Abstract

This is the second of two papers examining the role of equatorial Rossby (ER) waves in tropical cyclone (TC) genesis. Based on results from Part I, it is hypothesized that genesis resulting from the circulation of an ER wave alone is uncommon and that the majority of ER wave–related genesis events occur when a sufficiently intense ER wave interacts with a favorable background flow environment. This paper examines this contention by performing a series of simulations in which ER waves are imposed upon idealized background flows. The background flows are designed to resemble a region of a monsoon trough (MT), a flow feature observed at certain times of the year in all of the TC basins, and most dramatically, in the western North Pacific basin. It is believed that ER wave interactions with the MT may speed up the internal breakdown genesis mechanism of the MT, or even result in genesis when the MT is too weak to breakdown from in situ processes alone. The latter scenario is examined here. When just the MT is simulated without the ER wave anomaly fields, the MT remains quasi-steady and TC genesis does not occur. It is only when the ER wave is imposed on the MT that TC genesis is initiated. The results imply that the ER wave–MT interactions produce more TCs than would otherwise occur if no such interactions took place. Results demonstrate that wave breaking of the ER wave is a mechanism by which vorticity is organized on the scale of a TC. This process features a decrease in the initial horizontal scale of the cyclonic gyre of the ER wave to a scale comparable with a TC. This genesis mechanism is sensitive to the magnitude of the background cyclonic vorticity of the MT, as TC genesis is only initiated when the value of the 850-mb relative vorticity of the MT is larger than 2 × 10−5 s−1. This genesis pathway provides a unique interpretation of TC genesis and is compared with previous theories on TC genesis.

1. Introduction

The necessary but insufficient large-scale conditions for tropical cyclone (TC) genesis have been known for about 40 years (Gray 1968). They are the following:

  1. sea surface temperatures above 26.5°C coupled with a relatively deep oceanic mixed layer,

  2. organized deep convection in an area with large-scale ascending motion and high midlevel humidity,

  3. low-level cyclonic vorticity,

  4. weak-to-moderate (preferably easterly) vertical wind shear, and

  5. location sufficiently far from the equator.

While these conditions are often satisfied over large regions of the various ocean basins throughout many months of the year, genesis is the exception rather than the norm. The question then becomes what are the pathways by which we transition from these favorable large-scale conditions to TC genesis?

In Gall et al. (2010, hereafter Part I), we examined one particular genesis pathway resulting from an isolated equatorial Rossby (ER) wave. The ER wave–related genesis was investigated by simulating a convectively coupled ER wave in an initially quiescent background environment. This was done in order to examine potential genesis mechanisms internal to the ER wave. While it was demonstrated that certain regions of an n = 1 convectively coupled ER wave contained conditions favorable for TC genesis, only in the largest initial-amplitude ER wave simulation where the magnitude of the maximum initial 850-mb relative vorticity approached 2.5 × 10−5 s−1 was genesis observed to occur. Since numerous observational studies have demonstrated that ER waves play a prominent role in TC genesis (e.g., Frank and Roundy 2006; Bessafi and Wheeler 2006), it is hypothesized that TC genesis within an ER wave is much more likely when an ER wave interacts with (propagates into) a favorable background environment.

In this paper, we designed the background flow to be representative of the zonal wind component of an idealized monsoon trough (MT). The MT was selected because the majority of TC genesis events have been observed to occur within, or near, this synoptic-scale feature (e.g., Ramage 1974; Gray 1979). Because the western North Pacific basin is a global maximum for both convectively coupled ER waves (e.g., Wheeler and Kiladis 1999; Roundy and Frank 2004) and MTs (e.g., Briegel and Frank 1997), we believe that the TC-genesis scenario of an ER wave interacting with a MT is a likely one.

2. Background

a. Genesis within the MT

The MT is defined as the region between low-level equatorial westerlies on its equatorward side and low-level trade wind easterlies on its poleward side (Fig. 1). It is characterized by a local, zonally elongated sea level pressure minimum and enhanced rainfall. The eastern end of the MT is often associated with a low-level confluent zone with typical values on the order of 5 × 10−5 s−1 (e.g., Holland 1995; Ritchie and Holland 1999). As depicted in Fig. 1, this region of large-scale confluence features a shift in the zonal winds from equatorial westerlies to trade wind easterlies. The band of cyclonic relative vorticity; sustained convection; high-, mid-, and low-level moisture; and anomalously strong low-level confluence within the MT provides a favored region for genesis.

Fig. 1.

Idealized depiction of the near-surface streamlines associated with a MT flow configuration (Fig. 1 of Briegel and Frank 1997). The light-shaded region indicates the monsoon shear region of the MT while the darker-shaded region indicates the confluence region of the MT. The dots indicate the location of all genesis events in their 2-yr dataset.

Fig. 1.

Idealized depiction of the near-surface streamlines associated with a MT flow configuration (Fig. 1 of Briegel and Frank 1997). The light-shaded region indicates the monsoon shear region of the MT while the darker-shaded region indicates the confluence region of the MT. The dots indicate the location of all genesis events in their 2-yr dataset.

