1. Introduction

Rogers et al. (2015) documented the structure and evolution of Hurricane Earl (2010) utilizing a series of five NOAA WP-3D missions each 12 h long during 0000 UTC 29 August–0000 UTC 31 August 2010. While the Rogers et al. analysis was primarily based on the X-band tail Doppler radars on the WP-3Ds, they also incorporated GPS dropsondes from the WP-3D and the NOAA G-IV aircraft as part of the NOAA Intensity Forecasting Experiment (IFEX), and also utilized dropsondes deployed from the U.S. Air Force C-130 aircraft. Additional dropsondes were available from the NASA Genesis and Rapid Intensification Processes Experiment (GRIP; Braun et al. 2013), so Hurricane Earl was well observed over several days. An automated version of the Gamache (1997) variational algorithm takes the measured reflectivity and Doppler radial velocity to produce gridded three-dimensional analysis. As indicated in Reasor et al. (2009), the continuity and Doppler projection equations are simultaneously solved using least squares initialization to produce analyses on a 2-km horizontal and 0.5-km vertical grid. In the first two missions that will be discussed here, the flight tracks consisted of radial passes with an azimuthal separation of 45°–60°. Individual radial passes, which generally take ~1 h to complete, are thus merged into a single analysis that represents the conditions of the vortex over the time scale of the flight pattern, which is typically 4–5 h (Rogers et al. 2015).

Rogers et al. (2015) propose that rapid intensification (RI) defined as an increase in the peak 10-m winds of ~15 m s⁻¹ in 24 h occurred in two stages of Hurricane Earl. During the early stage RI that began at 0600 UTC 29 August, Earl was a tropical storm (TS) that was in an environment of moderate vertical wind shear (VWS). While the VWS magnitude was <4 m s⁻¹ from 1200 UTC 26 August to 0000 UTC 28 August (see Fig. 2a in Rogers et al.), the VWS increased to 9 m s⁻¹ by 0600 UTC 29 August from the northeast (see Fig. 2b in Rogers et al.) as Earl interacts with the outflow of Hurricane Danielle to the north (see section 2 in Rogers et al.). It is also noted that the sea surface temperatures (SST) along the path of TS Earl increased from 27.5°C at 1200 UTC 26 August to ~30°C at 0600 UTC 29 August (see Fig. 2c in Rogers et al.), which is a very favorable environmental factor for tropical cyclone intensification.

Rogers et al. (2015, their section 4a) attribute the early stage RI to vertical alignment processes that occurred during the 12-h period between mission 1 centered at 0000 UTC 29 August and mission 2 centered at 1200 UTC 29 August (i.e., 6 h after the beginning of the early RI). During mission 1, a broad, tropical cyclone–like vortex was analyzed at 2 km (Fig. 1e), but only a poorly defined, elongated circulation with a northwest–southeast orientation existed at 5 km (Fig. 1c). Although there is a critical observation gap in the eastern quadrant at 8 km (Fig. 1a), the circulation center at this elevation is clearly displaced ~50 km to the east-southeast of the 2-km circulation center.

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From Rogers et al. (2015): (a) Vertical vorticity (shaded, ×10⁻⁴ s⁻¹) and flow vectors (m s⁻¹) at 8-km altitude from merged analysis for mission 100828I1. (b) As in (a), but for mission 100829H1. (c) As in (a), but at 5-km altitude. (d) As in (b), but at 5-km altitude. (e) As in (a), but at 2-km altitude. (f) As in (b), but at 2-km altitude. Insets in (a) and (b) show the SHIPS-derived shear vector (green arrow, m s⁻¹) and storm motion vector (blue arrow, m s⁻¹) for the 6-h time nearest to the mission. Line A–B in (e) denotes the location of the cross section shown in Fig. 10 of Rogers et al. (2015).

Citation: Monthly Weather Review 145, 4; 10.1175/MWR-D-16-0301.1

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If this was a coherent vortex in a moderate-to-strong VWS [9.3 m s⁻¹, with a heading toward 223°; see Table 1 in Rogers et al. (2015)], one might expect that the 8-km circulation center would be tilted in the downshear direction. By contrast, the 8-km center is in the upshear-left quadrant relative to the 2-km vortex center. Rogers et al. suggest this upshear-left displacement may be explained as the 8-km vortex was precessing about the 2-km center during mission 1 but then became vertically aligned during mission 2 as has been proposed to occur with coherent vortices such as hurricanes in VWS (e.g., Reasor et al. 2004). With only the single analysis centered at 0000 UTC 29 August, Rogers et al. (2015) provide only a partial demonstration of such a vortex precession.

