Further examination of the thermodynamic modification of the inflow layer of tropical cyclones by vertical wind shear

Transcription

1 doi: /acp Author(s) CC Attribution 3.0 License. Atmospheric Chemistry and Physics Furr examination of rmodynamic modification of inflow layer of tropical cyclones by vertical wind M. Riemer 1, M. T. Montgomery 2,3, and M. E. Nicholls 4 1 Institut für Physik der Atmosphäre, Johannes Gutenberg-Universität, Mainz, Germany 2 Department of Meteorology, Naval Postgraduate School, Monterey, CA, USA 3 NOAA s Hurricane Research Division, Miami, FL, USA 4 University of Colorado, Cooperative Institute for Research in Environmental Sciences, Boulder, CO, USA Correspondence to: M. Riemer (mriemer@uni-mainz.d Received: 15 October 2011 Published in Atmos. Chem. Phys. Discuss.: 7 March 2012 Revised: 20 November 2012 Accepted: 1 January 2013 Published: 11 January 2013 Abstract. Recent work has developed a new framework for impact of vertical wind on intensity evolution of tropical cyclones. A focus of this framework is on frustration of tropical cyclone s power machine by induced, persistent downdrafts that flush relatively cool and dry (lower equivalent potential temperature, θ e ) air into storm s inflow layer. These previous results have been based on idealised numerical experiments for which we have deliberately chosen a simple set of physical parameterisations. Before efforts are undertaken to test proposed framework with real atmospheric data, we assess here robustness of our previous results in a more realistic and representative experimental setup by surveying and diagnosing five additional numerical experiments. The modifications of experimental setup comprise values of exchange coefficients of surface heat and momentum fluxes, inclusion of experiments with ice microphysics, and consideration of weaker, but still mature tropical cyclones. In all experiments, depression of inflow layer θ e values is significant and all tropical cyclones exhibit same general structural changes when interacting with imposed vertical wind. Tropical cyclones in which strong downdrafts occur more frequently exhibit a more pronounced depression of inflow layer θ e outside of eyewall in our experiments. The magnitude of θ e depression underneath eyewall early after is imposed in our experiments correlates well with magnitude of ensuing weakening of respective tropical cyclone. Based on evidence presented, it is concluded that newly proposed framework is a robust description of intensity modification in our suite of experiments. 1 Introduction 1.1 A new framework for intensity modification of tropical cyclones in vertical wind The intensity evolution of tropical cyclones (TCs) embedded in an environmental flow with vertical wind poses an important forecast problem. To date, physical processes that govern this intensity evolution are not well understood. In a recent publication (Riemer et al., 2010, referred to as 10 hereafter) a new framework for intensity modification of TCs in vertical wind was proposed. While previous hyposes have focused almost exclusively on processes above boundary layer, 10 showed that vertical wind has a significant impact on rmodynamic properties of TC s inflow layer 1. Strong and persistent, -induced downdrafts flush inflow layer with low moist-entropy (or equivalent potential temperature, θ e ) air anti-fuel for TC power machine. The replenishment of this air by surface heat fluxes is not complete while air spirals towards storm centre leading to a reduction of θ e values within inner-core updrafts in azimuthal mean. When viewed from simplified perspective of an idealised Carnot cycle, a decrease in potential intensity of TC can be expected (Tang and Emanuel, 2010). 1 In current study, term inflow layer will refer to layer of strong inflow associated with surface friction in lowest km where departure from gradient wind balance in radial direction is generally a maximum (e.g., Bui et al. (2009), ir Figs. 5 and 6 and accompanying discussion). Published by Copernicus Publications on behalf of European Geosciences Union.

2 328 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer The downdrafts that flush inflow layer with low-θ e air are associated with a quasi-stationary, azimuthal wavenumber 1, convective asymmetry outside of eyewall. This convective asymmetry is reminiscent of stationary band complex (Willoughby et al., 1984) and for this reason will be referred to as SBC hereafter. The SBC and associated downdraft pattern extends outwards to approximately km. On account of swirling winds, updrafts within SBC rise along a helical path. A simple kinematic model (Riemer and Montgomery, 2011) suggests that, at low levels above inflow layer, environmental low-θ e air approaches storm closely underneath helical updrafts in down and down-left quadrants 2. Evaporative cooling of precipitation falling out of SBC, and into this unsaturated air, most likely drives strong and persistent, vortex-scale downdrafts that cool and dry TC s inflow layer. In 10, evidence was presented that formation of SBC is connected to tilt 3 of TC vortex. When subject to vertical wind, tilt evolution of TC vortex was shown to be governed to zero order by asymmetricbalance dynamics. Vortex tilt can thus be described in terms of a standing vortex-rossby-wave (VRW) pattern with azimuthal and vertical wave-number 1 structure. Even though tilt of inner core is only km, VRW pattern associated with tilt of outer vortex extends outwards to radii of km ( 15a in 10) 4. After vertical wind is suddenly imposed, TC settles quickly (approx. within 3 h) into a quasi-equilibrium tilt direction that is to down-left. Thus, positive vorticity anomaly associated with standing wave-number 1 VRW pattern is found down-left at upper levels and down-right at low levels ( 16 in 10). Frictional convergence associated with this positive low-level vorticity anomaly n contributes to forcing of asymmetric convection within SBC. The foregoing results suggest an important connection between asymmetric-balance dynamics governing tilt evolution of vortex subject to vertical and rmodynamic impact on inflow layer. The findings of 10 were derived from idealised numerical experiments following setup of Bender (1997) and Frank and Ritchie (2001). In this experimental setup, a uni-directional vertical wind profile is imposed suddenly on a mature model TC. In an attempt to min- 2 In Riemer and Montgomery (2011), distribution of θ e was analysed at 2 km height. 3 In 10, as well as in current study, tilt is defined as vector difference between location of vorticity centroids at 10 km and 1 km height. 4 A considerable tilt of outer parts of TC-like vortices with small tilt of inner core has been noted previously by or authors also (see e.g. 6a in Jones, 1995; 10 in Reasor et al., 2004). imise complexity and to understand fundamental processes, 10 deliberately chose a simple set of model parameterisations. As is nature of results derived from such an idealised approach, uncertainties exist wher newly proposed pathway operates in real atmosphere. Although some preliminary observational support was offered in 10 a more comprehensive test of new hyposis with atmospheric data awaits future studies. Before undertaking such efforts we survey and diagnose here five additional numerical experiments with some modifications of experimental setup to assess robustness of 10 s results. 