Origin of outer tropical cyclone rainbands

Domain: earth_science
Published: 2023-11-03
Editorial outcome: major_revision

Abstract
Outer tropical cyclone rainbands (TCRs) are a concentrated region of heavy precipitation and hazardous weather within tropical cyclones (TCs). Outer TCRs pose considerable risk to human societies, but their origin remains unresolved. Here, we identify a total of 1029 outer TCRs at their formative stage from 95 TCs and present a large collection of radar observations in order to establish a robust foundation of the natural diversity of rainband origin. The results show the dominance of outer origin for the observed outer TCRs, in distinct contrast to theoretical modeling works of outer TCRs, which propose inner-origin scenarios. Our analysis also suggests that squall-line dynamics are a common, but not the sole, mechanism responsible for outer TCR formation. The nature of preexisting outer precipitation is found to be an important factor to influence the squall-line and non-squall-line outer TCR initiation.

Introduction
Tropical cyclones (TCs) are the most devastating storms in nature since they can result in the significant loss of human life and tremendous property damage due to torrential rainfall and intense winds1,2. In addition to eyewalls, tropical cyclone rainbands (TCRs) are a primary, concentrated region of heavy precipitation and hazardous weather within TCs3–10. TCRs not only play a vital role in influencing the development and intensity of TCs11–18 but also represent vast threats to societies because of their high potential to produce catastrophic rainfall and floods19–23. Therefore, improving our fundamental understanding of how TCRs form and develop is critically important for disaster mitigation and the prediction of the natural hazards and climate extremes in TC-prone regions.

TCRs are conventionally classified into inner and outer rainbands based on their location relative to the TC center. Inner TCRs are located within the TC inner core that has a radial distance of 100–200 km or ~3 times the radius of maximum wind (RMW), whereas outer TCRs are located beyond the inner core17,24. Moist convection of inner TCRs is usually weaker and organized into a more circular geometry due to the pronounced influence of the inner-core vortex and filamentation effect5,8,25. The precipitation features of outer TCRs are typically asymmetric but much more convective than those of inner TCRs due to a larger convective instability in the outer region of TCs5,8,17,26–31. Outer TCRs tend to have stronger and broader impacts on human and natural communities through the generation of severe weather conditions and flooding21,28,29,31,32.

Although the processes that form the inner TCRs have not been wholly conclusive33, a general consensus is that their appearance is related to the inner-core wave activities (e.g., vortex Rossby waves, VRWs) initiated near the eyewall34–38. However, the origin of the outer TCRs remains uncertain and the formative mechanisms proposed previously are diverse. Earlier modeling and theoretical investigations have suggested that outer TCRs are probably a manifestation of outward-propagating gravity waves (GWs) that are excited close to the TC center or inside the inner core39–42. In this view, the moist convection occurring in outer TCRs may be triggered by gravity-wave-induced upward motions42,43. Despite the potential discrepancy in the propagation speed between theoretical GWs and observed outer TCRs3,30,42–47, what we learned from these previous works is still unable to adequately address whether outer TCRs would be initially triggered by the GWs within the inner-core region and then propagate outward to the outer region of TCs.

Recently, the inner-origin scenario above was further explored by an idealized numerical TCR simulation by Li et al.48. That study demonstrates that convectively active outer TCRs form as weakly convective inner TCRs propagate to the outer region where filamentation and stabilization are reduced. Li et al.48 argue that their simulated inner TCRs would most likely be related to inner-core VRWs instead of GWs. In the context of the inner origin, the inner and outer TCRs are supposed to have no inherent distinction, although their associated precipitation characteristics may undergo some sort of convective transformation in response to the differences in environmental conditions between the inner and outer regions of TCs.

Although many previous theoretical and modeling works have emphasized the importance of the inner-origin processes for outer TCRs, they also seem likely to form locally near the inner-core boundary or in the outer region of TCs, which may be considered outer-origin. Understanding of the outer-origin processes has been limited due to scarce observations during the formative stage of outer TCRs. A particular, well-known type of rainband usually exists near the boundary between the inner-core vortex of TCs and environmental flow. This type of rainband has been referred to as the “principal band (PB)”5 and is typically quasi-stationary relatively to the TC center5,7,8,49,50. Outer TCRs are a broader class of rainband than just PB that exhibits unique precipitation and kinematic features tied to TC vortex dynamics. Although possible mechanisms responsible for the formation of PB have been explored by numerical modeling51, previous PB observational studies rely dominantly on the analyses of airborne flight-level and radar data collected over a relatively short period of time during the mature or late stage of oceanic TCRs. Hence, these observational works do not provide strong clues to where and how outer TCRs form within TCs.

With advances in high-resolution radar and surface observations and numerical simulations, a growing number of TC studies have improved our understanding of the detailed structural characteristics of outer TCRs28–31,44,45,52–56. These investigations have revealed the frequent presence of surface cold pool signatures and squall-line-like airflow patterns for outer TCRs, which imply the potential importance of squall-line dynamics on the development of moist convection associated with outer TCRs. However, none of the previous observational studies, except for the TCR case described in Yu et al.30, capture the formative stage of outer TCRs or confirm how relevant the squall-line dynamics would be in the outer TCR initiation process.

To the best of our knowledge, Yu et al.30 is the only observational study of TCRs to provide a complete picture of the outer-origin processes. By tracking the history of a long-lived outer TCR associated with Typhoon Jangmi (2008), Yu et al.30 documented that the outer rainband was initiated as it detached from the upwind segment of a stratiform precipitation region located slightly beyond the inner-core boundary. A distinct transformation from generally stratiform precipitation to highly convective precipitation, which was related to the increasing intensity of convectively generated cold pools and their interactions with low-level vertical shear57, was documented as the rainband propagated cyclonically outward.

The diurnal forcings and large-scale vertical wind shear have been both recognized to have a strong impact on the development and structure of TC convection. Previous studies have provided observational evidence that these two factors can influence convective intensities and distributions over a very broad area not only within the inner region of TCs but also beyond their inner core58,59. It is thus likely that the outer TCR origin would be also modulated by diurnal and shear effects. However, this likelihood has never been confirmed, and whether the formation of outer TCRs would exhibit diurnal cycles or some sort of dependence on large-scale vertical shear remains unclear.

A final possible contributor to the origin of outer TCRs, as proposed by a few earlier studies, is related to the boundary-layer instability from an Ekman-like flow4,60–62. On the basis of theoretical approaches, this kind of instability can occur in the rotational environment under the presence of suitable vertical shear in the boundary layer, taking the form of spiral-shaped roll vortices. Two of the most remarkable aspects for the instability-generated perturbations are their storm-relative stationary characteristics and a nearly constant crossing angle of about ~15o with respect to the TC center4. The crossing angle is defined as the angle between the rainband’s orientation and the tangent to a circle with radius from the band to the TC center3,4. Different wavelengths of roll vortices, ranging from sub-kilometers to several kilometers, have also been observed in the tropical cyclone boundary layer63–65. However, the potential relevance of the boundary-layer instabilities and roll vortices to the appearance of outer TCRs remains highly uncertain at present due to the lack of observational validation.

It is clear from the literature reviews above that current research is still far from adequate to clarify the relative prevalence of the inner-origin and outer-origin scenarios and of various possible realistic formative scenarios for outer TCRs. To establish a robust foundation of knowledge regarding the natural diversity of the rainband origin, a critical and challenging task is thus to collect detailed observational information from a very early stage of rainband development from a considerable number of outer TCR cases.

The primary objective of this study is to use long-term radar observations collected during 2002–2019 to identify the origin of numerous outer TCRs associated with TCs as they approach the ocean areas near Taiwan. The island of Taiwan is located within the main path of TCs that originate over the northwestern Pacific Ocean, a basin with the highest TC activity on Earth1. The statistics based on the typhoon database provided by the Taiwan Central Weather Bureau (CWB) (https://rdc28.cwb.gov.tw/TDB/public/warning_typhoon_list/) indicate that, since 1958, there have been approximately four to ten TCs that approach the area around Taiwan every year. In addition, an excellent ground-based Doppler radar observation network has been in operation in Taiwan since the 2000s. Both of the above aspects make it possible to collect a large dataset of outer TCR cases as TCs approach from the northwestern Pacific. The particular focus of this study is to explore the important characteristics of outer TCRs during their initiation stage in terms of their formative location and attendant propagation. The observations consisting of 1029 outer TCR cases associated with 95 TCs can provide important insight into the origin of outer TCRs.

Results
Formative location and dynamic regime

A plan view of the formative locations, with respect to the typhoon center and the direction of typhoon motion, for all identified TCRs is illustrated in Fig. 1. A diverse horizontal distribution of TCR formation over a broad region is seen, with the majority of the TCRs located within a radial distance of ~400 km. Nearly all TCRs are initiated beyond a radius of ~100 km. There are slightly more rainbands (~59% of the identified TCRs) in the front quadrants. This azimuthal variation of the outer TCR formation, however, would be due in part to the contamination by the inherent limitation of radar observations9,29. Specifically, the precipitation information of the front quadrants for a typical westward-moving TCs over the northwestern Pacific Ocean could be usually monitored by coastal radars in Taiwan for a longer period of time. In contrast, when the rear quadrants of TCs reach the observational coverage of coastal radars, the inner-core circulations of TCs have been closer to the land mass of Taiwan so both TC circulations and rainbands have greater chances to experience orographic modifications and/or make landfall. This sampling preference of coastal radars is expected to capture more outer TCR cases in the front quadrants than in the rear quadrants, consistent with the asymmetric characteristic of formative locations of the observed outer TCRs, as shown in Fig. 1.

The formative number of TCRs as a function of radial distance, as shown in Fig. 2a, indicates that the most concentrated regions of TCR formation are between 150 and 350 km from the TC center, and 589 rainbands (~57%) are initiated within this radial interval. Nevertheless, considerable TCRs are observed to form in far outer TC regions beyond the radius of 350 km. The formative number of TCRs expressed as a function of normalized radial distance by RMW, as shown in Fig. 2b, shows that a dominant portion of the identified TCRs (~97%) are initiated beyond the inner-core region (i.e., a distance of three times the RMW). Relatively higher formative numbers exist in the radii of 3–8 times the RMW, which accounts for ~47% of the identified TCRs. Peak TCR formation (108 cases) is located between 4 and 5 times the RMW. Outer TCRs that form in the outer vicinity adjacent to the inner-core boundary were also identified in a case study by Yu et al.30. Note that few of the outer TCRs (32 cases) are initiated inside three times the RMW (Fig. 2b), implying that the formation of these rainbands is related to the transition from outward-propagating inner TCRs to outer TCRs48. However, such an inner origin is not a frequent or dominant scenario for outer TCR formation because of a very low fraction of initiation within the inner-core region (only ~3% of the identified TCRs). It is fairly reasonable to conclude that actual outer TCRs tend to be initiated locally in the outer TC region (i.e., outer origin) and do not preferably originate from the inner-core region.

A complementary view of dynamic regimes for outer TCR formation can be provided by analyzing the filamentation time for each of the identified TCRs. As demonstrated in Rozoff et al.25, the inner-core flow of TCs tends to be strain-dominated and is characterized by a rapid filamentation zone with a timescale less than that of deep moist convective overturning (~30 min). Relative magnitudes of the filamentation time are useful for providing a dynamic distinction between the inner and outer regions of TCs25,66. In this study, the filamentation time, as defined in Rozoff et al.25, is calculated using the wind information at the formative location of each rainband at 1.5 km above mean sea level (MSL) from the ERA5 reanalysis data. The reason why the 1.5-km level is chosen for calculation is because this height is immediately above the typical top of TC boundary layer (0.5~1 km MSL) so the winds from this height are expected to better represent the TC intensity and circulation. Figure 2c indicates that outer TCR formation occurs in regions with filamentation times greater than 1 h. None of the outer TCRs is initiated within the rapid filamentation zone (i.e., filamentation time < 30 min). The dominant preference of outer origin for the observed rainbands supports what we see in Fig. 2b.

Since outer TCR formation is observed to be active over extensive outer regions of TCs, as shown in Figs. 1, 2a–c, one intriguing question emerges, what is the degree of prevalence for outer TCRs to form at radii larger than the storm radius of TCs? The size of a TC has been practically defined as the radius of a certain threshold of near-surface wind speed or by the radial extent of the outermost closed isobar67–69. Because the TC size may vary considerably with different thresholds chosen, we use the average radius of 34 kt winds (R34) as a storm radius for TCs in this study. R34 is commonly considered as the area of the TC warnings issued by operational forecasting centers31. The statistical distribution of the TCR formative number, as a function of normalized radial distance by JTWC-recorded R34, is shown in Fig. 2d. The peak outer TCR formation (139 cases) is observed within the interval of normalized radial distances between 0.75 and 1, which is close to the outer boundary of the storm radius of R34. Although the formative numbers tend to decrease generally with increasing radial distance in regions beyond the storm radius, the formative fractions of outer TCRs inside and outside the storm radius are dramatically different, which are calculated to be 29% and 71%, respectively. These statistics further indicate that the majority of outer TCR formation actually occurs in far outer regions beyond the operational TC alert area. This finding is impressive and suggests an essential need to expand the area of routine TC alerts, particularly given the frequent development of severe weather conditions associated with outer TCRs29,31.

It is noteworthy that diurnal forcings, as described in the Introduction, are well known to influence convective development of TCs. The formative times of all outer TCRs observed in this study are also analyzed to understand if there are any diurnal signals. It is found that the number of outer TCRs formed at different times in a day is similar and approximately equal to 80 cases for each time interval. This result generally reflects the lack of obvious diurnal variations for the formation of the studied outer TCRs.

Propagation and geometry characteristics

The large collection of TCR cases in this study provides a good opportunity to explore the generality and diversity of propagation and geometry characteristics for outer TCRs near Taiwan. Statistical results of the radial and tangential propagation velocities and the rainband’s width and crossing angles for all identified TCRs are shown in Fig. 3. The identified TCRs possess significant variabilities in the radial propagation speed, but the dominant majority (964 TCR cases, ~94%) are within the range of ±10 ms−1 (Fig. 3a). Outward propagation (i.e., positive radial velocities) tends to be more frequent (660 TCR cases, ~64%), whereas inward propagation is also evident from a considerable number of outer TCRs (369 TCR cases, ~36%). This statistical finding is significant and indicates that outward propagation is common but not dominant for outer TCRs. Whether these propagation characteristics are consistent with wave theories will be explored later in this section. The peak TCR number exists in the velocity interval of 2–4 ms−1, which is roughly comparable to the outward propagation speed of several outer TCRs (3–7 ms−1) reported in previous observational studies of TCs3,30,43. Small proportions of the observed outer TCRs have slow radial propagations within ±1 ms−1 (Fig. 3a), consistent with the quasi-stationary characteristics of PB5 and spiral-shaped disturbances generated by boundary-layer instabilities in a theoretical framework61. However, these rainbands are few (only 144 cases, ~14%), and the radially propagating feature is prevalent from our TCR dataset. Assuming the 2–5 times RMW as an approximate area for the outer boundary of the inner-core vortex of TCs, where PBs typically form, only 13 out of 144 outer TCR cases are actually located downshear within this area. Such a small number of TCR cases (~1% of all identified outer TCRs) suggests that the possible impact of PB-like rainbands on the outer TCR dataset analyzed in this study may be considered negligible. One of the primary factors contributing to the potential preclusion from the class of outer TCRs is related to the fact that PBs tend to occur preferentially inside the TC vortex core or near its outer boundary (~3 times RMW), as learned from the comprehensive examination of radar-observed precipitation field associated with 95 TCs investigated in this study.

Compared with the radial propagation, the tangential propagation of outer TCRs is generally much faster and predominantly cyclonic (i.e., positive tangential velocities) (Fig. 3b), which is consistent with the influence of TC vortex circulations. The mean tangential propagation for all identified TCRs is calculated to be 10.4 ms−1, which is somewhat slower than the average ambient tangential flow (14.4 ms−1) within the layer of precipitation associated with the rainbands (0.1~12 km MSL).