Another important feature in the 8-km plot (Fig. 1a) is the absence of any Doppler radar winds in the northern quadrant beyond about 25 km north of the 2-km center, and in the western quadrant beyond 40 km from the center, even though the WP-3D had long flight tracks through these regions. The implication is that these are regions of upper-tropospheric subsidence through which convection associated with the lower-tropospheric vortex (see 2-km plot in Fig. 1e) is not able to penetrate. Meridional wind components in an east–west cross section (see Fig. 10b in Rogers et al.) along the black line labeled A–B in Fig. 1e indicate very large local vertical wind shear between lower-tropospheric southerlies and the mid- to upper-tropospheric northerlies. Such a local vertical wind shear would be expected to inhibit deep convection over the circulation center.

The second WP-3D mission centered at 1200 UTC 29 August (12 h after the first mission and 6 h after the beginning of RI) observed a vertically stacked vortex from the 2-km (Fig. 1f) through the 5-km (Fig. 1d) and 8-km (Fig. 1b) levels. The tail Doppler radar wind coverage is more complete than in mission 1—including at 8 km in the outer northern and western quadrants that had no radar winds in the first mission (Fig. 1a). Thus, the key question is what physical processes explain these vortex structure changes between the first and second missions?

As mentioned above, Rogers et al. (2015, see their section 5a) attribute the change from a broad, shallow vortex during mission 1 to a deep, vertically stacked tropical storm structure during mission 2 to vortex alignment processes, and specifically that there was evidence of a cyclonic vortex precession during mission 1 that would by some mechanism lead to the “vortex alignment” during mission 2. The first source of confusion for us was this vortex alignment terminology. Davis and Ahijevych (2012) had previously attributed the genesis (nonredevelopment) of Hurricane Karl (Tropical Storm Gaston) during the 2010 PREDICT experiment to deep convection away from the lower-tropospheric circulation becoming (not becoming) vertically aligned with that circulation. Davis and Ahijevych also noted that Hurricane Matthew (2010) was vertically aligned through most of its early evolution.

In each of the three cases studied by Davis and Ahijevych, the key physical factor was the VWS magnitude. By contrast, the implication of the upper-tropospheric circulation center (and its associated convection) ~50 km to the east-southeast of the 2-km circulation center during mission 1 in TS Earl is that these two circulations were previously a coherent vortex, and vortex realignment would be a more accurate terminology in Rogers et al. (2015) to avoid confusion with Davis and Ahijevych (2012) rather than an internal process of somehow realigning the upper and lower circulation centers that existed during mission 1. An alternate explanation based on environmental VWS processes will be presented in the next section.

2. Alternate explanation for mission 1 and mission 2 vortex structures

The impacts on the TS Earl intensity due to the VWS associated with the outflow from Hurricane Danielle are evaluated based on the SHIPS (DeMaria et al. 2005) deep-layer (200–850 mb; 1 mb = 1 hPa) and low-level (500–850 mb) VWS estimates (SHIPS 2016), and also from the Cooperative Institute for Meteorological Satellite Studies (CIMSS) technique (Velden and Sears 2014). First, note that the SHIPS low-level VWS (designated as SHTS in Table 1) magnitudes are generally in the range of 2–3 m s⁻¹ and the headings are from 88° to 147° (i.e., from the east-southeast). These small VWSs are consistent with the Elsberry and Jeffries (1996, see their Fig. 11a) schematic in which the VWS is small in the tropical lower troposphere, but was concentrated in the mid- to upper troposphere in association with an adjacent tropical cyclone outflow (Fig. 2). This is also important because the special kind of VWS that impacts the TS Earl circulation and associated convection is primarily the upper-tropospheric flow.

Table 1.

Tropical Storm Earl (2010) intensity (m s⁻¹), and vertical wind shear magnitude (m s⁻¹) and direction estimates as a function of UTC from SHIPS low level (SHTS), deep layer (SHDC), and from CIMSS. The SHIPS shear directions have been converted to be headings to be consistent with the CIMSS convention (i.e., 270° indicates a shear vector heading from the west). The values at the center time of mission 1 (mission 2) is in boldface (italics).

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Schematics from Elsberry and Jeffries (1996) of the 200–850-mb vertical wind shear arising from (a) a low-latitude system with upper-tropospheric winds concentrated in a shallow layer vs (b) linearly distributed over a deep layer as might exist in a midlatitude trough.