1.2 Purpose of additional experiments The experimental setup in 10 features a simplified cloud microphysics scheme, a likely overestimation of surface exchange coefficients of momentum and enthalpy at high wind speed, and a very high TC intensity at time when is imposed, representative for a minority of TCs in real atmosphere only. The particular relevance of se features for 10 s framework is discussed in more detail below. One goal of this study is to assess robustness of 10 s results in a more realistic and representative experimental setup. Several environmental factors likely play a role for evolution of TCs in vertical wind also. Besides obvious importance of magnitude, such factors include vertical profiles of environmental wind speed and direction (Zeng et al., 2010; Wang, 2012), and environmental moisture and temperature profiles (cf. discussion in Riemer and Montgomery (2011)). Careful examination of importance of se environmental profiles is beyond scope of this study but constitutes an important topic for future research 5. The numerical experiments in 10 employed a microphysics scheme that considers warm cloud processes associated with collision-coalescence process only (hereafter termed warm rain ). The current study considers experiments with ice microphysics also. Adding ice processes introduces latent heat of fusion/ sublimation, new classes of hydrometeors with various fall speeds, and additional pathways to form precipitation. Details of ice microphysics scheme employed in this study are given in Sect Arguably, most significant of above processes is additional conversion of latent heat associated with freezing and melting of ice. Ice microphysics produce stronger updrafts than a warm-rain scheme due to additional latent heat release associated with freezing. In addition, inclusion of precipitation in form of ice may significantly enhance formation and intensity of downdrafts (Srivastava, 1987). 5 A brief discussion of potential consequences of environmental wind profile can be found in authors response to anonymous reviewer (item 1 and 2) on ACPD webpage.

3 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer 329 Previous studies have shown that inclusion of ice microphysics in numerical models may alter radial profile of swirling winds of TCs as compared to a warm-rain experiment (e.g., Lord et al., 1984; Fovell et al., 2009). In general, it is not well understood how se differences arise 6. Lord et al. have noted, albeit in an axisymmetric model framework, that ir experiment with ice microphysics exhibits more mesoscale convective features than ir experiment with warm rain. Fovell et al. have proposed a mechanism for change in radial profile of swirling winds that is based on sedimentation of ice particles from outflow anvil, subsequent sublimentation of se ice particles, and radiative feedback. In our suite of experiments, however, radiative processes are neglected. Neverless, potentially significant differences in TC-vortex structure between warm-rain and ice microphysics experiments do arise, indicating that mechanism suggested by Fovell et al. is not of primary importance. The potentially important differences in TC-vortex structure and ir implication for interaction with vertical wind will be discussed in some detail in Sect Recent studies have highlighted importance of representation of planetary boundary layer in numerical models for vortex intensification and structure changes of simulated storms (Braun and Tao, 2000; Smith and Thomsen, 2010; Montgomery et al., 2010; Smith et al., 2012). The exchange coefficients for enthalpy, C K, and momentum, C D, play a most prominent role. They govern energy extraction from ocean surface and dissipation of kinetic energy in frictional boundary layer, respectively. In framework of 10, values of C K and C D can be expected to play an important role in replenishment of depressed boundary layer θ e air while spiralling towards inner-core updrafts. The replenishment rate is proportional 7 to C K. The strength of inflow within frictional boundary layer is determined in part by C D. Smaller values of C D may lead to less radial inflow and thus to an increase of time that air parcels spend under influence of surface fluxes while spiralling inwards. Assuming that C K is not changed, and that wind dependence of fluxes is dominated by tangential wind speed, replenishment of depressed inflow layer θ e values is n more complete than for larger values of C D. Based on se considerations, one would expect that -induced flushing of inflow layer with low-θ e air has a more pronounced impact on TC intensity for smaller values of C K and larger values of 6 In his review of this study, Roger Smith has proposed that a first-order explanation of how se differences arise could be given in terms of conventional (balance model of vortex spin-up, noting that inclusion of ice microphysics substantially modifies diabatic heating rate. We are not aware, however, of published studies that elaborate on this idea. 7 The replenishment rate is proportional to air-sea rmodynamic disequilibrium also. C D. The interpretation of importance of C K and C D in an axisymmetric ory for a TC in vertical wind by Tang and Emanuel (2010) is consistent with foregoing considerations. Considerable uncertainties exist about values of C K and C D at high wind speeds occurring in TCs. Deacon s formula for C D was employed in 10 and ratio of C K /C D was set to unity. Recent results derived from observational data (Black et al., 2007; Zhang et al., 2008) strongly indicate that Deacon s formula overestimates C D at high wind speeds and that C K /C D is considerably less than unity. The observational data exhibit considerable scatter and are limited to wind speeds of marginal hurricane strength 8. To address likely overestimation of C K and C K /C D in 10, we employ in this study values of C K and C K /C D that are consistent with, but rar on lower end of range of values observed by Black et al. and Zhang et al. Furr details are provided in Sect The TCs considered in 10 were intense and rapidly intensifying at time when vertical wind profile was imposed. In current study we will consider, inter alia, weaker, but still mature TCs. Finally, our additional experiments now exhibit various rates of intensification just before vertical wind is imposed. We did not, however, find a sensitivity of subsequent TC evolution in vertical to this preceding intensification rate in our experiments. Thus, various rates of intensification just before vertical wind is imposed will not be considered hereafter. The next section provides an overview of numerical model employed and additional experiments performed, an expanded description of ice microphysics scheme, and values for surface exchange coefficients. In Sect. 3 we compare evolution of quintessential ingredients of 10 s newly proposed framework in different numerical experiments. One experiment with ice microphysics is examined in furr detail in Sect. 4, including an estimate of spindown timescale of simulated TC-vortex based on simple axisymmetric ory. Section 5 contains our conclusions. 2 Model setup and additional experiments 2.1 A brief model description For numerical experiments we employ Regional Atmospheric Modeling System (RAMS), developed at Colorado State University (Pielke et al., 1992; Cotton et al., 2003). The RAMS is a three-dimensional, nonhydrostatic numerical modeling system comprising timedependent equations for velocity, non-dimensional pressure 8 Some significant strides towards determining se coefficients at major hurricane wind conditions have been made recently by Bell et al. (2012).

