The effect of vertical shear orientation on tropical cyclogenesis

Transcription

1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5, April B The effect of vertical shear orientation on tropical cyclogenesis Eric D. Rappin* and David S. Nolan Rosenstiel School of Marine and Atmospheric Science, University of Miami, Florida, USA *Correspondence to: E. D. Rappin, RSMAS/MPO, Rickenbacker Causeway, Miami, FL 339, USA. erappin@rsmas.miami.edu The effect of the relative orientation of the vertical wind shear to the surface wind on tropical cyclogenesis is explored in environments of radiative-convective equilibrium (RCE) through numerical simulation. This study serves as a companion paper to an earlier study on the thermodynamics of genesis in RCE. It is found, when the mean surface wind and shear are aligned, a negative surface wind anomaly arises from the superposition of the mean and vortex surface flows left of the shear vector. The resulting weak surface enthalpy fluxes and up-shear quasi-balanced subsidence leads to dry air being located cyclonically down-wind of the down-shear convective anomaly. Thus convection is inhibited from propagating cyclonically around the core leading to a large down-shear vortex tilt. Conversely, in a counter-aligned orientation, the negative surface wind anomaly and driest air is found right of the shear vector. Hence the driest air rotates into the downshear flank where it moistened by shear-organized convection. Furthermore, the boundary layer is relatively moist left of shear due to the positive surface wind anomaly, therefore promoting the cyclonic propagation from down-shear and constraining the magnitude of the vortex tilt. Genesis is intimately tied to the magnitude of the tilt and is found to occur once the mid-level vortex has precessed into the up-shear flank. For smaller values of maximum tilt, vortex precession is comparatively rapid, aided by showerhead moistening provided by the up-shear advection of frozen condensate aloft. With the up-shear flank pre-moistened, rapid precession of the mid-level vortex, at smaller radii, leads to near saturation on the mesoscale and the onset of rapid intensification. When the magnitude of the tilt is quite large, precession is much slower and the showerhead effect is significantly reduced until just prior to the emergence of the mid-level vortex in the up-shear flank. Copyright c Royal Meteorological Society Key Words: tropical cyclones; genesis; wind shear; radiative-convective equilibrium Received January ; Revised August ; Accepted October ; Published online in Wiley Online Library 5 December Citation: Rappin ED, Nolan DS.. The effect of vertical shear orientation on tropical cyclogenesis. Q. J. R. Meteorol. Soc. 3: DOI:./qj.977. Introduction A recent article (Rappin et al., ; hereafter RNE) investigated the thermodynamics of tropical cyclogenesis in environments of radiative-convective equilibrium (RCE) in mean wind shear. The study presented here will focus on the kinematics of genesis in similarly sheared environments. The evolution of tropical cyclone (TC) strength vortices under the influence of large-scale vertical shear, and their subsequent intensity change, has seen considerable Copyright c Royal Meteorological Society

