PUBLICATIONS. Journal of Advances in Modeling Earth Systems

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1 PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE /2016MS Key Points: A new modeling framework is developed to allow smoothly transitioning environments of wind shear around tropical cyclones Point-downscaling combined with analysis nudging leads to a more realistic tropical cyclone response to increasing wind shear, which is steady weakening Simulations show that the steady weakening primarily results from intrusions of dry, relatively cool air from the midtroposphere to the boundary layer as wind shear increases Correspondence to: M. J. Onderlinde, monderlinde@rsmas.miami.edu Citation: Onderlinde, M. J. and D. S. Nolan (2017), The tropical cyclone response to changing wind shear using the method of time-varying pointdownscaling, J. Adv. Model. Earth Syst., 9, , doi: / 2016MS Received 1 SEP 2016 Accepted 27 MAR 2017 Accepted article online 31 MAR 2017 Published online 24 APR 2017 VC The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. The tropical cyclone response to changing wind shear using the method of time-varying point-downscaling Matthew J. Onderlinde 1,2 and David S. Nolan 1 1 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA, 2 Now at Innovim, LLC, Greenbelt, Maryland, USA Abstract Previous studies using idealized numerical simulations to understand the tropical cyclone (TC) response to time-varying wind shear have applied instantaneous changes in the TC environment. This was typically accomplished by pausing the simulation, constructing a new environmental vertical wind profile, rebalancing the mass field, and then restarting the simulation. A new modeling framework allows for smoothly transitioning environmental wind states: time-varying point-downscaling (TVPDS). TVPDS uses large-scale relaxation to smoothly transition between different vertical profiles of environmental wind (and/ or temperature and moisture) while coordinating the point-downscaling method such that the environment remains in balance. TVPDS simulations of quasi steady state, moderately intense (50 m s 21 ) TCs show that the response to increasing wind shear is a steady reduction in intensity without recovery to the preshear intensity. These results, which are consistent with the typical evolution of real TCs, stand in contrast to some previous studies that found a recovery to prestorm intensity after an initial weakening due to increased shear. TVPDS simulations also show that the rate at which the TC weakens depends on how rapidly the environment transitions to greater shear. Analyses of surface fluxes, regions of convection, and other variables are presented to determine how time-varying shear affects TCs. Finally, TVPDS simulations of TCs transitioning from environments characterized by high-shear into low-shear environments show that a similar but opposite response occurs. 1. Introduction Previous studies using idealized simulations of tropical cyclones (TCs) in changing vertical wind shear have imposed sudden changes to the environmental flow. Frank and Ritchie [2001] developed idealized TCs for 48 h under conditions without wind shear. At this point the simulation was paused, environmental shear was imposed, the temperature and pressure fields were recomputed to balance the imposed shear, and the simulation was resumed. Depending on the magnitude of the imposed shear, the TC either reached a quasi steady asymmetric state (e.g., shear 5 5ms 21 case) or dissipated completely (shear 5 15 m s 21 case). The authors admitted that the rapid weakening of the TC in the 15 m s 21 case may have been due partially to the shock from the sudden imposition of vertical wind shear. However, they pointed out that in most of their cases, after an initial adjustment period, the TCs once again attained balance with their environments, though this balance meant the TC was well below its maximum potential intensity. Frank and Ritchie [2001] described a series of events that result from the imposed shear and lead to weakening of the TC. First, the shear creates a wavenumber one asymmetry in the eyewall region at all altitudes throughout the TC circulation. Next, the asymmetry in the upper levels becomes strong enough to prevent parcels with high potential vorticity and equivalent potential temperature from entering the eye. This weakens the warm core of the TC and raises the central pressure. Finally, they found that the shear advects asymmetric features, which leads to a vortex that is tilted downshear. They suggested that a TC in vertical wind shear weakens from the upper to lower troposphere. Other previous studies pointed out the importance of diabatic effects on TC intensity in environments of increasing vertical wind shear [e.g., Wang et al., 2004; Schecter and Montgomery, 2007; Davis et al., 2008]. Wang et al. [2004] showed that diabatic processes are important when considering the ability of a mature TC to resist the imposition of vertical wind shear. They found that dry vortices could resist vertical wind shear to some extent; however, when full physics simulations including moist processes were considered, TC resiliency increased. Jones [2004] noted that comparing dry simulations to those which include full ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 908

2 physics may lead to the misinterpretation that moist processes are explicitly necessary for a TC to resist shear. The simulations of Wang et al. [2004] allowed a TC to develop over a 96 h period to an intense steady state with a minimum central pressure of approximately 925 hpa, after which, vertical wind shear of varying magnitude was imposed instantaneously. Their simulations found that shear stronger than that imposed by Frank and Ritchie [2001] was required to fully weaken the TC. In their four simulations with different values of environmental vertical wind shear (4.25, 12.75, 17.00, m s 21 ), only the simulation with shear of m s 21 caused the initial TC vortex to weaken to a depression and never restrengthen. Interestingly, the simulations with shear of and m s 21 weakened for approximately 24 h after shear imposition, but then reintensified to almost their initial intensity (925 hpa). Riemer et al. [2010] performed similar numerical simulations to Frank and Ritchie [2001] and Wang et al. [2004] in which a mature TC developed and then an environment with vertical wind shear was imposed. They suggested that lower equivalent potential temperature air enters the inflow layer of the core of a TC and that this process is a result of the balanced response to vertical shear forcing. They argued for a close linkage between environmental vertical wind shear and the thermodynamics of the boundary layer near the TC core. They performed simulations using the Regional Atmospheric Modeling System (RAMS) in which TCs spin up over an 48 h period. Following the methodology of Frank and Ritchie [2001], Riemer et al. [2010] imposed varying shear environments after 48 h into their simulations. As in the Frank and Ritchie [2001] simulations, Riemer et al. [2010] noted an imbalance when the shear environment was imposed; however, they claimed the brief adjustment to this imbalance did not affect the interpretation of their results. Much like the simulations discussed previously, the results of Riemer et al. [2010] showed a period of weakening when shear was imposed at 48 h followed by a recovery period during which the TCs resumed intensification. Even when the shear was set to 20 m s 21, the TC recovered and intensified to a strong hurricane (maximum sustained wind 85 m s 21 ) by 72 h after the imposition of shear. The authors pointed out that shear in their simulations was specified primarily through the initial conditions and by modifying the large-scale wind and temperature fields at a given time. Shear in their simulations was maintained via lateral boundary conditions, and they found that a strong TC was able to modify its environment. They speculated that strong TCs significantly reduce shear in the near-core region by axisymmetrizing the storm relative flow. Riemer et al. [2010] also pointed out that the intensity (and corresponding impacts) of lower equivalent potential temperature downdrafts may be sensitive to the prescribed background sounding and the microphysics parameterizations. They suggested future numerical experiments should test this sensitivity and performed additional simulations which varied microphysics parameterizations in a follow-up study [Riemer et al., 2013]. Increases in vertical wind shear do not necessarily lead to a decrease in TC intensity. Molinari et al. [2004] found that Hurricane Danny (1997) intensified from a depression to a tropical storm in vertical shear of 5 11 m s 21 and from a tropical storm to a hurricane in shear greater than 11 m s 21. The authors proposed that axisymmetrization of low-level vorticity and vertical mixing of moist entropy by convection allowed intensification despite strong shear. Molinari et al. [2006] analyzed Tropical Storm Gabrielle (2001) which intensified via downshear reformation in an environment characterized by shear of m s 21. Nguyen and Molinari [2012] discussed the rapid intensification of Hurricane Irene (1999) as it passed over the Gulf Stream. The intensity of Irene increased by 15.5 m s 21 despite shear increasing from 6.5 to 11.5 m 21. Nguyen and Molinari attributed the intensification to a dramatic increase in azimuthally averaged latent heating within the radius of maximum winds (RMW). However, while exceptions to the general response of TCs to vertical wind shear exist, statistical studies [e.g., DeMaria, 1996] show that the most typical response to an increase in shear is weakening. The point-downscaling (hereafter PDS) [Nolan, 2011] technique has been used to analyze TC intensity evolution for varying environmental wind profiles [e.g., Onderlinde and Nolan, 2014, 2016; Finocchio et al., 2016]. In these studies, environments with identical hpa wind shear vectors but variations in the midlevel flow led to different rates of TC intensification. These studies demonstrate the value of the PDS technique which allows for enhanced control of the environment around TCs and simplifies the analysis of vertical wind shear effects. The purpose of this study is to present an alternative to instantaneous shear imposition in idealized numerical simulations of TCs and to investigate the mechanisms that lead to TC weakening when environmental shear increases (or strengthening when shear decreases). This manuscript is organized as follows. Section 2 ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 909

