Idealized Numerical Simulations of Hurricane–Trough Interaction

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Idealized Numerical Simulations of Hurricane–Trough Interaction SYTSKE K. KIMBALL Department of Earth Science, University of South Alabama, Mobile, Alabama

JENNI L. EVANS Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania (Manuscript received 24 August 2001, in final form 24 January 2002) ABSTRACT A three-dimensional, nonhydrostatic, fine-resolution model, with explicitly resolved convective processes, is used to investigate the evolution of (a) a hurricane in two sheared flows, and (b) a hurricane interacting with four different upper-level lows. The negative impact of vertical shear on hurricane intensification is confirmed. The hurricanes display asymmetries that are most pronounced in higher shear flow. In both shear cases, the hurricane asymmetries seem to be related to a single upper-tropospheric outflow jet forcing convective activity below its right entrance region. Weak subsidence is confined to only part of the eye. Less eye subsidence leads to less inner-core warming, and hence a smaller fall in central surface pressure. A hurricane in zero flow (control) displays subsidence in the entire eye leading to a symmetric storm with a deep, strong warm core temperature anomaly and lower central surface pressure. In the weak shear and control cases, the radius of maximum wind (RMW) contracts as the storms intensifies via the mechanism of ‘‘symmetric intensification.’’ In the high-shear case the RMW and intensity remain almost steady. When hurricanes interact with troughs, asymmetries are evident in the hurricanes and their RMWs expand as the storms slowly intensify. During the interaction, the troughs are deformed by the hurricane flow. Remnants of the deformed troughs prevent an outflow channel from developing on the eastern side of the hurricanes, hampering storm intensification in three of the four cases. In the fourth case, a strong and shallow trough merges with the hurricane causing a three-dimensional split of the trough, reduction of vertical shear over the vortex, followed by rapid intensification and RMW contraction. This vortex reaches the highest intensity of all four trough-interaction cases and comes close in intensity to the comparable no-trough case.

1. Introduction Over recent years, hurricane track forecasts have improved but intensity forecasting has lagged substantially behind, reflecting the difficulty of this forecast challenge. Hurricane intensity is controlled by many factors, making it difficult to isolate the dominant processes in the evolution of a system. One of the most challenging factors is hurricane interaction with upper-tropospheric systems (e.g., Molinari and Vollaro 1990; Molinari et al. 1995; Molinari et al. 1998; Bosart et al. 2000; Hanley et al. 2001). Many synoptic and mesoscale disturbances coexist and interact with tropical cyclones in the atmosphere. The greatest potential for such interactions is found in the upper levels of the tropical cyclone due to the low inertial stability of the tropical cyclone outflow layer. Systems with which tropical cyclones may interact include midlatitude troughs, upper-level cold Corresponding author address: Dr. Sytske Kamminga Kimball, Department of Earth Science, LSCB 136, University of South Alabama, Mobile, AL 36688. E-mail: [email protected]

q 2002 American Meteorological Society

core lows, and tropical upper-tropospheric trough cells. For simplicity, the general term trough will be used in this paper to collectively refer to all such upper-level systems. Trough interaction has lead to sudden and rapid intensification of the tropical cyclone in some cases, while in others weakening (e.g., Lewis and Jorgensen 1978) or no change in intensity occurred. In intensification cases, upper-level eddy angular momentum flux forcing (e.g., Molinari and Vollaro 1989), enhanced upper-level divergence (Bosart et al. 2000; Shi et al. 1990), or superposition of potential vorticity (hereafter PV) anomalies (Molinari et al. 1995, 1998) were possible intensification mechanisms. Sometimes it is difficult to distinguish between these effects and other external influences: for example, the case of a hurricane, interacting with a midlatitude trough, intensifying over warm SST, or weakening because of large vertical wind shear associated with the trough. Because of its complex nature, hurricane–trough interaction is not well understood and poorly predicted. An additional complexity involves the vertical wind shear that accompanies upper-level troughs. On its own,

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vertical shear has an adverse effect on hurricane intensification, but during trough interaction its effects can be reduced by wave-breaking of the trough or diabatic erosion of the upper-level PV anomaly (Molinari et al. 1995; Molinari et al. 1998). Over the last decades, many researchers have investigated dynamical and thermodynamical mechanisms that cause tropical cyclones to intensify as a result of trough interactions. A large portion of these studies were observational. (e.g., Sadler 1976, 1978; Molinari and Vollaro 1989, 1990; Molinari et al. 1995; DeMaria et al. 1993; Hanley 1997, 2000, 2001; Bosart et al. 2000). Modeling efforts have included balanced vortex studies with hydrostatic, axisymmetric models (e.g., Challa and Pfeffer 1980; Pfeffer and Challa 1981; Holland and Merrill 1984), and hydrostatic three-dimensional models (e.g., Challa and Pfeffer 1990; Pfeffer and Challa 1992; Shi et al. 1990, 1995, 1997; Challa et al. 1998). No nonhydrostatic, three-dimensional, idealized hurricane–trough interaction modeling studies, with explicitly resolved convective processes, exist in the literature. The present study uses a model with these configurations. An idealized tropical cyclone and idealized upperlevel trough are inserted in an environment with weak vertical shear, over uniform and constant sea surface temperature on an f -plane. In this way, hurricane– trough interaction effects can be isolated, without too serious a departure from reality (e.g., axisymmetry or the hydrostatic approximation in small-scale convective environments). Since no feedback between the ocean and the vortex are possible in this model configuration, ocean upwelling cannot modify the storm intensity. It will also be possible to change the characteristics of the interacting systems and to study the effects of vertical wind shear on the hurricane vortex in isolation. 2. The numerical model and method of initialization The Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model (MM5; Dudhia 1993; Grell et al. 1994) is used with a coarse mesh of 45-km resolution (large enough to keep boundary effects away from the vortex) and two one-way nested domains of 15 and 5 km resolution, respectively. Twenty-four vertical sigma levels are chosen, seven of which are located in the first 1.5 km above the surface of the model. The Coriolis parameter ( f ) defined at 208N (where interactions between hurricanes and upper-level lows may often occur) is held constant, since the topic under investigation is vortex asymmetry and evolution forced by environmental flow. Therefore, asymmetries forced by a variable Coriolis parameter need to be excluded. The underlying sea surface temperature (SST) is uniform and constant, and has been assigned a value of 288C. The nonhydrostatic version of MM5 is used because

vertical accelerations are important in the highly convective region of the tropical cyclone core. The Betts– Miller cumulus parameterization scheme (Betts and Miller 1993) is used on the outer two model domains. It is also switched on for the first 36 h on the finest (5 km) grid to accelerate vortex spinup. The Reisner explicit moisture scheme (Reisner et al. 1993, 1998) and the Blackadar planetary boundary layer parameterization scheme (Blackadar 1979) are applied on all three grids. The horizontal wind profile of the initial, idealized, vortex is prescribed by Fiorino and Elsberry’s (1989) equation with a radius of maximum wind (RMW) of 135 km and a maximum wind of 20 m s 21 . By multiplying the horizontal wind profile with a vertical structure function that decreases monotonically with decreasing pressure (following Baik et al. 1990), the winds are tapered off with height. Temperature and height fields are derived from the wind field using hydrostatic and gradient wind balances. To investigate the complex problem of hurricane– trough interaction, the simplest form of an upper-level trough is chosen: a cold core upper-level low similar to the low pressure system, over the U.S. Gulf of Mexico coastal region, to the southwest of Hurricane Dennis on 30 August 1999. Figures 1a and 1b show the PV field of this upper-level low. PV is given by: PV 5 2vabs · =u/r, where vabs is the absolute vorticity, u the potential temperature, and r the density, and is a measure of the potential to create vorticity by changing latitude and by adiabatically changing the separation between isentropic layers (Hoskins et al. 1985). The PV is conserved under adiabatic and frictionless motion and its usefulness extends in analyzing the evolution of various diabatic flow features (e.g., Molinari et al. 1995; Molinari et al. 1998). The initialization of the idealized lows is similar to that of the hurricane vortex, except that the maximum winds now occur at 200 hPa and taper off with increasing pressure using a modified monotonically decreasing function. Care was taken to ensure that the tropopause structure of the idealized cases was reasonable compared to observations. The design of the idealized vortex and low is presented in more detail in Kamminga (2000). Table 1 summarizes the experiments of this study. Each experiment uses the same initial tropical stormlike vortex, while the upper-level lows differ in intensity and size. The control simulation consists of the initial vortex placed in a zero-environmental flow. In the following two simulations the vortex is placed in a westerly, vertically sheared regime: in experiment LOSHR the vertical shear has a low value of 2.5 m s 21 , in experiment HISHR the shear is increased to 8 m s 21 . The vertical shear in this case is measured at the location of the center of the vortex before the vortex is added to the flow. The vertical shear profiles can be seen in Fig.