2 3 E. D. Rappin and D. S. Nolan analytical, observational, and numerical study. In contrast, tropical cyclogenesis in a sheared environment has been given considerably less attention. Regardless, large-scale conditions under which tropical cyclogenesis is likely to occur have been well documented (Gray, 9; McBride and Zehr, 9; Bracken and Bosart, ) and low values of vertical shear are generally expected to be persistent in regions where genesis frequently occurs. Molinari et al. (, ) coined the term down-shear reformation in studies of hurricane Danny (997) and tropical storm Gabrielle () to describe the formation and development of a new low-pressure core resulting from deep convection organized by the large-scale vertical shear. In both cases, shear magnitudes were comparable to the commonly cited genesis threshold value of m s (Zehr, 99). Molinari et al. () likened their result to that of Enagonio and Montgomery (), which used numerical simulations of a shallow-water primitiveequation model. In their study of vortex intensification through axisymmetrization of convective anomalies, they found that, when a small intense vorticity anomaly located on the periphery of a weaker, large-scale anomaly is integrated with time, the weaker anomaly is axisymmetrized through the strong differential advection of the small anomaly, resulting in the amplification of the intense anomaly. A set of numerical simulations using a full-physics, cloudresolving model to simulate the formation of hurricanes Diana (9) and Humberto () were conducted by Davis and Bosart (,, ). An additional numerical study of Gabrielle () was performed by Musgrave et al. (). All of the above simulations imposed shear on the incipient disturbance through the presence of environmental potential vorticity (PV) gradients, mostly in the form of midlatitude troughs. Utilizing PV inversion techniques (Davis and Emanuel, 99), when the initial conditions were modified to reduce the shear over the disturbance, weaker or a total absence of development resulted. Development was argued to occur as the result of organized mesoscale ascent induced by shear. It was suggested that convective pulses and their diabatically generated PV anomalies could follow a number of evolutionary paths: first, they could pool and aggregate to form an enhanced vorticity centre; second, if the largescale circulation is of sufficient strength, they could be axisymmetrized and enhance the large-scale circulation; third, if the large-scale circulation is weak, then the large-scale circulation is axisymmetrized and the downshear perturbation would develop as discussed by Molinari et al. (). The numerical studies of tropical cyclogenesis undertaken by Frank and Ritchie (999; hereafter FR99) utilized idealized initial conditions in a full-physics, limited-area model (MM5). FR99 compared the vertical motion pattern in the boundary layer and the mid-troposphere under dry and moist conditions, with and without boundary-layer physics, and with and without shear or zonal flow. They also considered the intensity evolution of the array of experiments conducted. The current study has much in common with FR99 and in some ways may be considered an update. FR99 was concerned with intensification and therefore used a surface-based 5 m s initial vortex. The current study is concerned with genesis and therefore uses a weaker mid-level initial vortex as will be discussed in section. Additionally, FR99 was limited to 5 km horizontal resolution and hence made use of a convective parametrization. As a result, the intensity evolution of the various experiments showed little sensitivity. Here, we use a much finer resolution, making the parametrization of convection unnecessary. The article is organized as follows. The methodology and numerical set-up are discussed in section. Section 3 revisits the thermodynamic aspects considered in RNE as applied to the simulations conducted for this study. A kinematic analysis of the simulations is provided in section. The analysis considers the impact of vertical motion patterns on genesis, the temporal evolution of the vortex tilt, and the role of shear in the genesis process. Finally, section 5 provides a concluding discussion.. Methodology and experimental set-up A brief description of the experiment will be provided here; greater detail is discussed in Nolan et al. (7b), Nolan and Rappin (), and RNE. These references also provide justification for the use of environments of RCE. All simulations use the Weather Research and Forecast (WRF) mesoscale numerical weather prediction system version.. (Skamarok et al., 5) with 3 km horizontal grid spacing and vertical levels, of which lie below km. Physical parametrizations include the Yonsei University (YSU) boundary layer (Noh et al., 3) with modifications to the drag formulation following Donelan et al. () and implemented by Davis et al. (b) in the WRF model. The WRF single-moment six-class scheme (Hong and Lim, ) is used for microphysical processes. Radiation physics is handled by the Rapid Radiative Transfer Model (RRTM) for long-wave radiation (Mlawer et al., 997; Iacono et al., ) and the Goddard scheme (Chou et al., 99) for short-wave radiation. Due to the lengthy integration period required for RCE, a perpetual equinox is used while maintaining a diurnal cycle. First, a simulation initialized with random thermal perturbations is conducted on a 5 km square, doubly periodic grid to achieve a state of RCE. The mean sounding from this RCE state, taken as the horizontal mean of -hourly output over the last 3 days of a 9-day simulation, is then used to initialize a simulation of tropical cyclogenesis from a m s, mid-level, cold-core vortex on a km square, doubly periodic grid. A detailed description of initialization of the mid-level vortex can be found in Nolan et al. (7b). Briefly, the azimuthal wind profile is calculated from the radial integration of a Gaussian vorticity distribution such that a maximum wind, v max,ofms is located at a radius of maximum winds (RMW) of km. The vertical structure uses Gaussian decay above and below the height of the maximum winds z max. For the simulations here, a value of z max = 3.7 km is used and the vertical decay rate chosen so that the maximum surface wind has exactly one half the value of v max,or5ms. This structure is modelled after several case-studies of east Pacific easterly waves (Raymond et al., 99). Except for the shear sensitivity cases, all of the simulations, including the initial RCE simulations, include a 5 m s, 5 hpa piecewise linear shear profile in which the wind profile is constant from the surface up to 5 hpa and from hpa to the domain top. The three different shear profiles used in this study are shown in Figure. The Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

3 Tropical Cyclogenesis in Vertical Shear Zonal Wind (ms ) SF5W SH5E SF3W SH5W SF3E SH5W Figure. Initial zonal wind profiles. 3 3 Wind Speed (ms ) SF5W SH5E SF3W SH5W SF3E SH5W Figure. Position of the smoothed sea level pressure minimum for the first h for the three shear profiles utilized in this study at an SST of 3. C. Positions at -hour intervals are denoted by dots. All three storms start at the origin of the figure. naming convention describes two parameters, the mean surface wind and the large-scale vertical shear. SFXY gives the mean surface wind (u m )ofxms out of the Y direction. SHXY gives the large-scale shear of magnitude X m s directed from Y. For example, SF3E-SH5W corresponds to an easterly mean surface flow of 3 m s and westerly shear of 5 m s. Profiles SF3E-SH5W and SF5W-SH5E each have shear directed opposite that of the surface wind and the resulting translational motion (Figure ). Profile SF3W-SH5W is similar to the profiles used in RNE where the shear and surface wind are aligned. The shear profiles shown in Figure are taken from the RCE simulations that are used to initialize the genesis simulations. As such, weak nonlinearities are seen in the boundary layer and the tropospheric stratospheric interface. To incorporate vertical shear in a doubly periodic domain without largescale temperature gradients, the method introduced in Nolan and Rappin () was used. A more detailed explanation of this method can be found in the appendix of RNE. The shear profiles were chosen primarily for their consistency with the companion article RNE. These profiles can be considered the extreme cases of relative orientation of the mean surface wind and vertical shear, with other cases yielding evolutions that are intermediate to those presented here. Corbosiero and Molinari (3) compiled storm motion versus shear direction for all named storms within km of the US coastline between 95 and 999 at h periods, producing a sample size of 33. They found that roughly 5% of the cases fell between an aligned orientation and one in which the storm motion is left of shear. The distribution was even between the two orientations. The number of cases rapidly diminished as the angle of the motion relative to the shear increased beyond 9 left of shear and a minimum was found with motion right of shear. 5% of the cases were found to lie within 5 of a counter-aligned orientation. However, the counteraligned orientation is more consistent with climatological mean profiles in the Atlantic main development region, and thus may be more relevant to genesis (McGauley and Nolan, ). Two important parameters that are useful in understanding genesis in shear are the vortex tilt and the vertical shear of the horizontal wind. The vertical shear can be decomposed into a fixed, large-scale shear and a mesoscale, or self-induced, shear. Both quantities necessitate a definition of the vortex centre at various levels. During genesis, the vortex signature is weak in comparison to that of individual convective elements. However, the large-scale vertical shear flow organizes convection so that utilization of a statistical tracking technique may be applied. One such method, the centre of potential vorticity approach to vortex tracking has proven to be effective in previous shear studies (Jones, ; Davis et al., a) and will be employed here. To track the vortex at a given level, we define the mean PV position as: x = A (Qx)dxdy, () (Q)dxdy A where Q is Ertel PV and x is the position vector. The vertical tilt is taken to be the difference in 9 hpa and 5 hpa PV mean position, while the mesoscale vertical shear is calculated using the difference in horizontal winds at the same two levels within a 3 km radius circle centred on the PV centroid at 7 hpa. 3. Thermodynamic parameters and the time to genesis As in RNE, we would like to evaluate the likelihood of genesis as measured by the evolution of a seed vortex placed in explicitly simulated RCE states. The parameter χ m was introduced as an idealized predictor of the incubation period or time to genesis. χ m is defined as: χ m = s b s m s s. () b Here s m, s b,ands are the moist entropies of the midtroposphere (here taken as hpa), the boundary layer, and the sea surface at saturation, respectively. The moist Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

