1. Introduction and background
Tropical cyclones (TCs) and the extratropical jet have historically been analyzed separately due to their dynamical differences as well as their geographical separation. However, recent studies have shown that TCs approaching the jet stream can disturb the extratropical flow in such a way that induces Rossby wave amplification and breaking, potentially leading to extreme weather events downstream of the interaction (Harr and Dea 2009; Cordeira and Bosart 2010; Grams et al. 2011; Archambault et al. 2013; Grams et al. 2013a; Pantillon et al. 2013; Archambault et al. 2015; Grams and Archambault 2016; Pohorsky et al. 2019). This paper considers the extratropical flow response to recurving TCs in the North Atlantic from a climatological perspective with a view toward illuminating the characteristics and mechanisms that govern the interaction.
The extratropical jet is a planetary-scale phenomenon characterized by a westerly wind maximum located near the tropopause, typically residing near 40°–70°N. The jet provides a waveguide for Rossby waves due to the associated large gradients in potential vorticity (PV). Rossby waves on the jet are responsible for synoptic-scale troughs and ridges that may amplify in concert with surface cyclones via baroclinic instability. Breaking waves can lead to the formation of cutoff lows and PV streamers. As TCs approach midlatitudes, their structure and trajectory are affected by the midlatitude flow. During this period, a TC undergoes a structural transformation into an extratropical cyclone (EC) through the process known as extratropical transition (ET) (Jones et al. 2003). As the TC travels westward, the steering flow west of the subtropical high and/or ahead of an approaching trough will ultimately cause the storm to gain latitude and track eastward. This “recurvature” occurs as the storm moves poleward toward the extratropical jet, thus increasing its likelihood of interacting with the jet.
The large diabatically generated temperature anomalies within the TC’s inner core of O(10) K are associated with anomalies of high PV below the level of maximum heating and low-PV anomalies above the level of maximum heating (Grams et al. 2011, 2013b; Grams and Archambault 2016). The TC’s upper-level, divergent outflow advects low-PV air poleward (Bosart and Lackmann 1995; Agusti-Panareda et al. 2004; Riemer et al. 2008; Riemer and Jones 2010; Grams et al. 2013b; Archambault et al. 2013). The accumulation of this low-PV air on the equatorward side of the extratropical jet may result in a larger PV gradient across the jet and the intensification of a jet streak; farther downstream, a ridge may amplify and inhibit the eastward propagation of the upstream trough (Pantillon et al. 2015; Grams and Archambault 2016; Quinting and Jones 2016; Riboldi et al. 2019). The TC’s divergent outflow may continue to feed low-PV air into the downstream ridge, which may trigger an amplified Rossby wave train and downstream energy propagation (Agusti-Panareda et al. 2004; Riemer et al. 2008; Harr et al. 2008; Harr and Dea 2009; Anwender et al. 2010; Riemer and Jones 2010; Archambault et al. 2015; Grams and Archambault 2016; Quinting and Jones 2016). The ridge amplification may also result in the amplification of a downstream trough (Riemer and Jones 2010). The upper-level downstream trough then creates an environment conducive to cyclogenesis, similar to that seen following TC Helene in 2006 (Chaboureau et al. 2012; Pantillon et al. 2013), TC Hanna in 2008 (Grams et al. 2011), and TC Leslie in 2012 (Pantillon et al. 2015).
Until recently, the TC–jet interaction was investigated mainly in the context of case studies. Archambault et al. (2013, 2015) conducted the first extensive climatological analysis of recurving TCs in the western North Pacific. The interaction was shown to be regulated by a preexisting Rossby wave train whose amplitude is subsequently affected by the recurving TC. The strength of the interaction was determined by the magnitude of the negative PV advection by the irrotational wind from the TC. The enhanced flow anomalies that spawn from strong interactions with a TC typically lasted long enough to propagate over North America. Conversely, weak interactions were often associated with a shorter-lived, but still statistically significant flow amplification that generally dissipates before reaching North America (Archambault et al. 2015).
Compared to the Pacific basin, the North Atlantic TC–jet climatology has received less attention. Quinting and Jones (2016) indicated that while TCs have a role in altering the large-scale flow in the North Atlantic, the propagating Rossby waves downstream from the TC–jet interaction are not statistically different from climatology. Furthermore, the Rossby wave packets associated with ET in the Atlantic basin are generally weaker and therefore do not propagate as far downstream compared to midlatitude cyclone wave packets (Torn and Hakim 2015). These results, in combination with several Atlantic case studies (e.g., Grams et al. 2011; Pantillon et al. 2013, 2015), suggest that TC recurvature in the North Atlantic may not as readily lead to Rossby wave amplification and dispersion. Reasons for these differences may stem from the differences in the waveguides and storm tracks. For example, within the North Atlantic, the extratropical jet is shorter and weaker (Archambault et al. 2015).
Case studies have highlighted a variety of possible extratropical responses to recurving TCs. The factors regulating the interaction may be primarily related to characteristics of the preexisting large-scale flow pattern of the basin (Riemer et al. 2008; Harr and Dea 2009; Reynolds et al. 2009), including the strength of the jet (Riboldi et al. 2018) and the existence of a precursor Rossby wave upstream from the recurving TC (Archambault et al. 2015; Quinting and Jones 2016). The relative locations of the recurving TC and the nearest synoptic-scale trough have also been shown to impact the downstream evolution of waves on the jet (Archambault et al. 2013; Grams et al. 2013a; Keller et al. 2014; Archambault et al. 2015; Quinting and Jones 2016; Riboldi et al. 2019). Several studies (e.g., Harr and Elsberry 2000; Agusti-Panareda et al. 2004; Riemer and Jones 2010; Grams et al. 2013a; Keller et al. 2014; Quinting and Jones 2016) have indicated that the relative longitudes of the TC and the waves on the extratropical jet are a key component in the subsequent evolution of the flow pattern. The recurvature of TC Jangmi (2008) occurred when the TC was directly south and aligned with the nearest trough axis, but did not result in a significant extratropical flow response (Grams et al. 2013a). However, a PV surgery technique relocated the TC to the downstream flank of the nearest trough that then culminated with amplified extratropical flow and downstream cyclogenesis (Grams et al. 2013a). This study in particular elucidates the sensitivity of the TC–jet phasing in the resulting flow pattern and downstream high-impact weather. A recent study by Riboldi et al. (2019) elaborated on this theme by examining the phase speed of troughs during their interaction with TCs. It was found that decelerating troughs allowed the trough to remain positioned upstream of the TC, which promoted phase locking and subsequent downstream Rossby wave packets with above average amplitudes. Conversely, accelerating troughs outran the TCs, inhibited phase locking, and yielded a downstream wave pattern statistically similar to climatology.
In both the Atlantic and Pacific, TC intensity has been shown to have little impact on downstream wave characteristics (Riemer et al. 2008; Harr and Dea 2009; Riemer and Jones 2010; Archambault et al. 2013; Pantillon et al. 2015; Riboldi et al. 2018). While the most intense TCs were more often associated with larger deflection of the jet locally, both strong and weak TCs were capable of initiating a similar downstream response (Riemer et al. 2008; Riemer and Jones 2010; Archambault et al. 2013). In addition, whether or not the recurving TC reintensifies as an EC or decays cannot be used to establish the future amplitude of the jet downstream of the interaction (Harr and Dea 2009; Archambault et al. 2013). For these reasons, TC intensity is assumed to be a secondary factor compared to the preexisting large-scale flow and the relative location of the TC.
