The downstream impact of tropical cyclones on a developing baroclinic wave in idealized scenarios of extratropical transition

Transcription

1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 136: , April 2010 Part A The downstream impact of tropical cyclones on a developing baroclinic wave in idealized scenarios of extratropical transition Michael Riemer a,b *andsarahc.jones a a Karlsruher Institut für Technologie, Karlsruhe, Germany b Naval Postgraduate School, Monterey, CA, USA *Correspondence to: Michael Riemer, Department of Meteorology, Root Hall, 589 Dyer Rd, Naval Postgraduate School, Monterey, CA 93943, USA. mriemer@nps.edu The interaction of a tropical cyclone with a developing baroclinic wave is investigated in an idealized scenario of extratropical transition (ET). The impact of ET is examined by comparing and analyzing two numerical baroclinic-wave experiments: a traditional experiment in which baroclinic development is excited by a localized upper-level perturbation on a realistic jet profile and an experiment in which, additionally, a model tropical cyclone is inserted south of the jet at the initial time. ET occurs in a wavy upper-level flow while baroclinic surface systems are still weak. The characteristic direct impact of ET on the midlatitude flow is the formation of a distinct jet streak and the amplification of a ridge trough couplet in the adjacent downstream region. The subsequent rapid cyclogenesis downstream is a direct consequence of these upper-level flow modifications. This faster and stronger development constitutes the amplification of the leading edge of downstream development. Both the upper-level wave pattern and the surface development are subsequently amplified in the region further downstream. The formation of the ridge adjacent to the intensified downstream cyclone is analyzed in detail to elucidate the next stage in the downstream dispersion of the ET impact. Ridge-building in the ET scenario exhibits characteristics distinct from those in the life-cycle experiment. Wave breaking, feedback from the modified low-level frontal structure and diabatic processes all contribute to the high-amplitude wave pattern downstream of ET. The downstream impact of ET is highly sensitive to the initial storm location and intensity. The considerable amplification of the leading edge found in the reference experiment is the most widespread and rapidly propagating impact. We thus speculate that this leading edge represents an optimal location of the midlatitude circulation, where ET can lead to the most significant impact on the downstream flow. Copyright c 2010 Royal Meteorological Society Key Words: ridge building; potential vorticity inversion; tropical extratropical interaction Received 9 September 2009; Revised 22 January 2010; Accepted 10 February 2010; Published online in Wiley InterScience 30 March 2010 Citation: Riemer M, Jones SC The downstream impact of tropical cyclones on a developing baroclinic wave in idealized scenarios of extratropical transition. Q. J. R. Meteorol. Soc. 136: DOI: /qj Introduction About half of the tropical cyclones in the North Pacific and Atlantic basin transform at the end of their life cycles into midlatitude low-pressure systems, i.e. the tropical cyclones undergo extratropical transition (ET). The direct impact of ET on the synoptic-scale circulation in midlatitudes has been investigated in a number of case Copyright c 2010 Royal Meteorological Society

2 618 M. Riemer and S. C. Jones studies. A comprehensive review is provided by Jones et al. (2003). There is evidence that the impact of ET is not only localized but affects a much larger geographical region, in particular downstream. The formation of surface cyclones (Agusti- Panareda et al., 2005), rapid intensification (Hoskins and Berrisford, 1988) and severe precipitation events (Martius et al., 2008) have been linked to ET systems upstream. An impact on the region downstream of ET is also found in predictability studies. Recent analysis of ensemble prediction systems in the North Pacific and the North Atlantic (Harr et al., 2008; Anwender et al., 2008) have identified regions of reduced predictability characterized by enhanced ensemble spread in the downstream region following an ET event. Their results indicate that the impact of ET may reach near-hemispheric scales. In the cases studied the enhanced ensemble spread was associated with large variability in the representation of downstream midlatitude cyclones in the ensemble forecasts. Thus severe weather events (as cited above) may occur in regions of reduced predictability, highlighting the importance of achieving a better understanding of the physical processes that govern the downstream impact of ET. In order to reduce the high complexity of ET into its essential components, a recent study (Riemeret et al., 2008, hereafter RJD) investigated a highly idealized ET scenario in a numerical experiment: the interaction of a tropical cyclone with a straight jet. The prominent features of this interaction are the formation of a ridge trough couplet at upper levels and a jet streak just downstream of the ET system. This modification of the upper-level flow governs the development of the downstream system and rapid cyclogenesis takes place beneath the left exit region of the jet streak. The upper-level ridge trough pattern extends further downstream as a wave pattern and initiates a family of cyclones. Based on piecewise inversion of potential vorticity (PV), complemented by the partitioning of the flow into its nonrotational and non-divergent components, RJD showed that the ET system has a profound impact on the evolution of the ridge trough pattern over an extended period of time. The evolution downstream of ET can thus be regarded as downstream baroclinic development (Simmons and Hoskins, 1979; Orlanski and Sheldon, 1995), with