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FIG. 2. Vertical wind profiles of all six expts at the center of the vortex at t 5 0 h.

FIG. 1. The PV (in PVU) of Hurricane Dennis and an upper-level low to its southwest at 0600 UTC 30 Aug 1999 (a) at 300 hPa; (b) a vertical crosssection through Hurricane Dennis and the upper-level low, along the dashed line shown in (a).

2. On an f plane, westerly and easterly shear have the same effect on the vortex. In the final four experiments an idealized upper-level low is placed 800 km west of the vortex, illustrated in the PV crosssections in Fig. 3. This configuration is loosely based on Hurricane Dennis (1999). Initially, Dennis is located off the coast of the Carolinas and an upper-level low, slightly larger in horizontal extent than the hurricane, is located over the northern Gulf of Mexico (Fig. 1). This low had been cut off from a large midlatitude trough now located over the New England

region. The horizontal size of the upper low, located about 1300 km southwest of Dennis, was used as a guideline to construct the idealized lows used in this study. The PV maximum of the upper low in both Dennis and the idealized cases is located between 200 and 400 hPa. Both idealized systems are embedded in a low westerly vertical wind shear of 2.5 m s 21 . This allows the systems to approach one another: the hurricane is advected very slowly to the east by weak midlevel flow, while the stronger winds aloft move the upper-level low eastward at a faster rate. Low vertical wind shear was chosen so that the effects from the upper-level low on the storm will dominate the effects of the surrounding environmental flow; weak vertical shear has less effect on tropical cyclones than strong shear, as will be shown in section 3. Furthermore, low shear will allow the systems to approach one another slowly so that they can

TABLE 1. Summary of the experiments. Experiment name Control LOSHEAR HISHEAR LOLOW MIDLOW HILOW DEEPLOW

Experiment description Vortex in quiescent flow Vortex in westerly shear of 3 m s21 Vortex in westerly shear of 9 m s21 Vortex with upper low and westerly shear of 3 m s21 Vortex with upper low and westerly shear of 3 m s21 Vortex with upper low and westerly shear of 3 m s21 As lolow but larger and deeper upper low

Max PV

Depth of 2 PVU isopleth (hPa)

— — — 2 4 6 2

— — — 300 350 410 400

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interact, instead of advecting around one another (Montgomery and Farrell 1993). As mentioned earlier, the intensity and vertical depth of the upper-level low is different in each experiment (Fig. 3): experiment LOLOW has the weakest upper low, MIDLOW a slightly stronger low, and HILOW the strongest low. The low in experiment DEEPLOW has the same maximum PV value of 2 PVU (or PV units, where 1 PVU 5 10 26 m 2 K s 21 kg 21 , Hoskins et al. 1985) as experiment LOLOW, but the physical size of the low is closer to that of experiment HILOW. This way the effects of upper-level low’s strength and size on the hurricane can be distinguished. Figure 2 shows the vertical shear profiles of the upper-low cases at the initial location of the vortex. The vertical shear values range between 4 and 6.5 m s 21 and hence lie between the values of 2.5 and 8 m s 21 used in the shear-only simulations. 3. Vortex evolution Hurricanes, in nature, occur over a wide range of sizes, strengths, and intensities. Intensity is measured in terms of central surface pressure. Hurricane size measures the radial extent of the gale force winds (17 m s 21 ) averaged azimuthally, while strength gives the average wind speed between 100 and 300 km from the cyclone center (Merrill 1984). The radius of maximum winds is a further indicator of the horizontal extent of the tropical cyclone. Relative angular momentum (RAM) is defined as the radius times the azimuthal velocity anywhere on a cylindrical grid centered on the hurricane’s wind center. Time series of these quantities will be presented to illustrate the evolution of the model storms for a range of environmental forcings. To quantify the wind-related parameters—RMW, size, and strength—the wind speed is used to define the storm center: the smallest wind speed coincides with the center. In the simulations, the hurricane maximum wind speed occurs about 500 m above the sea surface; this level is therefore used to determine the wind-related parameters. The circular hurricane is divided into 24 equal azimuths (w). Each variable is determined at each azimuth, obtaining var(w), where var 5 RMW, size, or strength. The final value is obtained by azimuthally averaging. a. The control run The control experiment is used to validate model performance and to provide a comparison case for the remaining experiments. The results of this simulation are described in detail in Kamminga (2000), and demonstrate that the model is capable of simulating a realistic hurricane. The storm intensifies rapidly to an intense category 5 (Saffir–Simpson scale) hurricane (Fig. 4a) reaching its potential intensity or PI (Emanuel 1988) of

FIG. 3. Vertical crosssections of PV (shaded in PVU) and equivalent potential temperature (dashed in K) through the centers of the upper low and vortex at t 5 0 h for (a) LOLOW, (b) MIDLOW, (c) HILOW, (d) DEEPLOW.

905 hPa, and hence makes optimal use of the available thermodynamic energy in its environment. During the first 21 h of the simulation, the control vortex intensifies slowly while the RMW contracts rapidly from 135 to 65 km (Figs. 4a,b). The storm increases in size and strength (Fig. 4b) due to high RAM air moving from large radii towards r 5 30 km (Fig. 5). Weak descent takes place in the eye during this period. During the next 2 days (ending at approximately t 5 72 h) the control storm’s intensification rate increases and exceeds a value of 1 hPa h 21 (Fig. 4a). The storm’s size and strength remain steady (Fig. 4b), while RMW contraction and import of high RAM air gradually slow down and cease at around t 5 69 h (Fig. 5). Strong updrafts occur in the eyewall, between 700 and 250 hPa, forcing thermally indirect subsidence by continuity in the hurricane eye (Willoughby 1998). Weak eye subsidence (around 0.1 m s 21 ) is observed at all levels in the eye of the storm, primarily on the outer edges of the eye adjacent to the eyewall. This subsidence warm-

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FIG. 5. Time series for the control expt of relative angular momentum at 500-m height (shaded, in 310 5 m 2 s 21 , upper abscissa), radius of maximum wind (solid, in km, lower abscissa), and size (dotted, in km, lower abscissa).

ocean feedback in the model configuration is important here, since in reality a stationary hurricane would likely cool the underlying oceanic mixed layer and ultimately reduce its own PI. b. Vertical shear experiments

FIG. 4. Time series for the control expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); and (b) radius of max wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

ing results in a deep, strong temperature anomaly in the eye (with a maximum value of 148C) causing hydrostatic surface pressure falls in the center of the vortex and strong pressure gradients just inward from the RMW. As the vortex intensifies, the Rossby radius of deformation in the inner core, shrinks from 150 to 20 km, and remains comparable to the size of the eye (the RMW shrinks simultaneously from 135 to 25 km; Fig. 4b). Hence, the wind field will adjust to the pressure field. The tangential winds increase radially inward from the RMW, causing the RMW to contract as the vortex intensifies (Willoughby 1998; Shapiro and Willoughby 1982). Around t 5 90 h, the storm reaches its mature stage. The mature hurricane is small, intense, and symmetric with a few, short, rainbands of mostly azimuthal wavenumber 2. The formation of these bands in initially axisymmetric conditions on an f -plane, is caused by numerics and by resolving a circular feature on a square model grid. Asymmetric truncation and roundoff errors introduce small asymmetries in the finite difference equations, which grow as a result of inertial and/or barotropic instability (Anthes 1972). No distinct outflow channels exist, but strong outflow is distributed symmetrically around the center of the storm at upper levels. The absence of surrounding flow allows the storm to make optimal use of the thermodynamic energy available in its environment and to reach its PI. The lack of