4 330 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer perturbation, ice-liquid water potential temperature (Tripoli and Cotton, 1981), and mixing ratios of total water and hydrometeors. The experiments are carried out on an f-plane at 15 N and with a horizontal grid spacing of 5 km. The model does not include ocean feedback. The time-invariant sea surface temperature is set to 28.5 C. A standard first-order turbulence scheme developed by Smagorinsky (1963) is used for subgrid-scale mixing, with modifications by Lilly (1962) and Hill (1974) that enhance diffusion in unstable conditions and reduce diffusion in stable conditions. For simplicity, radiative processes are neglected. The bulk aerodynamic formulas are used to calculate momentum fluxes and sensible and latent heat fluxes from sea surface. The values of exchange coefficients are given in Sect We employ eir a warmrain microphysics scheme based on that of Kessler (1969) or RAMS standard ice microphysics scheme (Sect. 2.2). The mixing ratio equations for all prognosed hydrometeors include advection by three-dimensional flow. A more comprehensive description of RAMS, surface interaction parameterisation, and warm-rain scheme is given in Ice microphysics in RAMS The RAMS ice microphysics scheme has eight water categories: vapour, cloud droplets, rain, pristine ice, snow, aggregates, graupel and hail (Walko et al., 1995; Meyers et al., 1997). The liquid phase categories, cloud droplets and rain, may be supercooled. Pristine ice, snow and aggregates are assumed to be completely frozen, whereas graupel and hail are mixed phase categories, capable of consisting of ice only, or a mixture of ice and liquid. All hydrometeor categories except cloud droplets are assumed large enough to fall. Cloud droplets and pristine ice are only categories to nucleate from vapour. All or categories form from existing hydrometeors, but once formed may grow furr by vapour deposition. Pristine ice crystals form from heterogeneous nucleation, homogeneous nucleation, and secondary production that involves splintering of riming crystals. The snow category is defined in RAMS as relatively large ice crystals, which have grown from pristine ice category due to vapour deposition and may continue to grow by riming. Aggregates are defined as ice particles that have formed by collision and coalescence of pristine ice, snow and/or aggregates. Snow and aggregates retain ir identity with moderate amounts of riming, but convert to graupel if amount of riming is large. In addition to forming by heavy riming, graupel can also form by partial melting of snow or aggregates. Graupel is allowed to carry up to half its mass in liquid. If percentage becomes larger, by eir melting, riming or collection by rain, a graupel particle is re-categorised as hail. Hail is formed by freezing of rain drops or by riming or partial melting of graupel. Hail is allowed to be a large fraction liquid and converts to rain when completely liquid. The hydrometeor size distribution in RAMS is represented by a generalised Gamma function. A user specified shape parameter controls width of distribution. Also, a scaling diameter is often specified for a one-moment scheme that is related to mean diameter of distribution, with particular relation depending on chosen spectral parameters. For this study a one-moment scheme is employed for all categories except cloud droplets and pristine ice. A scaling diameter is specified and number concentration is diagnosed using predicted mixing ratio of hydrometeor scheme. A heat budget equation is formulated for rain, graupel, and hail hydrometeors. This allows temperature of a hydrometeor to differ from that of surrounding ambient air temperature due to latent heat release or absorption in hydrometeor, and sensible heating by collisions with or hydrometeors. The temperature of a hydrometeor often differs substantially from that of air, which can significantly influence rates of heat and vapour diffusion, as well as amount of sensible heat transfer that occurs in coalescence of hydrometeors. Collision and coalescence of hydrometeors is governed by stochastic equation derived by Verlinde et al. (1990). Gravitational settling of hydrometeors causes m to fall relative to air. Terminal velocities increase as a power of droplet diameter, and are based on empirical data. Pristine ice has very small fall speeds. Snow crystals fall faster than pristine ice, but still relatively slowly. Aggregates are large crystals that have moderate fall speeds. Graupel and hail have high fall speeds. Sedimentation in RAMS uses a Lagrangian scheme to transport mixing ratio from any given grid cell to a lower height in vertical column, so that a proportion is transferred to lower adjacent grid cell. 2.3 Modification of surface exchange coefficients Deacon s formula for dependence of drag exchange coefficient C D on wind speed is given by C D = V 1, (1) with V 1 being wind speed in m s 1 at lowest model level (here: 49 m). In 10 we used Deacon s formula toger with C K = C D. For reference, this formula furnishes values of exchange coefficients of , , and for 10 m s 1, 25 m s 1, and 50 m s 1, respectively. Zhang et al. (2008) found that The exchange coefficient of enthalpy flux shows no significant dependence on wind speed up to hurricane force with a value of and that The average ratio of C K /C D values is 0.63,.... We refore use se values and set C K = = constant (2) and C K /C D = (3)