The purpose of this study is to conduct a climatological analysis of the extratropical flow response to TC recurvature events in the North Atlantic. Rossby waves on the extratropical jet are diagnosed using a wavelet spectral technique as described in section 2, along with the data sources, the TC selection criteria, and the wavelet decomposition method. Given that the interactions may depend on the preexisting state of the extratropical flow and/or TC intensity, we separately investigate interactions that yield significantly modified extratropical flow from those that do not and present the results in section 3. The characteristics of these subsets are investigated to determine if certain aspects of recurving TCs and the large-scale flow influence extratropical flow amplification, and if the relative location and propagation speed of the nearest trough and the recurving TC are primary regulators of the downstream response. Conclusions are discussed in section 4 along with insight into future extensions of this study.
2. Data and methodology
The climatological analysis of TC–jet interactions conducted in this paper requires 1) identification of historical recurving TCs and their characteristics, and 2) a characterization of the extratropical jet evolution during periods of TC recurvature. This section describes the sources of data and the metrics used in the joint climatology, including the wavelet technique used to diagnose the amplitude and location of Rossby waves.
a. Data and sources
Rossby waves on the extratropical jet are diagnosed as disturbances in PV on the 320 K isentropic surface. For each recurving TC event, PV at 12 h intervals is obtained beginning 4 days (96 h) before recurvature and extending 7 days (168 h) after recurvature on a 1° × 1° global grid. Data is acquired from the ERA-Interim reanalysis dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF), which includes data starting in 1979 (Dee et al. 2011).
PV is a scalar quantity whose meridional gradient provides a waveguide for Rossby waves (Martius et al. 2010). Unlike relative and planetary vorticity, PV is conserved following frictionless, adiabatic flow and is therefore a convenient tracer for large-scale flow, especially on an isentropic surface (Hoskins et al. 1985). Rossby waves owe their existence to gradients in PV; therefore, PV is ideally suited for analyzing Rossby waves on the extratropical jet. The jet stream is situated near the elevation of the tropopause (Bosart and Lackmann 1995). The 1.5 potential vorticity unit (PVU; 10−6 m2 s−1 K kg−1) contour on the 320 K isentropic surface is used in this study to represent the approximate latitude of the jet stream. The 320 K isentropic surface is chosen because it reliably intersects the tropopause in midlatitudes near the latitude of the extratropical jet and is therefore appropriate for diagnosing Rossby waves.
Recurving TCs and their properties are diagnosed using data from the best track reanalysis hurricane database (HURDAT2) from the National Hurricane Center (Landsea and Franklin 2013). This dataset is a poststorm analysis that takes into account all observations, including those unavailable in realtime. HURDAT2 contains reanalysis data from all known TCs occurring in the Atlantic basin from 1851 to 2013, including best track data on location, pressure, size, and winds at 6-h intervals (Landsea and Franklin 2013). This study focuses on storms between 1979 and 2016 that experienced recurvature and reached a latitude of 35°N. These stipulations leave a total of 272 storms in the dataset whose tracks are shown in Fig. 1.
Tracks of the 272 recurving Atlantic TCs that occurred between 1979 and 2016 and reached a latitude of 35°N. Dots indicate the recurvature point of each track. Red track represents TC Harvey (1981).
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Tracks of the 272 recurving Atlantic TCs that occurred between 1979 and 2016 and reached a latitude of 35°N. Dots indicate the recurvature point of each track. Red track represents TC Harvey (1981).
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Tracks of the 272 recurving Atlantic TCs that occurred between 1979 and 2016 and reached a latitude of 35°N. Dots indicate the recurvature point of each track. Red track represents TC Harvey (1981).
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Recurving storms are selected as those with three consecutive time steps where the track of the TC moves eastward and northward. The point of recurvature is selected as the western-most point reached by the TC before it begins moving eastward. In the cases with multiple recurvatures, the first recurvature is selected as the recurvature point. If the point of recurvature occurs at 0000 or 1200 UTC, the exact point is used in this study. However, due to differences in time intervals between the data (6 h intervals for HURDAT2 and 12 h intervals for ERA-Interim), if recurvature occurs at 0600 or 1800 UTC, the point of recurvature is adjusted to the location and time at the prior time step (0000 or 1200 UTC). The storm tracks are normalized by the recurvature longitude and time. In a recurvature relative framework, a longitude of 0 represents the recurvature longitude and a time of 0 corresponds to the recurvature time. A time value less than zero represents hours before recurvature and a positive time value corresponds to hours after recurvature.
b. Rossby wave diagnosis
Rossby waves on the extratropical jet are diagnosed by the following procedure. At each longitude, a meridional average of PV between 40° and 70°N is calculated. The global midlatitude mean PV is then computed from 40° to 70°N across all longitudes and all timesteps (4 days before recurvature to 7 days after recurvature) for each case individually. The global midlatitude mean is subtracted from the meridional average PV at each longitude which yields a deviation of the meridionally averaged PV at each longitude from the overall midlatitude mean PV. A weighted running average is then applied spatially to filter finescale fluctuations due to PV streamers and subsynoptic-scale waves. The filtering is performed so that these small-scale features are not aliased onto the synoptic-scale features, which are the primary focus of this analysis. While such small-scale features are themselves worthy of analysis, especially given their ability to trigger precipitation events downstream, their diagnosis is beyond the scope of this study. Defining the global midlatitude mean PV as a different value for each case ensures the seasonality of the mean midlatitude PV does not affect the magnitude of the troughs and ridges. However, it should be noted that the wave amplitude diagnosed using the wavelet technique described below is insensitive to the definition of the zonal mean. Errors in the zonal mean affect only the wavenumber zero contribution to the spectrum.
A wavelet spectral decomposition is applied to this Rossby wave metric in order to identify the amplitude and location of troughs and ridges, as is described later in this section. Note that the spatial averaging of PV on an isentropic surface renders this Rossby wave metric a measure of the circulation anomalies associated with Rossby waves. Figure 2a demonstrates the ability of the Rossby wave metric to identify troughs and ridges in an example case of TC Harvey (1981) by comparing the Rossby wave metric to the raw PV field. To facilitate the comparison, the Rossby wave metric is translated and inverted (see figure caption) so that the contour may be mapped alongside the 1.5 PVU contour of the raw field. (Note, the raw calculation of the PV anomalies that comprise the Rossby wave metric are used for all calculations throughout this study.) Our Rossby wave metric accurately depicts the trough and ridge locations as well as their relative amplitudes while filtering subsynoptic variations and streamers.