4 3 E. D. Rappin and D. S. Nolan entropy is approximately (Emanuel, 99) s = c p ln T R d ln p + L vq T R vq ln H, (3) where c p and R d are the heat capacity and gas constant of dry air, respectively, R v is the gas constant for water vapour, L v is the latent heat of vaporization, q is the specific humidity, and H is the relative humidity. As described in Emanuel et al. (), χ m measures the relative importance of warming the boundary layer through surface fluxes and cooling of the boundary layer by convective downdraughts and turbulent mixing across the boundarylayer top. χ m is a non-dimensional measure of the time it takes for the vortex core to saturate and begin to warm through surface fluxes and upward convective heat transport and, as such, smaller values favour genesis. Large values of χ m indicate that the mid-levels are far from saturation and that convective downdraughts will disrupt the generation of the boundary-layer entropy gradient, or that the thermodynamic disequilibrium between the ocean surface and the overlying atmosphere is insufficient to produce a significant boundary-layer gradient. In RNE, χ m was referred to as the genesis parameter. Table I gives the values of CAPE, potential intensity V pot (Bister and Emanuel, 99), and χ m for the three shear cases (Figure ) and for sea surface temperature (SST) values of 7.5, 3, and 3.5 C. Note that in the table the values of χ m are normalized by the control case, that is the value obtained for simulation SF3W-SH5W at 3 C. As in RNE, for stronger mean surface winds (u m ) CAPE increases while the potential intensity decreases. Larger CAPE values are the result of the warmer, moister boundary layer while the decrease in potential intensity results from the decrease in thermodynamic disequilibrium between the sea surface and the overlying atmosphere. The shear orientation had little impact on the thermodynamic quantities. Furthermore, we see the genesis parameter increases (hence the favourability of genesis decreases) in value with both SST and u m, consistent with the results found in RNE. In order to relate the values of the large-scale derived genesis parameter to the genesis simulations, a measure of the time to genesis in the simulations is needed. RNE Table I. Thermodynamic and genesis parameters for atmospheres generated by small-domain simulations of RCE for various values of the environmental parameters SST, u m, and shear orientation. (The latter two are defined within the experiment name; see text.) SST ( C) Experiment SF3E-SH5W CAPE 5 5 V pot.3.5. χ m..9.7 SF3W-SH5W CAPE V pot χ m.9.. SF5W-SH5E CAPE 7 57 V pot χ m..3.5 Units: CAPE J kg ; V pot ms. (a) Pressure (hpa) Time (Days) (b) Pressure (hpa) Pressure (hpa) Time (Days) SF5W SH5E SF3W SH5W SF3E SH5W Time (Days) Figure 3. Surface pressure (hpa) traces for the initial vortex simulations: SST = (a) 7.5 C, (b) 3. C, 3.5 C. Time to genesis proxies are shown as: p max ( ), p qtmax (+), θ ediff ( ). compared three such genesis proxies ; the time to the maximum pressure fall in the simulated pressure trace (p max ), the time to a sustained -hour pressure fall that is 5% of the maximum pressure fall (p qtmax ), and the difference between θ e values straddling the minimum azimuthally averaged θ e gradient (θ ediff ). To compare longer gestation periods with smaller values of the genesis index, the inverse of the genesis time will be used for the proxy. While p max is included for completeness, it is not a valid genesis time as genesis usually occurs well before rapid intensification. Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