the tropical cyclone undergoing ET acting as the initial perturbation. Based on Hovmöller diagrams, the evolution of the upper-level flow can be interpreted as the excitation of a Rossby-wave train by the ET system and its subsequent propagation along the PV gradient associated with the jet (figure 5 in RJD). Although strong baroclinic feedback is evident, general characteristics of the evolution can be understood in terms of barotropic Rossby-wave dynamics. In the ET scenario of RJD, the upper-level Rossby-wave train can be considered to provide the precursor for lowlevel development. This interpretation is consistent with the results of Schwierz et al. (2004) and Martius et al. (2008). Schwierz et al. have shown that the PV gradient associated with a realistic jet profile can act as the wave guide for (barotropic) Rossby waves and Martius et al. argue that amplified Rossby-wave trains can constitute precursors to PV streamer formation and ultimately heavy precipitation events. Downstream baroclinic development is the characteristic response in all of the ET experiments conducted by RJD. Any localized perturbation to an unstable jet, however, can be expected to excite downstream development. For the long-term limit, Orlanski and Chang (1993) concluded that the response is independent of the initial perturbation. Questions therefore remain about how to attribute certain characteristics of the downstream development in RJD to the specific nature of the initial perturbation, i.e. the ET system. The current study thus considers a more realistic, albeit more complex ET scenario. The midlatitude flow is represented by a developing baroclinic wave excited by an upper-level ridge trough ridge pattern. In this scenario, the ET system is no longer the only perturbation to excite development but competes with the initial upper-level perturbation. The modification of a developing baroclinic wave is an impact distinct from the excitation of downstream baroclinic development in RJD and might be relevant to a larger number of real cases. We find that the interaction of the ET system with the developing baroclinic wave forces a high-amplitude ridge trough pattern and a jet streak, similar to the impact found in RJD. One focus of this study is on the downstream dispersion of this high-amplitude perturbation. Does this perturbation excite a coherent barotropic wave train that can trigger strong baroclinic and diabatic responses locally? Or does the feedback from developing low-level systems make a quintessential contribution to upperlevel wave propagation? We approach these questions, inter alia, by quantifying contributions to the building of the ridge associated with the downstream system. This ridge formation constitutes the leading edge of downstream baroclinic development in the earlier part of the experiment. The concept of downstream baroclinic development has been described in terms of local eddy kinetic energy (Orlanski and Sheldon, 1995). Harr and Dea (2009) have applied this methodology to four ET cases in the North Pacific. They show that ET systems can act as a source of kinetic energy for the midlatitude jet and demonstrate a considerable variety between individual ET cases. Nielsen- Gammon and Lefevre (1996) use a piecewise tendency diagnostic based on PV thinking in a case study of downstream trough formation. For the general concept of downstream baroclinic development, both approaches lead to consistent results. Here we adopt a piecewise PV analysis to study the evolution of the upper-level flow. Midlatitude flow features as well as the tropical cyclone can be identified and distinguished well in a PV framework. The paper is organized as follows. Section 2 describes the numerical model and the idealized initial conditions. Section 3 provides a brief description of the development of the baroclinic wave without the ET system and Section 4 discusses the impact of ET. A detailed analysis of the direct impact of the ET system and the downstream dispersion of this impact based on piecewise PV inversion is given in Section 5. The sensitivity of the evolution with respect to intensity and initial location of the tropical cyclone is examined in Section 6. Section 7 contains a discussion of the results and our conclusions. 2. Experimental design In the real atmosphere it is difficult to attribute specific developments to a particular ET event because it is not known how the atmosphere would have evolved

3 Tropical Cyclone Baroclinic Wave Interaction 619 without ET taking place. Here we investigate the impact of ET on midlatitude flow by comparing and analyzing two numerical baroclinic-wave experiments. In both experiments, baroclinic development is excited by a localized perturbation to an initially straight jet. The life cycle of this baroclinic development constitutes our benchmark experiment, referred to as the LC run. In the ET run a tropical cyclone is inserted in the quiescent environment south of the jet stream in addition to the midlatitude perturbation at the initial time. The differences that occur in the ET run can be attributed to the tropical cyclone undergoing ET and are thus considered to be the impact of the ET system on the midlatitude flow. We will also present sensitivity experiments with respect to the initial strength and position of the tropical cyclone. The initial perturbation is designed as an upperlevel ridge trough ridge-pattern in order to establish a southwesterly steering flow for the tropical cyclone early in the experiment. Hence the tropical cyclone starts moving towards the jet stream quickly and ET takes place in a wavelike upper-level flow before baroclinic low-level systems have developed significantly. Using our experience with preliminary experiments, the initial position of the tropical cyclone is chosen so that the impact of ET does not modify the phase of the