3 introduces the new modeling framework used to achieve smoothly varying environmental wind shear in TC simulations. Results are presented in section 3 and are divided into four subsections. Section 3.1 describes how different environmental shear transitions can be accomplished and how an idealized TC responds to differing magnitudes and rates of shear change. Simulations will examine to what extent reintensification occurs when the time-varying point-downscaling (TVPDS) method of the current study is applied. Simulations also will test the extent to which TC recovery is related to the limitations in the specification of environmental shear in previous studies. Section 3.2 investigates how variables like midlevel relative humidity and simulated reflectivity, surface latent heat fluxes, and near-surface equivalent potential temperature respond to changes in environmental shear. Section 3.3 discusses the TC-tilt response to changing shear and how sea surface temperature (SST) affects this tilt response. Section 3.4 presents the case where shear is smoothly reduced and shows how an idealized TC responds in a similar but opposite manner to the case when shear is increased. Finally, a summary section puts the results in context based on previous studies and briefly discusses the implications for future research of TCs simulated in time-varying environments. 2. A New Modeling Framework: Time-Varying Point-Downscaling Point-downscaling and idealized nudging [Stauffer and Seaman 1990; Stauffer et al. 1991] were combined to simulate TCs in environments with varying vertical wind profiles in simulations performed by Onderlinde and Nolan [2014, 2016]. In these studies, no time-varying vertical wind shear was imposed. In fact, timevarying profiles of environmental wind are not possible using only PDS. In the present study, this method is enhanced by modifying the framework to allow a time-varying component in the wind shear. To allow for smoothly transitioning background states in TC simulations, additional modifications to the numerical modeling framework (Weather Research and Forecast (WRF) model) beyond those made for the PDS technique were required. Idealized nudging is the method by which the background state is varied. A routine was developed to create three-dimensional (3-D) nudging fields that change in time. Specifically, these 3-D environmental states were defined at time intervals (every 6 h, for example) in a four-dimensional input data file read by the WRF model. To create the changing environment, the background state switches during one or more of the time intervals in the input nudging data. Typically the entire change in the environment is defined between two time intervals, but a shift defined smoothly over multiple intervals in the nudging data also achieves a changing background state. These nudging fields were then applied in the WRF model to smoothly transition between background states of environmental wind. In the default distribution of WRF, point-downscaling may be activated via the pert_coriolis option. When pert_coriolis is activated, WRF stores the vertical profiles of u and v from grid point (1,1) on the coarsest domain (d01) andthiswindprofileisdefinedasthemeanstate which is subtracted off when applying the Coriolis term in the momentum equations. This subtraction occurs at every model time step and at all grid points in three dimensions. Because of this default behavior, imbalances arise when nudging toward a state that does not match the pert_coriolis vertical wind profile. To overcome this, code was added in the WRF model to update the initial pert_coriolis profile at each time step to approximately match the profile that results due to the nudging. Nudging in the WRF model follows the methodology of Stauffer and Seaman [1990; Stauffer et al., 1991] in which nudging of the environment is defined such that: duðþ z 52 1 ½ dt s uz ðþ2u nðz; tþš (1) where uz ðþdefines the zonal wind at level z, u n ðz; tþ defines the prescribed nudging value for the zonal wind at level z for time t, and s is the nudging time scale. A similar equation can be applied to compute the time evolution of other variables, such as meridional wind, temperature, water vapor mixing ratio, etc. The new modeling framework used in this study, time-varying point-downscaling, allows smoothly transitioning background states of temperature, moisture, and wind with doubly periodic boundary conditions. TVPDS applies equation (1) at each model time step to update the base-state environmental profile on which the pert_coriolis feature operates so that PDS remains in balance with the idealized nudging. TVPDS is applied at all model grid points in three dimensions on the outermost domain in the simulations performed in this study. This is one of the key differences when compared to previous studies that imposed shear only by specifying the initial conditions, or by modifying the large-scale wind and temperature fields at a given time, with less ability to maintain the large-scale wind shear at a specific value. All simulations in this study use three domains: a parent domain, and two telescopic storm-following nested domains. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 910