5 Tropical Cyclogenesis in Vertical Shear 39 The pressure traces and the genesis proxies for the simulations of each of the three shear profiles for SST values of 7.5, 3, and 3.5 C are shown in Figure 3. As in RNE, the simulation with aligned surface motion and shear at 3.5 C failed to develop. The very large mid-level saturation deficit for this simulation could not be overcome and convective downdraughts hinder the development of a negative boundary-layer entropy gradient. The p qtmax proxy gives genesis pressures in the 5 hpa range while the θ ediff proxy gives pressures at the genesis time in the 5 hpa range. The genesis parameter, χ m, increases with mean surface wind regardless of the orientation of the shear (Table I). The genesis proxies, as seen in Figure 3, display different behaviour. When the shear and mean surface wind are aligned, the development is slower than counter-aligned shear with a larger mean surface wind. More succinctly, the SF5W-SH5E simulation shows more rapid development than the SF3W-SH5W simulation despite the larger mean surface wind. This suggests that shear orientation is as influential on the incubation period as thermodynamic disequilibrium, the value of which decreases with increasing u m.. Kinematic aspects of genesis in shear.. Overview The incipient tropical disturbance, from a finite-amplitude perspective, is viewed as a weak but coherent vortex. The tilt of the vortex under the influence of vertical shear generates a wavenumber-one asymmetry with upward motion down-shear and subsidence up-shear. To date, explanations for the wavenumber-one vertical motion pattern have used balanced dynamics. Bosart and Bartlo (99) and FR99 invoked differential thermal vorticity advection from quasigeostrophic theory to produce mesoscale lifting. Raymond and Jiang (99) and Raymond (99) introduced, with Jones (995) further exploring, a set of mechanisms that could account for the organization of vertical motion in the absence of moisture. Vertical motion is produced through vortex flow along slanted large-scale isentropes associated with the large-scale shear. Jones (995) discounted this mechanism as observed temperature perturbations could not be produced in her dry barotropic vortex simulations through vertical motion along isentropes. As noted in section, despite the use of a baroclinic vortex, the absence of large-scale temperature gradients in our set-up precludes this mechanism. A more significant mechanism accounts for the change in vertical shear of the vortex flow. As the vortex tilts, thermal balance necessitates a cold thermal perturbation down-shear and a warm thermal perturbation up-shear. These anomalies are generated through the development of a secondary circulation (Figure (b) of Jones, 995). DeMaria (99), along the same line, argued that the cold perturbation increases convective activity down-shear while the warm anomaly inhibits convection up-shear. Finally, Reasor et al. () found an optimal down-shear left configuration of the vortex tilt. Such an orientation accounts for the smallest net vertical shear when the self-induced shear associated with the vortex tilt (to be discussed at greater length shortly) is accounted for. A down-shear left configuration has been borne out in observations and numerical studies (review by Corbosiero and Molinari, ). The remainder of this study will largely focus on just two of the simulations, SF3E-SH5W and SF3W-SH5W with a 3 C SST, the two extremes of possible shear-mean surface wind orientations. Note that the only difference between the two simulations is the direction of the mean surface flow. A possible explanation for the more rapid intensification of SF3E-SH5W (and SF5W-SH5E) than SF3W-SH5W is a more symmetric vertical motion field from the combination of the shear-induced asymmetry and the boundary-layer convergence asymmetry in association with translational motion (FR99). Using a slab boundary-layer model, Shapiro (993) found convergence and vertical motion maximized in the front-right quadrant (front is defined with respect to the translational motion). Thus, when the shear and motion are aligned, the vertical motion asymmetries are located downshear, permitting unabated up-shear subsidence drying. Conversely, when the shear and motion are counter-aligned, as in SF3E-SH5W, the asymmetries are concentrated left of the shear vector. To test this hypothesis, simulations were conducted with the microphysics disabled so as to isolate the significance of vertical motion forced by the boundary-layer convergence of the translating vortex from the much stronger diabatic heating signal. For brevity, results from the dry simulations are not displayed. While there is a surface front-right asymmetry in the vertical motion, its magnitude is small compared to the downward projection of the low and mid-tropospheric tilt-induced asymmetry. However, with a low level of free convection in our tropical soundings, only a small amount of forcing is needed to produce moist convection. For SF3E-SH5W, the translational motion is small and there is no evidence of front-right convection (except for the initiation of a transient convective feature early in the simulation) until it propagates into the quadrant from down-shear. Thus we discount a more symmetric vertical motion field as a factor in the relative intensification rates. We now consider quantities that will likely be modified by the change in storm motion and vertical shear orientations of SF3E-SH5W and SF3W-SH5W. Figures 7 show a sequence of horizontal plots of the latent heat flux, surface θ e distribution, and column-integrated saturation deficit (CISDEF) for the two cases. As a result of the different temporal evolutions of the simulations, the times portrayed, though distinct for each simulation, are considered structurally consistent and have nearly equivalent surface pressure values. The initial time considered, the same for both simulations, is h. This time corresponds to just after development of a convergent boundary layer and the appearance of the down-shear vertical motion asymmetry (Figure ). Surface pressures are just over hpa. At this stage, the latent heat fluxes are largely associated with the asymmetry of the surface wind field generated by the superposition of the mean wind and the primary vortex (Figure (a, b)). With an easterly mean surface wind, the strongest winds and latent heat fluxes occur on the northern flank of the surface vortex. With a westerly mean surface wind, the strongest winds occur on the southern flank of the surface vortex. In addition to the surface wind asymmetry source, there are enhanced latent heat fluxes down-wind of the shear-organized convection Hereafter down-wind will refer to cyclonically down-wind with respect to the winds of the parent vortex. Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

6 E. D. Rappin and D. S. Nolan (a) (b) ms ms (d) (e) (f) Figure. (a, b) Latent heat fluxes (W m, colour shading) with 7 hpa vertical motion contours ( and 3 m s ) and m wind vectors. (c, d) Surface θe (K, colour shading) with vertical motion contours ( and 3 m s ) at 7 hpa (black) and hpa (white). (e, f) Column-integrated saturation deficit (mm, colour shading) and smoothed 5 hpa potential vorticity (contours). (a, c, e) show simulation SF3E-SH5W and (b, d, f) simulation SF3W-SH5W, both at hours. in association with low-level convective outflow. Both cases show the shear-organized convection shifted meridionally toward the direction of stronger surface winds, the result of both the surface wind asymmetry and the front-right boundary-layer convergence associated with translational motion. As such, with a mean surface wind opposite that of c Royal Meteorological Society Copyright the shear, the two sources of enhanced fluxes superimpose (Figure (a)). Conversely, the sources are isolated when the shear and surface wind are aligned (Figure (b)). At this time, the nature of the convection is similar for the two cases. At low altitudes, the convection is cellular with horizontal scales of 5 km (black contours of Q. J. R. Meteorol. Soc. 3: 35 5 ()