Most of the observed outer TCRs (748 cases; 73%) have cross-band widths ranging from 5 to 25 km (Fig. 3c), equivalent to a horizontal wavelength of 10 to 50 km, as approximated by twice the radar-observed TCR width. These rainband scales are much larger than the boundary-layer roll vortices, with typical horizontal wavelengths on the order of a few hundreds of meters to several kilometers62–65. The most frequent occurrence of the observed crossing angles is found between 10° and 30° (Fig. 3d), which is consistent with typical values of 20° to 25° reported in the literature4. However, a wide distribution of crossing angles, such as the evidence of larger and negative values for some observed rainbands, implies complexities in the TCR structures and dynamics.

To evaluate the relevance of wave activities to the initiation of outer TCRs, the theoretical phase velocities for two well-known, important wave types (GWs and VRWs) active within TCs are calculated and compared with the observed propagation velocities of outer TCRs presented above. The classical dispersion relation of internal gravity waves may be written as46,70:

Cgw = υ / k = ± N / sqrt(k^2 + m^2) (1)

where Cgw is the GW phase velocity, υ is the intrinsic wave frequency, k is the horizontal wavenumber, m is the vertical wavenumber, and N is the Brunt-Väisälä frequency that is computed from the ERA5 reanalysis data below 12 km MSL nearest the location of each identified TCR. The value equal to twice the radar-observed TCR width is again used to approximate the horizontal wavelengths. The vertical wavelength is assumed to be 12 km MSL based on the typical depth of convective motions associated with outer TCRs29. The scatterplot shown in Fig. 4a indicates the lack of consistency between the observational TCR radial propagation velocities and theoretical GW phase velocities. Most of the GW phase velocities are confined to a narrower range at approximately ±20 ms−1, which is the same order of magnitude as the typical radial propagation speeds of several meters per second for GWs excited within TCs42,44–47. These theoretical propagation estimates are distinctly separated from the primary velocity distributions of the observed radial propagation, which are within the range of ±10 ms−1 (Figs. 3a, 4a).

The theoretical VRW frequency (ω) and radial and tangential phase velocities (Cr, Cλ) are explored by Möller and Montgomery71:

ω = nΩ' + R n q' / (k^2 + n^2/R^2 + (n^2/R^2) * (N^2/m^2) * (∂q'/∂r + η'ξ' / N^2)) (2)

Cr = ω / k (3)

Cλ = ω / (n/R) (4)

where k, n, and m are the radial, tangential, and vertical wavenumbers, Ω' is the mean angular velocity, R is the reference radius, q' is the potential vorticity, ξ' is the inertial stability, η' is the absolute vorticity, and N is the Brunt-Väisälä frequency. The inertial stability and absolute vorticity are estimated by using the formulation of Möller and Shapiro72:

ξ' = f + 2V / R (5)

η' = f + 1/R * ∂(rV')/∂r (6)

q' = (ξ' η' N^2) / (ξ'^2 * (∂V'/∂z)^2) (7)

where V is the tangential wind; V' is the mean tangential wind; f is the Coriolis parameter; and N is the Brunt-Väisälä frequency. As described earlier, the radial wavelength (k) and the vertical wavelength (n) are again approximated as being twice the radar-observed TCR width and 12 km, respectively. The mean tangential wind in (5) and (6) is calculated by averaging tangential winds within the layer of 0.1–12 km MSL that is corresponding to the vertical wavelength of considered wave motions. The tangential vertical shear in (7) is approximated by the difference in the tangential wind between 0.1 and 12 km MSL. The reason why we choose the 0.1 km MSL as the lowest level in these calculations is that this height is well above the top of surface layer so the uncertainty on winds due to strong and direct impact of surface friction can be appropriately eliminated. A typical tangential wavenumber (n=2) that characterizes VRWs is assumed37,73. Note that the tangential wavenumber does not have a strong impact on the calculated propagation velocities, and choosing other tangential wavenumbers, such as n=1 or 3, for calculation in (2) gives rise to nearly identical propagation estimates. The radial distance of the observed TCRs is used to represent the reference radius (R) and Ω' = V'/R. The scatterplot of the observed TCR propagation velocities versus theoretical VWR phase velocities reveals quite diverse distributions, with low correlation coefficients equal to 0.1 and 0.2 for the radial and tangential velocities, respectively (Fig. 4b, c). In particular, the VRW theory predicts generally slower (<~3 ms−1) and predominantly outward propagations, in contrast to a very wide range of the observed velocities with evidence of both outward and inward propagation (Fig. 4b). Although some of the outer TCRs tend to have good agreement between observations and theory (i.e., lying closely along the diagonal line), the fraction of these TCR cases is small. For example, only 5.5% of the observed TCRs (i.e., 57 TCR cases) have magnitudes of differential velocity vectors between observational and theoretical propagations less than 2 ms−1. Indeed, the mean magnitude of the differential vectors calculated from all of the outer TCRs identified in this study can be as large as 10.6 ms−1. The statistical analyses provide evidence for a large discrepancy in propagation characteristics between the observed outer TCRs and theoretical GWs/VRWs. These results are considered robust, and suggest that the GW/VRW disturbances have little impact on the origin of outer TCRs.

Squall-line dynamics

As described in the Introduction, nearly none of the previous TC investigations are capable of clarifying the degree to which squall-line dynamics may contribute to the origin of outer TCRs. Moreover, the limited number of outer TCRs documented previously is also far from adequate to address how prevalent the squall-line dynamics would operate during the initiation process for outer TCRs. With a large dataset of outer TCRs collected during their formative stage in this study, it is now possible to evaluate the likelihood.

According to the classical squall-line theory proposed by Rotunno et al.57, the band-normal vertical shear toward the downshear side (i.e., frontward shear) and the warm, moist inflow (i.e., band-relative front-to-rear flow) present at low levels are two of the most fundamental characteristics of squall-line dynamics. The low-level front-to-rear flow that feeds warm air to the leading edge of squall lines can be considered a critical source of convective energy for the development of the precipitation of outer TCRs. If squall-line dynamics are responsible for the outer TCRs in this study, the observations should see some sort of preference in the distribution of the low-level band-normal vertical shear and band-relative flow consistent with the above outline. Using the TCR characteristics, orientation and position information and the ERA5 reanalysis data, a scatter plot of the low-level band-normal vertical shear vs. the band-relative flow for all outer TCR cases can be constructed, as shown in Fig. 5a. In this analysis, the low-level vertical shear is approximated by the difference in the band-normal wind between 0.1 and 2 km MSL. This layer is corresponding to the mean depth of cold pools associated with outer TCRs, as revealed by previous studies of TCs28–30. Similar to the consideration for the VRW calculations as described in the previous section, choosing the lowest level at 0.1 km MSL is to preclude the uncertainty on winds due to direct impact of surface friction. Moreover, the band-normal wind is calculated below 1.5 km MSL, corresponding to the mean depth of low-level inflow feeding the leading edge of the outer TCRs documented in this study. A large proportion of the outer TCRs (682 cases; 66%) is observed within the fourth quadrant (IV) of the analysis with positive band-normal vertical shear (i.e., frontward shear) and negative band-normal wind components (i.e., the front-to-rear flow) (Fig. 5a). There are relatively fewer TCR cases, with 20%, 9% and 5% observed in other quadrants (I, II and III). Interestingly, the percentage of outer TCR cases (i.e., 66%) that exhibits squall-line environmental characteristics is close to the degree of prevalence of outer TCRs (58%) with squall-line-like airflow structures reported in Yu et al.29. This striking environmental preference suggests that the squall-line dynamics is likely to operate and contribute to rainband initiation for a significant portion of the observed outer TCRs. However, it should be noted that a squall-line environment, as discussed herein, is not a sufficient condition but is merely a necessary condition to judge the relevance between outer TCRs and squall lines because the presence of the squall-line environment does not fully guarantee that squall-line dynamics is occurring.

Some clarification on the issue above may be performed by evaluating the relative consistency of whether the observed outer TCRs propagate at a speed similar to the atmospheric cold pool. In this evaluation, we simply classify the observed outer TCRs, according to their environmental characteristics, into the squall-line TCR group (i.e., 682 TCR cases seen in quadrant IV of Fig. 5a) and the non-squall-line TCR group (i.e., 347 TCR cases seen in quadrants I, II and III of Fig. 5a). The velocity of an atmospheric cold pool (Vcp) perpendicular to its leading edge can be approximated by the following expression75:

Vcp = k * sqrt(g * H * (θv2 - θv1) / θv2) + b * Vc (8)

where H is the depth of the cold air, θv2 and θv1 are the ambient and cold pool virtual potential temperatures, respectively, Vc is the ambient band-normal wind component ahead of the cold pool (negative for wind moving toward the cold air and vice versa), and k and b are empirical constants. The best fit of (8) to atmospheric observations gives constant k and b values equal to 0.9 and 0.6, respectively75. Considering the propagation of cold pools embedded within the moving TCs, we may need to approximate Vc in (8) by taking the TC motion into account so that the positive and negative Vcp calculated thus represent band-normal propagation motions away from and toward the TC center, respectively. Since direct measurements for the depth of the cold air and the cold pool virtual potential temperatures during the TCR initiation are not available, we attempt to determine the velocity range of Vcp by giving a possible range of values for H and the cold pool intensity (i.e., θv2 - θv1) and to check if the propagation velocity of the observed outer TCRs fit well into the calculated velocity range of Vcp. Based on previous observational studies of outer TCRs28–30, the most reasonable ranges of values for H and θv2 - θv1 may be 1–2.5 km and 0.5–3 K, respectively. The values of θv2 and Vc in (8) are obtained from the ERA reanalysis data nearest the location of each outer TCR observed in this study.

The calculations indicate that the percentage of the observed propagations that fit into the corresponding velocity ranges for the atmospheric cold pools is equal to 77.7% and 36.3% for the squall-line TCR group and non-squall-line TCR group, respectively. The contrasting percentage of the fit between the two TCR groups can be clearly seen from the statistical distribution of observed propagations and theoretically predicted velocity ranges of cold pools for each of the TCR cases, as shown in Fig. 5c, d. The observed propagation velocities for the squall-line TCR group (small blue circles) correspond generally to the cold pool velocity predictions (red shading) (Fig. 5c), whereas most of the observed propagation velocities for the non-squall-line TCR group are distributed beyond the theoretical velocity ranges of atmospheric cold pools (Fig. 5d). Not only is it evident that there is a much higher percentage of agreement between the observed propagation velocities and theoretically calculated cold pool velocities for the squall-line TCR group compared to that of the non-squall-line TCR group, but the majority of the TCR cases for the squall-line TCR group (530 cases out of 682 cases) also tend to have a cold pool-like propagation velocity, both of which suggest the relevance of squall-line dynamics to the squall-line TCR group. In addition, it has long been recognized that one of the representative characteristics for squall-line convective storms is their fast movement74,76. Compared to non-squall-line convective systems, one might see a more rapidly propagating nature for convective systems if they evolve with the operation of squall-line dynamics. Consistent with this expectation, the box and whisker plot of the observed propagation velocities, shown in Fig. 5b, indicates generally faster propagation characteristics for the squall-line TCR group than for the non-squall-line TCR group. The mean propagation velocities calculated from the squall-line and non-squall-line TCR groups are equal to 6.1 and 3.5 ms−1, respectively. According to the Student’s t test, such a velocity difference between the two TCR groups is calculated to have statistical significance at 99% confidence level. The assessment here provides further evidence supporting the importance of squall-line dynamics for the squall-line TCR group.

Two important implications may emerge from the above results. First, as shown in Fig. 5, a considerable number of the observed outer TCRs (i.e., the non-squall-line TCR group) do not actually exhibit squall-line environmental and propagation characteristics. The formative scenario closely related to squall-line dynamics is expected to occur frequently but not exclusively. Formative mechanisms other than squall-line dynamics must have existed and deserve future exploration. Second, in addition to the squall-line environment, the appearance of cold pools is equally important and can be treated as one of the key preconditions needed to start the scenario in which squall-line dynamics lead to the formation of outer TCRs. The cold pool signatures have been commonly observed in the vicinity of outer TCRs during their developing or mature stage and are most likely contributed by either the evaporative cooling associated with TCR precipitation or by the downward transport of low equivalent potential temperature air aloft via convective downdrafts9,13,28,30,55. However, during the preformation stage of an outer TCR, its associated precipitation is inherently weak, with scattered and disorganized distributions and a very limited horizontal extent (Fig. 9a presented in the Methods section). The aforementioned cooling mechanisms driven by the nascent TCR itself should be generally ineffective, and there must be other preexisting precipitation (i.e., separating from the considered outer TCR), which could act as an initial, critical provider of cold pools to initiate the operation of squall-line dynamics and contribute to the genesis of outer TCRs. In this context, the initiation of outer TCRs is expected to preferentially take place adjacent to some certain precipitation areas of TCs where evaporative cooling and/or convective transport is potentially active.

To validate the speculation above, an effort is made to construct the spatial composite of precipitation frequency (>15 dBZ) with respect to the location of each outer TCR at three particular time periods, 1 h prior to the preformation time (t0-2), the preformation time (t0-1) and the formation time (t0). The preformation time is defined as the earliest, unambiguous detection of TCRs by radar observations whereas the formation time refers to a time satisfying the formative criteria, as described in the Methods section. In this analysis, we choose the squall-line TCR cases with faster propagation velocities (i.e., greater than the mean cross-band propagation velocities of 6.1 ms−1 calculated from the squall-line TCR group) and corresponding to the theoretical velocity range of atmospheric cold pools to maximize composite signals for the squall-line outer TCRs. Similarly, those non-squall-line TCR cases that propagate relatively slower (i.e., less than the mean cross-band propagation velocities of 3.5 ms−1 calculated from the non-squall-line TCR group) and beyond the theoretical velocity range of atmospheric cold pools are chosen for the non-squall-line composite. As shown in the composite results, the position of the rainband is clearly marked by the highest precipitation frequency centered at (x=0 km, y=0 km) at t0-1 and t0 for both the squall-line TCRs and non-squall-line TCRs (Fig. 6). For the squall-line TCR composite, there is a concentrated area of preexisting precipitation on the rear flank of the rainband prior to its formation at t0-2 (Fig. 6a). In particular, the rainband tends to be initiated immediately adjacent to the outer boundary of the preexisting precipitation in the outer regions of TCs (Fig. 6b, c), consistent with our speculations above. For the non-squall-line TCR composite, there are generally scattered distributions of lower precipitation frequencies (18–30%) over a broad region in both front and rear sides of the rainband (Fig. 6d–f). These features suggest that the rainband formation occurs in a relatively precipitation-free area and is not frequently associated with prominent preexisting precipitation. The contrasting statistical distribution of outer precipitation between the squall-line and non-squall-line TCR composites further supports that the preexistence of suitable precipitation in the outer region of TCs would be critical to provide important sources of cold air to initiate the operation of squall-line dynamics for the squall-line outer TCRs. A schematic diagram is also prepared, as shown in Fig. 7, to help illustrate the two distinct types of outer precipitation and their associated formative scenarios of squall-line and non-squall-line outer TCRs.

In addition, given that the lack of consistency in the propagation characteristics between the observed outer TCRs and VRWs/GWs, as elaborated earlier, it seems unlikely that the VRWs/GWs play a direct role in triggering the outer TCRs. Because the generation of some convection/precipitation within TCs could be related to these wave activities, we cannot entirely rule out the wave-induced precipitation as a potential contributor that would favor the formation of cold pools and then initiate the operation of squall-line dynamics. To evaluate this likelihood and its underlying processes is beyond the scope of the study, but the potential, indirect roles of wave activities in facilitating the formation of outer TCRs deserve future investigation through detailed case studies using high-resolution observations and numerical simulations.