Ramage (1974) first documented that TC genesis was often associated with a near-equatorial trough in the Indian and Pacific Ocean basins, provided that this feature was sufficiently far from the equator. Briegel and Frank (1997) examined TC genesis within the MT region of the western North Pacific. Of the 41 total MT-related TCs in their 2-yr dataset, approximately 60% of these events occurred in the eastern end of the MT confluence zone, with the remainder occurring to the west of the confluence zone within the MT (Fig. 1). The authors found via composite analyses that the presence of both upper-level troughs to the west of the genesis location and low-level westerly wind surges prior to genesis played a significant role in the eventual genesis event. Briegel and Frank (1997) concluded that large-scale external forcings were crucial in triggering TC genesis within the MT region.

Ritchie and Holland (1999) further investigated the relationship between the MT and genesis in the western North Pacific Ocean basin by categorizing western North Pacific genesis events into five different large-scale dynamical patterns: monsoon shear line, monsoon confluence region, monsoon gyre, easterly waves, and Rossby energy dispersion. Of these five categories, three of these are associated with some aspect of the MT (monsoon shear line, monsoon confluence region, and monsoon gyre). While qualitatively similar to the Briegel and Frank (1997) description of the MT confluence zone, the Ritchie and Holland (1999) monsoon confluence categorization is quantitatively different. Of the total cases that were associated with the MT (147), 58 genesis events (39%) occurred within this confluence region. The authors stated that this MT-related genesis mechanism is essentially a wave accumulation mechanism (e.g., Webster and Chang 1988; Zehr 1992; Holland 1995). Ritchie and Holland (1999) describe the monsoon shear line categorization as when the pre-TC disturbance is located in a region of anomalously low sea level pressure associated with the MT and features westerly flow on the equatorward side of the genesis location throughout the 72 h prior to genesis. Of the total genesis cases that were associated with the MT, 84 cases (57%) were associated with this particular aspect of the MT. The authors demonstrated that nearly all genesis events associated with the MT in the western North Pacific basin were either associated with the shear line or the confluence region of the MT.

b. Motivation

In this paper, we concern ourselves with TC genesis1 within the MT shear region (i.e., the Ritchie and Holland (1999) monsoon shear categorization). Ritchie and Holland (1999) state that TC development within the shear region of the MT is internally forced via an in situ development of a convergent cyclonic circulation near the genesis location. This claim is supported by several observational studies (e.g., Hack et al. 1989; Schubert et al. 1991; Ferreira et al. 1996) and at least one modeling study (Wang and Frank 1999). These studies indicate that deep cumulus convection generated in situ within the MT produces a cyclonic potential vorticity (PV) anomaly that has a reversal of the meridional PV gradient on its poleward side and therefore satisfies the necessary condition for combined barotropic and baroclinic instability (Charney 1963). The MT may then start undulating because of combined barotropic and baroclinic instability and finally break down into one or more tropical disturbances.

We argue, however, that genesis within the shear region of the MT may be externally initiated (i.e., via an ER wave), in addition to the well-documented internally forced mechanism. Ritchie and Holland (1999) eliminate external phenomena as a potential driver for TC formation within the MT shear region by arguing that Hovmöllers of the 850-mb zonal and meridional winds show no such signature of zonally propagating phenomenon. They state that the increase in the meridional and zonal winds prior to genesis is a result of a “steady in situ” increase. However, as shown in the recent studies of Wheeler and Kiladis (1999), Roundy and Frank (2004), and Molinari et al. (2007), in order to identify zonally propagating phenomenon such as equatorially trapped tropical waves, filtering of the total zonal and meridional winds for certain zonal wavenumbers and frequencies must be employed. Additionally, it is possible that the “in situ” increase is due to the spinup of the pre-TC disturbance. That is, what we are seeing is a vortex intensifying via its own air–sea instability (e.g., Emanuel 1995), and the spinup is not some physical process related to the dynamics of the MT.

c. Equatorial waves in a background flow

Since we are focusing on the region of the MT that features significant background horizontal shear, much of the problem reduces to understanding how equatorial waves, and specifically convectively coupled ER waves, are modified by a horizontally sheared background flow. While numerous studies have concerned themselves with identifying a statistically significant link between equatorial waves and TC genesis (see Part I for a review of these), fewer studies have focused on how various background flows modify equatorial waves. These studies are discussed here.

Stewartson (1977) and Warn and Warn (1978) examined the evolution of an inviscid forced Rossby wave within a meridionally varying background zonal flow. Both of these studies demonstrated that an irreversible deformation of the material contours associated with the wave occur in and around the region where the propagation speed of the Rossby wave (c) is equivalent to the value of the background flow (U) (i.e., U = c). This nonlinear deformation of the wave is referred to as the process of wave breaking, and an idealized interpretation is presented in Figs. 2a–d. First, consider the idealized background flow depicted in Fig. 2a. This zonal flow configuration is representative of the horizontal shear pattern found within a MT. Superimposed on this background zonal flow is an idealized, westward-propagating wave (Fig. 2b). The critical latitude is given by the latitude at which the background zonal flow is equivalent to the propagation speed of the wave. Owing to horizontal shear of the background flow, the idealized wave begins to deform, as seen in Fig. 2c. The critical latitude represents the axis about which this deformation occurs, as regions poleward of the critical latitude feature (Uc) > 0, while regions equatorward of the critical latitude feature (Uc) < 0. This deformation continues and eventually the wave “breaks” (Fig. 2d). That is, a circulation forms whose horizontal scale is much smaller than the initial horizontal scale of the ridge or trough of the idealized wave. We contend that this process plays a vital role in TC genesis resulting from the interaction of an ER wave with a MT.