7 Tropical Cyclogenesis in Vertical Shear Figure (c, d)). Aloft, at roughly hpa, the vertical motion field becomes an aggregate of the low-level clusters with horizontal scales of 5 km (white contours of Figure (c, d)). Stronger updraught cores are embedded within the weaker, large-scale vertical motion shield. Conversely, a strong contrast is observed in the surface θ e fields. In SF3W- SH5W (Figure (d)), the enhanced latent heat fluxes on the southern flank of the vortex lead to a warming and moistening of the boundary layer. As the shear-organized convection is downwind of the enhanced θ e, convective downdraughts do not act to inhibit this boundary-layer moistening. In SF3E-SH5W the convection is up-wind of the enhanced surface fluxes, thus convective downdraughts on the down-shear flank inhibit boundary-layer moistening and the increase of θ e (Figure ). As was shown in RNE and other studies (Bister and Emanuel, 997; Nolan, 7), near-saturation of the core is observed prior to TC genesis. Therefore, plots of CISDEF and its average will be widely used in this study. Figure (e, f) show a plan view of CISDEF along with the smoothed 5 hpa PV for each simulation. Note that orange and red values correspond to low values of CISDEF and represent near-saturated conditions. The driest air is found in the southwest quadrant of simulation SF3E-SH5W and the northwest quadrant of SF3W-SH5W. These locations reflect dry regions in which weak surface winds fail to moisten the boundary layer and vortex tilt leads to subsidence drying. From Figures (e, f) it can be seen that SF3W-SH5W is more susceptible to dry air than simulation SF3E-SH5W. As dry air rotates cyclonically inward toward the centre, it does so on the down-shear flank of SF3E-SH5W where shear-organzied convection acts to moisten the atmosphere. Conversely, dry air in SF3W-SH5W builds on the northern flank and rotates into the up-shear flank where mid-tropospheric subsidence produces relative humidities as low as % (not shown), increasing the CISDEF with time (Figure 5(f)). Six hours later for simulation SF3E-SH5W and h later for simulation SF3W-SH5W, when the surface pressure for each has fallen just below hpa, down-wind fluxes are significantly enhanced (Figure 5(a, b)). A broader region of strong surface fluxes is found in simulation SF3E-SH5W due to the combination of the positive surface wind asymmetry and convective outflow. The outward propagating band of convection seen in this figure is a transient feature. Surface θ e in SF3E-SH5W is beginning to increase in association with convection in a near-saturated environment (Figure 5(c, e)). The transient convective arc is producing low θ e through downdraughts from radially inward-slanted convection. This short-lived low θ e spirals cyclonically inward but does not penetrate the core. θ e on the southern flank of SF3W-SH5W has increased significantly as there is no convection, and hence no convective downdraughts, to offset the warming produced by the surface wind asymmetry. In SF3W-SH5W, a mesoscale convective system (MCS) has formed on the eastern flank of the surface vortex with When considering genesis, the mid-levels of the initial parent vortex are dominated by the superposition of the shear-organized convective elements. Such a condition was alluded to in section in the discussion of the vortex tracking method. The initial mid-level vortex, if not decoupled from the surface vortex and advected down-shear, is dominated by the convective PV signature. The mid-level PV, when smoothed (accomplished here by passes through a simple -- convolution filter), allows one to visualize the mid-level vortex as opposed to an aggregation of PV elements. a zonal line of convection being forced by convergence between the primary circulation and the surface outflow of the MCS stratiform shield (Figure 5(b, d)). At this stage of both simulations, convection tends to form downshear and rotate cyclonically around the vortex core as it decays. For SF3E-SH5W, the convection can propagate into the northeastern quadrant as the northern flank is dominated by low CISDEF (Figure 5(e)). In simulation SF3W-SH5W, low surface θ e from the MCS divergent outflow (Figure 5(d)) coupled with dry tropospheric air (Figure 5(f)) on the northern flank inhibit convection from rotating down-wind. Instead, a strong MCS forms as older cells of the zonal convective line are carried to the northeast by the combination of the primary and large-scale flows, maintaining the stratiform shield. Note that only the and 3 m s contours are plotted for vertical motion. The hpa.5 m s contour (not plotted due to noisiness) portrays the stratiform region overlying the surface divergence field in Figure 5(b). Finally, the magnitude of the dry air on the western flank of the surface vortex in simulation SF3W-SH5W has increased significantly in magnitude as subsidence is uninhibited due to the localization of convection down-shear. Proceeding h for SF3E-SH5W and h for SF3W- SH5W, with surface pressures in both cases at 5 hpa, the largest surface fluxes appear down-wind of the deep convection in association with low-level convective outflow (Figure (a, b)). Both simulations show eyewall-like structure in the surface fluxes. SF3E-SH5W has developed a similarly coherent eyewall-like θ e structure. For SF3W- SH5W, the zonal convection line that was observed previously has rotated down-wind 5 and takes on a southwest northeast orientation. Likewise, the hemispheric region of high θ e has rotated 5 with a cool boundary layer and dry, but moistening, atmosphere ahead of the convection. The deep near-saturation is confined to the convective line which is quickly approaching the up-shear flank. Near-saturation exists throughout the core of SF3E- SH5W as genesis and intensification appear imminent. At the final time under consideration, 3 h into SF3E- SH5W and h into SF3W-SH5W, both simulations have passed the θ ediff genesis proxy and have surface pressures just below hpa. From Figure 7(a, c, e), eye-like structures are evident in the latent heat, surface θ e, and CISDEF fields of SF3E-SH5W. Also evident from Figure 7(c, e) is a succession of inner rainbands which form along the southern and eastern flanks and rotate cyclonically into the northern flank. The core of SF3E-SH5W has become compact as subsidence drying dominates the periphery of the domain shown in Figure 7(e). Note that from the beginning, the core of SF3E- SH5W was moist, allowing convection to propagate well down-wind of down-shear. SF3W-SH5W is nearly opposite, with relatively dry air dominating the domain and moisture confined to the region of active convection (Figure 7(f)). The MCS and its surface divergence have dissipated (Figure 7(b)) and the surface θ e is enhanced in all quadrants (Figure 7(d)). At this stage, one would wonder how SF3W-SH5W develops at all. At h, SF3W-SH5W has the appearance of squall line in shear with a long convective line and a book-end vortex on its northern end. The vortex proceeds to wrap up into a tropical cyclone-like structure as is often observed in subtropical genesis. Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