As is well documented in the literature (e.g., DeMaria et al. 1993; Merrill 1988; McBride and Zehr 1981; Gray 1968), vertical shear is unfavorable to hurricane intensification. Upper-level troughs (lows) have large values of vertical wind shear associated with them (Fig. 2); therefore, two simulations are performed to investigate the effects from vertical wind shear alone on the initial vortex. Once the simulations have begun the vertical shear is measured, after removing a symmetric vortex, between 0 and 500 km from the vortex center and between the 850 and 200 hPa pressure levels (following operational procedures; e.g., DeMaria et al. 1993). 1) LOSHR The negative effect of vertical shear on hurricanes is confirmed by experiment LOSHR (Fig. 6) where low vertical wind shear of 2.5 m s 21 causes the storm to reach a significantly lower maximum intensity (940 hPa or a weak Saffir–Simpson category 4) than the control vortex (905 hPa). Somehow, the vertical shear inhibits the storm from accessing all of its available thermodynamic energy and reaching its PI (900 hPa). The formation of asymmetries in sheared storms is often held responsible for this (DeMaria 1996; Jones 1995; Frank and Ritchie 1999a,b, 2001). The issue will be discussed further later. During the first 24 h, the storm’s size and strength increase and its RMW contracts (Fig. 6c); this coincides with an import of high RAM air towards small radii (about 40 km) in the storm (Fig. 7). Between t 5 24 and 42 h, RAM-import and RMW-contraction diminish, the size and strength of the vortex remain steady, and intensification rates exceed 1 hPa h 21 . At the mature stage, the LOSHR vortex is not as strong (22.5 m s 21 )

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FIG. 7. Time–radius series for the LOSHR expt of relative angular momentum at 500-m height (shaded, in 310 5 m 2 s 21 ), radius of maximum wind (solid, in km), and size (dotted, in km).

FIG. 6. Time series for the LOSHR expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); (b) vertical shear (solid in m s 21 ) and its tendency (dotted, in m s 21 h 21 ); and (c) radius of maximum wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

as the control vortex, but is of similar size (260 km), as seen by comparing Figs. 4b and 6c. Thus, the mature control and LOSHR vortices have similar size (radius of gale force winds), but the LOSHR vortex has a weaker and broader eye (RMW larger and intensity weaker). Maximum intensification of the LOSHR vortex occurs between t 5 24 and 48 h. Its maximum intensification rate (1.3 hPa h 21 ) is lower than that of the control vortex. Compared to the control case, the mature LOSHR vortex’s warm core temperature anomaly (128C) has a smaller magnitude and shallower vertical extent, and its PV anomaly is broader and shorter. The upper levels of the vortex seem most affected by the westerly shear. Immediately below the outflow layer, between 400 and 250 mb, the winds in the northwest quadrant of the storm have a large outward radial component and small tangential component. This is because the environmental westerlies directly oppose the cyclonic circulation of the vortex and the high inertial stability of the vortex winds prevents the colliding, and hence converging, flow from turning inward. As a result,

the upper-level tangential wind maximum occurs on the opposite side of the storm. The low-level wind maximum of the sheared vortex occurs in the western half of the vortex, as does the rainfall, the low-level upward motion, and the thermally indirect eye subsidence (not shown). In the control case eye subsidence is observed throughout the entire eye. Asymmetric vertical motion drives asymmetric convection (Kurihara 1976) and hence affects the distribution and amount of latent heat release and eye subsidence in the vortex. Less overall subsidence in the eye produces a weaker and shallower warm core anomaly, higher central surface pressure, and weaker low-level wind field than in the symmetric control vortex. A question that remains to be addressed is why the upward motion is concentrated in the western half of the vortex. One possible explanation is the existence of a single strong outflow jet, into the upper-level westerlies, with its right entrance region located over the northern half of the vortex. The Brunt–Va¨isa¨la¨ frequency below 500 hPa in that part of the eyewall is lower than in the southern half of the eyewall. The CAPE (convective available potential energy) is larger in the northern half than in the southern half of the eyewall. This supports the hypothesis (Sadler 1976, 1978; Willoughby 1995) that the outflow jet destabilizes the vortex eyewall below the jet, allowing upward motion and convection to occur in that location. Advection of hydrometeors by the cyclonic tangential winds is a possible explanation for the occurrence of rainwater and rainfall downstream of the jet, in the western half of the storm. No outflow jet can exist on the southeast side of the vortex because upper-level anticyclonic outflow is opposed by the environmental westerlies (Sadler 1976). Since the LOSHR vortex moves relatively slowly (0.5–2 m s 21 ), it is not likely that boundary layer convergence drives the convective asymmetries (Shapiro 1992). 2) HISHR As expected, stronger shear (case HISHR has an even larger impact on the vortex’s size, strength, and intensity

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FIG. 9. Time–radius series for the HISHR expt of relative angular momentum at 500-m height (shaded, in 310 5 m 2 s 21 ), radius of maximum wind (solid, in km), and size (dotted, in km).

FIG. 8. Time series for the HISHR expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); (b) vertical shear (solid in m s 21 ) and its tendency (dotted, in m s 21 h 21 ); and (c) radius of maximum wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

(Fig. 8). Vertical shear of 8 m s 21 is close to the DeMaria et al. (1993) sample mean of Atlantic tropical cyclones, and hence is considered moderate shear. The shear threshold above which no intensification occurs varies; DeMaria and Kaplan (1994) report 10 m s 21 , Zehr (1992) reports 12.5 m s 21 . However, our results are consistent with these findings: the shear remains below both threshold values and the vortex intensifies (slowly). The HISHR vortex is smaller, weaker, and less intense than the LOSHR vortex. The evolution of size and strength are again closely correlated to the import of high RAM air (Fig. 9). From t 5 0–99 h the import of high RAM air coincides with an increase in the size and strength. From t 5 126–204 h high RAM air is exported as the size and strength decrease. The RAM import (and export) occurs primarily at outer radii ($100 km) and hence is not linked with RMW contraction and the mechanism of vortex intensification that occurs in the control and LOSHR vortices (Willoughby 1998). Throughout 204 h of simulation time, the vortex’s central surface pressure remains well above its PI of

907 hPa. Its maximum intensity (973 hPa, or category 2 on the Saffir–Simpson scale) is reached at t 5 144 h. No sign of a mature stage is evident since the intensity of the vortex does not remain steady long enough. The RMW contracts in the first 24 h, but fluctuates between 50 and 75 km for the remainder of the simulation. The asymmetries in the HISHR vortex’s vertical motion, rainfall, and wind fields are more pronounced than in the LOSHR case. No distinct upper-level wind maximum can be seen; all of the upper-level tangential flow is disrupted by the strong environmental westerlies. Temperature anomaly and PV crosssections confirm this: the vortex is shorter, broader, and weaker than in the LOSHR case. Without a strong, deep temperature anomaly, the surface pressure cannot drop sufficiently to support strong low-level tangential winds. The low-level wind maximum is found in the western half of the storm, while the strongest upward motion in the storm core occurs in the northern half of the eyewall. Eye subsidence is weaker and covers less of the eye than the LOSHR case, creating a weaker and shallower warm core anomaly. The rainfall is concentrated in the northern half of the vortex, or to the left of the vertical shear vector, which is in good agreement with observed hurricanes in strong shear such as Olivia (1994) (HRD 2000), Norbert (1984) (Marks et al. 1992), and Gloria (1985) (Franklin et al. 1993), as well as modeled storms (Frank and Ritchie 1999b). Again the location of the convection is related to the location of a single, strong outflow jet to the north of the storm that links into the environmental westerlies. The jet’s right-front entrance region is located over the northern half of the storm and the jet is stronger than in the LOSHR case. Again lower values of the Brunt–Va¨isa¨la¨ frequency and higher CAPE values are seen in the northern half of the eyewall, possibly causing eyewall destabilization, stronger updraft velocities, and the formation of cloud water in the northern eyewall. Advection of hydrometeors downstream to the western half of the eyewall takes longer than in the LOSHR case due to the weaker tangential winds and larger eyewall radius of the HISHR storm. As a result cloud droplets have time to grow into raindrops, large

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FIG. 10. Time series for the LOLOW expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); (b) vertical shear (solid in m s 21 ) and its tendency (dotted, in m s 21 h 21 ); and (c) radius of maximum wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