Citation: Monthly Weather Review 145, 4; 10.1175/MWR-D-16-0301.1

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The schematics in Fig. 3 of the changing VWS directions and magnitudes (Table 1) relative to the positions of TS Earl prior to and immediately following mission 1 at 0000 UTC 29 August will be utilized to provide an alternate environmental control explanation of the upper-level vortex structure changes between mission 1 and mission 2. As indicated above, TS Earl was translating toward higher sea surface temperatures so that more vigorous diurnal convection each nighttime (local times are given in Table 1) may also be a contributing factor. In this environmental control explanation, the focus is on VWS in the mid- to upper troposphere associated with the Danielle outflow jet and what deep convection is allowed to exist or persist relative to the low-level circulation center of Earl.

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Schematics of three phases of the outflow jet (long, straight arrows) from Hurricane Danielle (2010) impinging on the outflow of Tropical Storm Earl (2010) (anticyclonically curved streamlines) at (a) 0600 UTC, (b) 1200 UTC, and (c) 1800 UTC 28 Aug. Panel (c) also applies to mission 1 centered on 0000 UTC 29 Aug if the TS Earl outflow pattern is shifted to the west-northwest to represent the storm translation (thick arrow) during the 6-h period. Dashed lines in (b) indicate a hypothetical flow if the Danielle outflow was so strong as to have sheared off the deep convection and outflow of TS Earl. Possible locations of deep convection are indicated by the scalloped regions in each panel.

Citation: Monthly Weather Review 145, 4; 10.1175/MWR-D-16-0301.1

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At 18 h prior to mission 1 (0600 UTC/0300 LT, Fig. 3a), the VWS (Table 1) is from the northwest with small magnitudes in both the SHDC (3.1 m s⁻¹) and the CIMSS (2.7 m s⁻¹). The interpretation is that TS Earl is remote from the Danielle outflow jet core and there is relatively little interaction with the Earl outflow. Based on many studies, the deep convection (at this time of a maximum diurnal convection) would be expected in the downshear-left quadrant of Earl. Just 6 h later (Fig. 3b), the VWS has rotated to be from the north, and there is a huge difference in magnitude between the SHDR (10.2 m s⁻¹) and the CIMSS (1.4 m s⁻¹). The expectation from the 10.2 m s⁻¹ SHDR is that the upper-level flow would be straight over Earl (Fig. 3b, dashed lines), and therefore the Danielle outflow jet would have prevented any deep convection.

As this time (0900 LT) is at the end of the diurnal convective maximum, the proposed explanation for the very small VWS from the CIMSS technique is the Earl outflow magnitude and direction are sufficient to oppose the Danielle outflow. As described in Elsberry and Jeffries (1996), the Danielle outflow will be forced to subside north of the interaction zone between the two outflows, or be diverted around the Earl outflow. The CIMSS technique will be able to detect this interaction of the cyclone outflow with the environmental flow phenomena because it is primarily based on the upper-tropospheric atmospheric motion vectors (AMVs). The Global Forecast System (GFS) wind analyses (on which the 1200 UTC 28 August SHDC VWS estimate is based) are provided hourly AMVs each 6 h. It is postulated that the small area of southerly AMVs associated with the Earl outflow opposing the large-scale northerly environmental flow associated with the Danielle outflow would likely not be properly analyzed (indeed, these AMVs with opposing directions would likely fail the quality control step and be omitted from the GFS data assimilation). With a relatively strong outflow being sustained in Earl, the small CIMSS VWS can be accepted as an alternate VWS explanation that is consistent with no change in the intensity at 1200 UTC 28 August (Table 1).

At 6 h prior to mission 1 (1800 UTC/1500 LT, Fig. 3c), both the SHDR and CIMSS VWS have further rotated relative to Earl to be from the northeast, and have similar magnitudes of 8.3 and 7.0 m s⁻¹, respectively (Table 1). These magnitudes suggest that Earl is relatively close to the Danielle outflow jet core. Since this time is closer to the diurnal convective minimum, this relatively large VWS would prevent deep convection in the northwest quadrant. With no deep convection to oppose the VWS in that quadrant, the Danielle outflow will pass through that quadrant (Fig. 3c) and contribute to the relatively large SHDR and CIMSS shear magnitudes. However, some deep convection may exist in the east quadrant where low-level convergence and upper-level divergence may be sufficient to sustain deep convection against the smaller vertical wind shear over that quadrant.

At the central time of mission 1 (0000 UTC 29 August, 2100 LT 28 August), the VWS directions of both SHDR and CIMSS continue to be from the northeast (Table 1). However, the rapid west-northwest translation of Earl is proposed to have brought Earl closer to the Danielle outflow jet maximum (thick arrow in Fig. 2c), and consequently the VWS magnitudes have increased (SHDR = 9.3 m s⁻¹; CIMSS = 10.3 m s⁻¹) during the last 6 h. Even though mission 1 was approaching the time of the diurnal convective maximum, no deep convection would exist in the northwest quadrant (see Fig. 1a) in the presence of such large VWS from the northeast. However, deep convection could develop (or be sustained from 6 h previous) in the southeast quadrant where the outflow is not opposing the VWS. Indeed, this asymmetric deep convection distribution was observed during mission 1 (Fig. 1a).