Fig. 2.

An illustration of the wave-breaking process for an idealized wave embedded within a zonal background flow representative of the shear region of an MT.

Fig. 2.

An illustration of the wave-breaking process for an idealized wave embedded within a zonal background flow representative of the shear region of an MT.

Zhang and Webster (1989) derived an analytic solution for the n = 1 ER wave in both constant background zonal flow, and meridionally varying background zonal flow. Their analytic model, however, assumes that the zonal wavenumber of the ER wave remains constant within a horizontally sheared zonal flow. As noted in Zhang and Webster (1989), this assumption is debatable since it removes any such wave-breaking mechanism given the constraint on the zonal wavenumber. Aiyyer and Molinari (2003) highlighted the importance of a background flow representative of the Madden–Julian oscillation (MJO; e.g., Madden and Julian 1994) in perturbing an equatorial wave in such a way as to result in genesis. While their background flow is different from the MT shear flow and the mixed Rossby–gravity wave is dynamically different from an ER wave, their main result demonstrates the significance of background flow–equatorial wave interactions in promoting TC genesis.

The recent “marsupial theory” of Dunkerton et al. (2008) contends that in the translating frame of reference, the critical latitude and nearby region represents a closed, stationary circulation that effectively separates air within the critical layer from outside air. The authors state that such a flow configuration provides a region of cyclonic vorticity, containment of moisture entrained by the gyre, and/or lofted by deep convection, confinement of mesoscale vortex aggregation, and a convective-type heating profile—all of which make this region favorable for genesis. While this theory was intended for TC genesis within TD-type waves, we believe that many of the features relevant for genesis within the TD-type wave are relevant for genesis within an ER wave. Namely, the cyclonic gyre of the ER wave represents a region of air of high moisture content that is relatively unaffected by nearby outside (drier) air. Furthermore, if the ER wave is embedded within a region of horizontally sheared flow, the critical latitude and nearby region of the ER wave may share many of the traits with the TD-type wave mentioned above that make the region favorable for genesis.

d. Outline

Section 3 of this paper features a description of the MT initialization procedure and describes the method by which the ER wave from Part I is added to the MT background flow. Section 4 presents results from both the MT simulations alone sans the ER wave and the combined MT–ER wave simulations. Section 6 gives a discussion of the results and presents additional avenues for future work.

3. Methodology

As in Part I, the Weather Research and Forecasting (WRF) model v. 2.1.1 (Michalakes et al. 2001) is employed to simulate an ER wave interacting with a MT. The domain configuration, grid spacing, and physical parameterizations are the same as those used in the full-physics ER wave simulations of Part I. The methodology used in this study can be broken down into two different steps. In the first step, a background zonal flow representative of the horizontal shear region of the MT is constructed. In the second step, a convectively coupled ER wave from Part I (ER-2) is added to the zonal background flow from Part I.

a. Model setup

The initial relative vorticity profile for the idealized MT is given by

 
formula

where ζ is the vertical relative vorticity, f is the Coriolis parameter, and ϕ refers to latitude. This initial relative vorticity profile is based on the observed structure of the shear region of the MT (e.g., Briegel and Frank 1997; Ritchie and Holland 1999). The analytic function for the relative vorticity profile is similar to the one employed in Ferreira et al. (1996). The initial horizontal variation of the zonal wind profile is calculated assuming υ(x, y) = 0, displaystyle ∂u/∂x = 0, and through integration of the relative vorticity profile with respect to y, that is,

 
formula

The vertical variation in the zonal wind is specified by multiplying u(x, y) by a vertical weighting function γ:

 
formula

The vertical profile of γ is given by Fig. 3. The structure of γ results in a significant background flow signature at low levels, which decreases toward upper levels.

Fig. 3.

The vertical variation of the weighting function γ used to specify the vertical variation of the background zonal flow. The top of the model lies at approximately 80 mb.

Fig. 3.

The vertical variation of the weighting function γ used to specify the vertical variation of the background zonal flow. The top of the model lies at approximately 80 mb.

