west orientation of A1, the buoyancy-gradient-induced horizontal vorticity vector would be mostly westerly. The tilting of this convectively generated vorticity by the along-band variations of vertical velocity is more likely to produce the east–west-oriented vortex pair. In principle, both updrafts and downdrafts associated with A1 could have the potential to tilt the horizontal vorticity into the vertical direction. However, the tilting of the leading updrafts at the line’s ends would be more plausible. The dual-Doppler analyses indicate that strong updrafts were generally confined to the region of strongest reflectivity (>40–45 dBZ) along A1 (cf. Fig. 6), with weaker upward motions over regions of less intense reflectivity (<40 dBZ) characterizing its line-end vicinity (cf. Fig. 5). The line-end tilting of the westerly horizontal vorticity vector would favor the initiation of a cyclonic and anticyclonic vorticity located on the western and eastern ends of A1, respectively, which is consistent with our radar observations. In contrast, the line-end tilting by the downward motions would give a completely opposite result.
c. Relation of structure to environmental conditions
One of the most important findings from the study is that the ASREs investigated herein exhibit unique airflow and precipitation structures that are different from the previously documented TCRs located closer to the inner core of tropical cyclones, such as principal bands. For a better demonstration of these differences, a schematic diagram of airflow and precipitation for the present case and the inner TCRs is presented in Fig. 10. An important but unresolved issue is how the studied ASREs could evolve into a squall-line-like convective circulation (Fig. 10a) and depart from the structures of the inner TCRs (Fig. 10b). To seek a complete answer for this question is actually beyond the scope of this study, but we propose several environmental factors that may play a role in influencing or determining the structural characteristics observed in this case.
First, the rainband environment for the present case was characterized by drier boundary layer air with a minimum relative humidity of 74% (cf. Fig. 2). This thermodynamic feature is expected to facilitate the evaporative process of hydrometeors and to contribute to the intensity of the observed cold pool. Perhaps owing to the subsidence surrounding the inner-core eyewall (or rainband) convection as well as stronger modulations by convection over the inner-core regions, the outer-core environment has been observed to exhibit generally lower humidity compared with the inner-core environment (e.g., Frank 1977). This environmental characteristic is consistent with a stronger (weaker) cold pool usually observed for the outer (inner) TCRs (Yu and Chen 2011). The presence of a stronger convectively generated cold pool as evident in the present case may further force the leading vertical motions to tilt rearward according to the theoretical vorticity argument (e.g., Rotunno et al. 1988). In addition, the nature of the weak ambient vertical shear in the cross-band direction in the lower troposphere, as evident in Fig. 3b, may also be considered an additional important coupler. Therefore, the combination of these two environmental characteristics may help explain the low-level rearward-tilting updraft features (cf. Fig. 10a) observed for the studied ASREs.
For the inner TCRs, a common airflow pattern in the mid- to upper levels is dominated by overturning upward motions rooted from the low-level inflow at the inner side (Fig. 10b), which to some extent reflects a strong constraint by a typical secondary circulation within tropical cyclones with storm inflow at low levels and an outflow layer in the upper troposphere. Given that the updraft behavior is strongly modulated by environmental airflow and shear in a manner similar to what we have discussed above, it is reasonable to suspect that the lack of overturning updrafts in the present case would be related to the upper-level typhoon outflow characteristics.
Supporting evidence is provided by a sequence of mean wind profiles averaged with respect to the typhoon center constructed from the National Centers for Environmental Prediction (NCEP)–NCAR reanalysis data. In particular, these observations reveal a dramatic change in the intensity of upper-level cyclone-scale outflow just prior to the occurrence of A1 and A2 (~1800 UTC 1 October) as the studied typhoon approached the eastern coast of Taiwan and increasingly interacted with the landmass. Specifically, the maximum intensity of the outflow associated with the landfalling typhoon was observed to decrease, and the height of the strongest outflow was found to become much lower (~4.5 km MSL). These evolving aspects were presumably related to the structural changes of the typhoon circulations due to the influence of topography (e.g., Yang et al. 2008) and resulted in an environmental wind transition from a strongly frontward shear to a slightly rearward shear at mid- to upper levels. This shear alternation in turn would favor the development of a rearward-tilting updraft at upper levels, as in the present case.