5 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer 331 Table 1. Overview of experiments that are considered in this study. The experiments and 10 are described in detail in 10. In column C K, Deacon denotes that Deacon s formula (see Sect. 2.3) is used to determine exchange coefficients. The last column gives TC s intensification rate just before vertical is imposed. Experiment initial C K C K /C D microphysics preceding int. intensity [m s 1 ] [m s 1 /12 km] rate [m s 1 /h] Deacon 1 warm Deacon 1 warm Deacon 1 warm warm warm Deacon 1 ice Deacon 1 ice Experiments that employ se values are referred to as below. Note that Deacon s formula and C K /C D = 1 furnishes values of C K and C D that, for V 1 = 50 m s 1, are approx. 2.7 and 4.2 times higher, respectively, than corresponding values. 2.4 Summary of experiments A summary of experiments examined in this study is given in Table 1. We refer to experiments that employ same parameterisations as in 10, i.e. warm rain and Deacon s formula for exchange coefficients (with C K /C D = 1), as. The experiments employ warm rain also. Experiments that include ice microphysics are referred to as. experiments use Deacon s formula with C K /C D = 1. Besides modifications that are mentioned explicitly, experimental setup is same as in 10. The profile employed in this study has a sine structure in vertical with zero winds at surface and maximum easterly winds at 12 km and above. We will follow convention of TC community to define vertical wind as vector difference between winds at upper and lower levels. Here, we use vector difference between 12 km and surface. The magnitude is thus given in m s 1. Unless orwise noted, we will consider TCs in vertical wind with a magnitude of 15 m s 1. The profile is imposed at a high intensity 9 of m s 1, after TCs have spun up in quiescent environment. These experiments are referred to as,, and, respectively. The intensity at time when is imposed will be referred to as initial intensity below. The conventions used in this study follow those in 10. Experiment is 15mps case of 10 and constitutes our reference experiment. We have performed experiments with a weaker initial intensity of 54 m s 1 also, referred to as 54 and 9 Our storm intensity metric is maximum azimuthallyaveraged tangential wind speed at 1 km height. 54. These experiments use same spinup runs as respective experiments with initial intensity of m s 1, but with vertical imposed earlier during intensification. Furrmore, an experiment has been performed with 10 m s 1 vertical ( 10 ) which will be compared briefly to 10mps case of 10 (here: 10 ). 3 Assessing robustness of new framework We shall focus on key features of 10 s new framework for intensity modification in vertical wind : vortex tilt, occurrence and location of SBC, flushing of inflow layer with low-θ e air, ensuing depression of inflow layer θ e, and associated weakening of TC. The general characteristics of se key features will be found to be common in all experiments. As can be expected, differences arise in specific characteristics of se key features. For some of se differences it is very difficult to establish causal link to changes in experimental setup. Most prominently, differences between evolution of TCs in and are partly due to enhancement of downdrafts by ice microphysics (Sect. 3.7), but very likely due also to changes in radial profile of swirling winds at time when vertical wind is imposed. Disentangling individual contributions requires a more complete understanding of processes at work, and extended numerical experimentation and diagnostic analyses, preferably in an ensemble-based framework. A more comprehensive examination of such differences is thus deferred to future research. 3.1 Importance of radial profile of swirling winds Impact on resiliency of TC-like vortices It is generally believed that presence of vertical wind increases interaction between a TC and dry environmental air (Riemer and Montgomery, 2011, and references

6 332 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer rein). Based on a simple kinematic model, Riemer and Montgomery (2011) argue that a TC with a broad radial profile of swirling winds should have a stronger ability to isolate itself from detrimental interaction with dry environmental air than a smaller-scale TC. Furrmore, radial profile of swirling winds has a profound impact on dynamic resiliency of TC-like vortices, i.e. ability to maintain vertical coherence in presence of differential advection by vertical flow (e.g., Jones, 1995; Reasor et al., 2004). These studies investigated resiliency of initially barotropic, dry vortices and are reviewed briefly below. Jones (1995) examined vortex evolution in terms of formation and subsequent interaction of potential vorticity (PV) anomalies. PV anomalies were defined as deviations from azimuthal mean. Due to differential advection by vertical flow, PV anomalies representing tilt of vortex form at lower and upper levels. These anomalies mutually interact through vertical penetration of ir induced quasi-horizontal circulations, causing vortex to precess. This precession helps vortex to counteract differential advection by vertical wind. The vertical interaction of se PV anomalies depends on Rossby penetration depth. The penetration depth increases with strength of background rotation and with horizontal scale of interacting anomalies 10. Jones noted that it is not entirely clear how to quantify penetration depth for a tilted TC-like vortex but concluded that intense and broad vortices are more resilient than ir weaker, smaller-scale counterparts. Reasor et al. (2004) re-visited problem of vortex resiliency and re-alignment using VRW concepts and models. Their results are in qualitative agreement with Jones s finding that vortex (and environment) parameters that increase penetration depth improve resistence of a vortex to tilting by an imposed vertical flow. In addition, Reasor et al. demonstrated that vortex precession is not only element in resiliency of TC-like vortices. An inviscid damping mechanism of vortex-tilt mode exists, associated with PV mixing at critical radius of near-discrete VRW that represents vortex tilt. The critical radius is typically located in skirt region of vortex, i.e. in region of small PV values outside of high PV values in inner core (approx. outside km in 1. The inviscid damping mechanism depends on radial gradient of skirt PV at critical radius (Schecter and Montgomery, 2003). Inviscid damping, and thus re-alignment of vortex, occurs when radial PV gradient in this region is negative. The damping rate increases with magnitude of gradient. For a positive skirt-pv gradient, a tilt instability may occur. The results of Reasor et al. clearly demonstrate that vortex resiliency may crucially depend on radial profile of swirling winds. 