upper-level wave train significantly. In a more complex scenario the ET system could interact with pre-existing low-level systems. The modification of such low-level systems may then also contribute to the downstream impact of ET Numerical model and initial background state The numerical model used in this study is the PSU/NCAR MM5V3 (Grell et al., 1995) run in a channel configuration on a Cartesian grid with periodic boundaries in the zonal direction. The Coriolis parameter varies in the meridional direction with the Earth s geometry. The Equator is located at the southern boundary of the domain. The outer domain has a horizontal resolution of 60 km and a zonal and meridional extent of and 8460 km, respectively. A vortex-following two-way interactive nest with a resolution of 20 km and a domain size of 1200 km 1200 km is used around the tropical cyclone/ ET system. Both domains use the Kain Fritsch 2 (Kain, 2004) scheme to parametrize convection, the Blackadar scheme (Zhang and Anthes, 1982) for boundary-layer processes and an explicit microphysical scheme (Reisner et al., 1998). The basic initial conditions consist of a zonally oriented straight jet stream in thermal wind balance with a baroclinic zone. The wind and temperature profiles are similar to those used by Simmons and Hoskins (1980), but the meridional scale of the profile in this study is contracted by a factor of 0.6, leading to a tighter low-level temperature gradient. The jet is centred on 42 N and has a maximum wind speed of 40 m s 1 at 175 hpa. While this jet magnitude is consistent with previous studies of baroclinic development (Simmons and Hoskins, 1980; Wernli et al., 1998), it somewhat underestimates the jet strength in the western North Pacific and the North Atlantic where ET takes place most frequently. For a stronger jet maximum, a higher group speed of downstream development and an increase in wavelength of the ridge trough couplet just downstream of ET can be expected (RJD). The numerical experiments are over water with a timeinvariant sea-surface temperature (SST) gradient. In the south of the domain a typical tropical value for the SST of 28 C is prescribed. To the north, the SST decreases in accordance with the temperature gradient at the lowest model level. The reader is referred to RJD for further details of the model configuration and the initial conditions Initial perturbation and model tropical cyclone Following Wernli et al. (1998), a combination of vortexlike disturbances is superposed on the initially straight jet to excite baroclinic development. The individual perturbations are in gradient wind balance and defined by their wind structure. The radial structure of the tangential wind is similar to the broad vortex profile of Smith et al. (1990), with modifications by Jones (1995) to confine the vortex circulation radially. The radius of maximum wind (RMW) is at 450 km and the circulation vanishes at a radius of 2500 km. The disturbances have maximum amplitude at the height of the jet core and decay exponentially in the vertical direction. The precise wind structure can be found in the appendix. One cyclonic and two anticyclonic perturbations are arranged to form a sharp trough that is flanked on both sides by weaker ridges. The cyclonic perturbation is centred 540 km south of the jet axis with maximum winds v max = 18 m s 1. An anticyclonic perturbation with v max = 9ms 1 is centred 1500 km west of the cyclonic perturbation and 540 km north of the jet axis. A somewhat stronger (v max = 12.7ms 1 ) anticyclone is centred 1380 km east of the cyclonic perturbation and 600 km north of the jet axis. In a separate model run, a tropical cyclone was spun up in a quiescent environment on an f -plane until a quasi-steady intensity was reached. This run used the same thermodynamic profile and SST as found in the southern part of the domain in the baroclinic-wave experiments and was performed at the resolution of the nested domain. This model tropical cyclone is inserted into the domain of the baroclinic wave at the initial time. The initial position in the reference ET run is 3600 km east of the trough axis and 1320 km south of the jet axis. Due to an inconsistency with high-resolution initial data for the nest and the moving nest option in MM5, the coarse-gridded data need to be used. The storm redevelops its finer-scale structure quickly and re-intensifies from an initial intensity of 967 hpa to 932 hpa in the first 36 h of the ET run. 3. Reference development of the baroclinic wave The evolution of baroclinic life cycles in a channel set-up has been studied extensively in the past. Compared with the classic baroclinic wave scenario, the following factors modify the evolution in our experiment: the SST gradient and the associated gradient in surface fluxes, enhanced diabatic processes due to the high moisture content south of the jet axis and the finite-amplitude nature of the localized initial perturbation. Thus, we need to provide a brief description of the LC run before the impact of the ET system on this development can be analyzed. At 36 h the ridge trough ridge structure of the initial perturbation is still apparent (Figure 1(a)). The surface

4 620 M. Riemer and S. C. Jones (a) (b) 1800 km 1800 km (c) (d) 1800 km 1800 km (e) (f) 1800 km 1800 km Figure 1. Overview of the synoptic development in the LC run at times (a) 36 h, (b) 72 h, (c) 108 h, (d) 144 h, (e) 180 h and (f) 240 h. Shading denotes the dynamic tropopause (θ on PV = 2 PVU). Contours show surface pressure, every 5 hpa, dashed for 995 hpa and lower. Thick contours depict horizontal wind speeds of 40 m s 1 and higher, every 5 m s 1. The vertical white lines indicate the position of the initial trough (solid), primary downstream trough (dashed), second downstream trough (short-dashed) and third downstream trough (dotted, at 240 h only), respectively.