Two different background flows (BF-1 and BF-2) representative of MT flow configurations are constructed, and the parameters ϕ1, ϕ2, ϕ3, ζ1, ζ2, and u(ymax) are summarized in Table 1. Figures 4a,b shows the initial meridional profile of relative vorticity, absolute vorticity, and f for BF-1 and BF-2, respectively. The maximum relative vorticity in BF-1 is 1 × 10−5 s−1, which is close to the maximum value from the Ritchie and Holland (1999) monsoon shear line composite for the 850-mb relative vorticity at 72 h prior to genesis (their Fig. 5a). Additionally, this value is between one-half and one-third as large as the maximum relative vorticity values from the Briegel (2002) 5-yr composites for western North Pacific MTs. The maximum relative vorticity of BF-2 is double that of BF-1 with a value of 2 × 10−5 s−1. The justification for this value is that it represents the maximum relative vorticity associated with a more intense monsoon shear line. Since the maximum relative vorticity of 1 × 10−5 s−1 from Ritchie and Holland (1999) was based on a compositing technique, it is likely that maximum vorticity values were larger than this for certain cases. Furthermore, this value falls within the range specified by Briegel (2002). Inspection of Figs. 4a,b reveals that the meridional gradients of absolute vorticity in both BF-1 and BF-2 do not feature a sign reversal; that is, they do not satisfy the necessary but insufficient condition for barotropic instability. Shown in Figs. 4c,d are the initial meridional profiles of the zonal wind. The magnitude of the zonal winds in both Figs. 4c,d are less than 10 m s−1, which are reasonable wind speeds for the MT region. For both background flow configurations, the base-state temperature and moisture soundings are specified with the Jordan (1958) tropical Atlantic soundings. As was done in Part I, a base-state pressure profile is calculated via vertical integration of the hydrostatic equation and through use of the Jordan (1958) temperature and moisture soundings.

Table 1.

Summary of the relevant parameters for the zonal background flows.

Summary of the relevant parameters for the zonal background flows.
Summary of the relevant parameters for the zonal background flows.
Fig. 4.

The initial meridional vorticity profile (s−1) for (a) BF-1 and (b) BF-2 and the initial meridional profile of zonal wind (m s−1) for (c) BF-1 and (d) BF-2.

Fig. 4.

The initial meridional vorticity profile (s−1) for (a) BF-1 and (b) BF-2 and the initial meridional profile of zonal wind (m s−1) for (c) BF-1 and (d) BF-2.

In the second step of the model setup, the initial t = 0 background wind fields of BF-1 and BF-2 are added to the t = 30-day wind fields of the ER-2 simulation ER wave. The resulting combined fields results in new initial conditions for a series of “combination” simulations. While the resulting initial condition is not considered to be “model balanced,” it is very close to a balanced state. The combination simulations allow for the modeling of convectively coupled ER waves in a monsoon shear region of varying intensity.

b. Experimental design

Four simulations are run in total—two background flow only simulations (BF-1 and BF-2) and two background flow plus ER wave simulations (ER-2 + BF-1 and ER-2 + BF-2). All four simulations are integrated forward in time for a period of 9 days. The background flow only simulations are run first in order to demonstrate the quasi-steady nature of the particular monsoon shear line structure, and to demonstrate that significant changes to the background flow only occur when the ER waves are inserted within this flow structure. The physical interpretation of this is a westward-propagating convectively coupled ER wave propagating into a quasi-steady monsoon shear line flow configuration.

4. Results

a. MT only

BF-1 and BF-2 are integrated forward in time for a period of 9 days in order to test their stability (i.e., to determine whether the zonal wind and vorticity fields remain relatively constant over the course of the simulations). Figure 5a shows the initial BF-2 meridional profile of relative vorticity and Fig. 5b shows the same profile at the end of the simulation period. The evolution of the relative vorticity field in BF-1 is qualitatively similar to that of BF-2 (figure not shown). While there are some slight differences in the overall structure of the relative vorticity profile, the monsoon shear line remains relatively intact over the course of the simulation. There is no breakdown of the general MT structure even though convection develops within the band of large cyclonic vorticity in the NH (figures not shown). Additionally, the MT structure exhibits minimal variation in the longitudinal direction throughout the simulation. Thus, the monsoon shear line structure remains quasi-steady and zonally uniform over the course of the 9-day simulation. As a result, we can eliminate internal forcings (i.e., in situ development of cyclonic vorticity) as the mechanism for breakdown and can focus on the externally forced breakdown mechanisms.

Fig. 5.

Meridional variation of the BF-2 850-mb relative vorticity (10−5 s−1) profile averaged over a 4° longitude band at (a) t = 0 and (b) t = 9 days.

Fig. 5.

Meridional variation of the BF-2 850-mb relative vorticity (10−5 s−1) profile averaged over a 4° longitude band at (a) t = 0 and (b) t = 9 days.

b. MT + ER wave simulations

A comparison of the 850-mb wind vectors and height field at t = 0 (Fig. 6a) to t = 12 h (Fig. 6b) shows that the height field quickly comes into balance with the wind field by t = 12 h for ER-2 + BF-2. The discrepancy between the t = 0 height field and wind field arises from the fact that only the background wind field was added to the ER wave and not the corresponding height anomalies. Furthermore, it should be noted that there is little change in the wind field at 850 mb between t = 0 and t = 12 h, as seen in a comparison of Figs. 6a,b. Thus, the time scale for adjustment is much faster than the time scale of any dynamical breakdown mechanism that we are investigating. It should be noted that we also experimented with introducing an artificial nudging term in the horizontal momentum equations to help balance the mass fields with the wind fields. Since a quasi-balance is achieved over a relative short time period without nudging terms, coupled with the fact that the nudging terms lack a physical interpretation, we decided to run the combined simulations without the nudging terms. The height field adjustment for ER-2 + BF-1 occurs over a similarly rapid time scale (figures not shown).

Fig. 6.

The ER-2 + BF-2 850-mb wind field and 850-mb z (m) at (a) t = 0 and (b) t = 12 h. The height field has been smoothed with a nine-point smoother.

Fig. 6.