A demonstration of the Rossby wave metric and the wavelet power spectrum at the time of TC Harvey’s recurvature at 1200 UTC 14 Sep 1981. (a) Potential vorticity on the 320 K isentropic surface (filled colored contours), the 1.5 PVU contour (black), which can be used to approximate the location of the jet stream, and the Rossby wave metric (blue), which has been inverted, translated north by 60°, and amplified by a factor of 10 to facilitate comparison with the 1.5 PVU contour. The purple line shows the complete track of Harvey with the purple dot indicating the position at this time step. The bold gray dashed line denotes the longitude of recurvature and the thin gray dashed line denotes 120° downstream of the recurvature longitude; “T” indicates a trough location, and “R” indicates a ridge. (b) Trough power as calculated by the wavelet decomposition technique. Synoptic-scale wavelengths (20°–60°) are considered in this study.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
A demonstration of the Rossby wave metric and the wavelet power spectrum at the time of TC Harvey’s recurvature at 1200 UTC 14 Sep 1981. (a) Potential vorticity on the 320 K isentropic surface (filled colored contours), the 1.5 PVU contour (black), which can be used to approximate the location of the jet stream, and the Rossby wave metric (blue), which has been inverted, translated north by 60°, and amplified by a factor of 10 to facilitate comparison with the 1.5 PVU contour. The purple line shows the complete track of Harvey with the purple dot indicating the position at this time step. The bold gray dashed line denotes the longitude of recurvature and the thin gray dashed line denotes 120° downstream of the recurvature longitude; “T” indicates a trough location, and “R” indicates a ridge. (b) Trough power as calculated by the wavelet decomposition technique. Synoptic-scale wavelengths (20°–60°) are considered in this study.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
A demonstration of the Rossby wave metric and the wavelet power spectrum at the time of TC Harvey’s recurvature at 1200 UTC 14 Sep 1981. (a) Potential vorticity on the 320 K isentropic surface (filled colored contours), the 1.5 PVU contour (black), which can be used to approximate the location of the jet stream, and the Rossby wave metric (blue), which has been inverted, translated north by 60°, and amplified by a factor of 10 to facilitate comparison with the 1.5 PVU contour. The purple line shows the complete track of Harvey with the purple dot indicating the position at this time step. The bold gray dashed line denotes the longitude of recurvature and the thin gray dashed line denotes 120° downstream of the recurvature longitude; “T” indicates a trough location, and “R” indicates a ridge. (b) Trough power as calculated by the wavelet decomposition technique. Synoptic-scale wavelengths (20°–60°) are considered in this study.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
c. Wavelet decomposition
Spectral techniques, such as the well-known Fourier transform, may be used to identify the individual wavelengths that contribute to a given signal. A drawback of using the Fourier transform is that it only provides information on which wavelengths are present in the signal with no information regarding the spatial or temporal location of those wavelengths within the signal. For this study, wavelet transforms are used. This approach allows one to identify which wavelengths in the dynamical wave structure contribute power and at what longitudes these waves occur (e.g., see Torrence and Compo (1998) for a review of wavelets in atmospheric science). The longitude dependence of Rossby wave activity makes wavelets an appropriate choice, and the use of PV is appropriate given the essential role of PV in the dynamics of Rossby waves.
The total power spectrum is separated into power contributed from troughs and ridges. An example of trough power at the recurvature time of TC Harvey (1981) is shown in Fig. 2b. It is not surprising that there is little power in the shortest of wavelengths since a filtering technique was applied during the creation of the Rossby wave metric. This study is primarily concerned with synoptic-scale wavelengths (20°–60°) that dominate weather on 3–7 day time scales. When comparing the trough locations extracted from the Rossby wave metric in Fig. 2a with the synoptic-scale trough wavelengths in Fig. 2b, each trough from the raw PV field is captured explicitly by the wavelet power decomposition, giving confidence in this technique’s ability to represent the location and amplitude of synoptic-scale troughs.
Despite the strengths of the wavelet technique, wave breaking events cannot be diagnosed using this procedure. At worst, due to the latitudinal-averaging, wave breaking may be aliased as reduced power. As will be presented in the next section, the evolution of power at synoptic wavelengths does not appear to suffer from this aliasing.
3. Results
The presentation of results begins with a demonstration of the wavelet decomposition of the Rossby wave metric and its evolution during several individual TC recurvature events (see section 3a). Because the characteristics of the extratropical response are not uniform across all TC-recurvature events, a subgrouping of similar events is then presented in section 3b. The properties of the TC and incipient extratropical flow that distinguish the different types of extratropical flow response are then analyzed and discussed. In section 3c, the results conclude with a comparison of the extratropical response for distinct subgroups based on the Rossby wave relative speed of the TC following recurvature.
a. Individual TC recurvature events
Hovmöller diagrams of the trough power contained in synoptic-scale wavelengths during four recurving TC events are shown in Fig. 3. Focusing mainly on the downstream region (0°–120°E), the four cases shown in Fig. 3 as well as the Hovmöllers from several other storms exhibit a disruption in downstream trough power near and slightly after the time of recurvature.
Hovmöller diagrams of average synoptic-scale trough power for TCs (a) Harvey (1981), (b) Frances (1992), (c) Helene (2000), and (d) Joaquin (2015). Black circles annotate the downstream region with trough power suppression and subsequent power return. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Hovmöller diagrams of average synoptic-scale trough power for TCs (a) Harvey (1981), (b) Frances (1992), (c) Helene (2000), and (d) Joaquin (2015). Black circles annotate the downstream region with trough power suppression and subsequent power return. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Hovmöller diagrams of average synoptic-scale trough power for TCs (a) Harvey (1981), (b) Frances (1992), (c) Helene (2000), and (d) Joaquin (2015). Black circles annotate the downstream region with trough power suppression and subsequent power return. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
In the cases of Harvey (Fig. 3a), Frances (Fig. 3b), Helene (Fig. 3c), and Joaquin (Fig. 3d), the synoptic-scale trough power diminishes around the time of recurvature (0–48 h after recurvature), but then returns back near prerecurvature levels. This general pattern is also prominent in an analysis of synoptic-scale ridge power (not shown explicitly with Hovmöllers but can be seen in Fig. 4). The change in downstream power over time is shown clearly by the time series of the sum of the downstream (0°–120°E) trough (ridge) power, represented by the solid (dashed) black lines in Fig. 4 for the same four previously mentioned cases.
Trough (solid black lines) and ridge (dashed black lines) power from 0° to 120° downstream of the TC’s recurvature longitude as a function of time for the cases of (a) Harvey (1981), (b) Frances (1992), (c) Helene (2000), and (d) Joaquin (2015), all of which are archetypical TC cases contained within the subset discussed in the text. The red line denotes the prototypical exponential decay and growth curve whose correlations with the trough power curves (solid black lines) are used to distinguish the subset of TCs.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Trough (solid black lines) and ridge (dashed black lines) power from 0° to 120° downstream of the TC’s recurvature longitude as a function of time for the cases of (a) Harvey (1981), (b) Frances (1992), (c) Helene (2000), and (d) Joaquin (2015), all of which are archetypical TC cases contained within the subset discussed in the text. The red line denotes the prototypical exponential decay and growth curve whose correlations with the trough power curves (solid black lines) are used to distinguish the subset of TCs.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Trough (solid black lines) and ridge (dashed black lines) power from 0° to 120° downstream of the TC’s recurvature longitude as a function of time for the cases of (a) Harvey (1981), (b) Frances (1992), (c) Helene (2000), and (d) Joaquin (2015), all of which are archetypical TC cases contained within the subset discussed in the text. The red line denotes the prototypical exponential decay and growth curve whose correlations with the trough power curves (solid black lines) are used to distinguish the subset of TCs.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
We have objectively created a subset of recurving TCs that exemplify this pattern of synoptic-scale trough power. The cases to be captured by our subset include those with a substantial amount of synoptic-scale trough power before recurvature, a steep decline in power near the time of recurvature, which persists for some time after recurvature, followed by an increase in trough power back toward prerecurvature values. This prototypical “decay-growth pattern” in the time series of trough power is illustrated by the red curves in Fig. 4. To objectively extract these storms and others with a similar evolution of Rossby wave power, each storm’s individual power time series is correlated with the prototypical decay-growth pattern, including leading and lagging the idealized function by 48 h in each direction. Cases with a correlation between the power time series and the decay-growth pattern of at least 0.7 are separated from the rest of the storms. After this first condition is satisfied, each individual case’s power time series is correlated with each of the other power time series in the subset and cases with an average intersubset correlation greater than 0.5 are retained. These correlation thresholds were determined through a series of sensitivity tests to ensure the values were “low enough” that all TCs exhibiting a decay-growth pattern in downstream synoptic-scale power were captured, but “high enough” that the cases retained exhibited a similar evolution of downstream power and resembled the prototypical decay-growth pattern such that a systematic behavior could be analyzed. These constraints leave a subset of 41 recurving TC cases, all of which are included in Table 1 and four of which are included in Figs. 3 and 4.