5 Tropical Cyclone Baroclinic Wave Interaction 621 systems at this time are very weak. Only two areas of high pressure can be seen with the contour interval used. After 72 h a surface cyclone has developed ahead of the trough (Figure 1(b)). We refer to this cyclone in the following as the initial low. Some of the initial perturbation energy propagates downstream and forms a new upper-level trough, exciting the development of a second surface low. These systems are referred to as the primary downstream trough and the primary downstream low, respectively. Weak surface development is also found upstream of the initial perturbation. The structure of the upper-level anomalies has changed significantly. The initial trough has broadened and the meridional orientation of the upper-level flow has decreased considerably. The ridge between the initial trough and the downstream trough is hardly discernable at this time. Baroclinic growth dominates the evolution in the next 36 h: the surface systems as well as the upper-level anomalies amplify (Figure 1(c)). The initial low and the primary downstream low intensify by about 10 hpa in this 36 h period. Both systems continue to deepen to about 975 hpa at 144 h (Figure 1(d)) and the associated upper-level troughs begin to wrap up. The low-level warm fronts associated with both systems extend 1000 km east of the surface pressure centres at this time and exhibit a predominantly zonal orientation (Figure 2). Heavy precipitation is found at the warm front of the primary downstream low on the northern tip of the warm sector. Diabatic enhancement of the associated ridge is indicated by a pronounced local maximum of potential temperature (θ) at the tropopause (highlighted in Figure 2, cf. Figure 1(d)). Further downstream, subsequent evolution follows the concept of downstream baroclinic development. An amplifying new trough, referred to as the second downstream trough in the following, excites the development of another surface cyclone (Figure 1(d)). Within the next 36 h the second downstream trough starts to wrap up (Figure 1(e)). The explosive intensification of the cyclone, with a pressure drop of 30 hpa in 36 h, is associated with this wrapup. The building of the next downstream ridge indicates significant diabatic impact again. The development of the third downstream system interacts, due to the periodicity of the domain, with the initial upstream development. At km Figure h accumulated precipitation (shaded), equivalent potential temperature at 850 hpa (thin contours, from K, every 7 K) and θ on PV = 2 PVU (thick contours) at 144 h in the LC run. For the sake of visual clarity, the tropopause structure is somewhat smoothed. This section of the total domain depicts the initial low (left) and the primary downstream system (right). The arrow highlights the local maximum of θ at the tropopause due to diabatic processes. 345 the end of the experiment (240 h, Figure 1(f)) four mature baroclinic systems are found in the integration domain. 4. Impact of ET on the developing baroclinic wave The synoptic-scale impact of ET on the developing baroclinic wave described in the previous section is investigated by comparing the ET and LC runs at selected times and by examination of Hovmöller diagrams of the upper-level meridional wind. A more detailed analysis to identify the relative importance of different physical processes based on piecewise PV inversion is presented in Section Comparison of synoptic evolution at selected times Evolution of the ET system Very early in the experiment the intense tropical cyclone (932 hpa) is embedded in the southwesterly flow ahead of the initial trough (36 h, Figure 3(a)). The outflow of the tropical cyclone, marked by the area of highest θ values on the tropopause, is found predominantly downstream of the storm. At 72 h the tropical cyclone moves towards midlatitudes between the initial and primary downstream lows (Figure 3(b)). The higher translation speed (not shown) suggests that the transformation stage of ET (Klein et al., 2000) has commenced. The storm intensity has decreased to 942 hpa. As the ET system moves further into the midlatitudes it becomes subject to strong vertical shear and deep convection around the centre decreases significantly (not shown). At 108 h, the outflow anomaly has decoupled from the storm s centre and is found predominantly to the south of the system (Figure 3(c); the ET system is marked by the solid line). The ET system, however, is still intense with a central pressure of 954 hpa. Low-θ values on the tropopause start to wrap around the centre cyclonically from the northwest. The wrap-up of high- and low-θ air at upper levels is a marked feature of the ET system at 144 h (Figure 3(d)). The ET system is still intense (954 hpa) but the surface pressure field has broadened considerably. At 180 h, the ET system has weakened and starts to merge with the primary downstream system (Figure 3(e)). At the tropopause, a filament of low θ is associated with the ET system. At the end of the experiment (240 h, Figure 3(f)) the ET system has completely merged with the primary downstream low and slightly re-intensified. A pronounced ridge has developed downstream of the merged system. This newly formed ridge has a phase shift of approximately 90 relative to the upper-level wave pattern in the LC run Midlatitude impacts during early interaction At 36 h, the impact of the tropical cyclone on the midlatitude flow is limited to a somewhat more pronounced jet streak in the crest of the ridge where the outflow impinges on the jet stream (cf. Figures 3(a) and 1(a)). In contrast to the LC run, a broad ridge is found 36 h later between the initial and the primary downstream trough, just downstream of ET (cf. Figures 3(b) and 1(b)). Both the jet streak and the primary downstream trough have amplified during this time, while the development of the initial low is hindered

6 622 M. Riemer and S. C. Jones (a) (b) 1800 km 1800 km (c) (d) 1800 km 1800 km (e) (f) 1800 km Figure 3. Same as Figure 1, but for the ET run: (a) 36 h, (b) 72 h, (c) 108 h, (d) 144 h, (e) 180 h and (f) 240 h. The white lines now indicate the respective systems in the ET run. The vertical black line denotes, when necessary, the position of the ET system.