10 The penetration depth increases also with a decrease in static stability. -4 vorticity [10 s -1-1 ], wind speed [ms ] vorticity in 10-4 s -1 radius [km] radius [km] ( Radial profiles of azimuthal mean 2 km (thin) and azimuthal mean tangential wind at 1. ( Radial profiles 1. of ( azimuthal Radial profiles mean vorticity of azimuthal at 2 km mean (thin) vorticity and azimuthal at 2 km mean (thin) tangential wind a radiusand of maximum azimuthal winds atmean 1 km height tangential (thick) at wind time when at vertical radius wind of ismaximum imposed in 54 radius of maximum winds at km height (thick) at time when vertical wind is imposed in CBLAS (re, winds at(blu, 1 kmand height (grey), (thick) respectively. at ( time Radial when vorticity vertical profiles as wind ( but zoomed is in on (re, skirt imposed (blu, regionand between in 50 km(grey), and 100respectively. km. ( Radial vorticity profiles as in ( but zoome 54 (re, (blu, and (grey), on skirt region respectively. between 50( km and Radial 100vorticity km. profiles as in ( but zoomed in on skirt region between 50 km and 100 km. The radial profile of swirling 27 winds has been confirmed to play a role in intensity evolution of vertically ed TCs in idealised, moist numerical experiments (Wong and Chan, 2004). In se experiments weakening of smallerscale TCs is found to be more pronounced than that of ir broader-scale counterparts. Wong and Chan based ir interpretation of this difference in intensity evolution on results of Jones (1995) derived 29from dry TC-like vortices. To us, however, it is not clear what underlying processes are that govern intensity evolution in Wong and Chan s experiments. In particular, role of moist processes and/or associated secondary circulation remains unclear. In real atmosphere, an indication of a higher susceptibility of smaller-scale TCs to vertical has been found by DeMaria (1996) based on a regression analysis Diagnosed radial vortex structure in our experiments Because radial profile of swirling winds may play a prominent role in evolution of TCs in vertical wind, we begin examination of our experiments with

7 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer intensity [ms ] -1 intensity [ms ] -1 intensity [ms ] -1 intensity [ms ] ( Intensity time 2. series Intensity for time seriesno- for experiment (re, 2. ( Intensity time series for no- experiment (re, 54 (light 54 re, (light re, (re, (dark re, 54 (light (dark re, no- re, (dark re, experiment (blu, 54 (light blu, and no- experiment (blu, (dark blu. The colour-coded arrows denote time when vertical wind 54 (light blu, and (dark blu. The colourcoded arrows denote time when vertical wind is imposed in respective experiment. As in is imposed in respective no- experiment. experiment ( As in (blu, (, but for 54 (light no- blu, experiment and (re, (dark (dark blu. re, The 10 colourcoded arrows (light re, no- experiment (black),, but denote for time (dark grey), and no- whenexperiment vertical (re, wind 10 (light grey). ( Time series of difference between intensity in (dark is imposed re, 10 in (light respective re, experiment. no- ( As in 54 (light re, (dark re, 54 (light blu, and (dark blu and respective no- experiment. Time 0 h denotes (, but time for when experiment vertical (black), no- wind experiment (dark is imposed grey), and (re, in 10 respective (light grey). (dark experiment. re, Time series 10 ( of As in difference (, (light butre, for between (dark no- re, 10 (re, (dark grey), intensity and 10 in 54 (light grey). re, (dark re, 54 (light blu, and (dark blu and experiment (black), (dark grey), and 10 (light grey). ( Time series of difference between respective no- experiment. Time 0 h denotes time when vertical wind is imposed in intensity in 54 (light re, (dark re, 54 (light blu, and (dark blu and respective experiment. As in, but for (dark re, 10 (re, (dark grey), and comparison of vortex structure at time when vertical Corresponding to smaller radius 10 of maximum vorticity, respective no- (light grey). experiment. Time 0 h denotes time when vertical wind is imposed in respective wind is imposed. The radial, azimuthal-mean profiles RMW is smaller (located at 30 km) than in of swirling experiment. winds( at this As in time (, are butillustrated for in (dark1. re, In 10 and (re, also. (dark grey), and 10 (light grey)., radius of maximum winds (RMW) is found As discussed above, resiliency of TC vortex may at 40 km ( 1. The vorticity maximum is s 1 crucially depend on gradient of (potential) vorticity at at a radius of 20 km. This vortex structure is very similar as in critical radius of (near-discret VRW mode that represents vortex tilt. The critical radius is found where (shown in 4 in 10) 11. For weaker TC in 54, vorticity structure outside a radius of 35 km azimuthal propagation of this VRW, i.e. vortex precession, equals speed of swirling winds. The precession is almost identical to. Inside this radius, vorticity is virtually constant with a value of approx s 1. rate, and thus critical radius, in our experiments is diffi- 28 The corresponding RMW is found at 48 km. The initial radial cult to determine. After vortices have re-aligned, a short structure of TC in 54 is very similar (not shown). precession period of 2 3 h is indicated in all experiments The vorticity structure of TC in exhibits some (see 4 below 12 ). Using values of axisymmetric notable differences as compared to warm-rain experiments and. The vorticity maximum is timate of critical radius is n km. swirling winds at 1 km, as depicted in 1a, our rough es- found inside a radius of 10 km with values of s 1, In, vorticity gradient is near-zero between 50 km i.e. approx. 60 % higher than in. Radially outside 30 and 65 km while in and 54 gradient is of this maximum, high vorticity values decrease rapidly. negative and of large magnitude ( 1. Between 65 km and 100 km radial vorticity profiles are broadly similar. At larger radii (not shown) average vorticity gradient is 11 A potential impact of barotropic instability associated with reversal of radial vorticity gradient in inner core on intensity evolution of ed TCs in our experiments is arguably negligible (see Sect. 3.1 in 10). 12 Note that temporal resolution of data in 4 is 1 h. It is thus most likely that vortex precession is undersampled.