At 6 h after mission 1, the SHDR magnitude has decreased by more than 50% to only 4.4 m s⁻¹ and the heading of 58° is more like east-northeast (Table 1). While the CIMSS magnitude decreases by 3.8 m s⁻¹, and continues to be from the northeast, this is a moderate VWS of 6.5 m s⁻¹. In conjunction with a time closer to the diurnal convective maximum, the much more favorable SHDR magnitude, and the deep convection on the eastern side possibly having a shielding effect against an east-northeast VWS, it is reasonable to suggest convective bursts would now be allowed to also develop in (or wrap around to) the western quadrant. The Ryglicki et al. (2016) convective burst explanation for rapid intensification during the development stage of some hurricanes may be applicable 6 h prior to mission 2. Either of these two scenarios would explain the vertically stacked vortex that Rogers et al. (2015) have analyzed from the mission 2 observations even though the SHDR (CIMSS) magnitude has increased to 7.7 (7.8) m s⁻¹ and mission 2 is at the end of the diurnal convective maximum. Even though this deep convection is of course essential to the RI, we prefer to describe the physical process as one of environment control of when and where this deep convection is allowed to develop and be sustained.

Park et al. (2012) examine case studies of the VWS and ocean heat content as environmental modulators of western North Pacific tropical cyclone intensification and decay. Because the western North Pacific frequently has multiple tropical cyclones spaced about 15° longitude apart, and the preceding tropical cyclone has an equatorward-directed outflow, the upper-level flow relative to the trailing low-level center is similar to this Earl case. The pre-Chaba (2010) case (Park et al.’s Fig. 1a) is similar to the Earl case in that an adjacent trough caused strong 200-mb northeasterly winds to impinge on the northeast quadrant of the tropical storm. Although the VWS over pre-Chaba was estimated to be 25 kt (12.9 m s⁻¹) from the north, upper-level convergence and likely strong subsidence was occurring where the outflow opposed the northeasterly winds. Based on this pre-Chaba case and two other cases, Park et al. (2012) conclude that what VWS is actually affecting the convection in the inner core of the developing tropical cyclone is an important intensity forecast question when the developing tropical cyclone is translating under a dynamically varying upper-tropospheric flow.

Note that it will be very challenging for a numerical model to forecast this phenomenon because the magnitude and orientation of the tropical storm outflow must be predicted in addition to its position and translation relative to the location, structure, and magnitude of the outflow from the leading tropical cyclone that may be recurving into the midlatitude flow. This challenge would be smaller in the pre-Chaba case with a strong, broad upper-tropospheric flow sweeping over the low-level circulation and completely removing the deep convection. For the Earl case, the numerical model must be able to replicate the shallow, broad vortex structure at 2 km in Fig. 1e while also predicting the mesoscale circulation with associated convection at 8 km in Fig. 1. Any numerical model that cannot replicate this precondition Earl vortex structure during mission 1 should not be utilized for testing the Rogers et al. (2015) precession explanation for the deep vortex structure observed during mission 2. Furthermore, we assert that the numerical model must properly represent the approaching Danielle outflow jet vertical structure as in Fig. 2a and horizontal structure as in Fig. 3.

In summary, the alternative proposed here is that the two vortices observed during mission 1 were independent (i.e., not coupled) vortices, and the shallow vortex structure during mission 1 and deep (vertically stacked) vortex structure during mission 2 were determined by the environmental influences of VWS and SST. Assuredly, convective bursts were important in creating that deep vortex structure observed in mission 2. However, it is proposed that the VWS associated with the time-varying effects of the Hurricane Danielle outflow, and in conjunction with the diurnal convective maxima and minima, are the explanation for the shallow vortex during mission 1. In addition to a decrease in the VWS as the paths of Danielle and Earl diverged, and in conjunction with a high SST, vigorous deep convection was then able to develop and offset the effects of moderate VWS, and allow a vertically stacked vortex to develop by the time of mission 2. As that deep vortex spun up, the small circulation at 8 km about 50 km to the east (Fig. 1b) would be axisymmetrized by the radial shear of the vortex flow. While no high temporal resolution observations necessary to validate this environmental control process are available at 0600 UTC 29 August between mission 1 and mission 2, this explanation is proposed as an alternative to the vertical realignment process of a fully coupled vortex as described in Rogers et al. (2015).