The ER-2 + BF-2 850-mb wind field and 850-mb z (m) at (a) t = 0 and (b) t = 12 h. The height field has been smoothed with a nine-point smoother.

Figures 7a–d and 8a–d show plots of the ER-2 + BF-2 850-mb wind vectors and 850-mb PV. The PV is calculated using

 
formula

where α is the specific density and θ is the potential temperature. Between about 60° and 90°E a reversal in the 850-mb zonal wind is apparent between 7° and 18°N at t = 0 (Fig. 7a). One day later at t = 1 day, the region of anomalously low PV associated with the anticyclonic gyre of the ER wave has taken on a northwest–southeast tilt. The initiation of the wave-breaking process is evident at this time, as indicated by the approximate north–south slope of the 0.2-, 0.15-, and 0.10-PVU contours on the western side of the low-PV ridges at both 50° and 90°E in the Northern Hemisphere (NH).

Fig. 7.

The ER-2 + BF-2 850-mb wind vectors and 850-mb PV field at (a) t = 0, (b) t = 1, (c) t = 2, and (d) t = 3 days plotted over two arbitrary wavelengths of the ER wave. The PV field is given in units of PVU and 1 PVU ≡ 10−6 K m2 kg−1 s−1. PV values larger than 0.15 PVU in magnitude are shaded. The horizontal dashed line indicates the location of the initial critical latitude assuming an ER wave speed of −2.7 m s−1 from Part I.

Fig. 7.

The ER-2 + BF-2 850-mb wind vectors and 850-mb PV field at (a) t = 0, (b) t = 1, (c) t = 2, and (d) t = 3 days plotted over two arbitrary wavelengths of the ER wave. The PV field is given in units of PVU and 1 PVU ≡ 10−6 K m2 kg−1 s−1. PV values larger than 0.15 PVU in magnitude are shaded. The horizontal dashed line indicates the location of the initial critical latitude assuming an ER wave speed of −2.7 m s−1 from Part I.

Fig. 8.

As in Fig.7, but for (a) t = 4, (b) t = 5, (c) t = 6, and (d) t = 7 days. The dark triangle in (d) indicates the location of genesis.

Fig. 8.

As in Fig.7, but for (a) t = 4, (b) t = 5, (c) t = 6, and (d) t = 7 days. The dark triangle in (d) indicates the location of genesis.

Between t = 0 and t = 3 days, there is a drastic change in the NH PV field as seen in Figs. 7a–d. At both t = 2 and t = 3 days, the tongue of anomalously low-PV air in the NH continues to be stretched in a northwest–southeast orientation and ejected poleward. Such a feature indicates the continuation of the wave-breaking process. By t = 3 days, the low-PV air has started to wrap around the NH cyclonic circulation. A comparison of the ridges of low-PV air near 95° and 58°E at t = 0 to those at t = 3 days reveal a significant decrease in the zonal extent of the low-PV ridge, which provides additional evidence of the wave-breaking process. Closed 0.3-PVU contours are evident at both t = 2 days centered near 12°N, 83°E and t = 3 days centered near 12°N, 2°E to the west of the tongue of low-PV air. Both of these closed cyclonic circulations form near the initial critical latitude. A comparison of the NH PV field to the Southern Hemisphere (SH) PV field in ER-2 + BF-2 reveals that no such drastic changes are observed in the SH PV field. Such a result is expected as all of the initial background horizontal shear associated with the MT was located in the NH. The initially constant background zonal flow has little impact on the structure of the ER wave in the SH.

Figures 8a–d demonstrates the continued deformation of the ER wave from t = 4 days to t = 7 days. The tongue of low-PV air continues to be stretched and deformed in a northwest–southeast orientation. The filament of low-PV air extending from 10°N, 92°E to 20°N, 73°E continues to wrap around the closed 0.3-PVU contour at 73°E. Even at this time, the finger of low-PV air remains attached to the near-equator zonal band of low-PV air. By t = 6 days, however, the narrow band of low-PV air has detached from the near-equator zonal band of low PV, and indicates that the ER wave has “broken.” At both t = 6 days and t = 7 days, the closed 850-mb PV contour situated near 15°N, 70°E continues to intensify and propagate farther west and north. By t = 7 days, the intensification of the low-level cyclonic circulation is evident, with 850-mb PV values above 0.5 PVU at 16°N, 68°E (Fig. 8d). Additionally, the horizontal scale of the cyclonic circulation at t = 7 days decreased by more than 50% when compared with the horizontal scale of the same cyclonic circulation at t = 0.

Figures 9a–d and 10a–d are the same as Figs. 7a–d and 8a–d, but for ER-2 + BF-1. The evolution of the 850-mb PV field is indicative of wave breaking, but in this case, the deformation is much more subdued when compared with results from the ER-2 + BF-2 simulation. For example, at t = 3 days in ER-2 + BF-1 (Fig. 9d), the decrease in the longitudinal extent of the ridge of low-PV air is much smaller when compared to the decrease in ER-2 + BF-2, as is the magnitude of the stretching of the low-PV filament in a northwest–southeast orientation. It should be noted that the deformation of the ER wave in the NH still occurs near the initial critical latitude in ER-2 + BF-1. Contrary to the ER-2 + BF-2 simulation, the tongue of low-PV air in ER-2 + BF-1 at t = 7 day remains attached to the near-equator zonal band of low-PV air (Fig. 10d). Furthermore, the substantial horizontal-scale decrease that was evident between t = 4 days and t = 7 days is much less apparent in ER-2 + BF-1, as the horizontal scale remains nearly unchanged over this time. These results indicate that the wave-breaking process in ER-2 + BF-1 is much more subdued when compared with results from the ER-2 + BF-2 simulation.