Methods
Data

The datasets used to identify TCRs in this study are provided by four S-band (10 cm) ground-based Doppler radars operated by the CWB at Wu-Fen-San (WFS), Chi-Gu (CG), Ken-Ting (KT) and Hua-Lien (HL), which are located in different coastal regions of Taiwan. The basic characteristics of these Doppler radars are described in Yu et al.29, and the locations of the four radar sites are shown in Fig. 8. These coastal radars provide volumetric scans of reflectivity, with a temporal interval ranging from 6 to 10 min between each volume, scanning elevations from 0.4° to 19.5° and a maximum observational range of ~460 km. The data coverage from these radars encompasses broad regions, extending from the island of Taiwan to approximately 300–400 km offshore (cf. Fig. 8). In addition to the radar measurements described above, the fifth-generation European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis data (ERA577) are also used to determine various environmental factors associated with the studied TCRs. Compared to other reanalysis data, the ERA5 reanalysis data have higher spatial and temporal resolutions at 0.25° × 0.25° and 1 h, respectively, thus providing a more realistic representation of TCs and their environment78–80. For convenience of relevant calculations and analyses, the ERA5 reanalysis data valid at different pressure levels are interpolated linearly to obtain vertical grid spacing at 0.1 km. The TC information, including center locations, RMW, and other storm characteristics, analyzed in this study comes from the best track data provided by the Joint Typhoon Warning Center (JTWC).

Although ERA5 data have been widely used to study relevant scientific issues for TCs, whether they can provide adequate representation of wind information nearby the studied outer TCRs is still somewhat uncertain. To fully address this issue is beyond the scope of this study, but the possible impact of this uncertainty on the calculated propagation velocity of VRWs presented in the Results section may be evaluated by comparing the ERA5 winds with other independent wind measurements nearby the rainband’s location. In making such comparisons, surface observations from eight offshore island stations [Pengjiayu (PJY), Yonaguni (YO), Hateruma (HTM), Iriomote (IM), Ishigaki (IG), Green island (GI), Penghu (PH) and Dongji (DJ)] near Taiwan (locations in Fig. 8) within a distance of 35 km from the formative location of outer TCRs are first collected. The reason why the threshold distance of 35 km is used herein is because it is approximately comparable to the grid spacing of ERA5. The island observations represent the ground truth measurements and are available from a total of 70 outer TCR cases. The near-surface winds at the 10-m (MSL) level from the ERA5 gridded data closest to the island stations for these TCR cases are then chosen to compare with station-measured winds. Firstly, we focus on the comparison of the tangential wind [i.e., V in (5), (6) and (7)] that is the ERA5-provided kinematic quantity involved with the calculation of VRWs.

A good correlation between the ERA5 data and offshore island observations is found, and the correlation coefficient, average error and root mean square error (RMSE) are calculated to be 0.74, 2.9 ms-1 and 4.5 ms−1, respectively. If we assume the calculated RMSE as potential errors for the tangential winds from ERA5, potential velocity errors in radial and tangential directions are estimated to be 0.2 and 4.4 ms−1, respectively, based on (2)–(7). The potential errors in the calculated propagation velocity for VRWs may be considered minor because they are unlikely to alter the statistical distributions of the scatterplots shown in Fig. 4b, c significantly.

Using the similar method of evaluating the uncertainty associated with ERA5-provided tangential winds in the rainband environment, the potential error of Vc (i.e., the band-normal wind component) from ERA5 is calculated be 2.9 ms−1, yielding a velocity error of 1.7 ms−1 in the estimate of theoretical cold pool velocity (Vcp) based on (8).

The error analyses above support the reasonable representation of the ERA5 reanalysis data for the rainband environment, although the accuracy of the ERA data to represent TC circulations and their ambient wind conditions is possible to vary case by case. This uncertainty may have greater chances to become a potentially serious problem if scientific approach is placed on the understanding of individual