4 Figure 1. Response of environmental vertical wind shear to different values of s, the nudging time scale, in a TVPDS simulation with shear transitioning from 5 to 15 m s 21. The nudging interval in each case is 24 h. The blue line represents the nudging field toward which the simulated wind field is nudged. Because the nudging component of TVPDS is imposed only on the outermost domain and not on the storm-following domains, the TC may modify its local environment inside these inner domains. The environmental shear imposed by the TVPDS technique is, therefore, only introduced to the TC through the boundary conditions of domain two. The primary caveat of the TVPDS technique is that, compared to a typical implementation of the WRF model, mass and momentum are not exactly conserved. This limitation is reduced somewhat because all simulations in this study occur on an f-plane at 208N where the horizontal midlevel temperature gradient required to balance shear of 10 m s 21 over the diameter of a TC is small (< 18C). Disallowing the environmental temperature gradient, therefore, compromises conservation less than it would if the simulations were performed at higher latitudes. The rate at which the environment transitions between environmental wind states depends on both the length of the interval over which the nudging fields change (i.e., the nudging interval) and the value of s, the nudging time scale. The length of the resulting transition period, defined as the period of time during which the shear makes the transition, depends on both the nudging interval and the nudging time scale. Figure 1 demonstrates how the environmental shear transitions more gradually as s gets larger. The nudging field to which the model wind field is nudged (blue line) transitions over a 24 h interval, but the actual simulated response transition period length depends on the value of s. By carefully choosing the nudging fields and the value of s, any shear transition period can be created. In this study, s was chosen based on hpa vertical wind shear calculated between 500 and 1500 km in annuli surrounding TCs in the ECMWF Reanalysis Interim [Dee et al., 2011]. This analysis showed that 44% of Atlantic TCs experienced a period in which shear magnitude changed by greater than 10 m s 21 and the average time required to make this transition was 38 h. Ensemble studies of Atlantic TCs have noted similar changes in vertical wind shear. Rios-Berrios et al. [2016a; Figure 3] found shear to decrease from 12 to 2 m s 21 over 36 h in ensemble simulations of Katia (2011). Much of the detailed analysis in sections considers environments that transition from 5 to 15 m s 21 (or vice-versa) over approximately 36 h. However, shear transition of this magnitude has been observed to occur much faster. Reasor et al. [2000] documented a change in shear from 3 5 to 15 m s 21 during a 3.5 h period during Hurricane Olivia (1994). 3. Results 3.1. Various Shear Values and Nudging Intervals In an effort to determine whether the instantaneous switch to shear is important in terms of the TC response to changing environmental wind shear, TVPDS simulations intended to mimic those of previous ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 911

5 Figure 2. Pretransition state (black-dashed line) of the vertical profile of the zonal wind, u, for all simulations and the posttransition state (solid lines) for the simulations with vertical wind shear transitioning from 5 m s 21 to 7.5 (cyan), 10 (green), 15 (red), and 20 (black) m s 21. The meridional wind, v, was fixed at zero for all times and at all vertical levels. studies [i.e., Frank and Ritchie, 2001; Riemer et al., 2010, 2013] were performed. TCs were initialized as moderately intense modified- Rankine vortices with a peak tangential wind speed of 30 m s 21. The SST for these simulations was fixed at 278C. The simulations were performed using a grid point parent domain with horizontal grid spacing of 18 km and two TC-following nested domains with grid spacing of 6 ( grid points) and 2 km ( grid points). Two-way nesting was used between the parent and nested domains. Idealized nudging was applied only on the parent domain. The simulations were performed with 41 vertical levels and used the same physics schemes as those listed in Onderlinde and Nolan [2014]. The hpa environmental vertical wind shear magnitude was held constant at 5 m s 21 for 264 h until the TC reached a quasi steady intensity with maximum surface wind speed around 55 m s 21. This long period of weak shear was chosen so that the TC could reach a steady state. At t h, shear began a transition to larger values. Four simulations were performed which transition from the initial shear of 5 m s 21 to magnitudes of 7.5, 10, 15, and 20 m s 21. The initial value of 5 m s 21 was chosen because this approximately matches the average vertical shear value computed from annuli around TCs in the Atlantic basin using ECMWF Reanalysis Interim (5.5 m s 21 ). Figure 2 shows the vertical profiles of the zonal component of the environmental wind before and after the shear transition occurs. The meridional flow in the environment was set to zero on all vertical levels and the shear in all simulations is westerly. During the transition, the profile shifts smoothly from the initial state to Figure 3. Environmental hpa wind shear (m s 21 ) versus time (h) for simulations with shear transitioning from 5 m s 21 to 7.5 (cyan), 10 (green), 15 (red), and 20 (black) m s 21. s for these simulations is 6 h. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 912

6 Figure 4. Minimum central pressure (hpa) versus time (h) for TVPDS simulations with environmental wind shear transitioning from 5 m s 21 (blue) to 7.5 (cyan), 10 (green), 15 (red), and 20 m s 21 (black). SST for these simulations is 278C and (a) s 5 6 h and (b) s 5 1h. the posttransition state. Figure 3 shows environmental hpa wind shear versus time for the four simulations with smoothly transitioning shear. The nudging time scale, s, is 6 h for these simulations. The combination of the 24 h nudging interval and the nudging time scale of 6 h used in these simulations produced a shear transition period similar to those frequently observed in the Atlantic basin (as discussed in section 2). The time series show that the transition period is approximately 48 h long although 90% of the transition occurs during the first 24 h of this transition period. Additional simulations were performed with s 5 1 h and these cases transitioned much faster, requiring only approximately 9 h to complete the transition to larger vertical wind shear (not shown). Results from the TVPDS simulations described above show that the TC response to increasing shear is a general weakening without a recovery to the prechange intensity. Figure 4a shows minimum central pressure versus time for the four simulations performed with a nudging time scale s 5 6 h. As the final-state environmental shear value becomes larger, the TC weakens both sooner and faster. The TC also reaches a final intensity that is weaker when the final-state shear is larger. Weakening occurs more quickly as the shear transition magnitude becomes larger. This is clear when comparing the 5 m s 21 control experiment (Figure 4a blue) to the simulations transitioning to 7.5 and 10 m s 21 (cyan and green, respectively). However, when the imposed shear reaches 15 and 20 m s 21, rapid weakening occurs during the first 48 h after ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 913