Although the discussions above imply that the upper-level structure of the studied rainband may be partly due to some complicated interactions of the typhoon circulations with Taiwan’s topography, the natural variability of outflow intensity at different radial distances for landfalling typhoons (like the present case) or tropical cyclones over the open ocean still cannot be ruled out as a potential factor that would influence the internal structure of TCRs. Radial variations of outflow and its associated shear could be clearly seen from the previously documented mean structure of tropical cyclones (e.g., Frank 1977; Gray 1979); however, our knowledge concerning the detailed aspects of these features and their impact on the rainband’s structures has not been well established. It is also noteworthy that the importance of the vertical shear associated with the large-scale tropical cyclone environment to the distribution of the clouds and precipitation of the eyewall has been generally recognized (e.g., Black et al. 2002). Nevertheless, there are still large gaps in our knowledge of how the structural changes of typhoon circulations, if any, influence local distributions of vertical shear and the subsequent development of TCRs. These scientific aspects remain unresolved and deserve future clarification through comprehensive investigations of TCRs developing over different storm-relative locations and different evolving stages of tropical cyclones.
Recent observational evidence has suggested the possibility that some tropical cyclone rainbands (TCRs) may exhibit a convective behavior toward the squall-line-like precipitation system, such as the development of convectively generated cold pools and arc-shaped radar echoes (ASREs) along the rainband. However, this issue remains unclear, and our knowledge of the structures of TCRs has mainly been confined to the principal band of tropical cyclones. This study used ground-based radar and surface observations to document the ASREs that developed along a propagating outer rainband of Typhoon Longwang as it approached the northern coastal regions of Taiwan on 1 October 2005. In particular, with the availability of dual-Doppler radar and surface observations, this study explores the possible distinction between the present case, previously documented TCRs, and squall lines.
The dual-Doppler-derived fields show that the leading precipitation of the studied ASREs exhibited a convective nature with a sharp horizontal gradient of reflectivity and a significant vertical extent with the 40-dBZ contour exceeding 4 km MSL. The regions behind the leading convection were characterized by obvious band-relative rear-to-front flow at low levels and associated with a broader area of stratiform precipitation. The typical depth of this flow was observed to be about 2–4 km MSL. The deep band-relative inflow extending from the surface to the upper troposphere was generally present ahead of the ASREs. The inflow appears to be lifted upward at and immediately ahead of the leading edge of the low-level rear-to-front flow to form a rearward tilt of updrafts. These airflow patterns are similar to those of the convective region of squall lines, but they differ fundamentally from those of previously documented TCRs located closer to the inner core of cyclones, as schematically summarized in Fig. 10. The cross-band circulations within the inner TCRs were usually dominated by low-level inflow from the outer to the inner side of the band, and the inflow was lifted upward near the inner side to produce radially outward-leaning convective motions (i.e., overturning updraft) (Fig. 10b). Moreover, the region of stratiform precipitation associated with the studied ASREs was observed on the inner side of the rainband, which is to some degree consistent with the presence of upper-level front-to-rear flow in the convective regions. Such a configuration of precipitation distribution is also different from that of the inner band, whose stratiform precipitation was preferably located on the outer side of the band.
Detailed analyses of the surface fluctuations that were observed as one of the studied ASREs (i.e., A2) passed over an offshore island station show an abrupt pressure rise (2 mb), a temperature drop (4°C), and a pronounced deceleration of inflow air coincident with the leading heavy precipitation. As suggested by the quantitative diagnosis of pressure perturbations, the combination of the evaporative cooling of hydrometeors, water loading, and dynamically induced nonhydrostatic pressure is required to explain the significant pressure jump observed at the leading edge for the present case. Moreover, based on the evaluation presented in section 6, it is suggested that the convectively generated cold pool would most likely be an important factor influencing the structures and propagation of the studied ASREs.
The results from this study imply that under favorable environmental circumstances (such as those discussed in section 6c), the outer TCRs may develop into squall-line-like airflow and precipitation structures; in addition, these results reflect our incomplete understanding of the general aspects of TCRs. More case studies of the outer TCRs and their corresponding modeling will be required to clarify whether the structural characteristics presented in this study are typical for propagating outer TCRs and to determine the environmental factors or storm stages that can promote the cold pool dynamics important for the development of moist convection within tropical cyclones.
The Doppler radar data and surface and sounding observations used in this study were provided by the Taiwan Central Weather Bureau. We thank Professor Zhiyong Meng and anonymous reviewers for providing helpful comments that improved the manuscript. This study is supported by the National Science Council of Taiwan under Research Grants NSC99-2111-M-034-002-MY3 and NSC100-2628-M-034-001-MY3.