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary:\nThe authors present a very nice radar climatology of outer-core tropical cyclone rainbands from 95\ntropical cyclones near Taiwan from 2002-2019. Tropical cyclone rainbands are an important hazard and\ntherefore this extensive climatology of their development and evolufion is of value to the community.\nThe authors use this radar climatology to document that outer-core tropical cyclone rainbands, defined\nas exisfing at least three fimes the radius of maximum winds from the storm center, predominantly\ndevelop within the outer-core region and do not commonly propagate outward from the inner-core\nregion. The authors also use ERA-5 reanalysis data to suggest that the outer-core rainbands often\npropagate in a manner consistent with squall line dynamics and not consistent with vortex Rossby waves\nor gravity waves. Despite some potenfial limitafions from using the relafively coarse ERA-5 reanalysis\ndata I believe this analysis is appropriate.\nMy concerns are primarily that (1) I believe the authors misuse the word ‘origin’ by not providing a\nconvincing descripfion of what inifiates the outer-core rainbands, (2) a lack of discussion on the diurnal\ncycle which is well established as influence tropical cyclone convecfion, and (3) a lack of discussion on\nverfical shear. Regarding (1), while I believe the authors adequately show that the convecfion associated\nwith the outer-core rainbands develops within the outer-core region of the tropical cyclone, they do not\nprovide a clear mechanism for their inifiafion. Instead, I believe the authors incorrectly use squall-line\ndynamics as an explanafion, which I believe to instead be an explanafion for their maintenance once\nconvecfion is ongoing, but not their formafion. With these concerns addressed, I believe the study can\nprovide a useful climatology of tropical cyclone rainbands to the community.\nMajor Comments:\n1) I am concerned by the fitle of the paper and the use of the word ‘origin’ throughout the arficle. In my\nopinion the authors do not clearly show the origin of outer tropical cyclone rainbands. Rather I believe\nthe authors demonstrate that the outer rainbands are often maintained through cold pool dynamics, not\ninifiated by them. I fail to see the authors clearly demonstrate what inifiates the outer rainbands. As a\nresult, I believe the authors overstate their results such as in L44-46, L245-247, L503-504, L508-510. I\nalso am not enfirely convinced that the authors can rule out the role of gravity waves, vortex Rossby\nwaves, or something else in triggering the inifiafion of the outer rainband convecfion before the cold\npool dynamics help to support their maintenance thereafter (L497-502).\n2) I understand that the authors used available radar data from Taiwan, but a natural quesfion from\nreaders will be how applicable are these results to tropical cyclones in other basins?\n3) One aspect missing from the introducfion and the analysis is the diurnal cycle, which is well known to\ninfluence tropical cyclone convecfion beyond the inner-core region (e.g., Dunion et al. 2014) The authors\nshould consider if there is a diurnal cycle to outer-rainband formafion and if the diurnal cycle may be an\nimportant mechanism to their formafion.\nDunion, J. P., C. D. Thorncroft, and C. S. Velden, 2014: The Tropical Cyclone Diurnal Cycle of Mature\nHurricanes. Mon. Wea. Rev., 142, 3900–3919, hftps://doi.org/10.1175/MWR-D-13-00191.1.\n4) A second aspect that appears to be missing from the analysis is a discussion on verfical wind shear,\nwhich is well known to influence tropical cyclone convecfion (e.g., Corbosiero and Molinari, 2002). I\nrecommend adding an addifional panel (Figure 3) that shows the formafion locafions relafive to the\ndeep-layer shear in an RMW relafive coordinate. The criteria menfioned for the classificafion of an outer\ntropical cyclone rainband required the rainband forming or propagafing into the region beyond 3 fimes\nthe RMW. Showing the formafion locafions relafive to the RMW and shear may yield addifional insights.\nCorbosiero, K. L., and J. Molinari, 2002: The Effects of Verfical Wind Shear on the Distribufion of\nConvecfion in Tropical Cyclones. Mon. Wea. Rev., 130, 2110–2123, hftps://doi.org/10.1175/1520-\n0493(2002)130<2110:TEOVWS>2.0.CO;2.\n5) I think the use of ERA5 for the TC presents potenfial for crificism. This may be unavoidable, but the\nauthors should add come discussion from using .25˚ data to represent the TC condifions and the\nassociated gravity wave and vortex Rossby wave calculafions within their analysis (L370-373, L432-433).\nAs an example, can we trust filamentafion fime esfimated from relafively coarse ERA5 data?\nMinor Comments:\nL41: I recommend adding “radar” before “observafions”.\nL53: “storm” should be changed to “storms”.\nL81: I think “inner-core” should be “outer-core”.\nL94: “would probably” can be changed to “could” and “but” can be removed.\nL100: “actually” can be removed.\nL102: “more” can be removed.\nL127: “evidence” can be removed.\nL184-186: It should be menfioned how the orographically generated rainbands were removed from the\nanalysis.\nL233: Do the authors mean this is a result of the Taiwan radars more frequently sampling the front\nquadrants as tropical cyclones approach Taiwan?\nL264-268: The size of a tropical cyclone is often considered to be larger than the radius of tropical storm\nforce winds. As menfioned by the authors other metrics are also commonly used including the\noutermost closed isobar and the radial extent of weaker wind speed thresholds, such as 10 or 12 m/s.\nThe authors should be careful in defining tropical cyclone size as the radial extent of tropical storm force\nwinds (34 kts). See also L490.\nL283: I recommend adding “near Taiwan” following “outer TCRs”.\nL284: “crossing angles” needs to be defined somewhere.\nL357: “actually” can be removed.\nL386: “circumstances to acfivate the operafion” can be removed.\nL462,510: I think the authors mean for “predominantly” to be “exclusively”.\nL465,504,519: The authors show that squall-line dynamics are often important for the maintenance of\nthe rainbands, not the “formafion”.", "reviewer_2": "Review of “Origin of outer tropical cyclone rainbands”\nSynopsis:\nThis is an important study that ufilizes a radar dataset to invesfigate the formafion locafion and\nmovement of outer tropical cyclone (TC) rainbands, as well as potenfial formafion mechanisms. As\ndiscussed in the introducfion, there are compefing theories on the formafion and origin of outer TC\nrainbands, with numerous (mostly modeling) studies indicafing that these rainbands are generated as a\nresult of TC inner core dynamic. In the current study, the authors provide convincing evidence that most\nouter TC rainbands form outside the inner core, and in some cases outside the radius of gale force winds.\nAddifionally, the rainbands propagate at radial and tangenfial velocifies that are inconsistent with inner\norigin theories. Instead, the authors show that a majority our outer TC rainbands propagate in a manner\nconsistent with squall line (and cold pool) dynamics. Therefore, I believe that this study is an important\ncontribufion to the research literature. However, I have major concerns associated with data and\nmethods, which are outlined below. Specifically, use of ERA5 data in certain parts of the study is not\njusfified and not likely to be sound. As a result, I recommend major revisions for this manuscript.\nMajor comments:\n1. Use of ERA-5 data: On lines 158-163, the authors provide some basic informafion about the ERA-5\ndataset and jusfify its use for it “more realisfic representafion of TCs and their environment.” It is\ngenerally true that the ERA-5 dataset provides more realisfic data about the TC environment as well as\nsome other TC-related metrics such as TC size. However, in this study, the authors have used ERA-5 data\nto capture informafion about lower-level (boundary layer) winds that are unlikely to be accurate due to\nthe low resolufion of the associated ERA5 model and the need for these winds to be calculated through\nparameterizafion. Could the authors find another dataset that would provide more accurate low-level\nwind info? Later in the results, the authors use ERA5 data to assess whether cold pool dynamical (and\nthermodynamical) processes are present, and these mesoscale processes are very unlikely to be\ncaptured by the low-resolufion (0.25°x0.25°) ERA5. I have major concerns about using ERA5 to assess\nmesoscale squall-line processes.\n2. Please provide more informafion about your “subjecfive screening” of the radar data to locate outer\nTC rainbands.\na. As described in the text, the first set of criteria include measurements of the rainband and other\nquanfitafive criteria, which suggest that it could have been applied algorithmically. Or was this part\napplied manually too? If manual, please provide jusfificafion for doing so. Manual/subjecfive applicafion\nof the length-to-wind-rafio and minimum length seems less than ideal.\nb. Do your data include the principal rainband? or have you excluded it using your subjecfive analysis?\nc. Lines 184-186: Please elaborate on how you idenfified orographically generated rainbands.\nd. Lines 236-237: “Nevertheless, considerable TCRs are observed to form in far outer TC regions beyond\nthe radius of 350 km.” How do you idenfify whether these rainbands are associated with the TC rather\nthan some other forcing? Please provide more details in the methods to describe how you decipher\nwhether the rainband is associated with the TC. Rainbands at distance ~1000 km from center seem like\nthey could be forming due to some other mechanism.\nMinor comments:\nLine 37: I don’t agree on the outer rainbands being the “most persistent.” The principal rainband is more\npersistent. It might be befter to focus on the hazardous weather part of this statement (or the extreme\nrain rates observed in these rainbands). For example, you menfion in the arficle that these rainbands can\nexist outside the TC gale force wind radius.\nLine 45: squall line dynamics “are” a common mechanism.\nLine 46: I don’t think the word “road map” is the right choice because you don’t specifically outline\nresearch direcfions and how those should be navigated.\nLine 54: There is not a clear connecfion between sea level rise and loss of life (it’s leading to enhanced\nstorm surges that lead to loss of life). Suggest rewording.\nLine 64-68: I disagree with characterizafion of inner vs. outer rainbands as transient (inner) and\npersistent (outer). Inner rainbands are usually dynamically driven and therefore persist (e.g., eyewall,\nprincipal rainband) whereas outer, convecfive rainbands are convecfive (thermo-driven) and less\npersistent in terms of their locafion and durafion. Of course, some of the inner rainbands within the\nstafionary band complex are more transient (such as secondary rainbands), but the eyewall and principal\nrainband in a major hurricane may be the most persistent and defining features of these storms. Some of\nthe arficles you cite (e.g., Willoughby et al. 1984) point out the persistent, stafionary nature of the\nprincipal rainband. Convecfive storms can persist for hours but not over mulfiple days as the eyewall and\nprincipal rainband do.\nLines 68-70: This sentence is about the impacts on human and natural communifies, but the references\n(28,29,31,32) are mostly about the structure of outer TC rainbands. The only cited arficle that seems\nrelevant here is the one about meteotsunamis. I suggest finding studies that focus on rainband/flooding\nimpacts instead.\nLine 71: I think you might want to cite more or different studies here, at the very least Part II by Moon\nand Nolan (2015), which I believe is the more relevant study about the formafion and propagafion of\ninner rainbands.\nMoon, Y., and D. S. Nolan, 2014: Spiral Rainbands in a Numerical Simulafion of Hurricane Bill (2009). Part\nII: Propagafion of Inner Rainbands. J. Atmos. Sci., 72, 191–215, hftps://doi.org/10.1175/JAS-D-14-0056.1.\nLine 73: There are a few more recent studies about observafions of inner rainbands and the VRW theory.\nSuggest cifing some here, primarily:\nGuimond, S. R., P. D. Reasor, G. M. Heymsfield, and M. M. McLinden, 2020: The Dynamics of Vortex\nRossby Waves and Secondary Eyewall Development in Hurricane Mafthew (2016): New Insights from\nRadar Measurements. Journal of the Atmospheric Sciences, 77, 2349–2374, hftps://doi.org/10.1175/JAS-\nD-19-0284.1.\nLine 75: delete extra word “be”\nLine 78: “Despite” doesn’t seem to be the right word choice here. Maybe “Due to”? Think about\nrewording this sentence on lines 78-82 to befter reflect the meaning you’re conveying.\nLines 93-95: I don’t follow how the principal rainband is related to outer or distant rainband formafion.\nYou say in the text “outer-origin scenarios would probably be related” to this rainband, but you don’t\nexplain how. Could you elaborate? Or maybe there is no underlying theory and this sentence should be\nreworded or removed.\nLines 97-99: “Previous PB studies rely dominantly on the analyses of airborne flight-level and radar data\ncollected over a relafively short period of fime during the mature or late stage of oceanic TCRs.” There\nare mulfiple modeling and idealized studies of the principal rainband by Michael Riemer and colleagues.\nPlease revise.\nRiemer, M., 2016: Meso-β-scale environment for the stafionary band complex of verfically sheared\ntropical cyclones. Q.J.R. Meteorol. Soc., 142, 2442–2451, hftps://doi.org/10.1002/qj.2837.\nLine 101-102: “To the best of our knowledge, Yu et al. (2019) is the only observafional study of TCRs to\nprovide a more complete picture of the outer-origin processes.” This may be true. However, there are\nmulfiple studies that observe the cold pools associated with these rainbands and their squall-line like\nstructure. I think you should also aftribute the idea to these other studies, rather than cifing them below\nas an afterthought (since the Yu et al. 2019 study came later and built on these former studies).\nEasfin, M. D., T. L. Gardner, M. C. Link, and K. C. Smith, 2012: Surface cold pools in the outer rainbands of\nTropical Storm Hanna (2008) near landfall. Mon. Wea. Rev., 140, 471–491, doi:10.1175/MWR-D-11-\n00099.1.\nMoon, Y., and D. S. Nolan, 2014: Spiral Rainbands in a Numerical Simulafion of Hurricane Bill (2009). Part\nI: Structures and Comparisons to Observafions. J. Atmos. Sci., 72, 164–190, hftps://doi.org/10.1175/JAS-\nD-14-0058.1\nYu, C.-K. & Tsai, C.-L. Structural and surface features of arc-shaped radar echoes along an outer tropical\ncyclone rainband. J. Atmos. Sci. 70, 56–72 (2013).\nLine 139: Can you provide a citafion or website for these stafisfics about the number of landfalling TCs\naround Taiwan from the Taiwan CWB?\nLine 143-145: The observafions cannot “aim.” Reword this sentence.\nLine 165: Please provide a website or reference for the JTWC best track data. It can be provided here in\nthe text, but you may want to actually provide this informafion in the data availability statement.\nLine 167-169: “The dataset comes from the four radars and contains observafions of 95 TCs during\n2002–2019, which the CWB issued typhoon warnings.” Here, you’re using “which” in a relafive clause,\nbut I think it needs to be used in a preposifion: “The dataset comes from the four radars and contains\nobservafions of 95 TCs for which the CWB issued typhoon warnings (during 2002–2019).”\nLines 213-222: It's good to include these limitafions. Could you provide even more informafion, such as\nthe distribufion of errors, not just the average value. It would be nice to see a table to histogram that\nsummarizes this informafion more fully, since the average might obscure other important informafion\nabout the full distribufion, including very large error values due to a non-normal distribufion.\nLines 232-233: “This weakly asymmetric characterisfic may not be stafisfically robust and would be due\nin part to the relafive configurafions between the generally westward-moving TCs in the northwestern\nPacific Ocean and the Taiwan area.” Elaborate and support this statement befter. I don't understand why\nthese would not be stafisfically significant, related to TC mofion.\nLine 254-255: “Relafive magnitudes of the filamentafion fime are useful for providing a dynamic\ndisfincfion between the inner and outer regions of TCs.” Has this been done in previous studies? If so,\ncite them.\nLine 257: Please define MSL. Also, I believe that you really want “above mean sea level.”\nLine 290: At this point, I was hoping for some commentary on the implicafions of your finding for the\ntheory of inifiafion/propagafion by gravity waves. It might be a good idea to make a note here in the text\nthat you will explore the implicafions later in the secfion.\nLine 299-302: This sentence seems to belong befter with the previous paragraph. I suggest beginning the\nnew paragraph with “Most of the observed outer TCRs …”\nLine 301: More informafion about whether principal rainbands are included in your dataset will help\nwith interpretafion here on the percentage of rainbands with “slow radial propagafions.”\nLine 355: Add citafion to support use of n=2 for tangenfial wave number.\nLine 393: Suggesfing changing “the squall-line characterisfics” to “the above outlined squall-line\ncharacterisfics.”\nLine 395: Please define “low-level,” “low-level band-normal verfical shear” and “band-relafive band-\nnormal wind component.” What levels and distances are used? How are the quanfifies calculated?\nInformafion can also be added to the Figure 7 capfion.\nLine 420-421: This is where I really started to get wary of your use of ERA-5 data for these mesoscale\ncirculafions associated with cold pool dynamics.\nLine 428-429: This is a good way to account for some of the uncertainty. Unfortunately, due to data\nquality issues, I think the uncertainty is much larger.\nLine 434-444: “that there is a much higher percentage of the squall line TCR group compared to that of\nthe non-squall-line TCR group.” I don't follow, do you mean a higher percentage of overlap? or do you\nmean the density of the lines in the plot? like you've squashed the data more in Figure 7c so that more\ncases fit into the plot?\nLine 448: characters  characterisfics\nLine 448: “fast movement” For clarity, are you referring to faster mofion (blue dots higher magnitude) in\nFigure 7c?\nLine 448-450: “One might see a more rapidly propagafing nature for convecfive systems if they evolve\nwith the operafion of squall-line dynamics.” More rapid compared with what?\nLine 490: When you refer to the rainbands being inside versus outside the “storm size,” I don’t think\n“storm size” is the word you want since you can’t really be inside the size. Rather, the rainbands are\nin/outside the storm radius, storm perimeter, or potenfially the storm area.\nLine 512: “must have existed”  must also exist\nLine 540-546: Please be sure that you are providing informafion about all the datasets you used in this\nstudy, including the JTWC best track data.\nFigure 1: I am wondering if there is a befter way than arrows to demarcate the rainband. Could you\nreduce the transparency of the rest of the radar reflecfivity regions? so that the rainband stands out\nmore.\nFigure 2: Could you add percentages or fracfion on the right axis to assist with interpretafion? This would\nbe especially helpful with comparing fracfion of inside vs. outside TC rainbands cited in the text.\nFigure 5a,b,d: For interpretafion, I manually added verfical lines along x=0 so that I could disfinguish\nposifive and negafive values more easily. I think it would be great to add these to the plots."}, "author_response": "NCOMMS-23-16082\nResponses to Reviewer#1\nReviewer #1 (Remarks to the Author):\nSummary:\nThe authors present a very nice radar climatology of outer-core tropical cyclone\nrainbands from 95 tropical cyclones near Taiwan from 2002-2019. Tropical cyclone\nrainbands are an important hazard and therefore this extensive climatology of their\ndevelopment and evolution is of value to the community. The authors use this radar\nclimatology to document that outer-core tropical cyclone rainbands, defined as\nexisting at least three times the radius of maximum winds from the storm center,\npredominantly develop within the outer-core region and do not commonly\npropagate outward from the inner-core region. The authors also use ERA-5 reanalysis\ndata to suggest that the outer-core rainbands often propagate in a manner consistent\nwith squall line dynamics and not consistent with vortex Rossby waves or gravity\nwaves. Despite some potential limitations from using the relatively coarse ERA-5\nreanalysis data I believe this analysis is appropriate.