FIG. 11. Time series for the MIDLOW expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); (b) vertical shear (solid in m s 21 ) and its tendency (dotted, in m s 21 h 21 ); and (c) radius of maximum wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

enough to fall to the ground, before they arrive in the western half of the storm. Rainwater and rainfall are therefore concentrated in the northern half of the storm in the HISHR case. Frank and Ritchie (1999a,b, 2001) concluded that shear contributed more than surface friction to the asymmetries observed in their vortices evolving in westerly and westerly sheared flows. This agrees with the current study: the vortex in larger vertical shear (HISHR), moved at almost the same speed as the LOSHR vortex; but displayed more pronounced asymmetries. Furthermore, an experiment with a vortex in uniform westerlies, moving at about the same speed as the sheared vortices, displayed as few asymmetries as the control vortex (Kamminga 2000). Therefore, low-level convergence is not the forcing mechanism for the asymmetric convection. Another explanation for the asymmetries observed in sheared hurricanes is vortex tilt (DeMaria 1996; Jones 1995). Some tilt is observed in the HISHR vortex (Kamminga 2000), but not to the extent of the dry simulations

performed by Jones (1995), who observed a vertical motion maximum on the right side of the shear vector instead of the left. A distinct midlevel warm anomaly, beneath the PV anomaly of the tilted vortex, is not present. DeMaria’s (1996) and Jones’s (1995) simulations were dry. The presence of moisture and convection in the current simulations makes detection of such an anomaly, and its cause, difficult. No tilt is observed in the LOSHR case, yet it displays asymmetries. It is therefore concluded that vortex tilt is not the cause of the asymmetries observed in the LOSHR and HISHR vortices. c. Hurricane–trough interaction The evolution of the four vortex–trough interaction cases is presented in Figs. 10–13. The initial (t 5 0 to about 24 h) strong intensification rates of all four storms drop when the vertical shear increases due to the approaching upper lows. None of the four cases reach their PI (ranging from 912 hPa for HILOW to 903 hPa for

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FIG. 12. Time series for the HILOW expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); (b) vertical shear (solid in m s 21 ) and its tendency (dotted, in m s 21 h 21 ); and (c) radius of maximum wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

FIG. 13. Time series for the DEEPLOW expt of (a) central surface pressure (solid, in hPa) and its tendency (dotted, in hPa h 21 ); (b) vertical shear (solid in m s 21 ) and its tendency (dotted, in m s 21 h 21 ); and (c) radius of maximum wind (solid, in km), size (dotted, in km), and strength (dashed, in m s 21 ).

LOLOW) in the 204-h (192 h in the DEEPLOW case) simulation time. Cases LOLOW and DEEPLOW are the furthest removed from their PI and reach Saffir–Simpson category 2 status. Case MIDLOW becomes a category 3 storm, and case HILOW a category 4 storm just like the shear case LOSHR. Since the larger-scale environmental shear in each trough case is equal to that of LOSHR a trough interaction will be termed favorable if the tropical cyclone exceeds the intensity reached by case LOSHR (942 hPa). Hanley et al (2001) termed a trough interaction favorable if the sea level pressure begins to fall or starts to fall more rapidly as a result of an interaction. In a modeling study, comparison with the no-trough situation is possible, and hence, one can determine if the trough enhances the storm’s intensification or merely delays it. The above definition indicates that cases LOLOW, MIDLOW, and DEEPLOW experience an unfavorable trough interaction. In HILOW, the trough temporarily delays the intensification of the hurricane (Figure 12a) which ultimately reaches the same maximum intensity

(944 hPa) as LOSHR. Even though the final intensities of these two cases are comparable, the ultimate size and strength of HILOW exceeds the size and strength of LOSHR significantly (compare Figs. 6c and 12c). The HILOW vortex reaches the largest size (478 km) of all seven cases, while the MIDLOW vortex becomes the strongest (40 m s 21 ) vortex of all seven cases. All four trough cases exceed the shear cases in size and strength, but have a lower maximum intensity. In the trough interaction cases both the hurricane and the upper low evolve differently than if they were left to evolve in isolation. Case LOSHR represents the situation where the hurricane evolves in the absence of an upper-level low, since both systems are embedded in 2.5 m s 21 vertical shear. Deformation of the four interacting upper-level lows at t 5 48 h is illustrated in Fig. 14, which shows the centers of the lows at four different levels in the atmosphere. Comparison of these figures shows that the lows evolve quite differently. Two distinct processes, that will be referred to as stretching and rotation, occur to varying degrees in each simulation.

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FIG. 14. Wind fields (shaded and arrows, in m s 21 ) at 400 hPa and t 5 48 h for (a) LOLOW; (b) MIDLOW; (c) HILOW; (d) DEEPLOW. The centers of the upper-level low are indicated by a solid triangle (200 hPa), solid circle (250 hPa), solid square (300 hPa), and cross (400 hPa). The low-level center of the vortex is indicated by a tropical cyclone symbol.

Figure 15 illustrates the stretching process. An initially vertically stacked upper-level low is located to the southwest of a hurricane (Fig. 15a). The hurricane’s anticyclonic outflow advects the low’s upper-level (200 hPa) center to the north, while the hurricane’s cyclonic flow advects the low’s lower-level (400 hPa) center to the south. As a result the low is stretched in a north– south direction, as shown in Fig. 15b. Figure 16 illustrates the process of rotation. Some amount of stretching of the low (in the north–south direction in Fig. 16) has to occur before rotation can take place. The arrows in Fig. 16a refer to the circulation associated with the cyclonic PV anomaly of the low, not the hurricane. The cyclonic circulation around the low’s 400-hPa PV anomaly (black arrow) extends through a depth proportional to its horizontal extent and PV (Hoskins et al. 1985). This induced circulation advects the low’s upper (200 hPa) center to the southwest. At the same time the cyclonic circulation at 400 hPa (gray arrow), induced by the low’s 200-hPa PV anomaly, advects the low’s 400hPa center to the northeast. The result is a more east– west-oriented low as shown in Fig. 16b. This process of cyclonic rotation of a system around itself is analogous to that of a rotating, tilted vortex described by Jones (1995).

Stretching and rotation occur in tandem; the dominating process depends on the relative intensities of the interacting upper low and hurricane; Fig. 17 helps explain this. The dashed arrows in Fig. 17 represent the upper-low circulation, while the solid arrows represent the hurricane flow. Upper-level (200 hPa) flow and the upper-low center (triangle) are represented in gray. Lower-level (400 hPa) flow, the lower-low center (square), and the lower hurricane center (hurricane symbol), are black. In other words, the gray dashed arrow is the 200hPa flow induced by the 400-hPa trough center, while the black dashed arrow is the 400-hPa flow induced by the 200-hPa low center. The black (gray) solid arrow represents the hurricane’s 400-hPa (200 hPa) flow. Once stretched a little by the vortex, rotation of the low about itself begins. The latter is indicated by the dashed arrows in Fig. 17. The solid arrows, on the other hand, illustrate the impact the hurricane has on the low (or stretching, see also Fig. 15, and the discussion in the previous paragraph). The hurricane and low circulations oppose one another at the upper-low center (triangle and gray arrows), as well as at the lower-low center (square and black arrows). Depending on the relative strengths of the low (dashed arrow) and hurricane (solid arrow), one or the other flow dominates.

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FIG. 15. Schematic illustrating the stretching process. Three centers of the upper-level low are indicated by a triangle (200 hPa), square (300 hPa), and circle (400 hPa). The center of the vortex is indicated by a tropical cyclone symbol. The light arrow indicates the hurricane’s anticyclonic outflow, the darker arrow corresponds to the lower-level cyclonic hurricane circulation. (a) The initially vertically stacked upper-level low located to the southwest of the vortex, and (b) after some time, the hurricane circulations stretch the upper-level low.

The processes of stretching and rotation can be used to explain the different lengths and orientations of the deformed upper lows at t 5 48 h shown in Fig. 14. The hurricane in case LOLOW is strong compared to the trough/low (Fig. 3a) and hence the solid arrows in Fig. 17 dominate, stretching the trough in a predominantly north–south direction to a length of 672 km (Table 2) in 48 h (Fig. 14a). Very little rotation of the trough about itself occurs causing the 400-hPa center to remain at a distance of 613 km from the hurricane center (Table 2). The MIDLOW trough is slightly stronger than LOLOW, but at lower levels the trough is still weaker than the hurricane (Fig. 3b). There is less stretching (Table

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FIG. 16. Schematic illustrating the rotation process. Three centers of the upper-level low are indicated by a triangle (200 hPa), square (300 hPa), and circle (400 hPa). The center of the vortex is indicated by a tropical cyclone symbol. The light arrow indicates the cyclonic flow around the lower center of the low, the darker arrow corresponds to the cyclonic flow around the upper center of the low. (a) The initially north–south-oriented upper-level low, and (b) after some time, the low has rotated cyclonically to a more east–west-oriented position.