7 Tropical Cyclone Baroclinic Wave Interaction 623 by the presence of the ET system. Ahead of the downstream trough, an area of low surface pressure indicates the development of the primary downstream low in the same region as in the LC run. The broad area of ridging evolves into a sharp upper-level ridge to the north and east of the ET system within the next 36 h (108 h, Figure 3(c)). Further downstream, the primary downstream trough is considerably more pronounced than in the LC run and starts to wrap up cyclonically. The formation of a sharp ridge has recently been analyzed in a barotropic framework by Scheck et al. (2010). In their set-up the circulation of a cyclone displaces the tropopause front, thereby creating a positive vorticity anomaly (trough) upstream and a negative anomaly (ridge) downstream of the cyclone. Downstream of the cyclone the circulation induced by these tropopause anomalies is parallel to the cyclone circulation, enhancing the formation of the ridge. Upstream of the cyclone the circulations of the anomalies and the cyclone oppose each other so that the trough formation is suppressed. This leads to a pronounced kink of the front close to the cyclone, strongly resembling the situation in Figure 3(c) Rapid downstream development and amplified baroclinic wave train The modification of the upper-level flow by the ET system provides very favourable conditions for surface development (detailed in Section 5.3). Hence, the primary downstream system develops rapidly, with the minimum central pressure dropping by 25 hpa between 72 and 108 h, 15 hpa more than in the LC run (cf. Figures 3(c) and 1(c)). The locations of the surface lows are virtually the same in both runs. In the adjacent downstream region the ridge is of significantly higher amplitude than in the LC run and the incipient second downstream trough is also more pronounced. The stronger development of the primary downstream low and the adjacent downstream ridge constitutes an amplification of the leading edge of the downstream development. The primary downstream trough has wrapped around the surface centre at 144 h (Figure 3(d)). The associated surface cyclone continues to be more intense (approximately 10 hpa) than in the LC run. The strong low-level circulation can be expected to support the pronounced wrap-up of the upper-level trough (Davis et al., 1993; Agusti-Panareda et al., 2005; RJD). The vertically stacked structure is characteristic for a mature baroclinic system. In the LC run the primary downstream system is still ahead of the trough at this time and continues to intensify. The primary downstream system in the ET run has thus undergone its baroclinic life cycle approximately 24 h faster than in the LC run. The surface centre has moved polewards and is located somewhat further to the east compared with the LC run. The high-amplitude ridge downstream of the primary downstream system is an exceptional feature at this time. The second downstream trough is in phase with its counterpart in the LC run. The associated surface low is 10 hpa deeper than in the LC run and develops in the same region (Figure 3(d)). The low-level frontal structure of the primary downstream system shows a strong meridional orientation (Figure 4). The region of heavy precipitation extends about 600 km further north than in the LC run (cf. Figure 2). In Section 5, we will show evidence that this modification of the frontal km Figure 4. Same as Figure 2, but for the ET run at 120 h. The primary downstream low is found to the right, the ET system in the middle, and the initial low to the far left. structure and associated precipitation pattern contributes to the building of the high-amplitude ridge. At 180 h (Figure 3(e)), during the merger with the ET system, the PV-anomaly associated with the primary downstream trough undergoes deformation and moves further polewards. The second downstream trough has become much sharper and extends further southward than in the LC run (cf. Figure 1(e)). The associated surface low has deepened by a further 15 hpa and a pronounced ridge has developed in the adjacent downstream region. Strong northerly and southerly jet streaks are found at the flanks of this ridge. Despite the larger amplitude of the upper-level wave pattern in the ET run, the second downstream low in the LC run (Figure 1(e)) has intensified strongly and attained the same intensity at this time. At the end of the experiment (Figure 3(f)), the phase shift associated with the merger of the ET system and the primary downstream low (indicated by the black line in Figure 3(f)) impacts the second downstream trough also. This trough is now located further to the west compared with the LC run (cf. Figure 1(f)). The third downstream trough extends further to the south in the ET run, the associated surface cyclone is very intense and the upper-level winds are stronger along the ridge in the adjacent downstream region A large-scale amplification of meridional moisture exchange? The frontal structure and precipitation pattern associated with the primary downstream low exhibit a more meridional orientation and extent under the influence of the ET system (see above). A similar effect is also found associated with the second downstream low. The moisture distribution in the ET and LC runs is compared using the 35 mm contour of column-integrated precipitable water at the later stage of the experiment (216 h, Figure 5). This contour represents the region of the strongest gradient between the moist air to the south (with typical values of mm) and the much drier air to the north (with typical values of mm, not shown). Figure 5 depicts a greater poleward extent of moist air in the warm sector of the merged ET/first downstream system, second downstream system and incipient third downstream system in the ET run. Extensive precipitation and flooding associated with ET systems have been documented previously (Jones et al., 2003 and references therein). Our results indicate that, in association with an amplified upper-level wave pattern, ET can enhance the meridional moisture exchange in