8 (a) E. D. Rappin and D. S. Nolan 5 (b) ms ms (d) (e) (f) Figure 5. As Figure, but at (a, c, e) hours, and at (b, d, f) 37 hours... Vortex tilt and precession applied PV analysis to the problem of a mid-level vortex in a shear flow to gain insight into self-sustained convection in To investigate more closely the significance of vortex tilt association with a mesoscale convective vortex (MCV). As on the intensity evolution, a PV perspective is employed noted earlier, Jones (995) applied the concepts put forth in which the mutual interaction of low- and mid-level in Raymond and Jiang (99) and Raymond (99) to a vortices can be examined. Raymond and Jiang (99) first dry, vertically coherent vortex in a sheared environment. c Royal Meteorological Society Copyright Q. J. R. Meteorol. Soc. 3: 35 5 ()

9 Tropical Cyclogenesis in Vertical Shear (a) 5 (b) ms ms (d) (e) (f) Figure. As Figure, but at (a, c, e) 3 hours, and at (b, d, f) 53 hours. Utilizing a primitive-equation model with an initially upright barotropic vortex, Jones (995) found that, as the vortex tilted down-shear with height, the mutual interaction of the low- and mid-level PV anomalies acts to oppose the vertical shear in two ways. First, as discussed previously, the response to vortex tilt is to generate adiabatic vertical motion c Royal Meteorological Society Copyright with upward motion down-tilt and downward motion uptilt to maintain the thermal perturbations required for balance. Second, should the tilt angle of the vortex exceed 9 relative to down-shear, the shear flow itself acts to oppose the tilt. Additionally, the magnitude of the final tilt was found to be a function of the Rossby penetration Q. J. R. Meteorol. Soc. 3: 35 5 ()

10 (a) E. D. Rappin and D. S. Nolan 5 (b) ms ms 5 (d) (e) (f) Figure 7. As Figure, but at (a, c, e) 3 hours, and at (b, d, f) hours. depth. Smith et al. () and Reasor et al. () followed the previous work using a two-layer model and a linearized primitive-equation model, respectively. Each found results similar to those of Jones (995), with the low- and midlevel vortices rotating around each other, until the vortices either break apart (increasing tilt with time) or cycle through alignment and separation. Breaking apart was found to occur when the differential advection rate dominated the precession rate. Precession cycles will be discussed shortly. c Royal Meteorological Society Copyright The vortex tilt angle and magnitude along with the mesoscale shear angle and magnitude are shown in Figure for simulation SF3E-SH5W. A fairly consistent relationship between the vortex tilt angle and shear angle is immediately observable. While the large-scale shear is fixed in direction as shown in Figure, the mesoscale shear plotted in Figure (a) is not. After the initial adjustment stage, the shear is largely fixed at 75 to the right of the vortex tilt. Such behaviour of the mesoscale shear is a result of vertical shear induced by the vortex tilt itself and is succinctly described by Figure of Q. J. R. Meteorol. Soc. 3: 35 5 ()