7 shear imposition and the TCs dissipate by the end of the simulation. Figure 4b shows simulations with shear transitioning to the same values as in Figure 4a, except with a nudging time scale s 5 1 h. The results are very similar despite the much more rapid transition to stronger shear. As in the case when s 5 6 h, there is no recovery after shear is imposed, although the case that transitions to 7.5 m s 21 (the cyan line in Figure 4b) does demonstrate some modest recovery (or at least a period of small changes in pressure) near the end of the simulation. Comparing the simulations that transition to 10 m s 21 (green lines; Figure 4) shows that TC weakening occurs more quickly when the nudging time scale decreases. The simulation transitioning to shear of 10 m s 21 with s 5 6 h reaches a final intensity of approximately 982 hpa, while the corresponding simulation with s 5 1 h weakens further to a final intensity of 992 hpa. This implies that TCs encountering environments characterized by moderate shear are indeed sensitive to the rate at which the transition occurs. This result (lack of recovery) stands in contrast to the results of Riemer et al. [2010, 2013], which showed a pause in intensification or a slight weakening after the imposition of shear followed by a recovery to intensity larger than the preshear intensity. This was the case in their results even when shear increased to a magnitude of 20 m s 21. Even though the TVPDS simulations above did not impose shear instantaneously as was the case in the Riemer et al. simulations, sensitivity to the transition rate is evident. The lack of recovery also is consistent with observational studies that show a negative correlation between environmental shear and TC intensity [e.g., DeMaria and Kaplan, 1994]. In addition to the simulations described above, numerous simulations (not shown) were performed with higher SST (up to 308C) and with various environmental lapse rates. Because the environmental temperature and moisture was set to the Dunion moist tropical sounding [Dunion, 2011] in the simulations discussed above, it was desirable to test the hypothesis that lapse rates steeper than the Dunion sounding could lead to more TC resiliency in environments of increasing shear. Both of these factors (steeper lapse rates and higher SSTs) proved, however, not to have a significant influence on the TC intensity response to changing vertical wind shear. Final-state intensity was higher when SST was larger, but recovery still did not occur. The rate at which TCs weakened when simulated in environments with higher SSTs also was very similar to the simulations performed with SST 5 278C. Figure 5 shows a time series of minimum central pressure versus time during the 96 h period after shear imposition for four simulations with environmental vertical shear transitioning from 5 to 15 m s 21 : two with SST 5 278C (red, blue), one with SST C (green), and one with SST 5 308C (black). The slopes of the time series are very similar despite the fact that the minimum pressures at shear imposition time are different by as much as 40 hpa. The primary difference in the simulations performed with SST 5 308C is that higher values of reflectivity at larger radii in rain bands and outside of the TC itself (not shown) are much more common. This additional precipitation at larger radii appears to play a minimal role in dictating changes in intensity. This result suggests that the rate at which TCs respond to shear is not necessarily tied to TC intensity. Figure 5. Minimum central pressure (hpa) versus time (h) for TVPDS simulations with environmental wind shear transitioning from 5 to 15 m s 21 with a SST 5 278C (red, blue), SST C (green), and a SST 5 308C (black). For each simulation, s 5 6 h. The 278C simulations (red and blue lines) are initially at different intensities because the TC was allowed to intensify longer before shear was imposed in the blue simulation. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 914

8 Figure 6. Minimum central pressure versus time (h) for two simulations performed with shear increasing from 5 to 13.5 m s 21 over a 24 h period (t h). The red line represents a simulation in which nudging is turned off after t 5 24 h and the blue line represents the case when nudging remains active for the duration of the simulation. In both cases, when nudging is active, the nudging time scale s 5 6 h. The one exception to this lack of recovery occurs when nudging is turned off after the shear transition has occurred. In this case, a temporary recovery occurs followed by an eventual weakening. Figure 6 shows a comparison of two simulations of intense TCs performed with SST of 308C and shear transitioning from 5 to 13.5 m s 21. This peak value of environmental shear (13.5 m s 21 ) was chosen because any values larger than this prevented TC recovery all together. In the simulation in which nudging is turned off after the shear transition is complete (Figure 6 red), a significant recovery occurs over a 62 h period, beginning 54 h after nudging ceases (Figure 6; t h). However, the TC then does return to a weakening state and is rapidly weakening at the end of the simulation. When nudging remains active throughout the simulation (Figure 6 blue), a much more stable response to shear occurs and no major weakening or strengthening occurs after the TC reaches a new quasi steady intensity around 955 hpa. These results suggest that when nudging is deactivated, the TC is able to modify the local environment near the TC primary circulation enough to overcome the environmental shear and temporarily reintensify. Figure 7 shows time series of mb shear Figure 7. (top) Time series of hpa wind shear (m s 21 ) inside a radius of 700 km (red, green) and between the radii of 700 and 2100 km (blue, black) for the simulations in which shear transitions from 5 to 13.5 m s 21 and then nudging is discontinued (red, blue) or is continued through the end of the simulation (green, black). (bottom) Time-height plot of potential temperature (K) between the radii of 700 and 2100 km for the simulation in which nudging is discontinued. SST is fixed at 308C for both simulations. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 915

9 inside of the TC (radius < 700 km; Figure 7a; red, green) versus shear outside of the TC (700 km < radius < 2100 km; Figure 7a; blue, black). The red and blue lines represent the simulation when nudging is deactivated after the transition is complete, while the green and black lines represent the case when nudging remains active through the end of the simulation. The shear outside the TC remains relatively constant even after nudging is turned off. Inside the vortex, shear decreases more when nudging is turned off (Figure 7a; red) than it does when shear remains active (Figure 7a; green) until late in the simulation when the TC becomes sufficiently weak. The shear outside the TC remains quasi steady because the PDS technique continues to enforce the quasi steady background wind profile on larger scales even after nudging is discontinued. Figure 7b shows a time-height diagram of potential temperature outside the vortex ( km radius). The environment gradually warms because of the transfer of energy from the ocean to the atmosphere by moist convection and large-scale ascent outside of the TC. This is the case whether or not nudging of the wind field remains active. The ability of the TC to modify its local environment in the case when nudging is discontinued allows a temporary recovery but ultimately the stabilizing environment in combination with vertical wind shear leads to the weakening of the TC. The differences between the two simulations shown in Figure 6 highlight one of the key aspects of the TVPDS method. The TVPDS technique nudges the environment in a way such that the TC experiences a nearly constant environmental hpa wind shear, with little ability to modify the near-tc environment. This is effectively as if the TC is experiencing an environment which is being forced to a given shear state by a strong synoptic scale weather system, such as a large midlatitude upper level trough. In this situation, when the large-scale is forcing vertical wind shear to be present, the TC circulation may not have a large effect on its environment. Riemer et al. [2010, 2013] attributed reintensification in their simulations to the fact that the TC was able to modify its local environment because shear was imposed only as a boundary condition on the outermost domain. While some of the differences between the TVPDS simulations of this section and the simulations of Riemer et al. [2010, 2013] likely are due to the differences in how shear is imposed, other differences may be due to differences in model resolution and physics. The simulations of Riemer et al. were performed using the Regional Atmospheric Modeling System (RAMS), developed at Colorado State University [Pielke et al., 1992; Cotton et al., 2003]. Their simulations were performed on an f-plane at 158N with horizontal grid spacing of 5 km. The primary difference between their 2010 and 2013 simulation were several upgrades to physics and surface exchange coefficients. The TVPDS simulations performed in this study used a horizontal grid spacing of 2 km. It is likely that the combination of higher resolution, updated parameterizations, and a smooth transition between shear regimes contributes to a more realistic TC response to changes in vertical wind shear. Because of modeling framework differences, it remains somewhat difficult to determine the primary physical cause of the differences between the TVPDS results and those of Riemer et al. [2010, 2013] TC Simulated Reflectivity and Surface Fluxes in Time-Varying TC Environments To examine the TC structural response to time-varying shear, time composites of reflectivity, surface latent heat fluxes, and low-level equivalent potential temperature (h e ) are computed during and after the period when shear is imposed. Riemer et al. [2013] discussed the sensitivity of intensification to midlevel dry air that moves downward into the boundary layer near the TC core. They described a process in which persistent shear-induced downdrafts deliver relatively cool air to the boundary layer near the TC core and that surface fluxes are insufficient to raise h e back to previous values. The more stable boundary layer then reduces the potential intensity of the TC. This process is different from the one described by previous studies which identified the mixing of midlevel low-entropy air directly into the TC eyewall as a means by which shear reduces TC intensity [Simpson and Riehl, 1958; Cram et al., 2007; Marin et al., 2009; Tang and Emanuel, 2012]. Riemer and Laliberte [2015] found that this incomplete low-level recovery was more pronounced than the midlevel ventilation mechanism in their modeling framework. Figure 8 shows time-averaged 700 hpa simulated reflectivity during the 24 h period after shear is imposed for a TVPDS simulation that transitions from 5 to 15 m s 21 (corresponding to the red line on Figure 4a). The nudging time scale is s 5 6 h for this simulation, the SST is 278C, and the environmental temperature and moisture profiles follow the Dunion moist tropical sounding [Dunion, 2011]. Immediately evident in Figure 8 is the steady degradation of the symmetry of the TC. By h after shear is initially imposed (Figure 8b), 700 hpa reflectivity in the downshear-right quadrant of the simulated TC has been substantially ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 916