8 624 M. Riemer and S. C. Jones 1800 km Figure 5. Column-integrated precipitable water at 216 h in the LC run (grey) and the ET run (black). The 35 mm contour depicted here represents the region of strongest gradient between the moist area in the south and the much drier midlatitudes (see text for details). The zonal location of the merged ET system is indicated by the solid line, the positions of the second and third downstream system with dashed and dotted lines, respectively. the downstream region on a much larger scale than the individual ET system. A quantification of this process by integrating over the life cycle of the baroclinic systems and over several wavelengths could provide an indication of whether the impact of ET might play a role in the moisture budget of the midlatitudes on seasonal to climatological time-scales. This assessment, however, is beyond the scope of the current study Impact of ET as seen in Hovmöller diagrams To investigate the impact of ET on the upper-level flow, we consider the 200 hpa meridional wind, meridionally averaged over a band around the initial jet axis with an extent of 1800 km (indicated by the horizontal black lines in Figure 1(a)). Hovmöller diagrams provide temporally continuous information at the expense of spatial resolution, and are particularly useful for identifying wave trains. In the LC run, the initial upper-level perturbation triggers a short wave-train which decays within the first 3 days (Figure6(a);thedecayofthewavetrainisindicatedbythe dashed arrow). A coherent wave train is found only after day 3, when surface development accompanies the upper-level perturbations. In the ET run, the amplification of the initial upperlevel wave pattern is apparent after day 1 (Figure 6(b)). In particular, the signature of the jet streak just downstream of ET is evident from the amplified northerlies between days2and5( km). A slight phase shift of the primary downstream trough relative to the wave pattern in the LC run is found after day 3. In contrast to the LC run, the meridional flow associated with the primary downstream trough decreases sharply between days 5 and 7. This decrease is consistent with the wrap-up of the trough and the mature stage of the baroclinic life cycle. During the merger of the ET and the primary downstream system, larger-scale ridging occurs in place of the polward-moving remnants of the primary downstream trough. Hence the meridional flow just downstream of ET changes from a jet-streak-dominated northerly flow to southerlies. This pronounced phase shift is evident between days 6 and 7 in Figure 6(b). The kink of the wind dipole around day 8 ( km) is the signature of the impact of this phase shift on the second downstream trough. Further downstream, the wave train is largely in phase with its counterpart in the LC run but of considerably larger amplitude. A simple way to quantify the impact of the ET system on the upper-level flow is to plot a Hovmöller diagram of the differences between the ET and LC runs (Figure 6(c)). The amplification of the upper-level wave pattern just downstream of ET dominates the impact in the first 5 days. We note that during this time the modification of the upper-level flow closely follows the phase lines of the ET system and the primary downstream trough. It is not apparent that the direct impact of the ET system early in the experiment excites a coherent wave train by itself. The impact of ET propagates with the group speed of downstream baroclinic development only after day 5. From the discussion of the synoptic evolution in Section 4, we conclude that this wave train denotes the amplification of the leading edge of downstream baroclinic development. The wave train has its origin in the faster and stronger development of the primary downstream system. The interaction of the amplified wave train with the development upstream of ET due to the periodic boundaries complicates tracking the impact of ET at the end of the experiment. The amplification of the wave train is a significant and coherent impact in this experiment. After day the magnitude of the differences between the ET and LC runs in the downstream region is comparable to that of the differences in the vicinity of ET. At the end of the experiment, the largest impact is associated with the phase shift of the upper-level wave pattern between the primary and second downstream trough. This impact, however, is rather local compared with the O(10 4 km) scale of the amplified wave train. 5. Quantitative analysis based on piecewise PV inversion 5.1. Methodology We apply a piecewise PV inversion diagnostic using nonlinear balance (Davis, 1992) to investigate the direct impact of ET and its propagation downstream in more detail. The PV anomalies are defined relative to a zonal background state and are divided into the positive PV tower of the transforming tropical cyclone, the negative PV anomaly associated with the outflow, low-level PV and lower boundary temperature anomalies and upper-level PV anomalies in the midlatitudes. The PV inversion is performed on a subdomain in which the system of interest is approximately centred. Only PV anomalies within this subdomain are considered. The domain size and location is adjusted for every time period under consideration. The upper-level flow in the midlatitudes is closely linked to the tropopause topology (θ on PV = 2 PVU; (Morgan and Nielsen-Gammon, 1998). On a PV surface, θ is conserved following adiabatic motion. In regions where diabatic

9 Tropical Cyclone Baroclinic Wave Interaction 625 (a) (b) (c) Figure 6. Hovmöller diagram of the meridional wind at 200 hpa (in m s 1 ), meridionally averaged over a zonal band of 1800 km width centred on the jet axis: (a) LC run, (b) ET run and (c) the differences (ET-LC) between these runs. Northerlies are shaded light to dark and southerlies vice versa. Open circles denote the zonal position of the ET system. Dotted lines indicate the axis of the primary (first), second (second) and third (third) downstream trough. Solid arrows indicate the propagation of upper-level wave trains, while the dashed arrow indicates the dissipation of the barotropic wave train excited by the initial perturbation. The periodic integration domain is extended to identify the upper-level wave train more easily. The origin of the horizontal axis has been matched to the initial zonal position of the ET system. processes are negligible, the evolution of the dynamic tropopause can thus be explained by advection of θ along the PV surface. By interpolating the balanced wind fields obtained by inversion of the aforementioned PV anomalies onto the 2 PVU surface we can infer the contribution of the respective anomalies to the evolution of the dynamic tropopause. The PV inversion reveals the non-divergent part of the flow only. It is known, however, that a considerable divergent component can be found in the outflow and in the vicinity of jet streaks. We thus complement the PV diagnostic with a Helmholtz partitioning of the flow in the non-divergent and non-rotational components. Further, we invert the quasigeostrophic (qg) ω-equationinitsq-vector form (Hoskins et al., 1978) using a domain-averaged Coriolis parameter and static stability to