8 334 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer positive in 54 (between 120 km and 200 km) and (between km). In contrast, in, vorticity decreases monotonically out to 200 km radius. It is questionable, however, wher se differences at a radius considerably larger than our estimate for critical radius play a role for TC-vortex evolution in our experiments. From discussion in this subsection it is clear that differences in evolution of TCs when interacting with vertical flow in various experiments potentially arise due to differences in radial vorticity profiles that exist before is imposed. The weaker vortices in 54 and 54, as well as smaller-scale vortex in, can be expected to be more susceptible to tilting than ir stronger, respectively broader-scale counterparts in and. In, susceptibility to tilting is potentially enhanced by near-zero gradient of skirt vorticity inside of 65 km. In Sect. 3.3 it will be shown that tilt evolution is broadly consistent with se expectations. Furrmore, based on results of Wong and Chan (2004), summarized at end of Sect , a more pronounced intensity decrease in can be expected due to smaller radial scale of vortex alone. The latter point needs to be borne in mind when attempting to attribute differences between and to ir different representation of cloud microphysical processes. 3.2 Intensity evolution An overview of intensity evolution in our experiments is presented in 2. First, a brief account of intensity evolution in quiescent environment, i.e. without vertical, is given. The intensity evolution in is described in some detail in 10. In ( 2, incipient TC slowly intensifies to 25 m s 1 in first 20 h. A period of rapid intensification ensues during which TC reaches an intensity of 53 m s 1 at 33 h. In subsequent 20 h, TC consolidates and slightly intensifies to 56 m s 1. Then, TC continues to intensify at a moderate rate until it reaches a quasi-steady intensity of m s 1 at 80 h. In ( 2, TC intensifies to approx. 40 m s 1 at 30 h after a short gestation period. Very rapid intensification ensues and intensity reaches 90 m s 1 at 50 h. The maximum, quasi-steady intensity of m s 1 is reached around 72 h. In all experiments, intensity decreases after vertical wind is imposed. As in 10, all TCs are resilient to detrimental impact of vertical wind. After a period of weakening TCs re-intensify; particularly rapidly in The re-intensification process in this experimental configuration is discussed in some detail in 10 (ir Sect. 6). 13 Because focus of this study is on structural changes of TCs during weakening phase, this experiment was discontinued at 84 h. To facilitate intercomparison of intensity evolution in various experiments, intensity difference from respective no- experiment is presented in 2c, d. Time 0 h in se figures denotes time when vertical wind is imposed in respective experiment. In all warmrain experiments ( 2, characteristics of this relative weakening are similar in first 20 h. The only exception being that weakening in 54 is delayed by 4 h. This detail will be examined in Sect After 20 h, experiments with weaker TCs ( 54 and 54 ) continue to weaken. In contrast, maintains its intensity difference for next 20 h and re-intensifies. Based on se plots alone it might refore be concluded that weaker storms are more susceptible to. However, this is not necessarily case here. Note that 20 h after is imposed in 54 and 54 respective reference TCs in a quiescent environment are still rapidly intensifying. In contrast, reference TCs in and intensify only slowly 20 h after vertical wind is imposed. Thus, differences in relative intensity evolution partly arise due to differences in contemporaneous evolution of reference TC. This brief discussion illustrates one of inevitable challenges to interpreting different TC simulations in vertical wind. The comparison of and experiments is less complicated because intensity evolution of reference runs in quiescent environment is similar ( 2b,. A comparison of intensity evolution in 10 and, respectively, clearly shows that TCs in experiments are more susceptible to than ir counterparts in warm-rain experiments. The differences between relative weakening in 10 and 10, i.e. experiments with imposed vertical of 10 m s 1, is on average approx. 10 m s 1 before 16 h, and on average approx. 5 m s 1 between 16 h and 36 h ( 2. After this time, it is no longer evident that weakening in 10 is more pronounced than in 10. For 15 m s 1, difference in intensity evolution between ice and warm-rain experiments is striking. The maximum relative weakening in is 60 m s 1 ( 2. The TC reaches a minimum intensity of 35 m s 1 ( 2. For, respective values are 25 m s 1 and 63 m s 1. Notwithstanding this distinct intensity evolution, it will be shown below that structural changes in and are very similar. In particular, pronounced weakening in is associated with by far most significant depression of inflow layer θ e (Sects. 3.6 and 4.1). The evolution in is thus consistent with results of 10, i.e. -induced frustration of inflow layer θ e plays a crucial role in intensity evolution in. Furrmore, it will be argued in Sect. 4.2 that this rapid weakening is consistent with frictional spindown of an axisymmetric vortex due to divergence above inflow layer associated with a significant reduction of inner-core convective mass flux.