10 Figure 8. Time-averaged 700 hpa simulated radar reflectivity (dbz) for a simulation with shear increasing from 5 to 15 m s 21 over the periods displayed. Row 1 shows reflectivity averaged from (a) 08 to 12 h, (b) 12 to 16 h, and (c) 16 to 20 h after shear begins increasing. Row 2 shows time-mean reflectivity from (d) 20 to 24 h, (e) 24 to 28 h, and (f) 28 to 32 h after shear imposition. reduced and this degradation continues into the following periods (Figures 8c 8f). Interestingly, despite that fact that the symmetry of reflectivity is quickly reduced over the first 18 h after shear imposition, the magnitude of the simulated reflectivity maximum remains approximately constant. This highlights the fact that with less convective symmetry, there is less total latent heating near the TC core. The azimuthal location of the maximum in reflectivity shifts very little while shear increases. During the time period corresponding to the plots of Figure 8, minimum central pressure rises from approximately 963 to 978 hpa. Figure 9 shows time-averaged surface latent heat flux for the same periods shown in Figure 8 (t h after shear imposition) along with time-averaged convergence on the lowest model level. While the symmetry of the surface latent heat fluxes and convergence are reduced, the peak magnitudes change very little over the 24 h period. The region of stronger surface convergence does appear to shift downshear (eastward) as shear increases (Figures 9c 9f). The reduction in symmetry of surface latent heat flux and low-level convergence occurs concurrently with the reduction in symmetry of 700 hpa simulated reflectivity. To determine if total diabatic heating changes as environmental shear increases and as the symmetry of reflectivity decreases, height-radius cross sections of time-composited azimuthal-mean diabatic heating are shown in Figure 10 for the same time periods shown in Figures 8 and 9. Initially, in the period 8 12 h after shear imposition (Figures 10a 10c), diabatic heating is relatively large near the RMW. Subsequently, there is a steady reduction in azimuthal mean diabatic heating during the period corresponding to the reduction in the symmetry of 700 hpa simulated reflectivity (Figures 8d 8f). Diabatic heating is particularly reduced above 500 hpa after time t 5 20 h after shear imposition (Figures 10e and 8f). These time composites illustrate how TC intensity is closely linked to diabatic heating at or inside the RMW [Shapiro and Willoughby, 1982; Nolan et al., 2007]. Another way to analyze the effects of increasing shear on TCs is to examine low-level h e. Previous studies have identified low-h e downdrafts induced by wind-shear-driven asymmetries as a mechanism for ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 917

11 Figure 9. Time-averaged surface latent heat flux (color-filled; Wm 22 ) and divergence (black contours, negative only; s 21 ) for a simulation with shear increasing from 5 to 15 m s 21 over the periods displayed. Row 1 shows latent heat flux and convergence averaged from (a) 08 to 12 h, (b) 12 to 16 h, and (c) 16 to 20 h after shear begins increasing. Row 2 shows timemean latent heat flux and convergence from (d) 20 to 24 h, (e) 24 to 28 h, and (f) 28 to 32 h after shear imposition. weakening TCs [Molinari et al., 2013; Riemer et al., 2010, 2013; Tang and Emanuel, 2012]. Figure 11 shows time-averaged h e on the lowest model level for the same simulation discussed above during the same time periods. More so than surface latent heat flux and low-level convergence, h e on the lowest model level shows relatively larger changes during the period when shear increases and the TC begins significant weakening. Initially, in the 8 12 h time range after shear is imposed (Figure 11a), lower values of low-level h e are present near the TC core, however, much lower h e air is flushed into the boundary layer near the TC core in the subsequent periods. This is particularly true by the h period (Figure 11c) when a large region of low-h e air arrives in the boundary layer in the upshear quadrants just outside the TC eye. This more conditionally stable near-surface air suppresses updrafts downstream in the upshear-right and downshear-right quadrants. This effect is evident in the simulated reflectivity fields in Figure 8 which show a steady reduction in these quadrants that are immediately downstream of the lower-h e air which enters the boundary layer. A steady reduction in surface h e in the eye also occurs during this period, which is predominantly related to the rising pressure of the TC. This reduction of h e in the eye continues beyond the time periods shown in Figure 11. To further investigate the role of relatively low h e boundary layer intrusions, radius-time Hovm oller diagrams of h e on the lowest model level are compared to Hovm oller diagrams of midlevel (700 hpa) relative humidity (RH). These levels were chosen in order to compare the relative impacts of midlevel drying and low-level low-h e intrusions since both mechanisms have been proposed to reduce TC intensity when vertical wind shear is present (i.e., midlevel ventilation mechanism described by Simpson and Riehl [1958]; Cram et al. [2007]; Marin et al. [2009]; Tang and Emanuel [2012], versus the low-level low-h e intrusion mechanism described by Riemer et al. [2010]). Hovm oller diagrams were generated for upshear (azimuth angles ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 918