List of TCs included within the subset as determined by the criteria described in the section 3. Whether the TC was on the east or west side of the trough at the time of recurvature is noted in the “TC at RC” column. A comparison of whether the TC or the nearest trough at the time of recurvature traversed a greater eastward distance in the 72 h following recurvature is recorded in the “RW rel speed” column.
b. Subset of similar TC recurvature events
The synoptic-scale trough power from the cases contained within the subset are composited to create the Hovmöller diagram shown in Fig. 5a, whereas the cases left out of the subset are composited to create the Hovmöller diagram shown in Fig. 5b. Despite the averaging applied to the subset of cases to produce these composites, the signal of trough power suppression near and just after the time of recurvature remains apparent along with the return of power approximately 96 h after recurvature (see Fig. 5a). The following t tests will reference the 48-h time periods outlined by the black boxes in Fig. 5. The prerecurvature time period extends from 4 days (96 h) before recurvature to 2 days (48 h) before recurvature, denoted as T − 96 to T − 48 h. The recurvature time period begins at the time of recurvature and continues through 2 days (48 h) after recurvature, denoted as T + 0 to T + 48 h. The postrecurvature time period encompasses 4 days (96 h) after recurvature to 6 days (144 h) after recurvature, denoted as T + 96 to T + 144 h.
Hovmöller diagrams of average synoptic-scale trough power (contours) composited for cases of (a) TCs contained within the subset and (b) TCs not encompassed by the subset. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black outlined boxes indicate 48-h intervals corresponding to the “prerecurvature,” “recurvature,” and “postrecurvature” time periods.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Hovmöller diagrams of average synoptic-scale trough power (contours) composited for cases of (a) TCs contained within the subset and (b) TCs not encompassed by the subset. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black outlined boxes indicate 48-h intervals corresponding to the “prerecurvature,” “recurvature,” and “postrecurvature” time periods.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Hovmöller diagrams of average synoptic-scale trough power (contours) composited for cases of (a) TCs contained within the subset and (b) TCs not encompassed by the subset. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black outlined boxes indicate 48-h intervals corresponding to the “prerecurvature,” “recurvature,” and “postrecurvature” time periods.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
One-sided t tests with 9999 bootstrap replications are used to determine if the difference in average downstream (0°–120°E) trough power between the recurvature time frame and the prerecurvature time frame is significantly less than zero. The t tests indicate that the synoptic-scale trough power in the recurvature time frame is significantly less than the synoptic-scale trough power in the prerecurvature time frame to the 95% confidence level. A similar one-sided t test with 9999 bootstrap replications was executed to diagnose whether the difference between the trough power in the postrecurvature time frame and the recurvature time frame is significantly greater than zero. Again, a low p value is evidence of a statistically significant difference between the average trough power in these time periods—the synoptic-scale trough power is greater 96–144 h after recurvature compared to the trough power 0–48 h immediately following recurvature. Together, this pair of t tests confirms that not only does the synoptic-scale trough power decrease just after the time of recurvature for this subset of recurving TC cases, but it also increases back toward its original level near 4 days following recurvature. It should also be noted that the same bootstrapped t-test technique was used to compare the average amplitude of the postrecurvature trough power to that in the prerecurvature time period. The average power within these two time periods was not significantly different, indicating that the postrecurvature power returns to levels near those of the prerecurvature time period. These same patterns of significant differences were also consistent within an analogous analysis of ridge power for the subset of TCs (not shown).
Two-sample t tests are used to compare the differences in the evolution of synoptic-scale trough power between the subset of TC cases (Fig. 5a) and the remaining storms (Fig. 5b). Both the change in average synoptic-scale trough power from the prerecurvature to the recurvature time frame and from the recurvature to the postrecurvature time frame yield significant differences (as indicated by the small p values) when the subset of cases was compared to the excluded cases. This result supports the objective creation of this subset and reveals that the response of the extratropical jet to the recurving TCs contained within the subset is statistically different from those excluded.
The analysis presented above has been conducted using the Rossby wave amplitude in wavelet spectral space. To determine what is physically happening during this period of synoptic-scale trough power suppression, several cases from the subset were thoroughly analyzed. The evolution of the PV field during the Harvey (1981) recurvature is included in Fig. 6 with Fig. 6b representing the prerecurvature time period, Fig. 6c depicting the recurvature time period, and Fig. 6d illustrating the postrecurvature time period. Mainly focusing on the Rossby wave metric (blue line in Fig. 6), the evolution of wave amplitude is consistent with the finding presented in spectral space. Keep in mind that our analysis focuses on synoptic-scale (20°–60°) waves. At the time before recurvature, the average 1.5 PVU contour exhibits wave power at about 40° wavelengths. At the time of recurvature, the synoptic-scale wave power has decreased, yielding flow that is more zonal. Several days after the time of recurvature, the synoptic-scale power has returned.