\nMy concerns are primarily that (1) I believe the authors misuse the word‘origin’\nby not providing a convincing description of what initiates the outer-core rainbands,\n(2) a lack of discussion on the diurnal cycle which is well established as influence\ntropical cyclone convection, and (3) a lack of discussion on vertical shear. Regarding\n(1), while I believe the authors adequately show that the convection associated with\nthe outer-core rainbands develops within the outer-core region of the tropical\ncyclone, they do not provide a clear mechanism for their initiation. Instead, I believe\nthe authors incorrectly use squall-line dynamics as an explanation, which I believe to\ninstead be an explanation for their maintenance once convection is ongoing, but not\ntheir formation. With these concerns addressed, I believe the study can provide a\nuseful climatology of tropical cyclone rainbands to the community.\nReply: We appreciate Reviewer#1’s positive and constructive comments, which help\nus improve the manuscript. A set of responses to your detailed comments is\nprovided below.\nMajor Comments:\n1\n1) I am concerned by the title of the paper and the use of the word‘origin’\nthroughout the article. In my opinion the authors do not clearly show the origin of\nouter tropical cyclone rainbands. Rather I believe the authors demonstrate that the\nouter rainbands are often maintained through cold pool dynamics, not initiated by\nthem. I fail to see the authors clearly demonstrate what initiates the outer rainbands.\nAs a result, I believe the authors overstate their results such as in L44-46, L245-247,\nL503-504, L508-510. I also am not entirely convinced that the authors can rule out\nthe role of gravity waves, vortex Rossby waves, or something else in triggering the\ninitiation of the outer rainband convection before the cold pool dynamics help to\nsupport their maintenance thereafter (L497-502).\nReply: In this study, we investigate the statistical aspects of where the outer TCRs\nbegin within the TC circulations (i.e., spatial origin) and of how the outer TCRs forms\n(i.e., mechanism origin) based on a large set of the outer TCRs observed during their\nformative stages. As for the spatial origin, we have shown the dominance of outer\norigin for the observed outer TCRs and this finding is well supported by our analyses\n(Figs. 3 and 4). As for the mechanism origin, although our analysis results have\nsuggested the squall-line dynamics as an important mechanism for a large portion of\nthe observed outer TCRs during their formative stage, we agree with the Reviewer’s\npoint that some more details about the mechanism origin need to be elaborated. To\naccommodate this issue, additional evidence is provided in the response here and in\nthe revised manuscript to better illustrate how squall-line dynamics relate to the\ninitiation of outer TCRs. As described in the Squall-line dynamics section of our\noriginal manuscript, during the preformation and formation stage of an outer TCR,\nits associated precipitation is inherently weak, with a very limited horizontal extent\n(Figs. 2a,b). The cooling processes accomplished by the nascent TCR itself should be\ngenerally ineffective, and there must be other preexisting precipitation separating\nfrom the considered outer TCR, which could act as an initial, critical provider of cold\npools to initiate the operation of squall-line dynamics and contribute to the genesis\nof the rainband. In this context, the initiation of outer TCRs is expected to\npreferentially take place adjacent to some certain precipitation areas of TCs where\nevaporative cooling and/or convective transport is potentially active.\nTo validate the speculation above, an effort is made to construct the spatial\ncomposite of precipitation frequency (>15 dBZ) with respect to the location of each\nouter TCR at three particular time periods, 1 h prior to the preformation time (t -2),\n0\nthe preformation time (t -1) and the formation time (t ). The preformation time is\n0 0\ndefined as the earliest, unambiguous detection of TCRs by radar observations\n2\nwhereas the formation time refers to a time satisfying the formative criteria, as\nexplained in the Data and rainband identification section. In this analysis, we choose\nthe squall-line TCR cases with faster propagation velocities (i.e., greater than the\nmean cross-band propagation velocities of 6.1 m s-1 calculated from the squall-line\nTCR group) and corresponding to the theoretical velocity range of atmospheric cold\npools to maximize composite signals for the squall-line outer TCRs. Similarly, those\nnon-squall-line TCR cases that propagate relatively slower (i.e., less than the mean\ncross-band propagation velocities of 3.5 m s-1 calculated from the non-squall-line TCR\ngroup) and beyond the theoretical velocity range of atmospheric cold pools are\nchosen for the non-squall-line composite. As shown in the composite results, the\nposition of the rainband is clearly marked by the highest precipitation frequency\ncentered at (x=0 km, y=0 km) at t -1 and t for both the squall-line TCRs and non-\n0 0\nsquall-line TCRs (Fig. R1). For the squall-line TCR composite, there is a concentrated\narea of preexisting precipitation on the rear flank of the rainband prior to its\nformation at t -2 (Fig. R1a). In particular, the rainband tends to be initiated\n0\nimmediately adjacent to the outer boundary of the preexisting precipitation in the\nouter regions of TCs (Figs. R1b,c), consistent with our aforementioned speculations.\nFor the non-squall-line TCR composite, there are generally scattered distributions of\nlower precipitation frequencies (18-30%) over a broad region in both front and rear\nsides of the rainband (Figs. R1d,e,f). These features suggest that the rainband\nformation occurs in a relatively precipitation-free area and is not frequently\nassociated with prominent preexisting precipitation. The contrasting statistical\ndistribution of outer precipitation between the squall-line and non-squall-line TCR\ncomposites supports that the preexistence of suitable precipitation in the outer\nregion of TCs would be critical to provide important sources of cold pools to initiate\nthe operation of squall-line dynamics for the squall-line outer TCRs. A schematic\ndiagram, as shown in Fig. R2, is also prepared to help illustrate the two distinct types\nof outer precipitation and their associated formative scenarios of squall-line and non-\nsquall-line outer TCRs. In response to the Reviewer’s comment, the above\ndiscussions along with Figs. R1 and R2 (i.e., Figs. 8 and 9) have been included in the\nSquall-line dynamics section of the revised manuscript.\nOn a different note, given that the lack of consistency in the propagation\ncharacteristics between the observed outer TCRs and VRWs/GWs, as elaborated in\nthe Propagation and geometry characteristics section, it seems unlikely that the\nVRWs/GWs play a direct role in triggering the outer TCRs. Because the generation of\nsome convection/precipitation within TCs would be probably related to these wave\nactivities, we cannot entirely rule out the wave-induced precipitation as a potential\n3\ncontributor that would favor the formation of cold pools and then initiate the\noperation of squall-line dynamics. To evaluate this likelihood and its underlying\nprocesses is beyond the scope of the study, but the potential, indirect roles of wave\nactivities in facilitating the formation of outer TCRs deserve future investigation\nthrough detailed case studies using high-resolution observations and numerical\nsimulations. In response to the Reviewer’s comment, we have also added these\ndiscussions in the Squall-line dynamics section of the revised manuscript.\nFig. R1. The spatial composite of precipitation frequency (>15 dBZ, color shading) and\nnormalized radial distance by RMW (contour) with respect to the location of each\nouter TCR (x=0 km, y=0 km) for 303 squall-line TCR cases at (a) 1 h prior to the\npreformation time (t -2), (b) the preformation time (t -1) and (c) the formation time\n0 0\n(t ). (d)-(f) as in (a)-(c), but showing the composite results for 140 non-squall-line TCR\n0\ncases. For the composites at t -1 and t -2 in (a), (b), (d) and (e), the location of each\n0 0\nTCR case is determined by the backward extrapolation from the TCR location at the\nformation time (i.e., t ) based on the calculated propagation velocities of TCRs.\n0\nnon-squall-line outer TCRs, and their embedded precipitation characteristics are\nparticularly highlighted. The solid circle denotes the inner-core boundary of TCs.\n2) I understand that the authors used available radar data from Taiwan, but a natural\nquestion from readers will be how applicable are these results to tropical cyclones in\nother basins?\nReply: We thank the Reviewer for raising the valid question. Despite the different\nevolving stages of outer TCRs, the cold pool signatures associated with outer TCRs\nhave been reported for TCs developing over different basins, such as the\nnorthwestern Pacific Ocean (e.g., Yu and Tsai 201328; Yu et al. 201829) and Atlantic\nOcean (e.g., Powell 1990b53; Eastin et al. 201255). In addition, outer TC circulations\nobserved over different basins seem to have similar characteristics of low-level winds\nwith the presence of some band-normal vertical shear (e.g., Powell 1990a52; Robe\nand Emanuel 200154; Yu et al. 201829). It is thus reasonable to expect that what we\nlearn from the study (i.e., the outer TCR origin and the importance of squall-line\ndynamics on the formation of outer TCRs) would be generally applicable to outer\nTCRs developing over other basins. However, a comprehensive dataset of outer TCRs\ncollected from different geographical locations during their formative stage will be\nstill required to clarify whether any possible basin-dependent characteristics of the\nTCR origin would exist. In response to the Reviewer’s comment, we have added\nthese points in the Summary section of the revised manuscript.\n5\n3) One aspect missing from the introduction and the analysis is the diurnal cycle,\nwhich is well known to influence tropical cyclone convection beyond the inner-core\nregion (e.g., Dunion et al. 2014) The authors should consider if there is a diurnal cycle\nto outer-rainband formation and if the diurnal cycle may be an important mechanism\nto their formation.\nDunion, J. P., C. D. Thorncroft, and C. S. Velden, 2014: The Tropical Cyclone Diurnal\nCycle of Mature Hurricanes. Mon. Wea. Rev., 142, 3900–3919,\nhttps://doi.org/10.1175/MWR-D-13-00191.1.\nReply: Thanks to the Reviewer for bringing this issue to our attention. In this revision,\nwe have included the aspect of diurnal cycles in the Introduction section, and\nrelevant articles have also been cited. In addition, the formation times of all outer\nTCRs observed in this study are also analyzed to understand if there are any diurnal\nsignals. The statistical distribution, as shown in Fig. R3, indicates that the number of\nouter TCRs formed at different times in a day is similar and approximately equal to 80\ncases for each time interval, although the peak and lowest numbers of TCR formation\nare found afternoon between 12 and 14 pm and between 14 and 16 pm,\nrespectively. This result generally reflects the lack of obvious diurnal variations for\nthe formation of the studied outer TCRs. In this revision, we have included these\ndescriptions in the Formative location and dynamic regime section of the revised\nmanuscript for clarity.\nFig. R3. Formative number of the outer TCR cases observed in this study at different\ntime intervals during a day.\n4) A second aspect that appears to be missing from the analysis is a discussion on\n6\nvertical wind shear, which is well known to influence tropical cyclone convection\n(e.g., Corbosiero and Molinari, 2002). I recommend adding an additional panel\n(Figure 3) that shows the formation locations relative to the deep-layer shear in an\nRMW relative coordinate. The criteria mentioned for the classification of an outer\ntropical cyclone rainband required the rainband forming or propagating into the\nregion beyond 3 times the RMW. Showing the formation locations relative to the\nRMW and shear may yield additional insights.\nCorbosiero, K. L., and J. Molinari, 2002: The Effects of Vertical Wind Shear on the\nDistribution of Convection in Tropical Cyclones. Mon. Wea. Rev., 130, 2110–2123,\nhttps://doi.org/10.1175/1520-0493(2002)130<2110:TEOVWS>2.0.CO;2.\nReply: Thanks to the Reviewer for bringing this issue to our attention. In this revision,\nwe have included the aspect of large-scale vertical wind shear in the Introduction\nsection, and relevant articles have also been cited. We also agree with the Reviewer\nthat the modulation of the outer TCR formation by deep-layer vertical wind shear is\nlikely to occur. However, as described in the Formative location and dynamic regime\nsection, the azimuthal variation of the outer TCR formation observed in this study is\ncontaminated by the inherent limitation of radar observations. Specifically, the\nprecipitation information of the front quadrants for a typical westward-moving TCs\nover the northwestern Pacific Ocean could be usually monitored by coastal radars in\nTaiwan for a longer period of time. In contrast, when the rear quadrants of TCs reach\nthe observational coverage of coastal radars, the inner-core circulations of TCs have\nbeen closer to the landmass of Taiwan so both TC circulations and rainbands have\ngreater chances to experience orographic modifications and/or make landfall. This\nsampling preference of coastal radars is expected to capture more outer TCR cases in\nthe front quadrants than in the rear quadrants, consistent with the asymmetric\ncharacteristics of formative locations of the observed outer TCRs, as shown in Fig.\nR4a (i.e., Fig. 3 of the original manuscript).\nIn addition, a plan view of formative locations for all analyzed outer TCRs with\nrespect to the large-scale deep-layer vertical shear is shown in Fig. R4b. The analysis\nseems to indicate that outer TCR formation would occur more frequently in the\nupshear quadrants than in the downshear quadrants. However, this asymmetric\ndistribution is also most likely contributed by the sampling preference of coastal\nradars as discussed above, in which the directions of large-scale deep-layer vertical\nshear are typically opposite to the motion vectors of TCs. As shown in Fig. R5, most\nof the studied TCR cases (~70%) have large differential angles between the TC motion\nvectors and shear vectors greater than 90o (i.e., obtuse angles). The mean directions\n7\nfor the TC motion vector and the shear vector are calculated to be 317o and 195o,\nrespectively. These statistical characteristics support the substantial contribution of\nthe radar sampling to the asymmetric distribution shown in Fig. R4b. This is the\nreason why we do not attempt to address the outer TCR formation in a spatial\ncoordinate relative to the TC motion and/or the deep-layer vertical shear. In the\nfuture, effective mitigation in the bias of radar sampling, such as by collecting long-\nterm observations from isolated island radars located over the open ocean, will be\ncritically required to document the natural variations of outer TCR formation over\ndifferent quadrants of TCs. For clarity, the inherent limitation of radar sampling and\nits potential impact on the observed asymmetric distribution of outer TCR formation\nhave been explained in more detail in the Formative location and dynamic regime\nsection of the revised manuscript.\nFig. R4. (a) Plan view of formative locations for all identified outer TCRs (1029 cases)\nrelative to the TC center and motion. The TC motion is toward the top of the page.\nThe range rings are indicated every 100 km. (b) Same as (a), but showing the\nformative locations with respect to the large-scale deep-layer vertical shear that is\ncalculated between 700 and 200 hPa within a radial distance of 150-500 km from the\nERA5 reanalysis data.\ndifferential angle is defined as the angle between the TC motion vector and deep-\nlayer shear vector.\n5) I think the use of ERA5 for the TC presents potential for criticism. This may be\nunavoidable, but the authors should add come discussion from using .25˚ data to\nrepresent the TC conditions and the associated gravity wave and vortex Rossby wave\ncalculations within their analysis (L370-373, L432-433). As an example, can we trust\nfilamentation time estimated from relatively coarse ERA5 data?\nReply: We thank the Reviewer for raising the concern with the ERA5 reanalysis data.\nAs described in the Data and rainband identification section, because ERA5 data have\nhigher spatial and temporal resolutions compared to other reanalysis data, it has\nbeen widely used to study relevant scientific issues for TCs and their environment.\nHowever, we agree with the Reviewer that whether ERA5 data can provide adequate\nrepresentation for the low-level winds nearby the studied outer TCRs is somewhat\nuncertain. To fully address this issue is beyond the scope of this study, but an effort is\nmade to evaluate this uncertainty in this study by comparing the ERA5 winds with\nother independent wind measurements nearby the rainband’s location. In making\nthis comparison, observations from eight offshore island stations [Pengjiayu (PJY),\nYonaguni (YO), Hateruma (HTM), Iriomote (IM), Ishigaki (IG), Green island (GI),\nPenghu (PH) and Dongji (DJ)] located near Taiwan (Fig. R6) within a distance of 35 km\nfrom the formative location of outer TCRs are first collected. The reason why the\nthreshold distance of 35 km is used herein is because it is approximately comparable\nto the grid spacing of ERA5. The island observations represent the “ground truth”\nmeasurements and are available from a total of 70 outer TCR cases. Compared to the\n9\nlarge number of outer TCRs analyzed in the study, this is a relatively small set of TCR\ncases, but they are valuable to provide a critical assessment of the representation of\nthe ERA5 data in the rainband environment. The 10-m (MSL) winds from the ERA5\ngridded data closest to these island stations for these TCR cases are then chosen to\ncompare with station-measured winds. Here, we focus on the comparison of the\ntangential winds [i.e., V in Eqs. (5), (6) and (7)] and band-normal winds [i.e., V in Eq.\nc\n(8)] because they are the ERA5-provided kinematic quantities involved with the\ncalculation of VRWs and the evaluation of squall-line dynamics.\nFigure R7a shows the scatterplot of tangential wind components calculated from the\nERA5 data and offshore island observations. The result indicates a good correlation\nbetween the two datasets, and the correlation coefficient, average error and root\nmean square error (RMSE) are calculated to be 0.74, 2.9 m s-1 and 4.5 m s-1,\nrespectively. If we assume the calculated RMSE as representative errors for the\ntangential winds from ERA5, potential velocity errors in radial and tangential\ndirections can be estimated to be 0.2 and 4.4 m s-1, respectively, based on Eqs. (2)-\n(7). Figure R7b shows the scatterplot of band-normal wind components calculated\nfrom the ERA5 data and offshore island observations. Similar to the tangential winds,\na good correlation is also evident for the band-normal winds. The correlation\ncoefficient, average error and root mean square error (RMSE) are calculated to be\n0.77, -0.1 m s-1 and 2.9 m s-1, respectively. The value of the calculated RMSE yields an\nerror of 1.7 m s-1 for the estimate of theoretical cold-pool velocity based on Eq. (8).\nThe potential errors in the calculated propagation velocity for VRWs and cold pools,\nas estimated above, may be considered relatively minor because they are unlikely to\nalter the statistical distributions of the scatterplots shown in Figs. 6b,c and Fig. 7c,d\nsignificantly.\nThe error analyses above generally support the reasonable representation of the\nERA5 reanalysis data for the rainband environment, although the accuracy of the ERA\ndata to represent TC circulations and their ambient wind conditions appears to vary\ncase by case (Fig. R7). This uncertainty may have greater chances to become a\npotentially serious problem if the scientific approach is placed on the understanding\nof individual TC/TCR events. However, because the present study focuses on the\nstatistical aspects of outer TCR formation using long-term reanalysis data for a very\nlarge set of TCR cases, the potential impact of this data uncertainty may be\nappropriately mitigated. In response to the Reviewer’s comment, we have included\ndiscussions given above in the Propagation and geometry characteristics section and\nSquall-line dynamics section in this revision.