12 Figure 10. Pressure-radius cross sections of time-averaged azimuthal mean diabatic heating rate (K h 21 ) for a simulation with shear increasing from 5 to 15 m s 21 over the periods displayed. Row 1 shows diabatic heating rate averaged from (a) 08 to 12 h, (b) 12 to 16 h, and (c) 16 to 20 h after shear begins increasing. Row 2 shows the heating rate from (d) 20 to 24 h, (e) 24 to 28 h, and (f) 28 to 32 h after shear imposition. SST for this simulation is fixed at 278C. The thick black line represents the radius of maximum winds ) and downshear (azimuth angles , 08 represents due east) quadrants to determine if one mechanism precedes the other and where these weakening effects are most apparent. Figure 12 shows upshear (a) versus downshear (b) 700 hpa relative humidity (%) radius-time Hovm oller diagrams for the 165 h period encompassing the shear transition period. Relatively low-h e intrusions on the lowest model level (Figure 12: black contours) are overlaid to show where these features are located radially and when they occur relative to drying in the midlevels. Approximately 9 12 h after shear is imposed (t h in Figure 12), low-h e intrusions in the boundary layer appear near the RMW in the upshear quadrant. Throughout the remainder of the simulation, periodic pulses of low-h e air appear near the RMW in the upshear quadrant, but remain mostly absent in the downshear quadrant. One notable effect in both quadrants is the tendency for larger RH values to expand radially outward beyond the RMW. A final approach to investigating the relative contribution of midlevel ventilation versus intrusions of reduced low-level h e involves generating a series of time-composite height-radius cross sections of the change in h e after shear imposition for different regions within the simulated TC. The composites are computed for the same experiment as above (shear increasing from 5 to 15 m s 21 ; SST 5 278C) except in 8 h intervals. Each plot represents the average cross section over the 8 h period minus the average cross section during the 8 h prior to shear imposition. Because individual intrusions of anomalously low h e are temporary, the longer time interval makes the trend in the intrusion occurrence easier to identify. Figure 13 shows these cross sections for the southeastern semicircle (covering 1808 in azimuth; centered on the downshearright quadrant; Figures 13a 13c) and the northwestern semicircle (covering 1808 in azimuth; centered on the upshear-left quadrant; Figures 13d 13f) within the TC. Anomalously low h e first appears primarily above the boundary layer outside the RMW in the northwestern semicircle. Then, over the following 16 h, these anomalies intensify and progress downward into the boundary layer and extend radially inward to the RMW. This process resembles a combination of the midlevel ventilation mechanism described in previous studies [Simpson and Riehl, 1958; Cram et al., 2007; Marin et al., 2009; Tang and Emanuel, 2012] and the insufficient boundary layer recovery process described by Riemer and Laliberte [2015]. It should be noted, ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 919

13 Figure 11. Time-averaged equivalent potential temperature (h e ; K) on the lowest model level for a simulation with shear increasing from 5 to 15 m s 21 over the periods displayed. Row 1 shows h e averaged from (a) 08 to 12 h, (b) 12 to 16 h, and (c) 16 to 20 h after shear begins increasing. Row 2 shows time-mean h e from (d) 20 to 24 h, (e) 24 to 28 h, and (f) 28 to 32 h after shear imposition. For each period, the minimum h e value is displayed in the upper right corner of the plot. however, that the substantial reductions in h e (excepting those located at high altitudes above the TC core) are confined to levels below 700 hpa. The progression of decreased h e moving downward into the boundary layer and inward toward the RMW is similar to the results of Riemer and Montgomery [2011] in which these intrusions frustrate the intensification of a TC. The process is most evident in the northwestern semicircle, however, h e does gradually decrease in the boundary layer near and just outside of the RMW in the southeastern semicircle. The large reduction in h e at high altitudes (above 400 hpa) within the RMW likely is due to the general weakening of the TC and a reduced warm core aloft. The increase of h e in the midlevels outside the RMW is radially collocated with decreased h e at low levels, leading to a more-stable vertical profile of h e. The outward expansion of convection during this period (as is evident in Figures 8d 8f) may be an effect of the redistribution of the dynamic and thermodynamic forcing for ascent due to increasing shear. The intrusions of reduced h e into the boundary layer appear to play the key role in weakening the TC Time-Varying Shear and TC Tilt In addition to affecting the distribution of reflectivity and boundary layer h e, vertical wind shear affects the vertical alignment of TCs. Numerous previous studies [e.g., Marks et al., 1992; Franklin et al., 1993; Jones, 1995, 2000; DeMaria, 1996; Corbosiero and Molinari, 2002; Molinari et al., 2006; Reasor et al. 2013] have outlined the impact of shear on TCs in terms of tilt and convective distribution. These studies noted that TCs in shear tilt downshear and favor convection in the downshear-left quadrant. Corbosiero and Molinari [2002] noted that this preference for downshear-left convection occurs in the inner-core regions (inside 100 km). Outside of this radius, convection reaches a maximum in the downshear-right quadrant. Reasor and Montgomery [2001] noted how TC tilt and subsequent precession can modify the rate at which TCs intensify or weaken. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 920

14 Figure 12. Radius-time Hovm oller diagrams of 700 hpa relative humidity (%; shaded) and relatively low equivalent potential temperature on the lowest model level (K; contoured at 1 K intervals from 340 to 345 K) for upshear locations (a; azimuths ) and downshear locations (b; azimuths ). The black arrows indicate the beginning time and approximate end time of the period during which shear transitions from5to15ms 21. The thick black line represents the radius of maximum wind for the quadrant. The times on the y axis are labeled relative to the time when shear is initially imposed. Figure 13. Time composite pressure-radius cross sections of the change in equivalent potential temperature (h e ) since shear imposition for (a c) the southeastern (centered on the downshear-right quadrant) and (d f) northwestern (centered on the upshear-left quadrant) semicircles (covering 1808 in azimuth) of a simulated TC. Figures 13a and 13d are for the period 0 8 h after shear imposition, Figures 13b and 13e represent 8 16 h after shear imposition, and Figures 13c and 13f represent h after shear imposition. The simulation with shear increasing from 5 to 15 m s 21 (corresponding to the red line in Figure 3a) and SST 5 278C was used. The thick black line represents the radius of maximum wind for the semicircle. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 921