2), especially in the upper levels (Fig. 14b), but a little more rotation occurs. This brings the 400-hPa center somewhat closer to the hurricane—595 km (Table 2). The HILOW trough is stronger than the hurricane (Fig. 3c) so the dashed arrows in Fig. 17 dominate. As a result, the trough stretches the least (Table 2), but rotates the most (Fig. 14c), bringing its 400-hPa center to 476 km from the center of the hurricane (Table 2). Little stretching means that the trough has remained more vertically stacked and as a result the trough and hurricane rotate cyclonically around one another (Fujiwhara 1923), until the entire trough is located to the southwest of the hurricane. Case DEEPLOW, while as weak as case LOLOW (Fig. 3d), stretches less than that case, and rotates more (Fig. 14d). Less stretching occurs because this trough is deeper and the circulation it induces at 200 hPa is stronger than that of LOLOW’s trough and can therefore better resist the circulation of the hurricane at that level. At the same time, the stronger 200-

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TABLE 2. Characteristics of the deformed upper-level lows at 48 h. Column 1 lists the case name, column 2 the distance between the 400- and 200-hPa centers of the deformed upper-level low, and column 3 the distance between the trough and hurricane centers at 400 hPa.

FIG. 17. Schematic illustrating deformation of a trough as a result of hurricane interaction. Light arrows are related to upper-level circulations, dark arrows represent low-level flow. The solid arrows are associated with the hurricane flow, the dashed arrows with the trough. The triangle represents the trough’s upper (200 hPa) center, while the square represents the trough’s lower (400 hPa) center.

hPa flow induced by the lower-trough levels causes more rotation of the trough bringing its 400-hPa center closer to the hurricane than LOLOW—564 km. The hurricane circulation also changes due to interaction with the lows. After 48 h (Fig. 14) a closed circular circulation remains in place close to the hurricane center in cases LOLOW, MIDLOW, and DEEPLOW, and surrounding both systems (hurricane and low) is a more elliptically shaped, closed circulation. With time, the troughs in these three cases dissipate and a closed circular circulation returns around the hurricane center. At 400-hPa in HILOW however, the trough is strong enough to disrupt the hurricane circulation at inner radii and a broad elliptical circulation encompasses both the trough and hurricane centers. Slowly, the two 400-hPa centers approach and by t 5 108 h they merge together, leaving a closed, circular, cyclonic circulation around the hurricane center at 400 hPa. Aloft, a shallow positive PV anomaly to the southwest of the storm remains as a remnant of the upper-level low. Initially, the trough’s strongest cyclonic circulation occurs at 230 and 300 hPa (Fig. 3). At these levels the hurricane’s cyclonic circulation is weak. As a result, the cyclonic circulation of the hurricane is disrupted at these levels by that of the trough. By t 5 72 h, a cyclonic circulation at 300 hPa around the hurricane center can be seen only in the case of the weakest trough (LOLOW). In the other cases the circulation around the troughs is still strong, and southerly winds blow across the hurricane center. This is reflected in the vertical shear values at 72 h: 4 m s 21 in case LOLOW, and between 8 and 9 m s 21 in the other three cases (Figs. 10b–13b). At 250 hPa (not shown) southerlies across the hurricane center occur in all four cases.

Case

Length of stretched low (km)

Distance between 400-hPa centers (km)

LOLOW MIDLOW HILOW DEEPLOW

672 628 375 515

613 595 476 564

At t 5 108 h, the location of the 200-hPa center of the low relative to the hurricane has become crucial. HILOW is the only case where the center of the low is located to the southwest of the hurricane, allowing the formation of strong, divergent outflow to the west of the storm in addition to an outflow channel to the storm’s east. At 400 hPa the trough and storm have completed their merger. At the levels in between there is no longer any southerly flow across the hurricane and consequently the vertical shear has dropped (Fig. 12b). After t 5 108 h the shear around the storm drops off further, the RMW shrinks, and the storm intensification rates increase (Fig. 12). In the other three cases, the deformed trough is stretched out along the western half of the hurricane and continues to affect it. A similar stretching of an upper-level low is observed by Molinari et al. (1998) during the interaction of an upper-level low with Tropical Storm Danny (1985). The outstretched low eventually splits in two, reducing the vertical shear over Danny and allowing the storm to intensify. In the current three cases the low does not get split in two. Instead, it prevents an outflow channel from developing aloft and on the west side of the vortex, and causes the vertical shear across the storm to remain high. It takes LOLOW until t 5 120 h, and case MIDLOW until t 5 144 h, for the lows to dissipate, the shear to decrease, and storm intensification rates to increase (Fig. 12). In DEEPLOW, the weak but deep trough affects the hurricane throughout the entire simulation, the shear does not drop off, and as a result the hurricane in this case does not intensify much beyond case HISHR (Fig. 13). 4. Vortex intensification In the previous section the evolution of the upperlevel low and the hurricane vortex were described. The split–merger of the HILOW case led to a reduction in vertical shear (Fig. 12) and subsequent intensification of the vortex. In this section, another possible intensification mechanism is presented: axisymmetrization of PV anomalies by the vortex (Montgomery and Kallenbach 1997; Mo¨ller and Montgomery 1999, 2000). A positive PV source, placed at or outward from the initial RMW of an idealized vortex in gradient balance, generates vortex Rossby wave packets, which travel radially outward from the RMW. These wave packets transfer

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their energy to the vortex, causing the tangential wind of the vortex to increase. The exact radius where the tangential wind increase occurs depends on the initial position and magnitude of the PV source and the initial structure of the vortex. When the PV source is placed at radii greater than the RMW, the intensification occurs outside the RMW, hence the RMW expands. When pulsing the PV forcing, to simulate convective bursts, Mo¨ller and Montgomery (2000) show that an initial tropicalstorm-like vortex intensifies to a hurricane in several days. This hurricane has a larger RMW than the initial storm when PV pulsing occurs at, or outside, the RMW. These findings can be related to hurricane–trough interaction, with the trough acting as a positive PV source, placed outside the initial RMW of the vortex. The RMW in the MIDLOW case (Fig. 11c) expands by 60 km (from 55 to 115 km) between t 5 24 h and 120 h and fluctuates for the remainder of the simulation. In the DEEPLOW case, larger (from 50 to 130 km) RMW expansion occurs (Fig. 13c) over the same time span. The RMW of the LOLOW vortex expands (from 50 to 70 km) between t 5 24 h and 114 h and then contracts for the remainder of the simulation to 45 km. The HILOW case contracts to only 65 km during the first 24 h, then fluctuates between that value and 100 km for the next 108 h and finally contracts down to 40 km at the end of the simulation (Fig. 12c). The temporary RMW contractions in MIDLOW and HILOW may be due to secondary eyewall cycles not caught by the coarse temporal output resolution of 6 h. Secondary eyewalls can take as little as 3 h to contract and are associated with vortex intensification (Willoughby et al. 1982). Expanding RMWs are usually associated with weakening hurricanes, but here coincide with a lowering of the central surface pressure. Hence, there is evidence that intensification via axisymmetrization of a positive PV source placed outside the RMW, may be occurring in the trough interaction cases. No significant RMW expansion is observed in the control and LOSHR cases (Figs. 4 and 6) and these storms intensify via the symmetric intensification mechanism discussed in section 3a. Symmetric intensification tends to be more rapid; the control vortex intensifies from a tropical storm to a hurricane in less than a day. During axisymmetrization of a positive PV source, a tropical storm takes several days to intensify to a hurricane (Mo¨ller and Montgomery 2000). Another important difference is that during symmetric intensification the RMW decreases, while the RMW expands during axisymmetrization of a PV source outside the storm’s RMW. Montgomery and Kallenbach (1997) and Kurihara (1976) propose that radially outward propagating vortex Rossby waves manifest themselves in hurricanes as spiral bands. Using a vortex in gradient balance on an f plane, they derive a dispersion relation for vortex Rossby waves. A typical value of the group velocity is around 4 m s 21 and is directed radially outward. With our tem-

VOLUME 130

FIG. 18. The 1500-m cloud and rainwater (g kg 21 ) fields for case HILOW at (a) t 5 168 h, and (b) t 5 174 h. The spiral band marked with a cross is tracked during the 6-h time frame.