(a) Hovmöller of average synoptic-scale trough power for TC Harvey (1981), as shown in Fig. 3a. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black dashed lines are drawn at the timesteps corresponding to panels (b)–(d). Filled colored contours on (b)–(d) illustrate potential vorticity on the 320 K isentropic surface (b) 96 h before recurvature (prerecurvature time period), (c) 24 h after recurvature (recurvature time period), and (d) 132 h after recurvature (postrecurvature time period). The 1.5 PVU contour (black) is used to approximate the location of the jet stream and the Rossby wave metric (blue) is inverted, translated north by 60°, and amplified by a factor of 10 to facilitate comparison with the 1.5 PVU contour. (Note, the raw calculation of the PV anomalies that comprise the Rossby wave metric are used for all calculations.) The purple line shows the complete track of Harvey with the purple dot indicating the position at each time step. The bold gray dashed line labels the longitude of recurvature and the thin gray dashed line denotes 120° downstream of the recurvature longitude. The longitudinal extent of the black dashed lines in (a) corresponds to the region between the dashed gray lines in (b)–(d). “T” indicates a trough location; “R” indicates a ridge.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
(a) Hovmöller of average synoptic-scale trough power for TC Harvey (1981), as shown in Fig. 3a. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black dashed lines are drawn at the timesteps corresponding to panels (b)–(d). Filled colored contours on (b)–(d) illustrate potential vorticity on the 320 K isentropic surface (b) 96 h before recurvature (prerecurvature time period), (c) 24 h after recurvature (recurvature time period), and (d) 132 h after recurvature (postrecurvature time period). The 1.5 PVU contour (black) is used to approximate the location of the jet stream and the Rossby wave metric (blue) is inverted, translated north by 60°, and amplified by a factor of 10 to facilitate comparison with the 1.5 PVU contour. (Note, the raw calculation of the PV anomalies that comprise the Rossby wave metric are used for all calculations.) The purple line shows the complete track of Harvey with the purple dot indicating the position at each time step. The bold gray dashed line labels the longitude of recurvature and the thin gray dashed line denotes 120° downstream of the recurvature longitude. The longitudinal extent of the black dashed lines in (a) corresponds to the region between the dashed gray lines in (b)–(d). “T” indicates a trough location; “R” indicates a ridge.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
(a) Hovmöller of average synoptic-scale trough power for TC Harvey (1981), as shown in Fig. 3a. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. “TC” denotes the longitude of the TC at the time of recurvature. Positive (negative) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black dashed lines are drawn at the timesteps corresponding to panels (b)–(d). Filled colored contours on (b)–(d) illustrate potential vorticity on the 320 K isentropic surface (b) 96 h before recurvature (prerecurvature time period), (c) 24 h after recurvature (recurvature time period), and (d) 132 h after recurvature (postrecurvature time period). The 1.5 PVU contour (black) is used to approximate the location of the jet stream and the Rossby wave metric (blue) is inverted, translated north by 60°, and amplified by a factor of 10 to facilitate comparison with the 1.5 PVU contour. (Note, the raw calculation of the PV anomalies that comprise the Rossby wave metric are used for all calculations.) The purple line shows the complete track of Harvey with the purple dot indicating the position at each time step. The bold gray dashed line labels the longitude of recurvature and the thin gray dashed line denotes 120° downstream of the recurvature longitude. The longitudinal extent of the black dashed lines in (a) corresponds to the region between the dashed gray lines in (b)–(d). “T” indicates a trough location; “R” indicates a ridge.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
To identify the features that distinguish the subset of cases described above, a comparison between the characteristics of the TC and the large-scale flow in the two subgroups is discussed next. Figure 7 presents a statistical comparison between the two subgroups, including the TC’s mean sea level pressure (Fig. 7a), average size (Fig. 7b), and wind speed (Fig. 7c) at the time of recurvature. Because the midlatitude jet is sensitive to temperature gradients causing it to shift latitudinally with season, here we examine the latitude (Fig. 7d) and date (Fig. 7e) of recurvature as factors that are associated with seasonal differences in the large-scale flow and could give insight into the extratropical flow response to the recurving TC. The TC–jet interaction is characterized by the Rossby wave relative location at the time of recurvature (Fig. 7f) and the average Rossby wave relative speed over the 72 h following recurvature (Fig. 7g).
Boxplots of the distributions of (a) mean sea level pressure at recurvature, (b) average size of the TC at recurvature, (c) wind speed at recurvature, (d) recurvature latitude, (e) date of recurvature, (f) the Rossby wave relative location measured by the distance between the TC and the nearest trough at the time of recurvature, and (g) the average speed of the TC relative to the Rossby wave speed from the time of recurvature to 72 h after recurvature. Red boxplots correspond to the distribution created by the subset of TCs and black boxplots correspond to the distribution created from all other TCs; p values from each two-sample t test are listed on each plot.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Boxplots of the distributions of (a) mean sea level pressure at recurvature, (b) average size of the TC at recurvature, (c) wind speed at recurvature, (d) recurvature latitude, (e) date of recurvature, (f) the Rossby wave relative location measured by the distance between the TC and the nearest trough at the time of recurvature, and (g) the average speed of the TC relative to the Rossby wave speed from the time of recurvature to 72 h after recurvature. Red boxplots correspond to the distribution created by the subset of TCs and black boxplots correspond to the distribution created from all other TCs; p values from each two-sample t test are listed on each plot.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Boxplots of the distributions of (a) mean sea level pressure at recurvature, (b) average size of the TC at recurvature, (c) wind speed at recurvature, (d) recurvature latitude, (e) date of recurvature, (f) the Rossby wave relative location measured by the distance between the TC and the nearest trough at the time of recurvature, and (g) the average speed of the TC relative to the Rossby wave speed from the time of recurvature to 72 h after recurvature. Red boxplots correspond to the distribution created by the subset of TCs and black boxplots correspond to the distribution created from all other TCs; p values from each two-sample t test are listed on each plot.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
On the basis of TC characteristics (see Figs. 7a–c), the comparison of the distributions created from the subset of cases to those from the remaining events show only slight differences between the groups. For each TC feature, the interquartile ranges align well between the groups. The medians and the extent of the tails for pressure and wind speed are nearly aligned between the subset and nonsubset cases. The median size of the average 34 kt (1 kt ≈ 0.5144 m s−1) wind radii is greater for the subset of cases (122.5 nm) compared to the excluded cases (80 nm), but the upper extreme for the subset of cases is less (178.75 nm) than the largest radii of the excluded cases (262.5 nm). Two-sample t tests were used on the distributions for each TC characteristic to deduce whether these TC qualities could be used to separate the subset from the remaining storms. For all three TC characteristics [pressure (Fig. 7a), size (Fig. 7b), and wind speed (Fig. 7c)], there is not a significant statistical difference in the distributions between the subset of cases and the excluded cases. Therefore, we conclude that the characteristics of the TC at recurvature are unlikely to affect the initial suppression and subsequent increase in downstream synoptic-scale trough power.
The latitude (Fig. 7d) and date (Fig. 7e) of recurvature give insight into the position and strength of the extratropical jet stream, which varies seasonally. The medians, total ranges, and interquartile ranges of the distributions are similar for the latitude of recurvature. Two-sample t tests reveal that the distributions of recurvature latitude are not statistically different between the two groups. Individual tracks of the TCs within the subset were also visually examined (not shown) to search for patterns, but no consistencies were revealed. The range and medians of the recurvature date distributions are comparable, but the main difference between these distributions is the interquartile range. The interquartile range of the subset of cases spans 61 days from 26 July to 25 September whereas the interquartile range of the excluded cases extends 43 days from 14 August to 26 September. Again though, two-sample t tests do not yield a significant difference between the two distributions and date of recurvature should not be used to predict which TCs would trigger extratropical flow modification in the Atlantic basin. The results of this study show that the seasonality and latitude of recurvature are not indicative of the probability of modifying the extratropical flow in the Atlantic, which is contradictory to the results from the western North Pacific.
Numerous previous studies (e.g., Harr and Elsberry 2000; Agusti-Panareda et al. 2004; Riemer and Jones 2010; Grams et al. 2013a; Keller et al. 2014; Quinting and Jones 2016) have described the importance of the “phasing” between the TC and the waves on the extratropical jet as a key indicator to the subsequent evolution of the extratropical flow amplitude. Traditionally, “phase” refers to the distance between the TC and an upstream trough. Along these lines, we compute the “Rossby wave relative location” at the point and time of recurvature for comparison between the two groups (Fig. 7f). The longitudes of all troughs are determined by finding the local maxima in the Rossby wave metric. The trough with the smallest displacement from the TC (regardless of whether it is upstream or downstream) is selected as the nearest trough. The Rossby wave relative location is essentially the distance between the TC and the nearest trough at the time of recurvature, calculated by subtracting the longitude of the TC from the longitude of the nearest trough (see Fig. 8). Therefore, positive (negative) Rossby wave relative location indicates a TC recurving on the west (east) side of the nearest trough.