estimate the relative importance of individual contributions to the upper-level divergent flow. Details of the definition of the PV anomalies, the PV inversion technique and the Helmholtz partitioning are giveninrjd. Special attention will be given to the formation of the ridge downstream of ET and downstream of the primary downstream system. It is reasonable to consider the associated θ anomalies at the tropopause as wave-like disturbances to a zonal basic state. For this configuration, only the meridional flow can lead to an amplification of the pattern. As in RJD, the ridge-building is analyzed by the meridional advection of θ (v θ/ y) into the crest of the ridge. We will present time series of v θ/ y due to individual flow components integrated over a predefined area around the ridge axis. The axis is defined by θ/ x = 0, evaluated at the tropopause. In order for our algorithm to find a continuous ridge axis at all times under consideration, it was necessary to smooth the θ distribution at the tropopause over a spatial scale of 600 km. By visual inspection, we have confirmed that the axis analyzed from the smoothed data matches the axis in the original data closely for all times. (Some examples are shown in Figures 7 and 12. The respective analyzed ridge axis is denoted by the thick solid line.) The area of integration is given by the region around the axis in which θ in the zonal direction does not differ by more than a prescribed value θ from the θ value on the ridge axis (thick dashed lines in Figures 7 and 12). As we consider the area-integrated values of v θ/ y, the values of the contributions due to individual anomalies usually increase when θ increases. However, the relative magnitudes of the individual contributions, and thus our interpretation of the results, are not sensitive to choices of θ between 0.5 and 2 K. In the following a value of θ = 2Kisused Direct impact of ET Ridge-trough amplification The patterns of v θ/ y associated with the PV anomalies of the tropical cyclone and the divergent flow in the early part of the interaction (36 72 h) are similar to the patterns in RJD (their figures 6 to 9) and are not shown in this study. It is obvious from these patterns that the anticyclonic circulation associated with the outflow anomaly continuously amplifies the trough downstream (see also Figure 7, where the downstream trough is marked by an arrow). The contributions from the upper-level wave pattern and the divergent flow to the formation of the downstream trough are small (not shown). The individual contributions to the building of the ridge during the early phase of the interaction (36 72 h) are presented in Figure 8. The most pronounced contribution throughout this period is due to the divergent flow. Technically, the divergent flow cannot be attributed to a specific flow feature. At 36 and 48 h, however, the midlatitude upper-level flow is largely similar in the ET and LC runs. A comparison of the divergent flow patterns shows that the divergent flow at these times is almost entirely The smoothing is performed using a two-dimensional boxcar average.

10 626 M. Riemer and S. C. Jones 1200 km Figure 7. Balanced wind (arrows) and v θ/ y (contours) associated with the outflow anomaly, and θ (shaded) at the dynamic tropopause (PV = 2PVU) at 36 h. Contour lines are drawn at 2, 4, 8 and Ks 1. White contours denote northward advection of high-θ air, black contours southward advection of low-θ air. For the sake of visual clarity, values are depicted for θ 355 K only. The location of the ET system is marked by an asterisk. The developing primary downstream trough is highlighted by a white arrow. The thick line depicts the ridgeaxisasanalyzedfromthesmootheddata.the thick dashed lines denote the zonal boundaries ( θ = 2K)overwhichv θ/ y is integrated (see text for details). K Figure 8. Integrated advection of θ into the crest of the ridge downstream of ET by the balanced circulation associated with the outflow anomaly (black), the positive anomaly of the PV tower (dark grey), the upper-level wave pattern (light grey) and the divergent flow (medium grey) for the times given on the x-axis. Negative values denote northward advection of high-θ air along the ridge axis and thus the amplification of the ridge. The values on the y-axis are in K s 1 km 2. associated with the tropical cyclone outflow and a typical outflow pattern can be recognized (not shown). This pattern still dominates the divergent flow at 60 and 72 h. Within and around the building ridge, the divergence calculated from the qg ω-equation is an order of magnitude smaller and exhibits a pattern unrelated to the observed one (not shown). Virtually the whole divergent flow can thus be attributed to the outflow from the tropical cyclone at these times. The increasing contribution to ridge-building by the divergent flow (Figure 8) is associated with the continuous movement of the ET system towards the jet axis. Due to the symmetry of the circulation with respect to the ridge axis (e.g. Figure 7, cf. discussion in RJD), the balanced outflow anticyclone makes only small, positive as well as negative, contributions to v θ/ y into the crest of the ridge (Figure 8). The advection of high-θ air into the crest of the ridge by the cyclonic circulation of the ET system gradually increases with time. This can be attributed to the movement of the ET system towards the jet axis and the gradual displacement of the storm centre away from the ridge axis, towards the western flank of the ridge (RJD). The direct impact of ET in the present study, as revealed by the piecewise PV inversion, is similar to the straight-jet case in RJD. Distinct differences, however, exist between the twoscenarios.inrjd,theetsystemistheonlyperturbation exciting development in the midlatitudes and can thus be considered as a local wave-maker. Here, the ET system interacts and competes with the high-amplitude initial upper-level perturbation. Due to the asymmetric structure of the initial upper-level perturbation, the midlatitude upperlevel flow contributes to the ridge-building until 36 h (shown at 36 h in Figure 8). Subsequently, however, the upperlevel flow counteracts the ridge formation (Figure 8). It is importanttonotethattheetsystemcanprevailoverthe tendency of the midlatitude flow at these times. Further, in RJD the outflow hinders the eastward propagation of the upper-level wave packet on a scale of 1 2 wavelengths downstream of ET. This distinct hindering promotes phase-locking between the ET system and the upper-level pattern. In the present study v θ/ y associated with the balanced-outflow anticyclone at the flanks of the ridge is approximately only half as strong as in RJD (cf. Figure 7 and figure 7(b) of RJD). Here, the ET system interacts earlier in the experiment and the outflow anomaly is less pronounced than during the interaction in RJD. Measured by the extent of the 365 K isentrope, the scale of the outflow anomaly is approximately 1200 km in diameter, whereas in RJD the diameter is approximately 2000 km (cf. Figure 3(a) and figure 2(a) in RJD). Consistently, the wave trains in the LC and ET runs in the present study have very similar group speeds (cf. Figure 6(a) and (b)). The ET system apparently hinders the upper-level wave packet much less and is thus more passively steered into the midlatitudes Jet streak formation The development of a jet streak is a prominent feature of the interaction of the ET system with the midlatitude flow. In general, the formation of a jet streak is the manifestation of upper-level frontogenesis. In our experiment, the