poral output resolution of 6 h, the bands thus move outward by around 85 km between output time steps. Furthermore, at a certain radius, called the stagnation radius, the spiral bands are shown to dissipate. The 850hPa cloud and rainwater fields for case HILOW at (a) t 5 168 h and (b) t 5 174 h are shown in Fig. 18. Several spiral bands can be seen and beyond a certain radius the field is clear. Some of the individual features can be tracked between the two output times, in particular the one marked with a cross at its tip. This feature moves radially outward and covers a radial distance of 80 km over the 6 h, in agreement with the value reported by Montgomery and Kallenbach (1997). Similar features are seen in the other trough-interaction experiments and it is therefore plausible that the spiral bands in the current simulations are vortex Rossby waves forced by asymmetric PV forcing. These features are not seen to the same extent in the symmetrically intensifying control and LOSHR cases. In the HISHR case some spiral bands are seen even though no trough is present. However, in this case, vortex Rossby waves

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may be generated by the convective asymmetry in the hurricane vortex. The formation of spiral bands and RMW expansion during vortex intensification provide evidence that axisymmetrization of a positive PV source, placed at a radius greater than the RMW, may be the mechanism of hurricane intensification in the trough-interaction cases, whether forced directly or indirectly by the presence of the trough. Montgomery and Kallenbach (1997) and Mo¨ller and Montgomery (1999, 2000) superimpose PV anomalies on their vortices in dry simulations, which directly force the formation of vortex Rossby waves. In the current work, the forcing may occur either directly via the positive PV anomaly associated with the upper lows, or indirectly by convective forcing induced by the lows, that is, by destabilization of the levels below and/ or upward motion ahead of a moving positive PV anomaly (see also Kurihara 1976). Careful examination of the convective activity shows a preference for such activity to occur on the western side of the vortex, where the trough is located. This asymmetric convective activity will generate positive PV on the western side of the vortex, which then forces the formation of vortex Rossby waves. It is not clear whether the asymmetric convective activity is forced by the troughs themselves (i.e., through destabilization and/or vertical motion) or by the southerly shear associated with the troughs. As was shown in section 3b, strong shear forces convective activity to the left of the shear vector (positioned across the storm’s center). For this reason a convective maximum occurs in the northern half of the HISHR vortex (westerly shear vector), while in the trough cases it occurs in the western half of the vortex (southerly shear vector). The hurricane vortex’s response to a positive PV anomaly depends, among other factors, on the radial distance between the anomaly and the center of the vortex (Montgomery and Kallenbach 1997). The further the anomaly is placed from the center, the longer it takes the vortex tangential winds to ‘‘axisymmetrize’’ the anomaly. Hence, it will act like a quasi-steady asymmetric source. Axisymmetrization is the process by which the radially varying tangential winds stretch the PV anomaly in the azimuthal direction and cause it to be wrapped around the vortex’s center in thin filaments (Montgomery and Kallenbach 1997). Once axisymmetrization is complete, the PV source is gone and symmetric intensification can resume. In the LOLOW case, the trough remains at a far distance from the center of the hurricane (Table 2) and the cyclonic circulation remains noncircular for a long period of time. This means that axisymmetrization takes a long time. Symmetric intensification, whereby the RMW contracts as the vortex intensifies, does not occur until t 5 150 h (Fig. 10). The HILOW trough approaches the hurricane center most closely (Table 2), meaning that axisymmetrization should occur more quickly. By t 5 120 h the lower portion of the trough has been axisymmetrized by

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(merged with) the vortex. The upper portion of the low has separated from the lower portion and is advected out of the vicinity of the vortex. The vortex is now embedded in weak vertically sheared flow just like case LOSHR (Fig. 12b), the RMW begins to contract (Fig. 12c), and intensification rates increase (Fig. 12a). It is concluded that the HILOW case intensifies more rapidly than the other trough cases because symmetric intensification dynamics get a chance to take over relatively early in the simulation. The ultimate intensity of the storm even comes within a few hPa of the minimum surface pressure of case LOSHR. This happens late in the vortex’s lifetime; the presence of the low temporarily halts the vortex’s period of rapid intensification, which would otherwise have occurred earlier, as in case LOSHR. RAM import forms an additional tool to diagnose whether symmetric intensification or axisymmetrization is occurring. As was shown in sections 3a and 3b, the symmetrically intensifying control and LOSHR cases display prolonged periods (t 5 24–69 h and t 5 24– 42 h, respectively) where the intensification rates exceed 1 hPa h 21 . During these periods, the RMW contracts, while high RAM air is imported from outer regions to the inner radii (r 5 35 km) of the vortex. Initially the size and strength of these vortices increase, but once the high RAM air reaches the inner core (around t 5 24 h), the size and strength remain steady. In other words, the larger-scale vortex intensifies during the first 24 h, followed by spinup of the inner core. Intensification rates $1 hPa h 21 are not seen in the trough cases. Initially, these storms intensify at rates approaching 0.5 hPa h 21 , their RMWs contract and high RAM-air import (Fig. 19) occurs. Then the vertical wind shear, associated with the approaching trough, increases (Figs. 10b through 13b) and intensification rates drop off. At t 5 24 h a period of RAM import at larger radii (beyond r 5 100 km), RMW expansion, and size increase begins. This period ends at t 5 99 h (LOLOW), t 5 120 h (MIDLOW), t 5 120 h (HILOW), and t 5 192 h (DEEPLOW). Axisymmetrization of the trough occurs during this time; the vortex spins up in the outer regions, and the RMW expands. 5. Conclusions and discussion The behavior of hurricanes in low and high vertical wind shear environments was explored first. This way the effects of vertical shear were isolated from the effects of trough interaction. The following conclusions could be drawn: • Even a vortex in relatively low shear (2.5 m s 21 ) shows a significant decrease (almost two Saffir–Simpson categories) in steady-state intensity, compared to a hurricane in zero flow. • The sheared vortices are asymmetric and hence only part of the eye experiences subsidence; the stronger

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VOLUME 130

FIG. 19. Time–radius series of relative angular momentum at 500-m height (shaded, in *10 5 m 2 s 21 , upper abscissa), radius of maximum wind (solid, in km, upper abscissa), and size (dotted, in km, lower abscissa) for (a) LOLOW, (b) MIDLOW, (c) HILOW, (d) DEEPLOW.

the shear, the more pronounced the asymmetry and the smaller the area of subsidence in the eye. The resulting warm core anomalies are weaker, broader, and shallower compared to a vortex in zero flow and hence the hurricanes are weaker and have larger RMW than their symmetric counterparts. • The formation of a single outflow jet, instead of two, is proposed as a possible forcing mechanism for the observed vortex asymmetries. Convective activity occurs at, and downstream from the outflow jet in both cases. In the remaining experiments, the trough-interaction problem is examined. Both hurricane and trough are embedded in weak vertical shear, equal to that of the low-shear case (2.5 m s 21 ). The structure of the upper low adds to the environmental shear experienced by the hurricane vortex, hence the vertical shear associated with the upper-level low at the storm center exceeds 2.5 m s 21 (see Fig. 2), but is still less than the shear values of between 10 m s 21 to 12 m s 21 (DeMaria and Kaplan 1994; Zehr 1992) empirically determined to be limiting for intensification. We define a trough interaction as favorable if it leads to a hurricane of greater intensity than that of the notrough and comparable vertical shear case. While none of the trough interactions resulted in a hurricane vortex as intense as the quiescent environment (control), the HILOW hurricane evolved to the same intensity as the LOSHR storm from an environment of much greater initial shear. Thus, the HILOW case would be regarded as a favorable trough interaction. The DEEPLOW vortex had lower initial shear than the HISHR case, but

became less intense (980 hPa compared to about 973 hPa), and hence may be termed an unfavorable trough interaction. Both the MIDLOW, and especially the HILOW, storms had a larger RMW and vortex size and also exhibited the greatest vortex strength of all of the cases examined (Table 3). Hence, the trough interaction also modified the evolving vortex structure, greatly increasing the area of damaging winds compared to either a linear shear or quiescent environment. In some cases (e.g., MIDLOW), the model vortex had not reached steady state by the end of the simulation, but the limited domain size precluded continuing the simulation further. None of the current trough interactions lead to hurricane decay, but a trough with above-threshold vertical shear, probably would. Such simulations are topics for future study. In contrast to the shear-only experiments, the shear associated with the upper-level lows acts on only one side of the vortex. Additionally, the vortex now has a chance to interact with and change the system that brings the potentially damaging values of vertical wind shear in its vicinity. The hurricane modification of the trough is illustrated by the stretching and rotation of the upperlevel low in three-dimensional space, the merger of the low with the vortex, and the subsequent vertical shear reduction. These results agree with the conclusions of Molinari et al. (1998) that ‘‘trough interaction is a coupled evolution of vertical shear and vortex interactions in the horizontal and vertical.’’ In their observational study of Tropical Storm Danny (1985), the outflow anticyclone of the storm causes the stretching of an upperlevel low interacting with the storm. The low eventually

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TABLE 3. Characteristics of the mature hurricane vortex (after 160 h). Here, pmin /Cat is the max intensity (min pressure and Saffir–Simpson category) and PI is the potential intensity for each case (based on the thermal structure of the initial conditions); the diff between the actual intensity and the PI indicate the negative influence of the environment. RMW, strength, and size are varying measures of the vortex wind structure and extent. Separation indicates the distance between the trough and hurricane centers at 400 hPa (from Table 2, column 3). Core shear is the vortex core value after a symmetric vortex averaged over 500 km has been removed: for initial and mature vortex.