\nat Wu-Fen-San (WFS), Hua-Lien (HL), Chi-Gu (CG) and Ken-Ting (KT) are denoted by\ntriangles. The locations of offshore island observations near Taiwan at Pengjiayu\n(PJY), Yonaguni (YO), Hateruma (HTM), Iriomote (IM), Ishigaki (IG), Green island (GI),\nPenghu (PH) and Dongji (DJ) are marked by solid circles. The outer curve denotes the\napproximate data coverage for these radars, extending from the island of Taiwan to\n300–400 km offshore.\nFig. R7. (a) Scatterplot of the tangential wind components (Vt) calculated from the\nERA5 data and offshore island observations. (b) Same as (a), but showing the\nstatistical results of the band-normal wind components (Vc).\nMinor Comments:\nL41: I recommend adding “radar” before “observafions”.\nL53: “storm” should be changed to “storms”.\nReply: Corrected as suggested.\nL81: I think “inner-core” should be “outer-core”.\nReply: The reason why “inner-core” is stated here is because we would like to\nemphasize a possible formative scenario, in which outer TCRs would be initially\ntriggered by gravity waves within the inner-core region and then propagate outward\nto the outer regions of TCs. This formative scenario of outer TCRs is so-called “inner\norigin” as described in the Introduction section. In this revision, this sentence has\nbeen reworded for clarity.\nL94: “would probably” can be changed to “could” and “but” can be\nremoved.\nReply: Reworded as suggested.\nL100: “actually” can be removed.\nReply: Removed as suggested.\nL102: “more” can be removed.\nReply: Removed as suggested.\nL127: “evidence” can be removed.\nReply: Removed as suggested.\nL184-186: It should be mentioned how the orographically generated rainbands were\nremoved from the analysis.\nReply: Thanks for raising this valid point. One of the most common features of the\ntopographically generated rainbands is that they are oriented approximately parallel\n12\nto the eastern coast of Taiwan without obvious curvature. In addition, these\nrainbands tend to be locked with coastal mountains and do not propagate rapidly\nwith cyclonic circulations of TCs. These characteristics contrast sharply with evolving\nand propagation aspects of TCRs. Hence, if rainbands are observed to form locally\nwithin the coastal zone (from coastline to ~25-100 km offshore) and meet the above\nsignatures, they are assumed to be the topographically generated rainbands and are\nthus removed during TCR identification. For clarity, these explanations have been\nadded in this revision.\nL233: Do the authors mean this is a result of the Taiwan radars more frequently\nsampling the front quadrants as tropical cyclones approach Taiwan?\nReply: Sorry for the confusing description. This part of the text has been significantly\nrewritten for clarity. Please also see our responses to Major comment#4.\nL264-268: The size of a tropical cyclone is often considered to be larger than the\nradius of tropical storm force winds. As mentioned by the authors other metrics are\nalso commonly used including the outermost closed isobar and the radial extent of\nweaker wind speed thresholds, such as 10 or 12 m/s. The authors should be careful\nin defining tropical cyclone size as the radial extent of tropical storm force winds (34\nkts). See also L490.\nReply: Thank the Reviewer for raising this good point. In this revision, we explicitly\ndefine R34 as “storm radius”, instead of simply using the term “TC size”, to avoid\nany possible ambiguity. For clarity, this part of the text has been reworded as below:\n“Since outer TCR formation is observed to be active over extensive outer regions of\nTCs, as shown in Figs. 3 and 4a–c, one intriguing question emerges, what is the\ndegree of prevalence for outer TCRs to form at radii larger than the storm radius of\nTCs? The size of a TC has been practically defined as the radius of a certain threshold\nof near-surface wind speed or by the radial extent of the outermost closed isobar73-\n75. Because the TC size may vary considerably with different thresholds chosen, we\nuse the average radius of 34 kt winds (R34) as a storm radius for TCs in this study.\nR34 is commonly considered as the area of the TC warnings issued by operational\nforecasting centers31. The statistical distribution of the TCR formative number, as a\nfunction of normalized radial distance by JTWC-recorded R34, is shown in Fig. 4d. The\npeak outer TCR formation (139 cases) is observed within the interval of normalized\nradial distances between 0.75 and 1, which is close to the outer boundary of the\n13\nstorm radius of R34. Although the formative numbers tend to decrease generally\nwith increasing radial distance in regions beyond the storm radius, the formative\nfractions of outer TCRs inside and outside the storm radius are dramatically different,\nwhich are calculated to be 29% and 71%, respectively. These statistics further\nindicate that the majority of outer TCR formation actually occurs in far outer regions\nbeyond the operational TC alert area.”\nL283: I recommend adding “near Taiwan” following “outer TCRs”.\nReply: Revised as suggested.\nL284: “crossing angles” needs to be defined somewhere.\nReply: The definition of crossing angles has been given in the Introduction section as\nbelow:\n“The crossing angle is defined as the angle between the rainband’s orientation\nand the tangent to a circle with radius from the band to the TC center.”\nL357: “actually” can be removed.\nReply: Removed as suggested.\nL386: “circumstances to activate the operation” can be removed.\nReply: Thanks for the suggestion. For clarity, this part of the sentence has been\nreworded as “present at low levels are two of the most fundamental characteristics\nof squall-line dynamics.”\nL462,510: I think the authors mean for “predominantly” to be “exclusively”.\nReply: Revised as suggested.\nL465,504,519: The authors show that squall-line dynamics are often important for\nthe maintenance of the rainbands, not the “formation”.\nReply: Thanks for raising the valid point. Please see our responses to Major\ncomment#1 for details.\nResponses to Reviewer#2\nReviewer #2 (Remarks to the Author):\nReview of “Origin of outer tropical cyclone rainbands”\nSynopsis:\nThis is an important study that utilizes a radar dataset to investigate the formation\nlocation and movement of outer tropical cyclone (TC) rainbands, as well as potential\nformation mechanisms. As discussed in the introduction, there are competing\ntheories on the formation and origin of outer TC rainbands, with numerous (mostly\nmodeling) studies indicating that these rainbands are generated as a result of TC\ninner core dynamic. In the current study, the authors provide convincing evidence\nthat most outer TC rainbands form outside the inner core, and in some cases outside\nthe radius of gale force winds. Additionally, the rainbands propagate at radial and\ntangential velocities that are inconsistent with inner origin theories. Instead, the\nauthors show that a majority our outer TC rainbands propagate in a manner\nconsistent with squall line (and cold pool) dynamics. Therefore, I believe that this\nstudy is an important contribution to the research literature. However, I have major\nconcerns associated with data and methods, which are outlined below. Specifically,\nuse of ERA5 data in certain parts of the study is not justified and not likely to be\nsound. As a result, I recommend major revisions for this manuscript.\nReply: We appreciate Reviewer#2’s positive and detailed comments, which help us\nimprove the manuscript. A set of responses to your detailed comments is provided\nbelow.\nMajor comments:\n1. Use of ERA-5 data: On lines 158-163, the authors provide some basic information\nabout the ERA-5 dataset and justify its use for it “more realistic representation of\nTCs and their environment.” It is generally true that the ERA-5 dataset provides\nmore realistic data about the TC environment as well as some other TC-related\nmetrics such as TC size. However, in this study, the authors have used ERA-5 data to\ncapture information about lower-level (boundary layer) winds that are unlikely to be\naccurate due to the low resolution of the associated ERA5 model and the need for\nthese winds to be calculated through parameterization. Could the authors find\nanother dataset that would provide more accurate low-level wind info? Later in the\n15\nresults, the authors use ERA5 data to assess whether cold pool dynamical (and\nthermodynamical) processes are present, and these mesoscale processes are very\nunlikely to be captured by the low-resolution (0.25˚x0.25˚) ERA5. I have major\nconcerns about using ERA5 to assess mesoscale squall-line processes.\nReply: We thank the Reviewer for raising the concern with the ERA5 reanalysis data.\nAs described in the Data and rainband identification section, because ERA5 data have\nhigher spatial and temporal resolutions compared to other reanalysis data, it has\nbeen widely used to study relevant scientific issues for TCs and their environment.\nHowever, we agree with the Reviewer that whether ERA5 data can provide adequate\nrepresentation for the low-level winds nearby the studied outer TCRs is somewhat\nuncertain. To fully address this issue is beyond the scope of this study, but an effort is\nmade to evaluate this uncertainty in this study by comparing the ERA5 winds with\nother independent wind measurements nearby the rainband’s location. In making\nthis comparison, observations from eight offshore island stations [Pengjiayu (PJY),\nYonaguni (YO), Hateruma (HTM), Iriomote (IM), Ishigaki (IG), Green island (GI),\nPenghu (PH) and Dongji (DJ)] located near Taiwan (Fig. R8) within a distance of 35 km\nfrom the formative location of outer TCRs are first collected. The reason why the\nthreshold distance of 35 km is used herein is because it is approximately comparable\nto the grid spacing of ERA5. The island observations represent the “ground truth”\nmeasurements and are available from a total of 70 outer TCR cases. Compared to the\nlarge number of outer TCRs analyzed in the study, this is a relatively small set of TCR\ncases, but they are valuable to provide a critical assessment of the representation of\nthe ERA5 data in the rainband environment. The 10-m (MSL) winds from the ERA5\ngridded data closest to these island stations for these TCR cases are then chosen to\ncompare with station-measured winds. Here, we focus on the comparison of the\nband-normal wind [i.e., V in Eq. (8)] because it is the only ERA5-provided kinematic\nc\nquantity involved with the evaluation of squall-line dynamics.\nFigure R9 shows the scatterplot of band-normal wind components calculated from\nthe ERA5 data and offshore island observations. The result indicates a good\ncorrelation between the two datasets, and the correlation coefficient, average error\nand root mean square error (RMSE) are calculated to be 0.77, -0.1 m s-1 and 2.9 m s-1,\nrespectively. If we assume the calculated RMSE as a representative error for the\nband-normal winds from ERA5, the potential velocity error in the calculation of\ntheoretical cold-pool velocity based on Eq. (8) can be estimated to be 1.7 m s-1. This\npotential error may be considered relatively minor and is unlikely to alter the\nstatistical distributions of the scatterplots shown in Figs. 7c,d significantly.\nreanalysis data for the rainband environment, although the accuracy of the ERA data\nto represent TC circulations and their ambient wind conditions appears to vary case\nby case (Fig. R9). This uncertainty may have greater chances to become a potentially\nserious problem if the scientific approach is placed on the understanding of\nindividual TC/TCR events. However, because the present study focuses on the\nstatistical aspects of outer TCR formation using long-term reanalysis data for a very\nlarge set of TCR cases, the potential impact of this data uncertainty may be\nappropriately mitigated. In response to the Reviewer’s comment, we have included\ndiscussions given above in the Propagation and geometry characteristics section and\nSquall-line dynamics section in this revision.\nFig. R8. Radar dataset used in this study. The locations of the coastal Doppler radars\nat Wu-Fen-San (WFS), Hua-Lien (HL), Chi-Gu (CG) and Ken-Ting (KT) are denoted by\ntriangles. The locations of offshore island observations near Taiwan at Pengjiayu\n(PJY), Yonaguni (YO), Hateruma (HTM), Iriomote (IM), Ishigaki (IG), Green island (GI),\nPenghu (PH) and Dongji (DJ) are marked by solid circles. The outer curve denotes the\napproximate data coverage for these radars, extending from the island of Taiwan to\n300–400 km offshore.\nERA5 data and offshore island observations.\n2. Please provide more information about your “subjective screening” of the\nradar data to locate outer TC rainbands.\nReply: In this revision, we have included more explanations on the method to\nidentify an outer TCR. Please see responses to Major comment#2a below for details.\na. As described in the text, the first set of criteria include measurements of the\nrainband and other quantitative criteria, which suggest that it could have been\napplied algorithmically. Or was this part applied manually too? If manual, please\nprovide justification for doing so. Manual/subjective application of the length-to-\nwind-ratio and minimum length seems less than ideal.\nReply: Sorry for the confusion. For clarity, this part of the text has been rewritten to\ninclude more detailed information for the identification of outer TCRs, as described\nbelow:\n“To seek TCRs, a very large set of radar reflectivity images and data from the lowest\nplan position indicator (PPI) scans (elevation ~0.4o) for TCs approaching Taiwan is\ninitially prepared. The dataset comes from the four radars and contains observations\nof 95 TCs during 2002–2019, which the CWB issued typhoon warnings. All of the\nreflectivity images produced are first screened visually to determine potential\ncandidates of TCRs whose radar echoes can be tracked backward from their mature\nto formative stages. The primary purpose of this subjective screening is just to retain\nReflectivity data from these tentatively chosen TCR cases are then calculated to\nobtain basic rainband information, such as location, length and width, for each of the\nTCRs. The specific location of rainbands at a given time is determined by averaging\nthe azimuthal angles and radial distances with respect to the TC center over the\nrainband entity with reflectivities ≥30 dBZ. The length of rainbands is determined by\nthe distance between two ends of the long axis of the rainband entity with\nreflectivities ≥20 dBZ. Similarly, the width of rainbands is approximated by a mean\ndistance in the band-normal direction along the rainband entity. With these\ncalculated rainband characteristics above, it is possible to identify an outer TCR\nbased on objective, quantitative criteria. The criteria used to identify a TCR are\nsimilar to those used by previous TCR studies9,29 but more specific criteria are used\nherein to define an outer TCR and determine its initiation. First, a precipitation\nfeature with a maximum reflectivity of at least 30 dBZ, a minimum length of 100 km\nand a large length-to-width ratio (>5) must be satisfied. Second, the precipitation\nsignature described above must persist for 1 h or longer. These two criteria can\nassure that a prominent and persistent rainband has been identified, and that a\nrelatively transient, non-banded or loosely organized precipitation feature could be\neffectively avoided. Third, a rainband is classified as an outer TCR as long as its\nprecipitation occurs in or propagates into regions beyond a radial distance of 3 times\nthe RMW for a certain time period during rainband formation and development. This\ncriterion allows us to include both possible formative scenarios: one is that the\nrainband begins development within the inner TC core and then propagates outward\nover time into the outer region, and the other is that the rainband is initiated locally\nin the outer region. Fourth, the formation time for an outer TCR is defined as when\nthe rainband initially satisfies the first criterion above.”\nb. Do your data include the principal rainband? or have you excluded it using your\nsubjective analysis?\nReply: In this study, we do not attempt to exclude principal bands using subjective\nanalysis. Identification of all outer TCRs analyzed in this study are based on the\nobjective, quantitative criteria, as described in our responses to Major comment#2a\nabove. An observed rainband is considered as an outer TCR as long as it satisfies\nthese criteria. So, we cannot rule out the possibility that the outer TCR dataset may\ncontain principal rainbands.\nc. Lines 184-186: Please elaborate on how you identified orographically generated\n19\nrainbands.\nReply: Thanks for raising this valid point. For clarity, we have added explanations for\nthe identification of orographically generated rainbands in this part of the text,\nas\nbelow.\n“One of the most common features of the topographically generated rainbands is\nthat they are oriented approximately parallel to the eastern coast of Taiwan without\nobvious curvature. In addition, these rainbands tend to be locked with coastal\nmountains and do not propagate rapidly with cyclonic circulations of TCs. These\ncharacteristics contrast sharply with evolving and propagation aspects of TCRs.\nHence, if rainbands are observed to form locally within the coastal zone (from\ncoastline to ~25-100 km offshore) and meet the above signatures, they are assumed\nto be the topographically generated rainbands and are thus removed during TCR\nidentification.”\nd. Lines 236-237: “Nevertheless, considerable TCRs are observed to form in far\nouter TC regions beyond the radius of 350 km.” How do you identify whether these\nrainbands are associated with the TC rather than some other forcing? Please provide\nmore details in the methods to describe how you decipher whether the rainband is\nassociated with the TC. Rainbands at distance ~1000 km from center seem like\nthey could be forming due to some other mechanism.\nReply: Thanks for raising the question and good point. As described in the “Data and\nrainband identification” section, the identification task for outer TCRs is focused only\non the time period with the official typhoon warnings issued by Central Weather\nBureau (CWB) of Taiwan. This ensures that TCs would be a primary circulation system\ninfluencing the Taiwan area and its surrounding ocean area. Moreover, all of the\nouter TCRs identified by radar observations in this study have also been checked if\nthey are mainly influenced by TC circulations and are not associated with any other\nsynoptic weather systems (e.g., fronts or cyclones). This checking is practically done\nby looking at both weather analysis maps provided from CWB of Taiwan and\natmospheric circulations nearby TCs seen from the ERA5 reanalysis data.\nIn addition, as the Reviewer kindly mentioned, rainbands at far distances from the TC\ncenter are also evident. Indeed, these exceptionally distant rainbands are quite rare;\nonly a single rainband located beyond 1000 km and 11 rainbands (~1 %) located\nbetween 800-1000 km (Fig. 3 and Fig. 4a). With the examination of CWB weather\n20\nanalysis maps (not shown), we can initially preclude the possibility for the influences\nof these outer TCRs by other synoptic weather systems. Also, as seen from the ERA5\ndata, these TCR cases are primarily associated with cyclonically rotational circulations\nin the outer region of TCs, as shown in Fig. R10. Based on these observational facts, it\nis reasonable to conclude that these distant TCR cases belong to precipitation\nfeatures exclusively induced by TC forcings.\nIn response to the Reviewer’s comment, we have included the explanations above\nin the Data and rainband identification section of the revised manuscript for clarity.\nFig. R10. The spatial composite of horizontal winds at 1.5 km MSL (streamline) with\nrespect to the TC center from the ERA5 data for 12 outer TCR cases with radial\ndistances beyond 800 km. Formative locations of these TCR cases are marked by red\nstars for reference.\nMinor comments:\nLine 37: I don’t agree on the outer rainbands being the “most persistent.” The\nprincipal rainband is more persistent. It might be better to focus on the hazardous\nweather part of this statement (or the extreme rain rates observed in these\nrainbands). For example, you mention in the article that these rainbands can exist\noutside the TC gale force wind radius.