9 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer tilt [km] tilt [km] 3. ( Time series 3. ( of Time 3. tilt Time series magnitude series of of for tilt tilt magnitude 54 (light for re, 54 (light (dark re, re, (dark (dark re, re, 54 (light 54 blu, (light 54 and blu, (light blu, (dark blu. Time 0 h denotes time when vertical wind is imposed in respective experiment. Vortex tilt is defined as vector difference and (dark blu. Time 0 h wind is imposed in respective between vorticity and centroids (dark at 10 km blu. and Time 1 km 0 height. h denotes For visual time clarity, when vertical 3 h running wind mean is of imposed time in series respective is shown. ( As in ( experiment. Vortex tilt is defined as vector difference between vorticity centroids at 10 km and 1 km but for experiment. (dark re, 10 Vortex tilt (light is defined re, as vector (dark grey), difference and 10 between (light vorticity grey). Note centroids that at 10 tilt kmmagnitude and 1 kmfor goes off scale between 33 height. h andfor 38visual h reaching clarity, amaximum 3 h runningvalue meanof 195 time km (not seriesshown). is shown. As in but for (dark height. For visual clarity, 3 h running mean of time series is shown. ( As in ( but for (dark re, 10 (light re, (dark grey), and 10 (light grey). Note that tilt magnitude for re, 10 goes off (light re, scale between 33 (dark grey), and h and 38 h reaching a 10 maximum (light grey). Note that tilt magnitude for value of 195 km (not shown). goes off scale between 33 h and 38 h reaching a maximum value of 195 km (not shown). tilt direction [degree] tilt direction [degree] tilt direction [degree] tilt direction [degree] tilt direction [degree] tilt direction [degree] Time series 4. of Time 4. tilt Time series direction series of offor tilt tilt direction (, for for (, (, 54 (, (, (, 54 (, 54 (, 54 (, 54 (, (, 54 (, and (, 10 (, (. Time 0 h denotes time when vertical wind is imposed in respective experiment. Vortex tilt is defined as vector difference between and 10 and 10 (. Time (. Time 0 h 0denotes h denotes time timewhen vertical wind is is imposed imposed in in respective respective experiment. vorticity centroids at km and 1 km height. Dashed line denotes 3 h running mean. Note that temporal resolution experiment. (1 h) of data is too coarse to resolve Vortex tilt is defined as vector difference between vorticity centroids at 10 km and 1 km height. Dashed Vortexatilt putative is defined high-frequency as vector precession differenceof between TC vortex. vorticity centroids at 10 km and 1 km height. Dashed line denotes 3 h running mean. Note that temporal resolution (1 h) of data is too coarse to resolve a line denotes 3 h running mean. Note that temporal resolution (1 h) of data is too coarse to resolve putative high-frequency precession of TC vortex. a putative high-frequency precession of TC vortex. 3.3 Evolution of vortex tilt Following 10, tilt of vortex is defined here as vector difference between vorticity centroids at 10 km and 1 km height. Details on calculation of vorticity centroids are given in 10. Here, tilt magnitude and tilt direction in our experiments are depicted in Figs. 3 and 4, respectively. A detailed examination of tilt evolution in was given in Sect. 5.1 of 10. There, evidence was presented that tilt evolution is governed to zero order by asymmetric-balance dynamics. The TC in settles 30

10 336 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer into a quasi-equilibrium tilt direction to down-left (south) shortly after is imposed (approx. within 3 h). A quasi-equilibrium tilt direction may be achieved when cyclonic precession of tilted vortex cancels differential advection by vertical flow. This quasiequilibrium vortex tilt can be described in a first approximation by balanced dynamics of an initially barotropic, dry TC-like vortex (Jones, 1995; Reasor et al., 2004). In, tilt amplitude decreases while maintaining quasi-equilibrium tilt direction. The TC virtually re-aligns within approx. 24 h, i.e. after this time tilt amplitude is comparable to tilt amplitude of TC in no- benchmark experiment (see 5 in 10). Once tilt amplitude has decreased considerably, a high variability in tilt direction ensues, indicative of a high-frequency precession of vortex ( 4. Figures 3 and 4 demonstrate that general characteristics of tilt evolution are similar in all of our experiments in first h after vertical wind is imposed. All TCs are resilient during this time and tilt direction is predominantly to South (180 ). In, maximum tilt magnitude, as well as temporal tilt evolution, is very similar to that of. The only exception being that local maximum at 23 h is more pronounced and, reafter, tilt magnitude remains 3 5 km larger. As can be expected from discussion in Sect. 3.1, weaker TCs in 54 and 54 clearly exhibit a larger tilt magnitude in first 24 h than more intense TCs in,, and. Maximum tilt amplitudes reach 40 km in 54 and 30 km in 54. Both TCs eventually re-align. The most striking feature in tilt evolution is disruption of TC vortex after 30 h in ( 3). Until this time TC tends to re-align slowly: local tilt maximum and minimum at 25 h and 30 h, respectively, are smaller than ir respective predecessors at 9 h and 15 h. At 30 h, intensity has decreased by over 30 m s 1 as compared to time when vertical wind is imposed and has reached smallest absolute value in all experiments (approx. 35 m s 1, 2). Based on discussion in Sect. 3.1, it is plausible that significantly weakened TC can no longer withstand differential advection associated with vertical wind. Note that distinct weakening in first 20 h precedes disruption of TC by more than 10 h. After 30 h, TC remains as a coherent entity with smaller vertical extent: tilt as inferred from vorticity centroid at 9 km height instead of 10 km height does not exceed 35 km (not shown). Arguably, survival as a vertically less extensive system allows for rapid re-intensification of TC after inflow layer θ e values have recovered (Sect. 4.1). The tilt magnitude in 10 remains below 10 km and quickly reduces to values smaller than 6 km after 12 h. Despite this small tilt magnitude a sourly tilt direction is preferred until late in experiment. Although evolution of tilt magnitude is similar in 10, tilt direction in 10 exhibits more variability after 30 h when tilt magnitude is small (not shown). 3.4 SBC formation and downward flux of low-θ e air into inflow layer A metric for downward flux of low-θ e air into inflow layer (DFX) has been defined in 10 (ir Sect ) as 14 DFX w θ e, (4) where w denotes downward vertical motion and θ e perturbation from azimuthal mean of θ e. The quantity DFX is evaluated at 1.5 km, approximate top of axisymmetric inflow layer. The time-averaged structure of SBC, represented by low-level upward motion, and distribution of DFX shortly after time when vertical wind is imposed is depicted in 5. In this early stage of evolution, general structure of SBC and distribution of DFX is consistent in all experiments. The SBC forms in downright quadrant 15 extending radially outwards to km. Small to moderate DFX values occur over a broad, banded region downwind of SBC, from down quadrant through down-left, and into up quadrant. In all experiments, azimuthal vertical cross-sections (as 18 in 10, not shown her indicate that associated downdrafts form underneath helical updrafts of SBC. It is of interest to note that SBCs in 54,, and 10, respectively, extend azimuthally furr into up quadrant than ir counterparts in,, and 54. In former experiments, tilt direction at early times exhibits a greater down (westwar component than in latter experiments ( 4). Thus, low-level vorticity anomaly associated with tilted vortex can be expected to extend into up quadrant. 10 have shown evidence that frictional convergence due to low-level vorticity anomaly associated with tilted vortex contributes to forcing of SBC. The correlation of location of SBC formation with tilt direction in our experiments presented here provides furr support for 10 s interpretation. 14 Our downward-flux metric DFX is virtually identical to that part of flux term θ e w for which w is negative (see 10, ir Sect , for details). 15 To describe azimuthal location of relevant features in this study following convention is used: First, centerline of azimuthal location is given with respect to vector. Then, azimuthal extent is given, e.g. quadrant or semicircle. For example, let 0 denote north and let vector point to west (270 ). Then, down-right is at 0 and down-right quadrant denotes region between 315 and 45. Note that this convention differs somewhat from one that is frequently used in TC community.