Schematic of Rossby wave relative location. In the left (right) case, the TC has a recurvature longitude west (east) of the trough axis yielding a positive (negative) Rossby wave relative location.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Schematic of Rossby wave relative location. In the left (right) case, the TC has a recurvature longitude west (east) of the trough axis yielding a positive (negative) Rossby wave relative location.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Schematic of Rossby wave relative location. In the left (right) case, the TC has a recurvature longitude west (east) of the trough axis yielding a positive (negative) Rossby wave relative location.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
The interquartile ranges as well as the values of the first and third quartiles of the Rossby wave relative location (Fig. 7f) are similar between the subset of TCs and the excluded cases. The skewness of the two groups is the most apparent difference. The subset has a negative skew with a median of +3.3° (TC recurves 3.3° to the west of the nearest trough) with a longer lower tail extending to −46.8° compared to the upper tail that reaches 33.2°. The distribution of excluded cases exhibits a positive skew with a median of −2.5° (TC recurves 2.5° to the east of the nearest trough) and a longer upper tail peaking at 56.0° compared to the lower tail that only reaches −33.0°. Though the medians suggest that the TCs associated with the subset of cases tend to recurve further west in comparison to the TC events excluded from the subset, this result is not statistically significant. Within the context of this study, the Rossby wave relative location at the time of recurvature is not a significant detector of whether the power of synoptic-scale troughs will diminish following recurvature.
Motivated by Riboldi et al. (2019) who identified the importance of the trough’s deceleration in its ability to phase lock and promote Rossby wave amplification downstream, the final metric hypothesized to distinguish the subset of TCs from the excluded TCs is referred to as the “average Rossby wave relative speed,” which is plotted in Fig. 7g. This metric is an average zonal speed from the time of recurvature to 72 h after recurvature. For each time step after recurvature, the longitude of the trough nearest the trough of interest at the previous time step is recorded. The total zonal distance traveled by the TC in those 72 h is subtracted from the total zonal distance traveled by the trough. Essentially, the average Rossby wave relative speed determines whether the TC or the nearest trough traverses a greater eastward distance in the 72 h following recurvature. If the average Rossby wave relative speed is positive, the trough moves farther eastward than the TC. Conversely, a negative Rossby wave relative speed indicates the TC traveling faster than the nearest trough. In the distributions of Fig. 7g, the most noticeable difference is between the ranges. The subset of TCs has a smaller range of average Rossby wave relative speed extending from −7.7° (12 h)−1 to 8.35° (12 h)−1 whereas the range of the distribution of the excluded TCs is nearly double, reaching −14.7° (12 h)−1 and 15.6° (12 h)−1. Notice, too, the difference in sign of the medians—the subset has a median of −0.7° (12 h)−1 and the median of the excluded cases is +1.1° (12 h)−1. A two-sample t test between these two distributions yields significance with 95% confidence, suggesting that the TCs contained by the subset of cases tend to move faster eastward with respect to their nearest trough compared to the TCs excluded from the subset. This result however does not imply that the TCs contained by the subset necessarily have an average forward speed greater than that of their nearest trough, but rather a faster average Rossby wave relative speed than those TCs excluded from the subset. A one-sample t test was executed to determine if the average Rossby wave relative speed of the storms within the subset is significantly greater than zero, or in other words, if the TCs of the subset travel a greater zonal distance in the 72 h following recurvature than the nearest trough. The t test indicates the average Rossby wave relative speed for TCs within the subset is significantly less than zero with 88% confidence. Therefore, cases that experience significant suppression of synoptic-scale trough power in the 48 h following recurvature are often those with TCs that outrun their nearest trough.
c. Subgrouping based on Rossby wave relative speed
Given the statistical significance of the average Rossby wave relative speed in distinguishing the downstream wave amplitude pattern, a separate subgrouping analysis based on the sign of the average Rossby wave relative speed was conducted. Of the full group of 272 TCs, 111 storms exhibited negative Rossby wave relative speed on average (i.e., moving eastward relative to the Rossby wave) and their total synoptic-scale power is composited and plotted as a function of recurvature relative time and longitude in Fig. 9a. An examination of the downstream power at times before, during, and after recurvature shows a similar evolution of power compared to the evolution of synoptic-scale trough power for the previously discussed subset (Fig. 5a). Downstream power is present before these storms recurve, decreases near the time of recurvature, and returns to the downstream region about 4 days (96 h) after recurvature. The time step revealed to have the lowest downstream power is 48 h after recurvature, which is the last time step encompassed by the recurvature time period. The power suppression however appears to last just beyond the previously defined time period, extending to nearly three days (72 h) after recurvature. The only statistically significant difference in power among the three time periods exists between the prerecurvature and the recurvature time periods. Therefore, the subgroup of cases comprised of all TCs that travel farther eastward in the 72 h after recurvature than their nearest trough is able to capture the trend of the synoptic-scale power suppression following recurvature, but unable to explain the subsequent amplification of synoptic-scale Rossby wave power shown by the previous subset.
Hovmöller diagrams of average synoptic-scale power (contours) composited for cases of TCs that exhibit (a) negative Rossby wave relative speed and (b) positive Rossby wave relative speed. Note, in order to display total power, the color bar is altered compared to Fig. 5 which plotted only trough power. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. Eastern (western) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black outlined boxes indicate 48-h intervals corresponding to the “prerecurvature,” “recurvature,” and “postrecurvature” time periods.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Hovmöller diagrams of average synoptic-scale power (contours) composited for cases of TCs that exhibit (a) negative Rossby wave relative speed and (b) positive Rossby wave relative speed. Note, in order to display total power, the color bar is altered compared to Fig. 5 which plotted only trough power. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. Eastern (western) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black outlined boxes indicate 48-h intervals corresponding to the “prerecurvature,” “recurvature,” and “postrecurvature” time periods.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Hovmöller diagrams of average synoptic-scale power (contours) composited for cases of TCs that exhibit (a) negative Rossby wave relative speed and (b) positive Rossby wave relative speed. Note, in order to display total power, the color bar is altered compared to Fig. 5 which plotted only trough power. Both time and longitude are normalized by the recurvature point. Positive (negative) time values indicate times after (before) recurvature. Eastern (western) longitudes refer to regions downstream (upstream) of the TC’s recurvature location. Black outlined boxes indicate 48-h intervals corresponding to the “prerecurvature,” “recurvature,” and “postrecurvature” time periods.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
The remaining 161 cases displayed a positive Rossby wave relative speed on average (i.e., a Rossby wave packet moving eastward faster than the TC). The total synoptic-scale power surrounding the recurvature of these cases is composited and plotted in Fig. 9b. Visually, the evolution of average synoptic-scale downstream power from before, during, and after recurvature appears to be nearly the converse of the evolution in Fig. 9a. Instead of a decrease in synoptic-scale power immediately following recurvature, there is an increase in power, which is significant at the 95% confidence level. It should also be mentioned that the time step with the maximum downstream power is 60 h after recurvature, which is not included by the recurvature time period.