\nReply: Thanks for the valid point. Currently, there is no relevant research to\ndocument the statistical differences in the duration between individual principal\nbands and outer TCRs observed in the real atmosphere. Although our experiences\nlearned from looking at numerous TCs approaching Taiwan indicate that the\n21\nappearance of principal bands within TCs seems less frequent than outer TCRs, we\nagree with the Reviewer that saying “most persistent” for outer TCRs may be\noverstated. In this revision, we have removed the description of “most persistent”\nand this part of the text has also been reworded to emphasize the aspects of outer\nTCRs that are a concentrated region of heavy precipitation and hazardous weather\nwithin tropical cyclones (TCs).\nLine 45: squall line dynamics “are” a common mechanism.\nReply: Revised as suggested.\nLine 46: I don’t think the word “road map” is the right choice because you\ndon’t specifically outline research directions and how those should be navigated.\nReply: For clarity, the “road map” and its associated sentences in the Abstract and\nSummary sections have been removed in this revision.\nLine 54: There is not a clear connection between sea level rise and loss of life (it’s\nleading to enhanced storm surges that lead to loss of life). Suggest rewording.\nReply: In response to the Reviewer’s comment, this sentence has been reworded for\nclarity.\nLine 64-68: I disagree with characterization of inner vs. outer rainbands as transient\n(inner) and persistent (outer). Inner rainbands are usually dynamically driven and\ntherefore persist (e.g., eyewall, principal rainband) whereas outer, convective\nrainbands are convective (thermo-driven) and less persistent in terms of their\nlocation and duration. Of course, some of the inner rainbands within the stationary\nband complex are more transient (such as secondary rainbands), but the eyewall and\nprincipal rainband in a major hurricane may be the most persistent and defining\nfeatures of these storms. Some of the articles you cite (e.g., Willoughby et al. 1984)\npoint out the persistent, stationary nature of the principal rainband. Convective\nstorms can persist for hours but not over multiple days as the eyewall and principal\nrainband do.\nReply: We agree with the Reviewer that the precipitation feature of eyewalls could\nbe more persistent compared to outer TCRs. However, tropical cyclone rainbands\n(TCRs) defined in the literature usually refer to spirally banded features of\n22\nprecipitation (i.e., spiral rainbands) outside the eyewall. TCRs are conventionally\nclassified into inner and outer TCRs based on their location relative to the TC center.\nTherefore, the terminology of inner TCRs usually excludes the rainband type of\neyewalls, although the eyewall is actually located within the inner-core region of TCs.\nIn addition, regarding the principal bands, we choose to follow our responses to\nMinor comment # Line 37 above, and the “persistent” and “transient” words have\nbeen both removed from this part of the text for clarity.\nLines 68-70: This sentence is about the impacts on human and natural communities,\nbut the references (28,29,31,32) are mostly about the structure of outer TC\nrainbands. The only cited article that seems relevant here is the one about\nmeteotsunamis. I suggest finding studies that focus on rainband/flooding\nimpacts instead.\nReply: Thanks for raising this concern. The references 28 and 29 cited provided\nstrong, comprehensive observational evidence of squall-line-like precipitation and\nairflow signatures (i.e., severe weather signals) associated with outer TCRs. The\nreference 31 described analysis results about how outer TCRs contributed to the\noccurrence of hazardous weather and how they impacted a fatal airline crash. The\nreference 32 provided evidence of how TCRs trigger meteotsunamis. Therefore, the\nfour references appear relevant to the statement herein. In response to the\nReviewer’s comment, one more reference related to severe flooding due to the\ninteractions of landfalling TCRs with topography is also cited herein.\nLine 71: I think you might want to cite more or different studies here, at the very\nleast Part II by Moon and Nolan (2015), which I believe is the more relevant study\nabout the formation and propagation of inner rainbands.\nMoon, Y., and D. S. Nolan, 2014: Spiral Rainbands in a Numerical Simulation of\nHurricane Bill (2009). Part II: Propagation of Inner Rainbands. J. Atmos. Sci., 72,\n191–215, https://doi.org/10.1175/JAS-D-14-0056.1.\nReply: Thanks for pointing this out. Yes, Moon and Nolan (2015) (Part II) above is a\nmore relevant study and it has been cited in this revision.\nLine 73: There are a few more recent studies about observations of inner rainbands\nand the VRW theory. Suggest citing some here, primarily:\nGuimond, S. R., P. D. Reasor, G. M. Heymsfield, and M. M. McLinden, 2020: The\nDynamics of Vortex Rossby Waves and Secondary Eyewall Development in Hurricane\nAtmospheric Sciences, 77, 2349–2374, https://doi.org/10.1175/JAS-D-19-0284.1.\nReply: Thanks for recommending the nice article related to VRW/inner TCRs. This\narticle has been cited herein in this revision.\nLine 75: delete extra word “be”\nReply: Deleted as suggested.\nLine 78: “Despite” doesn’t seem to be the right word choice here. Maybe\n“Due to”? Think about rewording this sentence on lines 78-82 to better reflect the\nmeaning you’re conveying.\nReply: For clarity, this sentence has been reworded for clarity.\nLines 93-95: I don’t follow how the principal rainband is related to outer or distant\nrainband formation. You say in the text “outer-origin scenarios would probably be\nrelated” to this rainband, but you don’t explain how. Could you elaborate? Or\nmaybe there is no underlying theory and this sentence should be reworded or\nremoved.\nReply: Given that there is no underlying theory, this sentence has been reworded and\nother relevant descriptions are also revised for clarity.\nLines 97-99: “Previous PB studies rely dominantly on the analyses of airborne\nflight-level and radar data collected over a relatively short period of time during the\nmature or late stage of oceanic TCRs.” There are multiple modeling and idealized\nstudies of the principal rainband by Michael Riemer and colleagues. Please revise.\nRiemer, M., 2016: Meso-β-scale environment for the stationary band complex of\nvertically sheared tropical cyclones. Q.J.R. Meteorol. Soc., 142, 2442–2451,\nhttps://doi.org/10.1002/qj.2837.\nReply: Thank the Reviewer for bringing this article to our attention. We have cited\nthis article in this revision and this part of the text is also reworded for clarity.\nLines 101-102: “To the best of our knowledge, Yu et al. (2019) is the only\nobservational study of TCRs to provide a more complete picture of the outer-origin\n24\nprocesses.” This may be true. However, there are multiple studies that observe the\ncold pools associated with these rainbands and their squall-line like structure. I think\nyou should also attribute the idea to these other studies, rather than citing them\nbelow as an afterthought (since the Yu et al. 2019 study came later and built on\nthese former studies).\nEastin, M. D., T. L. Gardner, M. C. Link, and K. C. Smith, 2012: Surface cold pools in the\nouter rainbands of Tropical Storm Hanna (2008) near landfall. Mon. Wea. Rev., 140,\n471–491, doi:10.1175/MWR-D-11-00099.1.\nMoon, Y., and D. S. Nolan, 2014: Spiral Rainbands in a Numerical Simulation of\nHurricane Bill (2009). Part I: Structures and Comparisons to Observations. J. Atmos.\nSci., 72, 164–190, https://doi.org/10.1175/JAS-D-14-0058.1\nYu, C.-K. & Tsai, C.-L. Structural and surface features of arc-shaped radar echoes along\nan outer tropical cyclone rainband. J. Atmos. Sci. 70, 56–72 (2013).\nReply: This is a valid point. In this revision, we have re-organized this part of the text\nby moving the paragraph starting with “With advances….” to the position before the\nparagraph starting with “To the best of …..” to better reflect the subsequence of\nscientific thought.\nLine 139: Can you provide a citation or website for these statistics about the number\nof landfalling TCs around Taiwan from the Taiwan CWB?\nReply: We have provided the website information\n(https://rdc28.cwb.gov.tw/TDB/public/warning_typhoon_list/) along with the\ndescription of the statistics.\nLine 143-145: The observations cannot “aim.” Reword this sentence.\nReply: Reworded as suggested.\nLine 165: Please provide a website or reference for the JTWC best track data. It can\nbe provided here in the text, but you may want to actually provide this information in\nthe data availability statement.\nReply: The website information for JTWC best track data has been provided in the\nData availability statement, as the Reviewer suggested.\nLine 167-169: “The dataset comes from the four radars and contains observations\n25\nof 95 TCs during 2002–2019, which the CWB issued typhoon warnings.” Here,\nyou’re using “which” in a relative clause, but I think it needs to be used in a\npreposition: “The dataset comes from the four radars and contains observations of\nReply: Revised as suggested.\nLines 213-222: It's good to include these limitations. Could you provide even more\ninformation, such as the distribution of errors, not just the average value. It would be\nnice to see a table to histogram that summarizes this information more fully, since\nthe average might obscure other important information about the full distribution,\nincluding very large error values due to a non-normal distribution.\nReply: We have prepared the statistical histogram for the differences between the\nJTWC-calculated and radar-estimated propagation velocities, as shown in Fig. R11.\nThe differences are characterized by a normal distribution centered at nearly zero\nvalues (±1 m s-1) for both radial and tangential propagation velocities. Although large\ndifferences (i.e., beyond ±6 m s-1) are also evident, their occurrence is rare, with\nmuch lower percentages. The statistics indicate a general consistency between the\ntwo independently estimated propagations. Given no perfect observation is available\nto estimate the TC motions, the differences discussed herein do not actually\nrepresent errors, and they just imply a possible uncertainty for the estimation of TC\nmotions based on independent datasets and methods. In response to the Reviewer’s\ncomment, more statistical information about the differences has been included in\nthis revision.\nFig. R11. (a) The statistical histogram for the differences between the JTWC-\n26\ncalculated radial propagation velocities and radar-estimated radial propagation\nvelocities from the 174 outer TCR cases. (b) As in (a), but showing the results of the\ndifferences for the tangential propagation velocities.\nLines 232-233: “This weakly asymmetric characteristic may not be statistically\nrobust and would be due in part to the relative configurations between the generally\nwestward-moving TCs in the northwestern Pacific Ocean and the Taiwan area.”\nElaborate and support this statement better. I don't understand why these would not\nbe statistically significant, related to TC motion.\nReply: In response to the Reviewer’s comment, more explanations have been added\nin this revision and relevant descriptions are also revised for clarity, as below:\n“This azimuthal variation of the outer TCR formation, however, would be due in part\nto the contamination by the inherent limitation of radar observations9,29. Specifically,\nthe precipitation information of the front quadrants for a typical westward-moving\nTCs over the northwestern Pacific Ocean could be usually monitored by coastal\nradars in Taiwan for a longer period of time. In contrast, when the rear quadrants of\nTCs reach the observational coverage of coastal radars, the inner-core circulations of\nTCs have been closer to the landmass of Taiwan so both TC circulations and\nrainbands have greater chances to experience orographic modifications and/or make\nlandfall. This sampling preference of coastal radars is expected to capture more outer\nTCR cases in the front quadrants than in the rear quadrants, consistent with the\nasymmetric characteristic of formative locations of the observed outer TCRs, as\nshown in Fig. 3.”\nLine 254-255: “Relative magnitudes of the filamentation time are useful for\nproviding a dynamic distinction between the inner and outer regions of TCs.” Has\nthis been done in previous studies? If so, cite them.\nReply: Additional references have been cited here for clarity.\nLine 257: Please define MSL. Also, I believe that you really want “above mean sea\nlevel.”\nReply: In this revision, “MSL” has been defined in this sentence for clarity.\nLine 290: At this point, I was hoping for some commentary on the implications of\n27\nyour finding for the theory of initiation/propagation by gravity waves. It might be a\ngood idea to make a note here in the text that you will explore the implications later\nin the section.\nReply: A note is added right after the sentence, as the Reviewer suggested.\nLine 299-302: This sentence seems to belong better with the previous paragraph. I\nsuggest beginning the new paragraph with “Most of the observed outer TCRs …”\nReply: Revised as suggested.\nLine 301: More information about whether principal rainbands are included in your\ndataset will help with interpretation here on the percentage of rainbands with\n“slow radial propagations.”\nReply: As described in our responses to Major comment#2b, we cannot rule out the\npossibility that our outer TCR dataset may also contain principal rainbands. The\nobserved outer TCRs with slow radial propagations would probably belong to\nprincipal bands. However, these quasi-stationary rainbands are quite few (only\n~14%), and most of the outer TCRs analyzed in this study are characterized by radially\npropagating nature. In this revision, this part of the text has been reworded to make\nthis point clear. What’s radial distances for these slow-propagating rainbands?\nLine 355: Add citation to support use of n=2 for tangential wave number.\nReply: Supportive references have been cited in this revision.\nLine 393: Suggesting changing “the squall-line characteristics” to “the above\noutlined squall-line characteristics.”\nReply: Reworded as suggested.\nLine 395: Please define “low-level,” “low-level band-normal vertical shear”\nand “band-relative band-normal wind component.” What levels and distances\nare used? How are the quantities calculated? Information can also be added to the\nFigure 7 caption.\nReply: Height information for the calculation of low-level vertical shear and band-\n28\nnormal wind component has been added in the caption of Fig. 7.\nLine 420-421: This is where I really started to get wary of your use of ERA-5 data for\nthese mesoscale circulations associated with cold pool dynamics.\nReply: Please refer to our responses to Major comment#1.\nLine 428-429: This is a good way to account for some of the uncertainty.\nUnfortunately, due to data quality issues, I think the uncertainty is much larger.\nReply: Please refer to our responses to Major comment#1.\nLine 434-444: “that there is a much higher percentage of the squall line TCR group\ncompared to that of the non-squall-line TCR group.” I don't follow, do you mean a\nhigher percentage of overlap? or do you mean the density of the lines in the plot?\nlike you've squashed the data more in Figure 7c so that more cases fit into the plot?\nReply: Yes, we mean a much higher percentage of agreement between the observed\npropagation velocities and the theoretically estimated cold pool velocities for the\nsquall-line TCR group compared to that of the non-squall-line TCR group. This part of\nthe text has been reworded for clarity.\nLine 448: characters  characteristics\nReply: Revised as suggested.\nLine 448: “fast movement” For clarity, are you referring to faster motion (blue\ndots higher magnitude) in Figure 7c?\nReply: The “fast movement” described here is referring to squall-line convective\nsystems that typically have faster propagations. Relevant articles are also cited,\nalong\nwith this statement.\nLine 448-450: “One might see a more rapidly propagating nature for convective\nsystems if they evolve with the operation of squall-line dynamics.” More rapid\ncompared with what?\nReply: This sentence has been reworded for clarity.\nsize,” I don’t think “storm size” is the word you want since you can’t really\nbe inside the size. Rather, the rainbands are in/outside the storm radius,\nstorm perimeter, or potentially the storm area.\nReply: Thank the Reviewer for raising the valid point. In this revision, we explicitly\ndefine R34 as “storm radius”, instead of simply using the term “TC size”, to avoid\nany possible ambiguity. For clarity, this part of the text has also been reworded in this\nrevision.\nLine 512: “must have existed”  must also exist\nReply: Reworded as suggested.\nLine 540-546: Please be sure that you are providing information about all the\ndatasets you used in this study, including the JTWC best track data.\nReply: Yes, the website information for the JTWC best track data has been added in\nthe Data availability section.\nFigure 1: I am wondering if there is a better way than arrows to demarcate the\nrainband. Could you reduce the transparency of the rest of the radar reflectivity\nregions? so that the rainband stands out more.\nReply: Following the reviewer’s suggestion, Figure 2 has been improved to highlight\nthe rainband by reducing the transparency of the rest of the radar reflectivities. In\naddition, after we remove the arrows, the rainband position is not very easy to\nidentify visually, especially during the preformation stage (i.e., Fig. 2a). Thus, we also\nchoose to include the arrows in this revision for clarity.\nFigure 2: Could you add percentages or fraction on the right axis to assist with\ninterpretation? This would be especially helpful with comparing fraction of inside vs.\noutside TC rainbands cited in the text.\nReply: After adding percentages on the right axis, we found that it makes the figure\nillustration very busy and that the digits of percentage are difficult to read especially\nfor the area closer to the inner core of TCs, where many rainbands form. So, we\n30\nchoose not to add the percentages on the figure. However, alternative information\ncan be provided by Fig. 4a, which shows the number of TCR cases formed at different\nintervals of radial distances.\nFigure 5a,b,d: For interpretation, I manually added vertical lines along x=0 so that I\ncould distinguish positive and negative values more easily. I think it would be great to\nadd these to the plots.\nReply: Vertical lines at x=0 have been added in these plots, as the Reviewer\nsuggested.\nReviewer #1 (Remarks to the Author):\nThe authors revisions have substanfially improved the manuscript, which presents a very nice radar\nclimatology of outer-core tropical cyclone rainbands from tropical cyclones near Taiwan from 2002-2019.\nIn parficular, the addifion of Figure 8 clearly highlights the importance of pre-exisfing precipitafion in the\nvicinity of the region where the outer TC rainband later develops. This preexisfing precipitafion is a likely\nsource of cold pools which may help to inifiate the outer TC rainband. I also commend the authors for\nthe addifion of the schemafic in Figure 9 which nicely summarizes both squall-line and non-squall-line\nouter TC rainband development.\nMinor comments:\nL45-47: The addifion of this sentence I believe strengthens the abstract greatly and makes the\nunderstanding of the outer TC rainband origin much clearer.\nL60: “the prevenfion and predicfion” should be changed to “disaster mifigafion and the predicfion”. It is\nnot possible to prevent the natural hazard (the TC) but it may be possible to mifigate some of the\nimpacts.\nL69: I recommend the authors remove the comparison with inner TCR impacts here. For example,\nremove “In contrast to inner TCRs” and instead say “Outer TCRs tend to have strong and broad\nimpacts…”.\nL97-103: I think it is important within this secfion to clearly state that outer TCRs are a broader class of\nrainbands than just a principal rainband that extends into this region.\nL139: “hypothefical” should be changed to “uncertain”.\nL186: “calculated to obtain” can be rewriften as “used to calculate”.\nL327-334: I appreciate the authors verifying that there is no diurnal variafion in outer TCR formafion.\nThis is a noteworthy and useful result.\nL332-333: I think “although the peak and lowest…” porfion of this sentence can be removed because\nthere is no clear diurnal signal anyway.\nFigure 8: I suggest adding grid lines to this figure to make the distance relafive to the origin locafion\neasier to see.\nL604-605: “would be probably” should be changed to “could be”.