Fig. 9.

As in Fig.7, but for ER-2 + BF-1.

Fig. 9.

As in Fig.7, but for ER-2 + BF-1.

Fig. 10.

As in Fig.8, but for ER-2 + BF-1.

Fig. 10.

As in Fig.8, but for ER-2 + BF-1.

From t = 0 to t = 7 days, the deformation of the ER wave in ER-2 + BF-2 is associated with a shift in the location of convection as well as the development of a cyclonic vortex at the surface as seen in Figs. 11a–d. At t = 3 days, most of the convection in the NH remains located within the eastern half of the broad cyclonic circulation extending from about 65° to 85°E (Fig. 11a). At this time, there is little signature in the sea level pressure field (Fig. 11b) associated with this broad cyclonic circulation at 850 mb. Four days later at t = 7 days, the picture has changed substantially. Most of the convection is located near the center of an intense 850-mb cyclonic circulation as seen in Fig. 11c. By this time, there is a significant sea level pressure minimum associated with this cyclonic circulation with a minimum value near 1009 mb. Thus, by t = 7 days in ER-2 + BF-2, the end result is a finite-amplitude cyclonic circulation whose horizontal scale is comparable to that of a tropical cyclone. This circulation features intense convection in and around its center of circulation.

Fig. 11.

The ER-2 + BF-2 t = 3 days 850-mb wind vectors and (a) 850-mb vertical velocity (m s−1), (b) sea level pressure field (mb) and the t = 7 days 850-mb wind vectors, (c) 850-mb vertical velocity, and (d) sea level pressure field. Vertical velocities greater than 0.025 m s−1 are shaded. The horizontal dashed line indicates the location of the initial critical latitude for the ER-2 + BF-2 simulation. The dark triangle in (b) and (d) indicates the location of genesis. The sea level pressure fields are smoothed with a nine-point smoother.

Fig. 11.

The ER-2 + BF-2 t = 3 days 850-mb wind vectors and (a) 850-mb vertical velocity (m s−1), (b) sea level pressure field (mb) and the t = 7 days 850-mb wind vectors, (c) 850-mb vertical velocity, and (d) sea level pressure field. Vertical velocities greater than 0.025 m s−1 are shaded. The horizontal dashed line indicates the location of the initial critical latitude for the ER-2 + BF-2 simulation. The dark triangle in (b) and (d) indicates the location of genesis. The sea level pressure fields are smoothed with a nine-point smoother.

As was the case in ER-2 + BF-2, the broad cyclonic circulation at t = 3 days in ER-2 + BF-1 between about 63° and 83°E features convection within its eastern half (Fig. 12a). No distinct sea level pressure minimum is associated with this circulation at this time. Between t = 3 days and t = 7 days, the strengthening of the 850-mb cyclonic circulation is smaller in ER-2 + BF-1 when compared to the strengthening observed in ER-2 + BF-2. By t = 7 days, the convection remains broadly scattered about the 850-mb cyclonic circulation (Fig. 12c) and no significant decrease in the horizontal scale of the circulation is evident over this time. Additionally, the surface cyclonic circulation remains relatively weak as evidenced by the small seal level pressure anomaly at t = 7 days in ER-2 + BF-1 (Fig. 12d).

Fig. 12.

As in Fig.11, but for ER-2 + BF-1.

Fig. 12.

As in Fig.11, but for ER-2 + BF-1.

Figure 13 illustrates the effect of the initial intensity of the MT with regards to genesis. In ER-2 + BF-2, the genesis process takes about 6.5 days to complete. Subsequent to this is a rapid intensification period, as indicated by the increase in the maximum 850-mb relative vorticity from t = 6 days to t = 9 days. In ER-2 + BF-1, however, the genesis process never fully completes as indicated by the ER-2 + BF-1 maximum relative vorticity time series. The TC-scale cyclonic circulation that was observed to form in ER-2 + BF-2 never forms during the 9-day simulation in ER-2 + BF-1 because the wave-breaking mechanism is much more subdued in this simulation. Thus, a comparison of the maximum intensities from both simulations reveals, in this case, that a MT with an initial maximum 850-mb relative vorticity value of at least 2 × 10−5 s−1 coupled with a sufficiently intense convectively coupled ER wave is needed for genesis to occur.

Fig. 13.

Time series of the maximum 850-mb relative vorticity for ER-2 + BF-1 (solid black) and ER-2 + BF-2 (dashed black). The relative vorticity fields were smoothed in the horizontal with a nine-point smoothing function prior to identification of the maximum values.

Fig. 13.

Time series of the maximum 850-mb relative vorticity for ER-2 + BF-1 (solid black) and ER-2 + BF-2 (dashed black). The relative vorticity fields were smoothed in the horizontal with a nine-point smoothing function prior to identification of the maximum values.