Expt name

pmin /Cat (hPa)

PI (hPa)

RMW (km)

Strength (m s21 )

Size (km)

Separation (km)

Core shear (initial/mature) (m s21 650 hPa21)

Control LOSHR HISHR LOLOW MIDLOW HILOW DEEPLOW

905/5 942/4 973/2 970/2 960/3 944/4 980/2

905 900 907 903 906 912 912

25 40 50 60 100 40 90

25 22.5 20 24 35–40* 35* 28

250 250 220 260 420* 440* 380

— — — 613 595 476 564

0 2.5/4 8/10 4/12 5/3 6/2 6/14

*These values do not settle down to steady state, but are still increasing at the end of the model run.

splits in two, reducing the vertical shear over Danny, allowing it to intensify. The split is observed on the (two-dimensional) 350-K potential temperature plane. In case HILOW, a three-dimensional split of the upper low also occurs, with the lower (400 hPa) portion of the upper-low merging with the hurricane circulation, while the upper (200 hPa) portion moves to the southwest of the storm. The split results in a vertical shear drop over the storm, while the 200-hPa remnant PV anomaly allows the formation of an extra outflow channel (Molinari et al. 1998; Sadler 1976, 1978). Either phenomenon could have been responsible for the subsequent intensification that occurs. Hence, an important result from the current study is the significance of the troughs’ vertical structure. A shallow, but strong trough (HILOW) undergoes three-dimensional split–merger, resulting in a reduction of horizontal scale of the trough and subsequent vertical shear reduction. This was possible because the circulation of the lower portion of the trough (at 400 hPa) and the circulation of the hurricane at that level, were comparable. In LOLOW the circulation of the lower portion of the trough is too weak for a merger to take place, and the vertical shear did not drop. If the vertical extent of the trough is deep but weak (DEEPLOW), the trough remains more vertically stacked (Table 2), no split– merger occurs, and high values of vertical shear persist during the interaction. Bosart et al. (2000) point out that favorable troughs are likely to be those similar in lateral extent to the storm they are interacting with, that is, subsynopticscale troughs (or lows) and PV fragments from synopticscale troughs. In the current study all four troughs were comparable in lateral extent to the hurricane (compare the 2 PVU contours in Fig. 3). They were of subsynoptic scale, similar to the trough interacting with Hurricane Danny (1985), described by Molinari et al. (1998). Indeed, in all four cases the hurricane intensified, consistent with the observational definition of a favorable trough (Hanley et al. 2001).

Besides the formation of an extra outflow jet or splitting of the upper low leading to vertical shear reduction, another possible intensification mechanism could be axisymmetrization of a positive PV source, placed outside the storm’s RMW (Mo¨ller and Montgomery 1999, 2000). The positive PV anomaly (upper-low) could force the hurricane intensification directly (the PV anomaly is absorbed into the existing hurricane PV anomaly through axisymmetrization) or indirectly (by driving enhanced convection). The further the PV source is removed from the RMW, the slower the intensification process for each mechanism. During axisymmetrization, the PV source is axisymmetrized by the vortex’s differential tangential flow (Montgomery and Kallenbach 1997), and is eventually absorbed completely into the flow of the vortex; at this stage, more rapid, symmetric intensification dynamics can take over. The existence of radially outward propagating vortex Rossby waves and expansion of both size and RMW during intensification indicate that these processes may be operating in the trough-interaction cases presented here. In HILOW the upper-level low approaches the storm more closely than in the other trough interaction cases, and hence the axisymmetrization process takes less time. In summary, the vertical as well as horizontal structures of both systems are important in hurricane–trough interaction, with each system acting to deform and change the other. Given the adverse effects of vertical shear on hurricanes, one would have expected weaker lows with less vertical shear (e.g., LOLOW) to be advected away by the storm or to dissipate sooner, allowing the hurricane to resume intensification earlier and to become more intense ultimately. Instead, the hurricane interacting with the strongest trough (HILOW) becomes the most intense. The current study indicates that: • A deep trough (maximum PV located between 200 and 450 hPa) produces strong and deep shear that persists for a long time and prevents significant deepening of the storm.

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• Shallow troughs (maximum PV anomaly located between 300 and 200 hPa), temporarily delay and reduce overall vortex intensification. This reduction is smallest in the case where the 400-hPa trough and hurricane circulations are comparable and the vertical shear is reduced due to a split–merger of the trough. • Hurricanes interacting with troughs evolve to be larger and stronger, but less intense than hurricanes intensifying in vertical wind shear alone. The larger size can be attributed to the mechanism of axisymmetrization whereby the positive PV forcing associated with the trough allows the storm to intensify while its RMW expands. The second point agrees with the results of Mo¨ller and Montgomery (2000): a stronger initial PV source produces a more intense vortex than a weaker source. Out of the shallow trough cases, the least intense storm is produced by interaction with the weakest trough (LOLOW), while the most intense storm is associated with the strongest trough (HILOW). The finding that trough interaction increases the size of the hurricane is supported by Guard (1995), who observed that interaction with midlatitude troughs was associated with the largest and most intense western North Pacific typhoons (these occur in October/November), but often occurred without rapid deepening. Large storms may not necessarily have the strongest low-level winds, but the areal coverage of destructive winds and rainfall is larger. Bosart and Bartlo (1991) and Bosart et al. (2000) suggested that the ability of a tropical cyclone to intensify during trough interaction may depend upon its intensity and its proximity to its PI. While the vortices in the current study were generally far removed from their PI when the trough interaction occurred, both MIDLOW and HILOW evolved significantly toward their respective PI (approx. 40 and 60 hPa). It does seem plausible that a hurricane close to its PI would not have much room for further intensification with or without the presence of a trough. An interesting question is whether a trough can take a hurricane to its PI when, without the trough’s presence, it would not have gotten there. These are important issues to be addressed in future work. Acknowledgments. The authors thank Keith G. Blackwell for his thorough review of this document and many helpful comments. For their discussions and ideas offered throughout this project, we express our gratitude to Mike Fritsch, Bill Frank, Craig Bishop, and Peter Bannon. We appreciate the constructive and thoughtprovoking comments received by three anonymous reviewers. The second author gratefully acknowledges the support of the National Science Foundation (ATM9911212). An equipment grant from SUN Microsystems to the University of South Alabama has significantly contributed to the production of diagnostics and figures.