4. Summary and discussion
This study has demonstrated the climatological association between recurving Atlantic TCs and synoptic-scale Rossby waves at higher latitudes, specifically focusing on the period from 1979 to 2016. Case studies have previously demonstrated that amplified Rossby waves on the extratropical jet sparked by recurving TCs are responsible for extreme weather events downstream, including cyclogenesis, heavy precipitation, flooding, wind gusts, and cold-air outbreaks. Given the significance of recurving TCs to high-impact weather downstream, a better understanding of the characteristics regulating the TC–jet interaction and the resulting extratropical flow is valuable from a operational weather prediction standpoint.
This study utilized a wavelet decomposition technique to diagnose Rossby waves on the extratropical jet. Wavelet transforms were applied to latitude-averaged PV anomalies on a 320 K isentropic surface. A comparison between waves evident on the 1.5 PVU contour and our wavelet-based metric in individual cases demonstrated the reliability of the wavelet technique in identifying the evolution of Rossby wave amplitude. A limitation of this method is its inability to diagnose PV folds or tilts that may be present during an ongoing wave break. However, the main objective of this study was to illuminate amplitude changes in synoptic-scale Rossby waves following TC recurvature, which is within the capability of the designed method. Nevertheless, given the importance of wave breaking in triggering extreme precipitation events downstream, a separate analysis of wave breaking should be conducted in a future investigation.
The pattern of Rossby wave amplification following a TC recurvature event was not uniform across all 272 storms analyzed. A subset of 41 events demonstrated a distinct class of systematic behavior. For these events, the synoptic-scale trough power significantly decreased abruptly near the time of recurvature and remained reduced throughout the recurvature time frame (T + 0 to T + 48 h) before increasing in the postrecurvature time period (T + 96 to T + 144 h) back toward levels near those present in the prerecurvature period (T − 96 to T − 48 h). This suppression of synoptic-scale trough power is also evident in the examination of ridge power as well as planetary-scale (60°–120°) trough power near the time of recurvature (not shown). The average planetary-scale trough power at the recurvature time period (T + 0 to T + 48 h) is significantly less than that of the prerecurvature time period (T − 96 to T − 48 h) at the 95% confidence level. Therefore, the suppression of synoptic-scale trough power during the recurvature time period is not due to a transfer of power to longer wavelengths.
Additional analysis was conducted in order to identify which properties of the recurving TC and preexisting extratropical flow might distinguish this subset of 41 events. The key conclusions of this study are as follows:
Recurving Atlantic TC events are capable of disrupting and modifying the amplitude of the extratropical flow.
Characteristics of the TC itself have little/no significance in predicting the evolution of the amplitude of the resulting extratropical flow.
The nature of the extratropical flow response is most strongly linked to the average Rossby wave relative speed of the recurving TC during the 72 h after recurvature.
The average Rossby wave relative speed of TCs in the subset indicates that these TCs traverse a greater zonal distance relative to their nearest trough compared to the excluded cases. The forward speed of these cases is also significantly greater than the forward speed of their associated trough at the 88% confidence level. The result of this relative speed within the 41-case subset is a sharp decline in synoptic-scale trough power just after the time of recurvature, followed by an increase in power back toward the prerecurvature average about 4 days after recurvature. Additionally, we have separated the TC events strictly based on the sign of the average Rossby wave relative speed of the TC. Of the cases including only TCs with a negative Rossby wave relative speed (meaning that in the 72 h after recurvature the TC traveled a greater zonal distance eastward than the nearest trough) the resulting downstream synoptic-scale evolution of power resembled that of the 41-case subset. However, only the initial power suppression was significant—the ensuing return of the power in the postrecurvature period was not. In the cases with TCs exhibiting positive Rossby wave relative speed (trough traveled a greater eastward distance in the 72 h after recurvature compared to the TC), nearly the opposite pattern was present with a significant increase in power in the timesteps of the recurvature period compared to the prerecurvature period. Again though, there was no significant difference in the average power from the recurvature period to the postrecurvature period. Other classifications of the individual TCs (perhaps upper-level mass divergence or net heating within the TC) and the large-scale flow (PV gradients in the vicinity of recurvature or jet intensity) should be examined in future studies aiming to account for other features that control the response of the extratropical jet to recurving Atlantic TCs.
We propose three possible physical and dynamical mechanisms that may explain this extratropical flow response to a recurving TC. We preface this discussion by noting that a climatological study alone, such as the one presented in this paper, can only provide circumstantial evidence for these mechanisms. Detailed case study analysis, including simulation and observation, could discriminate between the importance of each of these mechanisms to the TC–Rossby wave interaction. The three mechanisms that we propose are as follows.
Modification of the midlatitude PV gradient by the TC outflow.
Direct constructive/destructive interference with the nearest trough or ridge.
Action at a distance via barotropic vorticity dynamics.
Concerning the first mechanism, the diabatically modified low-PV outflow in the upper levels of the TC deposits low-PV air along the equatorward side of the extratropical jet. This low-PV air may therefore act to tighten the PV gradient across the jet, effectively decreasing the jet’s ability to sustain synoptic-scale wave power. It has been demonstrated previously (e.g., Riemer et al. (2008)) that the divergent outflow from the TC can indeed modify the PV gradient locally. However, the mechanism discussed here requires that the TC outflow modifies the extratropical waveguide (i.e., the zonal mean meridional PV gradient). We expect that the time scale for this modification would be long compared to the time scale associated with the relatively rapid Rossby wave amplification that has been diagnosed in this paper. We therefore do not suspect that this mechanism is the dominant mechanism governing the interaction diagnosed in this study.
Concerning the second mechanism, if the low-PV air of the TC’s outflow is distributed preferentially into a ridge, then a constructive interference may amplify that ridge. Conversely, a nearby trough may be de-amplified by the destructive interference with the low-PV outflow. If this mechanism were dominant, then we would expect the mean location of the TC relative to the Rossby wave pattern to govern the interaction. For example, a TC residing downstream of a trough could readily deposit its low-PV outflow into the low-PV ridge downstream, thus leading to amplification of the ridge by constructive interference. This result was seen in western North Pacific studies by Grams et al. (2013a), Keller et al. (2014), and Quinting and Jones (2016) who concluded that optimal phasing for a significantly amplified downstream flow is achieved when the TC recurves just east of the nearest trough. However, in this study, we do not diagnose a statistically significant connection between the location of the TC relative to the Rossby wave pattern at recurvature and the subsequent evolution of Rossby wave power. We therefore do not suspect that this is the lone mechanism dominant in our climatology, although we do not have enough evidence to reject its relevance to individual cases. These differences were also revealed by the methods used in Quinting and Jones (2016) who examined Rossby wave amplitude following TC recurvatures in both basins. Although the large-scale flow was modified following the recurvature of Atlantic TCs, the Rossby waves characteristics were not shown to be statistically different from the climatological values (Quinting and Jones 2016). Reasons for these differences between basins may stem from fundamental differences in size and strength of the waveguides in each basin—within the North Atlantic, the extratropical jet is typically shorter and weaker (Archambault et al. 2015).