It should be pointed out that both the background flow only simulations (BF-1 and BF-2) and the combined ER wave–background flow simulations (ER-2 + BF-1 and ER-2 + BF-2) were run at a horizontal resolution of 81 km. To examine potential sensitivities of the results to horizontal resolution, these 4 simulations were rerun at a horizontal resolution of 27 km (results now shown). In the 27-km BF-1 and BF-2 simulations, the MT structure remained quasi-steady over the 9-day run, consistent with results from the 81-km simulations. In the 27-km ER-2 + BF-1 simulation, TC genesis did not occur, as the deformation of the ER wave by the background flow was minimal. This result agrees with the findings from the 81-km ER-2 + BF-1 run. As was the case with the 81-km ER-2 + BF-2 experiment, TC genesis occurred in the 27-km ER-2 + BF-2 run by about t = 7 days. Between t = 7 days and t = 9 days, however, the resulting TC in the 27-km simulation is more intense. The insensitivity of TC genesis to horizontal resolution suggests that the main drivers for genesis are large-scale processes, and that these mechanisms are well resolved by the 81-km resolution. Since the focus of this study is on TC genesis (as opposed to TC intensification), we contend that the 81-km resolution is sufficient for modeling the ER wave–background flow interaction.

5. Discussion and future work

The results show how an ER wave interacting with a MT can cause TC genesis. The interaction between the ER wave and the shear region of the MT increases the likelihood of genesis relative to the genesis potential in either the MT or the ER wave alone. When both the MT and ER wave were simulated on their own, genesis did not occur. When a convectively coupled ER wave was combined with a favorable background environment representative of the shear region of a MT, however, TC genesis was observed to occur given that the MT circulation was sufficiently strong. The genesis location resided within the eastern half of the cyclonic gyre of the ER wave and supports the hypothesized favored regions obtained from both the results of Part I as well as the ER wave-genesis composites of Frank and Roundy (2006) and Molinari et al. (2007). With regards to the ER-2 simulation from Part I, while genesis did not occur, it was hypothesized that the eastern half of the cyclonic gyre of the ER wave was the most favorable location for TC genesis, as this location featured enhanced convection, low-level cyclonic vorticity, and weak vertical shear.

The combined ER wave and background flow simulations allowed for the mechanisms by which ER waves promote TC genesis to be examined, and for cause–effect relationships to be established. It was demonstrated that wave breaking of an ER wave is a mechanism by which vorticity can be organized on the scale of a TC. An ER wave propagating into a MT region of sufficient intensity (i.e., strong background vorticity) results in an irreversible deformation of the ER wave. This deformation leads to a significant decrease in the horizontal scale of the cyclonic circulation, and ultimately results in a vortex with the horizontal scale of a TC when the initial 850-mb relative vorticity associated with the MT is at least 2 × 10−5 s−1. The formation period of this TC-scale circulation was associated with a concurrent shift in convection from east of the cyclonic circulation to an area collocated within the center of circulation. Given a sufficient intensity of both the ER wave and MT, the resulting dynamics give way to a smaller cyclonic vortex capable of intensifying via its own air–sea instability.

The Zhang and Webster (1989) analytic solution for an n = 1 ER wave in a horizontally sheared flow fails to account for the nonlinear processes crucial to wave breaking. The time scale of this wave-breaking process was shown to be proportional to the initial background relative vorticity. That is, the larger the background vorticity, the faster the breakdown of the ER wave. Such an observation is in good agreement with the analytic studies of Stewartson (1977) and McIntyre and Palmer (1985) on wave breaking. Since low-level vorticity was crucial to wave breaking and the low-level convergence was important for the location of convection, it was also concluded that the low-level vorticity and convergence anomalies of the ER wave were far more important in the genesis process than were vertical shear modulations associated with the ER wave.

Results from the ER-2 + BF-1 and ER-2 + BF-2 simulations demonstrate the possible significance between the location of the critical latitude and the environmental profile of absolute vorticity. In ER-2 + BF-1, the initial background vorticity associated with the MT is insufficient to produce a large-scale reversal in the meridional gradient of absolute vorticity near the location of the critical latitude, as seen in Fig. 14a. In the stronger MT of ER-2 + BF-2, however, there is a reversal in the meridional gradient of absolute vorticity at t = 0 as indicated by the shaded region of Fig. 14b. In this case, the critical latitude is embedded within this region of negative absolute vorticity gradient. It is believed that such a configuration is important for ER wave–induced genesis, as genesis occurred in ER-2 + BF-2 but not in ER-2 + BF-1. While the PV fields of both ER-2 + BF-1 and ER-2 + BF-2 were materially deformed, only in ER-2 + BF-2 did the ER wave fully “break.” Such a result agrees with the findings of Dunkerton et al. (2008) in which it was argued that easterly waves (TD-type waves) become unstable when the critical latitude lies within a region where the effective beta is negative (i.e., a region featuring a negative meridional absolute vorticity gradient).

Fig. 14.