VOLUME 130 REFERENCES

Anthes, R. A., 1972: Development of asymmetries in a three-dimensional numerical model of the tropical cyclone. Mon. Wea. Rev., 100, 461–476. Baik, J.-J., M. DeMaria, and S. Raman, 1990: Tropical cyclone simulations with the Betts convective adjustment scheme. Part I: Model description and control simulation. Mon. Wea. Rev., 118, 513–527. Betts, A. K., and M. J. Miller, 1993: The Betts–Miller scheme. The Representation of Cumulus Convection in Numerical Models. Meteor. Monogr., No. 46, Amer. Meteor. Soc., 107–121. Blackadar, A. K., 1979: High resolution models of the planetary boundary layer. Advances in Environmental Science and Engineering, J. R. Pfafflin and E. N. Ziegler, Eds., Vol. 1, Gordon and Briech, 50–85. Bosart, L. F., and J. A. Bartlo, 1991: Tropical storm formation in a baroclinic environment. Mon. Wea. Rev., 119, 1979–2013. ——, C. S. Velden, W. E. Bracken, J. Molinari, and P. G. Black, 2000: Environmental influences on the rapid intensification of Hurricane Opal (1995) over the Gulf of Mexico. Mon. Wea. Rev., 128, 322–352. Challa, M., and R. L. Pfeffer, 1980: Effects of eddy fluxes of angular momentum on model hurricane development. J. Atmos. Sci., 37, 1603–1618. ——, and ——, 1990: Formation of hurricanes from cloud clusters and depressions. J. Atmos. Sci., 47, 909–927. ——, ——, Q. Zhao, and S. W. Chang, 1998: Can eddy fluxes serve as a catalyst for hurricane and typhoon formation? J. Atmos. Sci., 55, 2201–2219. DeMaria, M., and J. Kaplan, 1994: A Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic basin. Wea. Forecasting, 9, 209–220. ——, 1996: The effect of vertical shear on tropical cyclone intensity change. J. Atmos. Sci., 53, 2076–2087. ——, J.-J. Baik, and J. Kaplan, 1993: Upper-level eddy angular momentum fluxes and tropical cyclone intensity change. J. Atmos. Sci., 50, 1133–1147. Dudhia, J., 1993: A nonhydrostatic version of the Penn State–NCAR Mesoscale Model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121, 1493–1513. Emanuel, K. A., 1988: The maximum intensity of hurricanes. J. Atmos. Sci., 45, 1143–1155. Fiorino, M., and R. L. Elsberry, 1989: Some aspects of vortex structure related to tropical cyclone motion. J. Atmos. Sci., 46, 975– 990. Frank, W. M., and E. A. Ritchie, 1999a: Effects of environmental flow upon tropical cyclone structure. Mon. Wea. Rev., 127, 2044–2061. ——, and ——, 1999b: Environmental effects on hurricane core structure. Preprints, 23d Conf. on Hurricanes and Tropical Meteorology, Dallas, TX, Amer. Meteor. Soc., 680–681. ——, and ——, 2001: Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 129, 2249–2269. Franklin, J. L., S. J. Lord, S. S. Feuer, and F. D. Marks Jr., 1993: The kinematic structure of Hurricane Gloria (1985) determined from nested analyses of dropwindsonde and Doppler radar data. Mon. Wea. Rev., 121, 2433–2451. Fujiwhara, S., 1923: On the growth and decay of vortical system. Quart. J. Roy. Meteor. Soc., 49, 75–104. Gray, W. M., 1968: Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev., 96, 669–700. Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR TN-398 1 STR, 138 pp. Guard, C., 1995: Some synoptic and dynamic aspects of the processes involved in rapid intensification of western North Pacific tropical cyclones. Preprints, 21st Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 389–391.

SEPTEMBER 2002

KIMBALL AND EVANS

Hanley, D. E., 1997: The effect of trough interactions on tropical cyclone intensity change. Preprints, 22d Conf. on Hurricanes and Tropical Meteorology, Fort Collins, CO, Amer. Meteor. Soc., 354–355. ——, 2000: A comparison of favorable and unfavorable hurricanetrough interactions. Preprints, 24th Conf. on Hurricanes and Tropical Meteorology, Ft. Lauderdale, FL, Amer. Meteor. Soc., 191–193. ——, J. Molinari, and D. Keyser, 2001: A composite study of the interactions between tropical cyclones and upper-tropospheric troughs. Mon. Wea. Rev., 129, 2570–2584. Holland, G. J., and R. T. Merrill, 1984: On the dynamics of tropical cyclone structural changes. Quart. J. Roy. Meteor. Soc., 110, 723–745. Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877–946. HRD, cited 2000: Windfield and reflectivity structure and evolution of Hurricane Olivia on 25 September 1994. [Available online at http://www.aoml.noaa.gov/hrd/project2000.html.] Jones, S. C., 1995: The evolution of vortices in vertical shear. I: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821–851. Kamminga, S., 2000: The evolution of hurricane-like vortices in three-dimensional flow. Ph.D. thesis, The Pennsylvania State University, 139 pp. Kurihara, Y., 1976: On the development of spiral bands in a tropical cyclone. J. Atmos. Sci., 33, 940–958. Lewis, B. M., and D. P. Jorgensen, 1978: Study of the dissipation of Hurricane Gertrude (1974). Mon. Wea. Rev., 106, 1288–1306. Marks, F. D., Jr., R. A. Houze Jr., and J. F. Gamache, 1992: Dualaircraft investigation of the inner core of Hurricane Norbert. Part I: Kinematic structure. J. Atmos. Sci., 49, 919–942. McBride, J. L., and R. Zehr, 1981: Observational analysis of tropical cyclone formation. Part II: Comparison of non-developing versus developing systems. J. Atmos. Sci., 38, 1132–1151. Merrill, R. T., 1984: A comparison of large and small tropical cyclones. Mon. Wea. Rev., 112, 1408–1418. ——, 1988: Environmental influences on hurricane intensification. J. Atmos. Sci., 45, 1678–1687. Molinari, J., and D. Vollaro, 1989: External influences on hurricane intensity. Part I: Outflow layer eddy angular momentum fluxes. J. Atmos. Sci., 46, 1093–1105. ——, and ——, 1990: External influences on hurricane intensity. Part II: Vertical structure and response of the hurricane vortex. J. Atmos. Sci., 47, 1902–1918. ——, S. Skubis, and D. Vollaro, 1995: External influences on hurricane intensity. Part III: Potential vorticity structure. J. Atmos. Sci., 52, 3593–3606. ——, ——, ——, F. Alsheimer, and H. E. Willoughby, 1998: Potential vorticity analysis of tropical storm intensification. J. Atmos. Sci., 55, 2632–2644. Mo¨ller, J. D., and M. T. Montgomery, 1999: Vortex Rossby-waves

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and their influence on hurricane intensification in a barotropic model. J. Atmos. Sci., 56, 1674–1687. ——, and ——, 2000: Tropical cyclone evolution via potential vorticity anomalies in a three-dimensional balance model. J. Atmos. Sci., 57, 3366–3387. Montgomery, M. T., and B. Farrell, 1993: Tropical cyclone formation. J. Atmos. Sci., 50, 285–309. ——, and R. J. Kallenbach, 1997: A theory for vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes. Quart. J. Roy. Meteor. Soc., 123, 435–465. Pfeffer, R. L., and M. Challa, 1981: A numerical study of the role of eddy fluxes of angular momentum in the development of Atlantic hurricanes. J. Atmos. Sci., 38, 2393–2398. ——, and ——, 1992: The role of environmental asymmetries in Atlantic hurricane formation. J. Atmos. Sci., 49, 1051–1059. Reisner, J., R. T. Bruintjes, and R. J. Rasmussen, 1993: Preliminary comparison between MM5 NCAR/Penn State model generated icing forecasts and observations. Preprints, Fifth Int. Conf. on Aviation Weather Systems, Vienna, VA, Amer. Meteor. Soc., 65– 69. ——, R. J. Rasmussen, and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124B, 1071–1107. Sadler, J. C., 1976: A role of the tropical upper tropospheric trough in early season typhoon development. Mon. Wea. Rev., 104, 1266–1278. ——, 1978: Mid-season typhoon development and intensity changes and the tropical upper tropospheric trough. Mon. Wea. Rev., 106, 1137–1152. Shapiro, L. J., 1992: Hurricane vortex motion and evolution in a three-layer model. J. Atmos. Sci., 49, 140–153. ——, and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39, 378–394. Shi, J. J., S. W. Chang, and S. Raman, 1990: A numerical study of the outflow layer of the tropical cyclone. Mon. Wea. Rev., 118, 2042–2055. ——, ——, and ——, 1995: The possible role of upper-tropospheric environmental forcings on the intensification of Hurricane Florence (1988). Preprints, 21st Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 392–393. ——, ——, and ——, 1997: Interaction between Hurricane Florence (1988) and an upper-tropospheric westerly trough. J. Atmos. Sci., 54, 1231–1247. Willoughby, H. E., 1995: Mature structure and evolution. Global perspectives on tropical cyclones. WMO Tech. Doc. WMO/TD693, 43–44. ——, 1998: Tropical cyclone eye thermodynamics. Mon. Wea. Rev., 126, 3053–3067. ——, J. A. Clos, and M. G. Shoreibah, 1982: Concentric eyes, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci., 39, 395–411. Zehr, R. M., 1992: Tropical cyclogenesis in the western North Pacific. NOAA Tech. Rep. NESDIS 61, 181 pp.