11 Tropical Cyclone Baroclinic Wave Interaction 627 midlatitude θ gradient on the tropopause north of the outflow anomaly increases significantly between 36 and 72 h (Figure 3). To investigate the jet streak formation, we examine upperlevel frontogenesis in a simplified framework. Davies and Rossa (1998) have proposed that upper-level frontogenesis can be regarded as the two-dimensional process of PV frontogenesis along an isentrope intersecting the tropopause. Their methodology, however, is limited by the use of a single isentrope and thus does not capture the threedimensional upper-level PV structure. A more complete and still concise representation of upper-level PV is the distribution of θ on a PV surface representing the tropopause (Morgan and Nielsen-Gammon, 1998). We propose that frontogenesis of θ on the tropopause provides an improved estimate for upper-level frontogenetic processes in a simple framework. This approach is similar to that of Wandishin et al. (2000), who have analyzed upper-level frontogenesis as the steepening of the tropopause in height coordinates. We consider the period from h and calculate Petterssen s frontogenesis function F, interpolating the quasi-horizontal flow and θ to the PV = 2PVUsurface: F = d dt θ = 1 [ θ 2 ( ) x u x + θ x θ y vx + u y + θ 2 ] y v y. (1) θ The subscripts denote the partial derivative in the respective direction. The quasi-horizontal derivatives are taken on the constant-pv surface of the dynamic tropopause. We calculate F using the total flow, the flow associated with the respective PV anomalies (as in Morgan, 1999), the background and divergent flow. A significant region of frontogenesis is found on the western flank of the ridge, just upstream of the jet streak (Figure 9). This result is consistent with Bosart (2003), who appliedthe approach ofwandishinet al. in an observational case study of upper-level frontogenesis. Bosart s results suggested that air parcels are undergoing frontogenesis in the jet entrance region and then carry their frontal properties well downstream km Figure 9. Petterssen s frontogenesis function F for θ at the tropopause (shaded, in K(ms) 1, positive values denote frontogenesis) for the ET run at 48 h. For visual clarity F has been smoothed by a 300 km running mean in two dimensions. Thick contours denote θ on PV = 2PVU.The thin contours show wind speed at 200 hpa, every 5 m s 1 starting at 40 m s 1. At early times (36 and 48 h), the divergent flow makes the largest frontogenetic contribution in this region (not shown). Subsequently, the divergent contribution remains large but the contribution from the upper-level wave pattern becomes equally important. At 72 h, the frontogenesis region extents further into the crest of the ridge (not shown). There is no persistent and significant contribution from the balanced flow associated with the ET system, nor from the background flow. Thus the divergent flow plays an important role, not only in the building of the ridge downstream of ET butalsointheformationofthejetstreak. In addition, the jet streak appears to be partly formed by the superposition of the outflow anticyclone and the midlatitude jet (cf. the jet streak in Figure 3(a) and the outflow circulation in Figure 7). This mechanism is not associated with frontogenesis within the midlatitude θ gradient but rather with the elevation of the tropopause south of the jet due to the high-θ outflow air. Similar formation mechanisms for jet streaks have been discussed in a barotropic framework by Cunningham and Keyser (2000). Further investigation of the jet streak formation and its role in the downstream impact of ET is an interesting subject for future research Rapid development of downstream cyclone The characteristic downstream impact of the ET system, i.e. the amplification of the upper-level wave pattern and the formation of the pronounced jet streak, constitutes a very favourable environment for surface cyclogenesis. The development of a surface cyclone can be explained by vortex stretching due to ascending motion. We quantify the augmentation of the upper-level forcing for low-level development by calculating the vertical motion at 700 hpa from the qg ω-equation, retaining forcing terms above 650 hpa only (650 hpa is our separation level between the upper and lower PV anomalies). The forced rising motion in the genesis region in the ET run from h is at least twice as strong as in the LC run (exemplified for 72 h in Figure 10). From a PV perspective, the amplification of the low-level warm anomaly by the flow associated with the upper-level PV anomalies can be considered as the upper-level forcing for baroclinic development in the early stage of development (Hoskins et al., 1985, section 6e). Applying piecewise PV inversion, we find an increase of the southerly flow into the incipient warm sector at the lower boundary associated with the upper-level anomalies. Values of v θ/ y increase by about 50% in the ET run (not shown). Both diagnostics show a significant enhancement of the dry dynamics of baroclinic development. Moist processes play an important role in the intensification of the baroclinic systems in this experimental set-up (cf. DRY experiment in RJD). The enhanced low-level southerly flow due to the stronger upper-level PV anomaly leads to a larger advection of moisture into the system. Maximum values of moisture advection in the ET run are % larger than in the LC run (not shown). The stronger forcing for vertical motion can be expected to augment the release of latent heat further. Therefore the modification of the upper-level flow in the ET run supports the diabatic processes in the developing system as well. Thus we conclude that the rapid development of the primary downstream low