The t = 0 meridional profile of absolute vorticity (dashed) centered on the t = 0 850-mb relative vorticity maximum and the meridional profile of the t = 0 uc 850-mb zonal wind (solid) for (a) ER-2 + BF-1 and (b) ER-2 + BF-2. The zonal wind profile was offset by the phase speed of the ER-2 wave in order to identify the critical latitude (star). The shaded box identifies large-scale reversals in the meridional absolute vorticity gradient.

Fig. 14.

The t = 0 meridional profile of absolute vorticity (dashed) centered on the t = 0 850-mb relative vorticity maximum and the meridional profile of the t = 0 uc 850-mb zonal wind (solid) for (a) ER-2 + BF-1 and (b) ER-2 + BF-2. The zonal wind profile was offset by the phase speed of the ER-2 wave in order to identify the critical latitude (star). The shaded box identifies large-scale reversals in the meridional absolute vorticity gradient.

This wave-breaking genesis pathway differs from some of the recent theories on genesis (e.g., Ritchie and Holland 1997; Simpson et al. 1997; Bister and Emanuel 1997; Montgomery and Enagonio 1998; Reasor et al. 2005; Holland 1995) in at least one of three ways. First, the wave-breaking mechanism is largely a downscale process whereby the initial cyclonic circulation of the ER wave decreases in horizontal scale as opposed to an upscale energy transfer from the convective scale to the mesoscale. Second, rather than starting our genesis argument with vorticity on the scale of a TC, we demonstrate the process by which this scale is achieved. Apart from the assumptions of the initial structure of the ER wave and MT, no other assumptions were made to simulate TC genesis resulting from the wave-breaking process. Third, the wave accumulation mechanism is dependent upon background confluence. The initial structure of our highly idealized MT was zonally uniform, and as result, contained no initial background confluence. Since wave accumulation requires background confluence to decrease the zonal wavelength, wave accumulation was most likely not the relevant genesis mechanism.

Results from this study suggest that increased ER wave activity is likely to produce a net increase in the number of TCs formed in an ocean basin, particularly in an ocean basin containing a MT. Such a result agrees with the findings of Frank and Roundy (2006) in which it was demonstrated that increased ER wave activity in a particular ocean basin was associated with increased TC genesis. Based on this result, it is hypothesized that the number of TCs will be larger in regions where there is more ER wave activity and more intense MTs. Results from a climatology of potential genesis forcings such as MT duration or intensity and tropical wave activity (including ER waves) may be used to improve upon large-scale diagnostics (e.g., vertical wind shear, SST, etc.) used to predict the number of TCs in different climate scenarios. Thus, TC activity may be increased or decreased in future climates relative to current TC global climatologies depending on such potential factors as MT intensity or duration and tropical wave activity in addition to changes in such large-scale parameters as SST and vertical wind shear.

The wave-breaking mechanism may often be obscured in nature owing to the complexities of the flow. In the simulations performed herein we have identified two characteristics that were indicative of wave breaking—a significant reversal in the meridional gradient of absolute vorticity near the eventual genesis location and the formation of a critical latitude near the genesis location. This begs the question of how important the existence of a critical latitude is when compared with the magnitude of the meridional shear. Would genesis still occur if the critical latitude is removed but the magnitude of the horizontal shear resulting from the combined ER wave–MT remains unchanged? We would like to address this question with an additional idealized modeling study and an observational study utilizing a large dataset (e.g., Frank and Roundy 2006) of TC genesis events in which ER waves played a significant role.

Another potential limitation of this study is that the effects of the confluent region of the MT (as depicted in Fig. 1) were neglected. This was done to isolate the relationship between the magnitude of the background vorticity of the MT to the subsequent deformation of the ER wave. Inclusion of additional physical processes such as background confluence, while resulting in a more realistic MT, would simultaneously weaken cause–effect arguments. It is believed that if an ER wave were to interact with a region of background confluence, that wave accumulation and ultimately, TC genesis, may occur. Such a result has been suggested by Molinari et al. (2007) and shown to occur when other convectively coupled equatorial wave types lie within a region of background confluence (e.g., Maloney and Hartmann 2001; Aiyyer and Molinari 2003). Since both wave breaking and wave accumulation are means by which a horizontal-scale decrease can occur, the existence of background confluence may lower the magnitude of the background vorticity necessary for TC genesis. This hypothesis will be examined in a future study.

Acknowledgments

Insightful comments from Dr. Matthew Wheeler improved both the ideas expressed herein and the manuscript itself. The authors thank Dr. Lee for her useful comments on the subject of wave breaking. This work was supported by National Aeronautics and Space Administration Grant NNG05GQ64G and National Science Foundation Grant ATM-0630364. Many of the plots were generated using the Grid Analysis and Display System (GrADS), developed by the Center for Ocean–Land–Atmosphere Studies at the Institute of Global Environment and Society.

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Footnotes

Corresponding author address: Jeffrey S. Gall, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. Email: gall@meteo.psu.edu

1

Recent studies on TC genesis within the MT (e.g., Cheung and Elsberry 2002; Chen et al. 2004) have highlighted the difficulty in differentiating between a TC and a cyclonic circulation whose horizontal scale is on the order of a TC. As a result, we are careful in not referring to the formation of a TC-scale circulation as TC genesis until a period of subsequent intensification (e.g., a significant sea level pressure decrease) is observed. We refer to the preintensification disturbance as a cyclonic circulation or cyclonic vortex.