15 Figure hpa TC tilt (km) as measured by the relative vorticity centroids for TVPDS simulations transitioning from 5 to 7.5 m s 21 (cyan), 5 to 10 m s 21 (green), 5 to 15 m s 21 (red), and 5 to 20 m s 21 (black). These simulations correspond to the simulations shown in Figure 3a. To examine the extent to which tilt and precession affect TC resiliency and the rate of weakening in the TVPDS simulations, time series of tilt were generated for the simulation transitioning from 5 to 15 m s 21 (corresponding to the red curve in Figure 4a). Figure 14 shows these time series of the hpa vorticity centroid tilt versus time for all four of the TVPDS simulations transitioning into larger shear regimes with a constant SST 5 278C (from 5 to 7.5 m s 21 : cyan, to 10 m s 21 : green, to 15 m s 21 :red,to20ms 21 : black). Smoothed vorticity centroids are computed at 850 and 400 hpa and then the horizontal distance between the centroids is identified hourly. Figure 15 shows the evolution of smoothed relative vorticity to demonstrate the hpa tilt. Relative vorticity is smoothed 200 times with a filter on the 400 and 850 hpa levels. Initially, TC tilt is near zero when shear is 5 m s 21 in each simulation. Considering the case when shear transitions from 5 to 15 m s 21 (red curve in Figure 14), tilt steadily increases to approximately 50 km by t 5 54 h after shear imposition. At this point, a notable precession pattern develops and Figure 15. Smoothed relative vorticity (s 21 ) at 400 (black contours; from to with a contour interval of ) and 850 hpa (color filled) (a c) for the simulation transition from 5 to 15 m s 21 and (d f) for the simulation transitioning from 5 to 10 m s 21. Relative vorticity is smoothed 200 times with a filter. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 922

16 continues through the end of the simulation. Interestingly, this precession corresponds with minor fluctuations in the minimum central pressure as shown by the red line of Figure 4a. Whenever the upper level (400 hpa) vorticity centroid precesses near or upshear of the 850 hpa centroid the TC minimum pressure stabilizes or decreases slightly. However, the overall trend of weakening continues. As the TC becomes weaker, the general trend is for the tilt to continue to increase through 96 h when tilt reaches 235 km. By this time, the TC has weakened substantially to a minimum central pressure of approximately 1000 hpa. While it does appear that the precession process acts to reduce the impact of the vertical shear (15 m s 21 ) by periodically realigning the vortex vertically, the large magnitude of shear disallows any significant sustained recovery. The time series shown in Figure 14 show that this large tilt and precession process occurs only when shear increases to greater than 10 m s 21. When shear increases to only 10 m s 21 or less, the TC resists tilting and precession with hpa tilt remaining less than 15 km for the duration of the simulation. Despite the lack of larger tilt, minimum pressure does rise in both of these cases (Figure 4a). This again suggests that the asymmetry of reflectivity and the flushing of lower h e air into the boundary layer near the TC core are the primary reasons for the weakening of the TC. When shear increases to 20 m s 21, both tilt and precession begin sooner, although the precession frequency (i.e., revolutions per day of the upper level vorticity centroid about the low level centroid) is very similar to the case where shear increases to 15 m s 21. The precession rates in these TVPDS simulations (s 5 6 h) are approximately s 21 (precession period h). Reasor and Montgomery [2015] found slightly faster precession rates between 5.5 and s 21 (precession period h). The simulation transitioning to 20 m s 21 also experiences fluctuations in minimum central pressure corresponding to the precession process as seen in the 15 m s 21 simulation (Figure 4a). Another factor reducing tilt during shear imposition is TC intensity. The hpa tilt computed from a simulation performed with SST 5 308C and shear transitioning from 5 to 15 m s 21 shows that a stronger TC can resist tilting (Figure 17a). This was not the case when SST 5 278C. Tao and Zhang [2014] found that TCs simulated with warmer SSTs produced a less tilted vortex due to larger diabatic heating near Figure 16. Pressure-radius cross sections of time-averaged azimuthal mean diabatic heating rate (K h 21 ) versus pressure (hpa) for a simulation with shear increasing from 5 to 15 m s 21 over the periods displayed. Row 1 shows diabatic heating rate averaged from (a) 08 to 12 h, (b) 12 to 16 h, and (c) 16 to 20 h after shear begins increasing. Row 2 shows the heating rate from (d) 20 to 24 h, (e) 24 to 28 h, and (f) 28 to 32 h after shear imposition. SST for this simulation is fixed at 308C. The thick black line represents the radius of maximum winds. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 923

17 Figure 17. (a) hpa TC tilt (km) as measured by the relative vorticity centroids and (b) minimum central pressure (hpa) versus time (h) for TVPDS simulations with environmental shear transitioning from 5 to 15 m s 21 with SST 5 278C (red), SST C (blue), and SST 5 308C (black). The nudging time scale s 5 6 h for each simulation. The red lines correspond to the red line shown in Figures 3a and 10. Figure 18. Minimum central pressure (hpa) versus time (h) for TVPDS simulations with environmental wind shear transitioning from 15 to 5ms 21 (red) and a control experiment in which shear remains at 15 m s 21 throughout (blue). SST for these simulations is 28.58Cands 5 6h. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 924

18 Figure 19. Time-averaged 700 hpa simulated radar reflectivity (dbz) for a simulation with shear decreasing from 15 to 5 m s 21 over the periods displayed. Row 1 shows reflectivity averaged from (a) 0 to 6 h, (b) 6 to 12 h, and (c) 12 to 18 h after shear begins decreasing. Row 2 shows time-mean reflectivity from (d) 18 to 24 h, (e) 24 to 30 h, and (f) 30 to 36 h after the shear begins decreasing. the TC center. TVPDS simulations show a similar result in which azimuthal mean diabatic heating is degraded less as shear increases when SST is 308C.Figure16showstimecompositesin4hintervalsover a 24 period after shear is imposed (t h after shear imposition; as in Figure 10). Diabatic heating is particularly larger relative to the 278C simulation in the h period (Figures 10d and 10e). Despite the fact that tilt is resisted, minimum central pressure steadily rises throughout the simulation. Figure 17a shows hpa vorticity centroid tilt versus time for three simulations that transition from shear of 5 15 m s 21 (SST 5 278C red, SST C blue, SST 5 308C black). Comparing the three time series, it is evident that tilt increases with decreasing SST. Precession is quite evident when the SST is 278C, somewhat evident when SST is 28.58C, and substantially reduced when SST is 308C, implying that precession is reduced for stronger TCs. Although all three TCs show about the same increase in minimum pressure over the 90 h period (Figure 17b), the amplitude of the tilt precession decreases drastically with storm intensity, with almost no tilt or precession at all for the case where SST 5 308C. h e cooling rate on the lowest model level inside a radius of 40 km is computed for these three simulations over the first 24 h after shear imposition. This cooling rate equals 0.05, 0.04, and 0.02 K h 21 for the simulations with SST 5 278C, 28.58C, and 308C, respectively. When these rates are computed over the radial range km, h e actually warms slightly as shear increases when SST and 308C. The lack of a clear relationship between boundary layer h e cooling rate near the TC core and TC intensity change suggests that additional factors (i.e., reduced diabatic heating in the midlevels; reduced reflectivity symmetry) also contribute to TC weakening rate, particularly at higher SSTs. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 925