11 Tropical Cyclogenesis in Vertical Shear 5 (a) (W) Angle (degrees) 9 (N) (E) 9 (S) Tilt Shear (W) (b) Tilt (km) CISD (mm) 5 Tilt Shear NE NW SW SE Figure. Simulation SF3E-SH5W. Time evolution of (a) 9 5 hpa vertical shear and vortex tilt angles (rotating counterclockwise from due east at ), (b) 9 5 hpa vertical shear and vortex tilt magnitude (km), and quadrant- and radial-averaged column-integrated saturation deficit (mm). This figure is available in colour online at wileyonlinelibrary.com/journal/qj Davis and Bosart (). In the present study, the mesoscale shear took on a 7 9 anticyclonic phase shift relative to the vortex tilt in all of the simulations conducted. Recently, Raymond and Lopez-Carillo () provided a different explanation for this behaviour. They argued that the lowand mid-level vortices are located where the cyclonic flow of the parent vortex offsets that of the environmental shear flow (their Figure ). As in all of the simulations conducted for this study, the first 5 h of simulation SF3E-SH5W are dedicated Hereafter, shear in the text will refer to the fixed, large-scale shear as given by the zonal wind profiles of Figure. Shear (ms ) to the development of a convergent boundary layer and a secondary circulation, during which the mid-level vortex is advected down-shear of the surface vortex. After the initial balancing stage, the vortex tilt continues to rapidly increase, reaching a maximum just after 5 h while the mid-level vortex begins a cyclonic precession into the down-shear left quadrant. The precession continues at a near constant rate of h (estimated from Figure (a)) for the next 5 h while the magnitude of the tilt settles into an equilibrium value of approximately 3 km. At roughly hour 37, the mid-level vortex enters the up-shear flank of the storm (9 ) as seen in Figure (a). At this time, the vortex tilt, and hence the mesoscale shear, rapidly decrease in magnitude. The small vortex tilt leads to a faster precession rate so that by 5 h the mid-level vortex is located in the up-shear-right quadrant with a negligible tilt. To relate changes in the vortex tilt magnitude and angle to tropospheric moisture content, we consider the CISDEF azimuthally averaged in quadrants and radially averaged from to km. The result for simulation SF3E-SH5W is shown in Figure. During the early h development stage, there is little variation in CISDEF in the inner km core. After h, the northeast quadrant moistens to near-saturated conditions as convection that develops down-shear begins to propagate into that quadrant. The southeast quadrant maintains a constant CISDEF through the first h as the down-shear development of convection occupies a fraction of the quadrant. Additionally, unlike both western quadrants which dry out by h due to quasi-balanced subsidence, the southeast quadrant is downshear. After h, both eastern quadrants begin to dry. The southwest and southeast quadrants maintain their dryness until the mid-level vortex has entered the up-shear flank around hour 3. The evolution of simulation SF5W-SH5E mimics that of SF3E-SH5W. Both have a similar tilt and therefore experience a similar precession rate (not shown) and nearly equal times to genesis. This suggests that shear orientation with respect to surface wind is more influential than mean surface wind as long as sufficient thermodynamic disequilibrium exists. We speculate that the slight delay in genesis of SF5W-SH5E is the result of the stronger mean surface wind which results in a larger mid-level saturation deficit and decreased thermodynamic disequilibrium as discussed in detail in RNE. Of course with easterly shear in SF5W-SH5E, the CISDEF and mid-level vortex angle evolutions are the mirror image of the SF3E-SH5W simulation (not shown). The vortex tilt is much larger in magnitude for simulation SF3W-SH5W. The associated slow precession rate, half of that seen in the other two cases (Figure 9(a, b)), results in a significantly longer time to genesis (Figure 3(b)). The rapid increase in tilt at hour 3 can be explained with the aid of the smoothed PV field seen in Figure 5(f). With the development of the MCS northeast of the surface vortex, the PV centroid calculation produces a larger tilt as the upperlevel PV of the MCS is superimposed with the down-shear convective PV signature. It takes nearly twice as long for the mid-level vortex to precess into the up-shear quadrant (the vortex angle passes through 9 at approximately h). The CISDEF time evolution in Figure 9 does not differ significantly from the other cases except for the increasingly large magnitude of the CISDEF itself. The large values result from the sustained quasi-balanced subsidence occurring Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

12 E. D. Rappin and D. S. Nolan (a) (W) Angle (degrees) 9 (N) (E) 9 (S) Tilt Shear which depends on the inertial stability and length-scale of the vortex as well as the ambient dry stability, but these are roughly equivalent in all simulations. (For a discussion on changes to the dry stability with SST and mean surface wind, refer to Nolan and Rappin,.) Since the shear-induced convective asymmetry defines the vortex, hereafter down-tilt will refer to the location of shearorganized convective development. So while the down-shear direction is fixed, the down-tilt direction rotates as defined by the tilt angle..3. Path to genesis (W) (b) Tilt (km) CISD (mm) 5 Tilt Shear NE NW SW SE Figure 9. As Figure, but for simulation SF3W-SH5W. This figure is available in colour online at wileyonlinelibrary.com/journal/qj along the western flank. In addition, the CISDEF curves have a much more monotonic appearance, the result of a slower precession rate. It is found that there is close agreement between the time to genesis parameter θ ediff (RNE) and the precession of the mid-level vortex into the up-shear flank of the vortex and the rapid diminishment of vortex tilt, not only for simulation SF3W-SH5W, but for the other two cases as well (compare Figure 3 with Figures and 9). Finally, once the mid-level vortex has been advected up-shear, rapid moistening to near-saturation occurs on the southern flank, much as in SF3E-SH5W. Within the context of the simulations presented here, it is the magnitude of the vortex tilt which controls the precession rate. Of course the precession rate will be strongly influenced by the Rossby penetration depth (Jones, 995), Shear (ms ) Recent work has focused on two primary routes to genesis, a top-down path in which a mid-level MCV plays a fundamental role in the development of the surface circulation (Ritchie and Holland, 997; Bister and Emanuel, 997; Molinari et al., ; Nolan, 7), and a bottomup path, where low-level diabatically generated PV builds upward through a variety of mechanisms (Hendricks et al., ; Montgomery et al., ; Tory et al., 7a). For the top-down route, it is thought that convective-stratiform processes, such as mid- and upper-level diabatic heating associated with decaying convective cells in a stratiform shield, can spin up a mid-level vortex, which through a number of mechanisms can extend to the surface to become warm core and ignite genesis. Conversely, bottom-up theory suggests that development of a low-level warm core vortex precedes development aloft. Low-level vertical vorticity is generated through diabatic heating and tilting of horizontal vorticity produced by vertical shear of the baroclinic vortex or of the boundary-layer flow. The vorticity is then enhanced through vertical advection, vortex tube stretching, and on the system scale by the balanced adjustment to heating (Hack and Schubert, 9; Montgomery et al., ; Nolan et al., 7a). It is also possible that these distinct approaches are not mutually exclusive, as suggested by Raymond et al. (99) and Tory et al. (7b), and that a hybrid development is possible in which both routes are fundamental to development. An example of this has been shown here and in RNE in which bottom-up development occurred as the result of sustained convergence forced by divergent outflow from a MCS that formed down-shear of the surface vortex. To further explore the process of genesis in shear, we will explore height-time Hovmöller diagrams for the logarithm of all condensate (given by 3 plus the base logarithm of the condensate mixing ratio in units of g kg ), the diabatic heating, and the tangential velocity, as seen in Figures. Each quantity has been radially averaged between and km and azimuthally averaged in quadrants just as in the CISDEF figures discussed previously. After the initial development of a frictional boundary layer in simulation SF3E-SH5W, deep convection is observed to propagate down-wind, in the northeast quadrant, at approximately 7 h as observed in the condensate and diabatic heating (Figures (b), (b)) and from the earlier overview. The vertical advection of cyclonic momentum, as seen in the rapid increase of cyclonic momentum aloft in Figure (a), accompanying the down- Referred to simply as condensate hereafter. Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