11 M. Riemer et al.: Thermodynamic impact of vertical wind on inflow layer f) fluxtext of 1 θe for, DFX (colour, in 0.1 Kms, see definition), top(colour, of inflow axisymmetric 5. text Downward flux of θate, DFX in 0.1layer, Kms 1,defined see text foras definition), at top 5. Downward flux of θe0, DFX (colour, in 0.1 K5.mDownward s 1, see definition), at top offor axisymmetric 5. Downward flux of θe0, DFX (colour, in 0.1 Km s, see text forupward definition), atcontour: top of km, 1 axisymmetric inflow layer, as 1.5 km, and low-level motion 0.25,and thick contour: 1 msaveraged, inflow (thin layer, defined as 1.5ms low-level upward motion (thin contour: 0.25 ms 1, th 1.5 km, and low-level upward motion (thin contour: 0.25 m defined s 1, thick contour: 1 m s 1, averaged from km height) both from 1, averaged from 1.25 km -motion 2 km both averaged 1 h - 6m hfrom after averaged 1.25 km - 2 km averaged 1 h - 6arrow h after vertical is im. The layer, defined as 1.5for km, low-level upward contour: 0.25 s54 1, thick contour: s,from 1 6 h afterinflow vertical is imposed (and, height) ( (thin, vertical (, imposed and both (1form, ( 54, (from isheight) 10 54is, in 10 arrow 54 direction, of and 10. The arrow indicate, scale., The 54,indicates, indicates direction of deep-layer. The horizontal km. 54,, and averaged from km height) both averaged from 1 6 h after vertical is imposed for (, ( deep-layer. The horizontal scale is in km deep-layer. The horizontal scale is in km, ( 54, ( 54, (, and ( 10. The arrow indicates direction of search is needed to clarify formation mechanism of se A distinct maximum of The DFXhorizontal is found scale in isup deep-layer. in km. quaddowndrafts, as well as relative importance of confined rant close to eyewall. This maximum is most pronounced DFX maximum and broad region of moderate DFX for in experiments ( 5e,. In 10, this DFX maximum was not given special attention. A pronounced TC intensity evolution. maximum in up quadrant occured in 20mps case of 10 (ir furr noted a localized region of downdrafts in up 1region close to 3.5 Vortex-tilt induced dynamic instability? 5. text Downward flux of θate, in 0.1 Kms, see text for definition), at top of axisymmetric of θe, DFX (colour, in 0.1eyewall Kms 1, see for definition), top(colour, of axisymmetric after TCs indfx 10mps and 15mps cases 31 1 and low-level upward 1 inflow (thin layer,contour: defined 0.25 as 1.5ms km, (thin contour: 0.25 ms 1, thick contour: 1 ms 1, km, and low-level upward motion 1 ms motion, discussion). have re-aligned (ir 11a, thick andcontour: associated averaged from 1.25 km 2 km height) both averaged from 1 h 6 h after vertical is imposed for, - 2 km height) both averaged from 1 h - 6 h after vertical is imposed for, A non-linear, Kelvin-Helmholtz type instability in inner The DFX maximum is located at downwind end of,,,, and. The arrow indicates direction of N54, 54,, and 10. The arrow indicates direction of core of a tilted, dry TC-like vortex has been found in a nubanded region of positive DFX values. A pronounced θ dee deep-layer. The horizontal scale is in km orizontal scale is in km merical experiment by Reasor et al. (2004, ir Sect. 5. In pression is found at top of inflow layer in this region ir experiment, this instability contributed to enhanced lo(not shown). Therefore, large negative values of θe0 contribute calized, three-dimensional mixing. Such mixing is one pathto high values of DFX (Eq. 4). However, downward motion into inflow layer is particularly strong in this region also33 way to dissipate kinetic energy in TC s inner core. The role of this mixing for intensity evolution of TCs in ver(not shown). A preliminary examination of distributions tical wind is hirto unexplored. of vertical motion, hydrometeors, and θe suggests that The necessary condition for such an instability is that downdrafts close to eyewall may form by evaporation of gradient Richardson number, R, drops below unity (Abarprecipitation falling out of tilted eyewall. To us, however, banel et al., 1986). Here, R is calculated as it is not clear wher more pronounced localized maximum in experiments is solely due to inclusion of ice microphysics or to what extent differences in radial structure of TC vortex contribute. Clearly, more rer = N 2 /((du/dz)2 + (dv/dz)2 ), (5) 10 10