19 Figure 20. Pressure-radius cross sections of time-averaged azimuthal mean diabatic heating rate (K h 21 ) versus pressure (hpa) for a simulation with shear decreasing from 15 to 5 m s 21 over the periods displayed. Row 1 shows diabatic heating rate averaged from (a) 0 to 6 h, (b) 6 to 12 h, and (c) 12 to 18 h after shear begins decreasing. Row 2 shows the heating rate from (d) 18 to 24 h, (e) 24 to 30 h, and (f) 30 to 36 h after shear imposition. SST for this simulation is fixed at 28.58C. The thick black line represents the radius of maximum winds The TC Response to the Reduction of Environmental Wind Shear To determine if the opposite sequence of events occurs when environmental wind shear is reduced, simulations were performed in which a quasi steady state TC in relatively strong wind shear transitions smoothly into an environment of less shear. In these simulations, the TC is allowed to develop for 234 h until the quasi steady state is reached. Figure 18 shows a time series for a simulation with shear transitioning from 15 to 5ms 21. The blue line represents minimum central pressure for the control simulation in which environmental shear remains at 15 m s 21, and the red line shows minimum pressure for the simulation with shear reduced to 5 m s 21 over a 36 h period. As in the experiments described in previous sections, approximately 90% of the transition in shear occurs during the first 24 h after the shear transition begins. The transition of TC intensity takes longer, approximately 60 h. For these simulations, the SST C and the nudging time scale s 5 6 h. The slightly higher SST (28.58C as opposed to 278C) is chosen so that the simulation can produce an intense quasi steady state TC (category-1 hurricane with minimum central pressure of 990 hpa and maximum sustained 10 m wind speed of 40 m s21) despite environmental shear of 15 m s 21. In the control simulation, the minimum central pressure fluctuates in the hpa range. In the case in which shear is reduced the TC steadily intensifies, reaching a value of 943 hpa at the end of the simulation. As was the case for the simulations when shear increased, the symmetry of reflectivity, boundary layer h e, and TC tilt provide insight into the reasons why the TC intensifies as shear decreases. Figure 19 shows a sequence of time-averaged 700 hpa simulated reflectivity for 6 h periods during the 36 h period after shear begins to decrease. Figure 19a shows a very asymmetric system in the presence of environmental wind shear of nearly 15 m s 21. Despite the asymmetry and strong shear, the region of maximum reflectivity in the downshear left quadrant is relatively intense and widespread compared to the subsequent five periods. However, the asymmetric nature and radial distance of the maximum in reflectivity from the center suggests that it is less efficient at releasing latent heat near the TC core. Over the following time-averaged periods symmetry steadily increases, first encircling the eye in the t h (Figure 19d) period after shear transition begins. By the final period shown in Figure 19f (t h), strong reflectivity fully ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 926

20 Figure 21. Time-averaged equivalent potential temperature (h e ; K) on the lowest model level for a simulation with shear decreasing from 15 to 5 m s 21 over the periods displayed. Row 1 shows h e averaged from (a) 0 to 6 h, (b) 6 to 12 h, and (c) 12 to 18 h after shear begins decreasing. Row 2 shows time-mean h e from (d) 18 to 24 h, (e) 24 to 30 h, and (f) 30 to 36 h after the shear begins decreasing. For each period, the minimum h e value is displayed in the upper right corner of the plot. encompasses the eye and the TC has acquired a much more symmetric appearance with slightly higher values of reflectivity upshear (west) of the center. Despite the symmetry, the magnitude of the strongest reflectivity is no more intense than when shear is initially imposed. Time composites of azimuthal mean diabatic heating rate show a steady increase in diabatic heating as shear decreases. Diabatic heating is relatively small during the first 12 h after shear begins to decrease (Figures 20a and 20b). Figure 20c shows the first period (t h after shear reduction begins) in which diabatic heating in the midlevels near the TC core significantly increases. After a brief reduction in heating in the subsequent 6 h period (Figure 20d), diabatic heating again increases significantly in the TC eyewall during the final two periods (Figures 20e and 20f). The relationship between the symmetry of 700 hpa reflectivity (Figure 19) and azimuthal mean diabatic heating (Figure 20) is similar to that seen when shear increases. In the case of decreasing shear, both the symmetry of simulated reflectivity and the azimuthal mean diabatic heating increase. Time-averaged plots of h e on the lowest model level show that relatively stable air near the TC core becomes steadily less widespread as shear decreases. Boundary layer recovery was also noted by Riemer et al. [2010, 2013] in the reintensification portions of their simulations. Figure 21 shows time-averaged plots of near-surface h e for 6 h intervals during the 36 h period after shear begins to decrease. Initially, in the first 6 h when shear still is near 15 m s 21 (Figure 21a), a large region of low-h e air in the boundary layer exists in the upshear quadrants, maximized in the upshear-left quadrant. Throughout the following periods (Figures 21b 21f) there are bouts of relatively lower h e entering the boundary layer, but the magnitude of these intrusions is reduced and their radial distance from the TC core increases. The combination of these factors is to reduce the effect of these low-h e intrusions on TC intensification and to allow more conditionally ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 927

21 Figure 22. Radius-time Hovm oller diagrams of 700 hpa relative humidity (%; shaded) and relatively low equivalent potential temperature on the lowest model level (K; contoured at 1 K intervals from 335 to 340 K) for (a) upshear locations (azimuths ) and (b) downshear locations (azimuths ). The black arrows indicate the beginning time and approximate end time of the period during which shear transitions from 15 to 5 m s 21. The thick black line represents the radius of maximum wind for the quadrant. The times on the y axis are labeled relative to the time at which shear begins to decrease. unstable air to be present near the TC core. h e in the TC eye steadily increases during this 36 h period as the TC responds to the reduction in shear and intensifies. Radius-time Hovm oller diagrams of quadrant mean h e on the lowest model level are compared to Hovm oller diagrams of quadrant mean mid-level (700 hpa) relative humidity for the upshear (Figure 22a) and downshear (Figure 22b) quadrants. Figure 22 shows the diagrams for the 115 h period encompassing the shear transition period. Low-h e intrusions are contoured in black in 1 K intervals from 335 to 340 K. The behavior of midlevel RH and low-level low-h e when shear decreases is essentially opposite of what occurs when shear increases (shown in Figure 12). Relatively higher values of 700 hpa RH contract inward to radii Figure hpa TC tilt (km) as measured by the relative vorticity centroids for a TVPDS simulation with environmental shear transitioning from 15 to 5 m s 21 (red) and a control experiment with environmental shear of 15 m s 21 throughout (blue). SST C and the nudging time scale s 5 6 h for both simulations. ONDERLINDE ET AL. TC RESPONSE TO TIME-VARYING WIND SHEAR 928