The third mechanism that we have proposed involves ‘action at a distance’ between the extratropical Rossby wave and the low-PV anomaly associated with the TC’s divergent outflow. The hypothesized mechanism works as follows and is depicted schematically in Fig. 10. We conceive of this mechanism as acting in a manner similar to the barotropic instability, but instead of two interacting edge waves (e.g., as in Heifetz et al. (1999)), we have one Rossby wave and one propagating monopole source. As in the barotropic instability, the effect of the monopole on the Rossby wave depends on the tilt of the vorticity pattern relative to the background shear. Amplification results when the pattern tilts into the shear; when the tilt is in the direction of the shear, the interaction is dampening. The optimal configuration for amplification is one for which the components (i.e., the Rossby wave and the TC monopole) are counterpropagating and tilted into the shear. The pattern of Rossby wave de-amplification and reamplification that we have diagnosed in this climatological study is consistent with this proposed mechanism. Specifically, the period of de-amplification occurs for storms moving eastward ahead of the Rossby wave while the tilt of the combined vorticity pattern is conducive for dampening. Once the TC source moves past the axis of the downstream ridge, the tilt of the pattern is into the shear and conducive for reamplification. This mechanism is consistent with the observation made by Scheck et al. (2011) and Grams et al. (2013b) that optimal interaction occurs when the phase speed of the Rossby wave matches the translation speed of the TC; in this optimal scenario, the barotropic growth rate could be sustained over a longer period than for a TC whose translation speed does not match the Rossby wave phase speed. However, the mechanism proposed here highlights that the tilt of the pattern also regulates the growth or decay, such that the optimal interaction requires phase locking and optimal tilt. To establish whether this hypothesized mechanism is important to the TC–Rossby wave interaction, we recommend that it be evaluated in future case study analysis and in idealized simulations. Case studies afford a more detailed analysis of the PV tendencies and meridional velocity perturbations associated with the TC and Rossby wave packet (e.g., via a PV surgery technique). Such information would be needed in order to establish whether the tendencies associated with each feature are constructive to the other and support the propagation of the pattern in the manner described in Heifetz et al. (1999).
Schematic diagram depicting the hypothesized interaction between a Rossby wave packet and a moving vorticity source provided by a tropical cyclone (TC) that is positioned equatorward of the Rossby wave. The interaction resembles the barotropic instability between two edge waves in a sheared flow, except here the TC is a negative monopole that replaces one of the edge waves. Plus and minus signs indicate the PV anomalies. Block arrows show the phase speeds of the Rossby wave (CRW) and the TC (CTC). Gray arrow shows the shear. The location of the TC at two hypothetical times are shown for the moving TC with the first time (t0) drawn in green and the second time (t1) drawn in blue. Dotted lines illustrate the lines of equal phase of the combined pattern. This diagram displays a TC with negative Rossby wave relative speed, meaning that the TC travels faster eastward than the Rossby wave. The TC monopole suppresses the Rossby wave where and when the tilt of the combined vorticity pattern is in the same direction as the shear. Once the TC has moved beyond the axis of the ridge, the tilt is into the shear and becomes favorable for amplification.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Schematic diagram depicting the hypothesized interaction between a Rossby wave packet and a moving vorticity source provided by a tropical cyclone (TC) that is positioned equatorward of the Rossby wave. The interaction resembles the barotropic instability between two edge waves in a sheared flow, except here the TC is a negative monopole that replaces one of the edge waves. Plus and minus signs indicate the PV anomalies. Block arrows show the phase speeds of the Rossby wave (CRW) and the TC (CTC). Gray arrow shows the shear. The location of the TC at two hypothetical times are shown for the moving TC with the first time (t0) drawn in green and the second time (t1) drawn in blue. Dotted lines illustrate the lines of equal phase of the combined pattern. This diagram displays a TC with negative Rossby wave relative speed, meaning that the TC travels faster eastward than the Rossby wave. The TC monopole suppresses the Rossby wave where and when the tilt of the combined vorticity pattern is in the same direction as the shear. Once the TC has moved beyond the axis of the ridge, the tilt is into the shear and becomes favorable for amplification.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
Schematic diagram depicting the hypothesized interaction between a Rossby wave packet and a moving vorticity source provided by a tropical cyclone (TC) that is positioned equatorward of the Rossby wave. The interaction resembles the barotropic instability between two edge waves in a sheared flow, except here the TC is a negative monopole that replaces one of the edge waves. Plus and minus signs indicate the PV anomalies. Block arrows show the phase speeds of the Rossby wave (CRW) and the TC (CTC). Gray arrow shows the shear. The location of the TC at two hypothetical times are shown for the moving TC with the first time (t0) drawn in green and the second time (t1) drawn in blue. Dotted lines illustrate the lines of equal phase of the combined pattern. This diagram displays a TC with negative Rossby wave relative speed, meaning that the TC travels faster eastward than the Rossby wave. The TC monopole suppresses the Rossby wave where and when the tilt of the combined vorticity pattern is in the same direction as the shear. Once the TC has moved beyond the axis of the ridge, the tilt is into the shear and becomes favorable for amplification.
Citation: Monthly Weather Review 148, 2; 10.1175/MWR-D-19-0216.1
This study has identified some key similarities and differences between the North Atlantic and Pacific with regard to the extratropical flow response during TC recurvature. In the Pacific, Archambault et al. (2013) has shown that an optimal phasing between the TC and preexisting Rossby wave pattern can systematically lead to amplification of the Rossby wave packet. Such a signal was not evident in the Atlantic climatology presented in this paper. Instead, we have shown that the relative propagation speed of the TC versus the Rossby wave pattern can systematically determine a de-amplification (later followed by a reamplification) of the wave pattern. The precise reasons for the different basin-dependent behavior have not yet been identified but may be related to differences in the orientation and length of the storm tracks as well as the upstream characteristics of wave packets exiting the continents.
Aligned with our conclusions, previous studies that focused on western North Pacific TCs also deduced that properties of the TC itself were not directly linked to the resulting extratropical flow response. While Archambault et al. (2013) found that the most intense storms (defined by lowest central pressure and highest maximum wind speed) were the most likely to initiate a downstream response, it was also noted that an amplified extratropical flow could still be observed following the recurvature of both strong and weak, and large and small TCs.
In a departure from what has been observed in the North Pacific, this study did not find an association between the TC’s recurvature date or recurvature latitude with the resulting evolution of the extratropical flow pattern. In the western North Pacific, the latitude of recurvature is a significant indicator of the resulting amplification of the large-scale flow. Specifically, western North Pacific TCs recurving between 20° and 35°N were found by Archambault et al. (2013) to be more likely to amplify the jet compared to those that recurved farther south. Concerning the seasonal dependence, this study concluded that the recurvature date of Atlantic TCs had no influence on the resulting synoptic-scale trough amplitude, whereas in the western North Pacific basin, the date of the TC’s recurvature is found to be a significant predictor in the resulting flow amplification. Western North Pacific TCs occurring in August–November were found to have the highest probability of disturbing the jet in such a way that a statistically significant amplified large-scale flow would result (Archambault et al. 2013).
A future study will make use of historical ECMWF ensemble forecasts to investigate the TC–jet interaction from a predictability viewpoint. The current study highlighted the ability of recurving TCs to significantly alter the amplitude of Rossby waves on the jet, especially downstream from the point of recurvature, which may increase the difficulty in forecasting downstream weather. A future objective is to examine how well this extratropical flow amplification is forecasted, including identifying the key physical processes that are responsible for error growth and skill degradation within numerical weather prediction models.
Acknowledgments
The authors thank three anonymous reviewers for insightful feedback that significantly enhanced this manuscript. We acknowledge the National Hurricane Center for compiling and providing their Best Track reanalysis database. We also thank the European Centre for Medium-Range Weather Forecasts for contributing the ERA-Interim reanalysis data.
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