\nL641-644: This sentence is very clear and gets at the importance of cold pools in inifiafing many of the\nouter TC rainbands.\nReviewer #2 (Remarks to the Author):\nReview of “Origin of outer tropical cyclone rainbands”\nSynopsis:\nThe authors have addressed most of my concerns from the first review. However, I have a few remaining\nconcerns that need to be addressed before I can recommend this study for publicafion.\nMajor comments:\n1. Regarding the use or ERA5 data, thank you for taking the fime to verify that the winds are similar to\nobservafions. In this latest revision, though, I am left with some confusion about the wind data that was\nused throughout the study. What verfical levels are chosen? and for which parts of the analysis? On lines\n430-454, the authors discuss the verificafion that they completed to ensure that the ERA5 winds are\nconsistent with observafions. However, they do not specify the verfical level that they use in this\ncomparison. Is if the 1.5 km MSL that you use in the filamentafion fime calculafion? Please specify the\nverfical levels that are used in the following places:\na. What verfical level(s) are used in the verificafion on lines 430-454\nb. What verfical level(s) are used in the filamentafion fime calculafion (here, I think that the wind\ninformafion is specified more clearly in the text, but I include it to emphasize that the authors are using\nERA5 wind data in mulfiple places)\nc. ERA5 wind data are also used in the VRW calculafions, with the mean tangenfial wind being averaged\n“within the layer of precipitafion associated with outer TCRs (0.1-12 km MSL). How do you jusfify using\nwinds within the boundary layer in this calculafion?\nd. What verfical level(s) are used in the squall line dynamic secfion, i.e., low-level verfical shear and\nband-normal wind calculafions. In the Figure 7a capfion, the authors describe the low-level verfical wind\nshear as being “calculated and averaged below 1.5-2 MSL.” Does this include all ERA5 verfical levels\nbelow 1.5 -2 km above MSL? If so, then the authors are also including wind data within the boundary\nlayer, which might be problemafic. This might be specified on line 524, but it’s not clearly stated in my\nopinion.\ne. Are there other places that I have missed?\nI am asking that the authors provide a summary of the ERA5 data used in the study, and some\njusfificafion for its use throughout. If boundary layer winds are being used, is this jusfified and how?\n2. Thank you for providing addifional details about the subjecfive screening of radar data to locate outer\nTC rainbands. This is helpful. The addifional details about the spafial measurements and idenfificafion of\norographically generated rainbands, etc. are also welcome and provide important details about your\nmethods.\na. I think that it would be possible to remove principal rainbands from this study, since these rainbands\nare large, prominent, and persistent, and located downshear/downshear left. I believe that the origin\nmechanisms for outer TCRs and PBs are likely to be different and the inclusion of PBs in this study is likely\n“contaminafing” the results. Please provide some addifional discussion of this fact. I think this should be\nconsidered a limitafion in the conclusions secfion.\nMinor comments:\nLine 185: remove the word “just”\nLine 186: Rather than, “Reflecfivity data … are then calculated”, I think you mean “Reflecfivity data … are\nused”\nLines 187-207: Why are 20 dBZ and 30 dBZ threshold selected in this secfion. Please elaborate and/or\nprovide jusfificafion.\nNCOMMS-23-16082A\nResponses to Reviewer#1\nReviewer #1 (Remarks to the Author):\nSummary:\nThe authors revisions have substantially improved the manuscript, which presents a\nvery nice radar climatology of outer-core tropical cyclone rainbands from tropical\ncyclones near Taiwan from 2002-2019. In particular, the addition of Figure 8 clearly\nhighlights the importance of pre-existing precipitation in the vicinity of the region\nwhere the outer TC rainband later develops. This preexisting precipitation is a likely\nsource of cold pools which may help to initiate the outer TC rainband. I also\ncommend the authors for the addition of the schematic in Figure 9 which nicely\nsummarizes both squall-line and non-squall-line outer TC rainband development.\nReply: We sincerely appreciate Reviewer#1’s positive and encouraging comments on\nour revision. Thank you so much. A set of responses to your further comments is\nprovided below.\nMinor comments:\nL45-47: The addition of this sentence I believe strengthens the abstract greatly and\nmakes the understanding of the outer TC rainband origin much clearer.\nReply: Thank you very much.\nL60: “the prevention and prediction” should be changed to “disaster mitigation\nand the prediction”. It is not possible to prevent the natural hazard (the TC) but it\nmay be possible to mitigate some of the impacts.\nReply: Thank Reviewer#1 for the good point. This sentence has been revised as\nsuggested.\nL69: I recommend the authors remove the comparison with inner TCR impacts here.\nFor example, remove “In contrast to inner TCRs” and instead say “Outer TCRs\ntend to have strong and broad impacts…”.\nL97-103: I think it is important within this section to clearly state that outer TCRs are\na broader class of rainbands than just a principal rainband that extends into this\nregion.\nReply: Thank Reviewer#1 for the good point. We have clearly stated this point in this\nparagraph for clarity.\nL139: “hypothetical” should be changed to “uncertain”.\nReply: Revised as suggested.\nL186: “calculated to obtain” can be rewritten as “used to calculate”.\nReply: Revised as suggested.\nL327-334: I appreciate the authors verifying that there is no diurnal variation in outer\nTCR formation. This is a noteworthy and useful result.\nReply: Thank you.\nL332-333: I think “although the peak and lowest…” portion of this sentence can\nbe removed because there is no clear diurnal signal anyway.\nReply: Removed as suggested.\nFigure 8: I suggest adding grid lines to this figure to make the distance relative to the\norigin location easier to see.\nReply: In this revision, grid lines have been added in Fig. 8 as suggested.\nL604-605: “would be probably” should be changed to “could be”.\nReply: Revised as suggested.\nL641-644: This sentence is very clear and gets at the importance of cold pools in\n2\ninitiating many of the outer TC rainbands.\nReply: Thank you very much.\nResponses to Reviewer#2\nReviewer #2 (Remarks to the Author):\nReview of “Origin of outer tropical cyclone rainbands”\nSynopsis:\nThe authors have addressed most of my concerns from the first review. However, I\nhave a few remaining concerns that need to be addressed before I can recommend\nthis study for publication.\nReply: We appreciate Reviewer#2’s positive and further comments, which help us\nimprove the manuscript. Thank you very much. A set of responses to your detailed\ncomments is provided below.\nMajor comments:\n1. Regarding the use or ERA5 data, thank you for taking the time to verify that the\nwinds are similar to observations. In this latest revision, though, I am left with some\nconfusion about the wind data that was used throughout the study. What vertical\nlevels are chosen? and for which parts of the analysis? On lines 430-454, the authors\ndiscuss the verification that they completed to ensure that the ERA5 winds are\nconsistent with observations. However, they do not specify the vertical level that\nthey use in this comparison. Is if the 1.5 km MSL that you use in the filamentation\ntime calculation? Please specify the vertical levels that are used in the following\nplaces:\na. What vertical level(s) are used in the verification on lines 430-454\nb. What vertical level(s) are used in the filamentation time calculation (here, I think\nthat the wind information is specified more clearly in the text, but I include it to\nemphasize that the authors are using ERA5 wind data in multiple places)\nc. ERA5 wind data are also used in the VRW calculations, with the mean tangential\nwind being averaged “within the layer of precipitation associated with outer TCRs\n(0.1-12 km MSL). How do you justify using winds within the boundary layer in this\ncalculation?\nd. What vertical level(s) are used in the squall line dynamic section, i.e., low-level\nvertical shear and band-normal wind calculations. In the Figure 7a caption, the\nauthors describe the low-level vertical wind shear as being “calculated and\naveraged below 1.5-2 MSL.” Does this include all ERA5 vertical levels below 1.5 -2\n4\nkm above MSL? If so, then the authors are also including wind data within the\nboundary layer, which might be problematic. This might be specified on line 524, but\nit’s not clearly stated in my opinion.\ne. Are there other places that I have missed?\nI am asking that the authors provide a summary of the ERA5 data used in the study,\nand some justification for its use throughout. If boundary layer winds are being used,\nis this justified and how?\nReply: We thank you for raising the issue of what vertical levels of ERA5 data are\nused in this study. Below is a summary of vertical levels used for different parts of\nour analysis and their justification. Additional descriptions/explanations have been\ngiven in appropriate places of this revised manuscript for clarity.\na. Verification of ERA5 wind data: Surface observations from eight offshore island\nstations represent “ground truth” measurements and are used to evaluate the\nreliability of ERA5 wind data. For a meaningful comparison with surface\nobservations, the vertical level of the ERA5 wind data at 10-m (MSL) (i.e., near-\nsurface winds) is chosen for this verification. This information has been stated\nclearly in the Propagation and geometry characteristics section. As elaborated in\nthe text of the revised manuscript and previous responses, these comparisons\nshow general consistency between island surface observations and ERA5 data,\nwhich in turn suggests that ERA5 can provide generally reliable boundary-layer\nwind information in the environment of outer TCRs.\nb. Filamentation time calculation: In this study, the vertical level of the ERA5 wind\ndata at 1.5 km (MSL) is chosen for the filamentation time calculation. It has been\nrecognized that most intense winds associated with TCs usually occur\nimmediately above the top of the boundary layer. Given a typical height of TC\nboundary layer at around 0.5-1 km MSL (e.g., Zhang et al. 2011,\nhttps://doi.org/10.1175/MWR-D-10-05017.1), the wind data from the vertical\nlevel used here are expected to better reflect the TC intensity and circulation so\ntheir calculated results for the filamentation time could be more representative.\nThese explanations have been added in the Formative location and dynamic\nregime section of this revision.\nc. VRW calculations: The vertical levels of the ERA5 wind data from 0.1 to 12 km\nMSL are used to calculate the mean tangential wind expressed in Eqs. (5) and (6)\nfor the VRW calculations. The tangential vertical shear in Eq. (7) is approximated\nby the difference in the tangential wind between 0.1 and 12 km MSL. As\ndescribed in the Propagation and geometry characteristics section of the original\n5\nand revised manuscript, the vertical wavelength of both GWs and VRWs in this\nstudy is assumed to be the typical depth of convective motions associated with\nouter TCRs extending from the oceanic surface to ~12 km MSL (Yu et al. 201829).\nThe deep layer chosen for the VRW calculations is corresponding to the\ncharacteristic scale of wave motions. In addition, the reason why we choose the\n0.1 km MSL as the lowest level in these calculations, instead of simply using the\nnear-surface level, is that this level is well above the top of surface layer so the\nuncertainty on winds due to strong and direct impact of surface friction can be\nappropriately eliminated. The explanations above have been added in this\nrevision. It should be noted that the theoretically calculated VRW phase velocities\nare not sensitive to the different choices of the lowest level. Specifically, the\nchanges in the calculated radial and tangential phase velocities of VRWs for all\nstudied outer TCR cases are found to be within 0.1 and 1.0 m s-1, respectively,\nwhen using different heights of the lowest level from the 0.1 km MSL to a height\nabove the top of the boundary layer (1.5 km MSL).\nd. Evaluation of squall-line dynamics: In this study, the low-level mean band-normal\nvertical shear is approximated by the difference in the band-normal wind\nbetween 0.1 and 2 km MSL. This layer is corresponding to the mean depth of cold\npools associated with outer TCRs, as revealed by previous studies of TCs28-30.\nSimilar to the consideration for the VRW calculations as described above,\nchoosing the lowest level at 0.1 km is to preclude the direct influences of surface\nfriction. In addition, the reason why the mean band-normal wind is calculated\nbelow 1.5 km MSL is because this layer is corresponding to the mean depth of\nlow-level inflow (i.e., front-to-rear flow) feeding the leading edge of the outer\nTCRs documented in this study. These explanations have been added in the\nSquall-line dynamics section of this revision.\ne. Please see our responses to Major comment#1c above for details.\n2. Thank you for providing additional details about the subjective screening of radar\ndata to locate outer TC rainbands. This is helpful. The additional details about the\nspatial measurements and identification of orographically generated rainbands,\netc.\nare also welcome and provide important details about your methods.\na. I think that it would be possible to remove principal rainbands from this study,\nsince these rainbands are large, prominent, and persistent, and located\ndownshear/downshear left. I believe that the origin mechanisms for outer TCRs and\nPBs are likely to be different and the inclusion of PBs in this study is likely\n“contaminating” the results. Please provide some additional discussion of this\nfact. I think this should be considered a limitation in the conclusions section.\nReply: We thank you for pointing out the possible inclusion of PBs. In this study, a\nprecipitation feature is identified as outer TCRs as long as it satisfies several\nobjective, quantitative criteria, as described in the Data and rainband identification\nsection of the manuscript. The propagation characteristics and formative locations of\nthese identified rainbands may provide some helpful hints on the degree to which\nthe outer TCR dataset analyzed in this study contain PBs. One of the most important\ncharacteristics for PBs are their quasi-stationary nature relative to the TC center.\nPBs\nalso tend to be located downshear (as Reviewer kindly mentioned) and near the\nouter boundary of the inner-core vortex of TCs. It is found that there are small\nproportions of the identified outer TCRs (144 TCR cases, ~14%) that exhibit slow\nradial propagations within ±1 m s-1 (Fig. 5a) and are consistent with quasi-stationary\nnature. Statistical analyses for the locations of these quasi-stationary cases (i.e., the\nPB candidates) further indicate that they are distributed over different quadrants\nwith respect to the large-scale shear vector (Fig. R1) and over a broad range of radial\ndistance (Fig. R2), with a mean of 331 km and 10.5 times RMW. Assuming the 2-5\ntimes RMW as an approximate area defining the outer boundary of the inner-core\nvortex of TCs, only 13 out of 144 outer TCR cases are actually located in the large-\nscale downshear quadrants within this area. Such a small number of rainbands with\nPB characteristics (~1% of all outer TCRs identified in this study) suggests that the\npossible impact of PBs on the outer TCR dataset and on the statistical results\npresented in this article may be considered negligible.\nOne of the primary factors contributing to the potential preclusion from the class of\nouter TCRs is related to the fact that PBs tend to occur preferentially inside the TC\nvortex core or near its outer boundary (~3 times RMW), as learned from the detailed\nexamination of radar-observed precipitation field from 95 TCs analyzed in this study.\nAn example of TCRs observed from Typhoon Linfa (2015) is chosen to illustrate this\ncommon situation, as shown in Fig. R3. In this case, one PB-like rainband and several\nouter TCRs, located in the northern and eastern portion of the typhoon, respectively,\nare co-existing but they are well separate from each other. The rainband segment for\nthe PB-like rainband is mostly located well within and close to the ring of 3 times\nRMW, although its upwind segment is located slightly beyond 3 times RMW. In\ncontrast, the observed outer TCRs are primarily located in outer regions of the\ntyphoon. The inner PB-like rainband shown in Fig. R3 is not included in our outer TCR\ndataset not only because its initiation scenario is not well captured by radar\nobservations but also because it does not satisfy the criterion of radial distance (i.e.,\n> 3 times RMW) used to identify outer TCRs.\nIt is noteworthy that whether PBs belong to inner rainbands, outer rainbands or\nsome sort of their mixed behavior still remains ambiguous in the literature due to the\nlack of large collection of both inner/outer TCRs and PB cases and their relevant\nstatistical analyses and comparisons. To clarify this scientific issue deserves future\nexploration but will be very challenging because it is usually difficult for atmospheric\nobservational platforms to provide complete and continuous pictures of TC\nprecipitation over the open ocean. Complicated organization and rapidly evolving\nnature of TC precipitation also represents an additional challenge for the\ninvestigation of this topic.\nWe thank you very much again for bringing the PB issue to our attention. In response\nto the Reviewer’s comment, discussions on the possible inclusion of PBs as described\nabove have been added in the Propagation and geometry characteristics section of\nthis revised manuscript for clarity.\nFig. R1. (a) Plan view of formative locations for 144 quasi-stationary outer TCR cases\nrelative to the TC center and large-scale deep-layer vertical shear. The large-scale\nshear is calculated within the deep layer between 700 and 200 hPa over a radial\ndistance of 150-500 km from the ERA5 reanalysis data. (b) Same as (a), but showing\nthe formative locations as a function of normalized radial distance by RMW.\nintervals of (a) radial distance (km) and (b) normalized radial distance by RMW. In (b),\nthe number of outer TCR cases located beyond 15 times RMW (20 cases) are not\nshown.\nFig. R3. Low-level composite radar reflectivity (dBZ) from Typhoon Linfa valid at 0030\nUTC on 8 July 2015. The dashed circle denotes the inner-core boundary (3 times\nRMW) of the typhoon. The principal band discussed in the text of our responses is\ndenoted by PB. The solid ellipse encompasses the primary region with outer TCR\nactivities.\nMinor comments:\nLine 185: remove the word “just”\nReply: Removed as suggested.\nmean “Reflectivity data … are used”\nReply: This sentence has been revised as suggested for clarity.\nLines 187-207: Why are 20 dBZ and 30 dBZ threshold selected in this section. Please\nelaborate and/or provide justification.\nReply: We have provided justification within this paragraph for the 20 and 30 dBZ\nthreshold used in this study.\nReviewer #2 (Remarks to the Author):\nReview of “Origin of outer tropical cyclone rainbands”\nSynopsis:\nThe authors have addressed my concerns, and I am happy to recommend this study for publicafion.\nMinor comments:\nLine 194: Suggest further jusfificafion for using 20 and 30 dBZ. In parficular, the jusfificafion for 30 dBZ is\nflimsy and seems to be somewhat arbitrary.\nLine 197: missing the word “is”: “The reason why a lower reflecfivity threshold of 20 dBZ IS used here is\nbecause...”\nNCOMMS-23-16082B\nResponses to Reviewer#2\nReviewer #2 (Remarks to the Author):\nReview of “Origin of outer tropical cyclone rainbands”\nSynopsis:\nThe authors have addressed my concerns, and I am happy to recommend this study\nfor publication.\nReply: The authors appreciate Reviewer#2’s positive and encouraging comments on\nour revised manuscript. Thank you so much.\nMinor comments:\nLine 194: Suggest further justification for using 20 and 30 dBZ. In particular, the\njustification for 30 dBZ is flimsy and seems to be somewhat arbitrary.\nReply: Following Reviewer’s suggestion, further justification for using 20 and 30 dBZ\nhas been provided in the Methods section of the revised manuscript.\nLine 197: missing the word “is”: “The reason why a lower reflectivity threshold\nof 20 dBZ IS used here is because...”\nReply: Corrected as suggested.\n1"}]

Decision letter