13 Tropical Cyclogenesis in Vertical Shear 7 (a). (b) (d) Figure. Simulation SF3E-SH5W. Quadrant-averaged height time Hovmöller of the logarithm of all condensate, approximately given by 3 plus the base logarithm of the mixing ratio in units of g kg : (a) northwest, (b) northeast, southwest, and (d) southeast. wind propagation of convective elements results in the down-wind advection of frozen condensate into the northwest quadrant (Figure (a)). An angular momentum budget for the northeast quadrant at h shows that vertical advection is the primary forcing between the boundary and outflow layers where friction and asymmetric flows are large (not shown). The frozen condensate evaporates in the sub-saturated air, producing mid- and upper-tropospheric diabatic cooling (Figure (a)) and northwest quadrant moistening (Figure red curve between 5 and 3 h). The moistening is aided by continued down-wind propagation of deep convection that forms down-tilt, and whose frequency increases as the mid-level vortex approaches the up-shear flank. Thus a positive feedback is set up in which the shearmotion orientation creates a more favourable down-wind environment for long-lived convective cells organized by the large-scale shear. These down-wind propagating convective cells act to moisten the down-wind (notably in the the up-shear flank) regions by the showerhead effect, in which deep near-saturation is brought about by evaporation from stratiform precipitation (Bister and Emanuel, 997), thus providing an even more suitable environment for the further down-wind propagation of deep convection. At 3 h, when the northwest quadrant is near saturation, deep sustained convection begins. As noted previously, the convection spirals around the storm core at a decreasing radius (as indicated by the rapid increase in mid-level vortex precession). When coupled with upper-tropospheric cyclonic winds of approximately m s, the southwest quadrant, followed shortly by the southeast quadrant (where the cyclonic wind acts in concert with the shear), begin to moisten. Diabatic cooling in the southwest quadrant begins shortly after the sustained convection erupts in the northwest quadrant and becomes strong just prior to 35 h (Figure ). Deep diabatic cooling in the souheast quadrant begins at this time (Figure (d)) and moistening of the southern flank occurs rapidly so that around h there is a near-saturated core (Figure ), small vortex tilt (Figure (b)), and rapid intensification (Figure 3(b)). Prior to onset of deep sustained convection in nearsaturated conditions, we have found evaporative cooling in a stratiform environment to be a key contributor to moistening, particularly on the southern flank of the surface vortex. Mapes and Houze (995), in a study of tropical MCSs, found that stratiform precipitation areas have their peak convergence aloft, just above the melting level. It is therefore not surprising to see the mid-level strengthening of the tangential wind prior to the onset of deep convection. This is Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()

14 E. D. Rappin and D. S. Nolan (a) x 3.. (b) x x 3.. (d) x Figure. As Figure, but showing diabatic heating (K s ). particularly evident in the southeast quadrant (Figure (d)) where an increase in the mid-level tangential circulation is observed beginning around hour 3. For SF3W-SH5W, the inability of convective cells to propagate down-wind inhibits the development of an upperlevel cyclonic circulation. In fact, upper-level mean cyclonic winds of 5 m s do not develop until after 5 h (not shown). The lack of upper-level cyclonic flow leaves the organized down-shear convection to be advected by the southwesterly flow formed by the superposition of the largescale westerly flow and the broad southerly flow of the primary vortex. Hence the development of a MCS northeast of the surface vortex. Little to no evaporative moistening of the up-shear northwest quadrant occurs due to the absence of upper-level cyclonic flow and upper-level frozen condensate accumulates in the northeast quadrant (the MCS stratiform shield) from the down-shear convection as seen in Figure 9 and Figure 3(a). It is the steady precession of the mid-level vortex into the up-shear flank that ultimately leads to the moistening of SF3W-SH5W. Closer inspection of the northwest quadrant curve in Figure 9 reveals rapid moistening at hour 57, prior to the onset of tilt reduction (Figure 9(b); hour 3). Recall that the mid-level vortex position is a mean PV calculation, where the PV field is largely composed of convective-scale anomalies. Prior to the tilt angle exceeding 9, convection has already begun to moisten that quadrant. The second moistening period in the northwest quadrant, starting at hour 3, is associated with the sustained deep convection in this quadrant as the tilt angle exceeds 9 (Figure 9(a, c)). Combining the decreasing radius at which convection spirals into on the southern flank with the strong upper-level advecting flow, the southern quadrants begin to near-saturate rapidly at hour 5 due to cooling associated with melting and evaporation (Figure 9). A downward extension of the evaporative cooling from the upper to lower levels occurs in conjunction with the thickening of the condensate from an anvil to deep convective towers (Figure 3(c, d)). Ten hours later, there is a near-saturated mesoscale core with sustained deep convection in all quadrants (Figure 9). There is an absence of mid-level tangential wind intensification prior to the bottom-up intensification in SF3W-SH5W (not shown). There is however a cyclonic wind increase in the km layer associated with melting from a thin stratiform layer on the southern flank of the vortex (not shown). In the simulations conducted, there was no evidence of top-down development in terms of the downward advection of a mid-level vortex. However, the showerhead effect is observed. This is particularly evident in simulation SF3E-SH5W. Copyright c Royal Meteorological Society Q. J. R. Meteorol. Soc. 3: 35 5 ()