The Role of Equatorial Rossby Waves in Tropical Cyclogenesis

Part II: Idealized Simulations in a Monsoon Trough

Environment

Jeffrey S. Gall and William M. Frank

Department of Meteorology, Pennsylvania State University,

University Park, Pennsylvania

Submitted as to Monthly Weather Review

June 12, 2009

Corresponding author: Jeffrey S. Gall, 503 Walker Building, University Park, PA 16802<gall@meteo.psu.edu>

Abstract

This is the second of two papers examining the role of equatorial Rossby (ER) waves in tropical

cyclogenesis. Based on results from part one, we 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 envi-

ronment. 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 tropical cyclone basins, and most dramat-

ically, the western North Pacific basin. We believe 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. We examine the latter scenario here.

When just the MT is simulated without the ER wave anomaly fields, the MT remains quasi-steady

and tropical cyclogenesis does not occur. It is only when the ER wave is imposed on the MT is

tropical cyclogenesis initiated. The results imply that the ER wave-MT interactions produce more

tropical cyclones 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 tropical cyclone. This process features a decrease in the initial

horizontal scale of the cyclonic gyre of the ER wave to a scale comparable with a tropical cyclone.

This genesis mechanism is sensitive to the magnitude of the background cyclonic vorticity of the

MT, as tropical cyclogenesis is only initiated when the strength of the MT is sufficiently intense.

This genesis pathway provides a unique interpretation of tropical cyclogenesis and is compared

with previous theories on tropical cyclogenesis.

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1. Introduction

The necessary but insufficient large-scale conditions for tropical cyclogenesis have been known for

about 40 years (Gray 1968). They are:

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 mid-level

humidity

3. low-level cyclonic vorticity

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

5. location sufficiently far from the equator

While these conditions are often satisfied over large regions of the various ocean basins through-

out 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 tropical cyclogenesis?

In Gall et al. (2009, henceforth GFW), we examined one particular genesis pathway - genesis

resulting from an isolated ER wave. In GFW, ER wave-related genesis was investigated by sim-

ulating 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 contain conditions

favorable for tropical cyclogenesis, only in the largest initial-amplitude ER wave simulation was

genesis observed to occur. Since this simulation represented an approximate upper-bound on the

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maximum amplitude of an ER wave, coupled with the fact that ER waves have been observed in

nature to play a prominent role in tropical cyclogenesis (e.g. Frank and Roundy 2006; Bessafi and

Wheeler 2006), we hypothesized that genesis 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 compo-

nent of an idealized monsoon trough (MT). The MT was selected because the majority of tropical

cyclone (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 2004a)

and MTs (e.g. Briegel and Frank 1997), we believe that the 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 confluent zone (e.g. Holland 1995; Ritchie and Holland 1999). As depicted

in Fig. 1, this region of large-scale convergence 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 anomalous low-level convergence within the MT provides

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a favored region for genesis.

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 two-year data set, 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 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 tropical cyclogenesis

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, mon-

soon 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 quantita-

tively 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

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the MT and features westerly flow on the equatorward side of the genesis location throughout the

72 hours 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 confluence region of the MT.

b. Motivation

In this paper, we concern ourselves with TC genesis within the MT shear region, i.e. the Ritchie

and Holland (1999) monsoon shear categorization. Ritchie and Holland (1999) state that TC de-

velopment 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 ob-

servational studies (e.g. Hack et al. 1989; Schubert et al. 1989; 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 due to 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 hovmollers of the 850 mb zonal and meridional winds show no such

4

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 re-

cent studies of Wheeler and Kiladis (1999), Roundy and Frank (2004a), Molinari et al. (2007), and

others, 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 fre-

quencies must be employed. Additionally, it is possible that the “in situ” increase is due to the

spin-up 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 spin-up is not some physical process related to the

dynamics of the MT.

The remainder of this section reviews previous work that is related to the topic of equatorial

waves within a background flow. Section 3 of this paper features a description of the MT initial-

ization procedure and describes the method by which the ER wave from GFW 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 plus ER wave simulations. Section 6 gives a discussion of the results and

presents additional avenues for future work.

c. Equatorial Waves in a Background Flow

Since we are focusing on the region of the MT that features significant background horizon-

tal 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 be-

tween equatorial waves and TC genesis (see GFW for a review of these), fewer studies have fo-

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cused 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 demon-

strated 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 non-linear deformation of the wave is referred

to as the process of wave-breaking, and an idealized interpretation is presented in Fig. 2a-d. First,

consider the idealized background flow depicted in Fig. 2a. This zonal flow configuration is rep-

resentative 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 (U − c) > 0, while regions equatorward of the critical lati-

tude feature (U − c) < 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.

Zhang and Webster (1989) derived an analytic solution for the n = 1 ER wave in both con-

stant 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 de-

6

batable since it removes any such wave-breaking mechanism given the constraint on the zonal

wavenumber. Aiyyer and Molinari (2002) highlighted the importance of a background flow rep-

resentative 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 MRG wave is dynamically different from an ER wave, their main

result demonstrates the significance of background flow-equatorial wave interactions in promoting

tropical cyclogenesis.

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. Further, 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.

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3. Methodology

As in GFW, 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 GFW. The methodology used in this study can be broken down into two different parts. In

the first part, a background zonal flow representative of the horizontal shear region of the MT is

constructed. In the second part, a convectively-coupled ER wave from GFW (ER-2) is added to

the zonal background flow from part one.

a. Model setup

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

ζ(x, y) =

0.0, φ < φ1

ζ1, φ2 ≥ φ ≥ φ1

ζ2 − f(y), φ3 > φ ≥ φ2

0.0, else

(1)

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 is similar to the one employed in Ferreira et al. (1996). The initial horizontal variation of

the zonal wind profile is calculated assuming v(x, y) = 0, ∂u∂x

= 0, and through integration of the

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relative vorticity profile with respect to y, i.e.

u(x, y − 1) = u(x, y) +[ζ∆y

], for 2 ≤ y ≤ ymax and all x (2)

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

function γ:

γ =

1.0, p > 500 mb

p−200300

, 500 mb ≥ p > 200 mb

0.0, else

(3)

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 towards upper-levels.

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. Fig-

ure 4a and 4b 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 hr 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) five-year 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. Further, this value falls within the range specified by Briegel (2002). Inspection

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of Fig. 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 Fig. 4c and 4d are the initial meridional profiles of the zonal

wind. The magnitude of the zonal winds in both Fig. 4c and 4d are ≤ 10 m s−1, which are rea-

sonable 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 sound-

ings. As was done in GFW, 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.

In the second part of the model setup, the initial t = 0 background wind fields of BF-1 and BF-2

are added to the t = 30 d 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 result-

ing initial condition is not considered to be “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 nine 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-

10

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 nine 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 nine 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.

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b. MT+ER wave simulations

A comparison of the 850 mb wind vectors and height field at t = 0 (Fig. 6a) to t = 12 hr (Fig. 6b)

shows that the height field quickly comes into balance with the wind field by t = 12 hr 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. Further, it should be noted that there is little change in the wind field at 850 mb between

t = 0 and t = 12 hr, as seen in a comparison of Fig. 6a to 6b. Thus, the timescale for adjustment

is much faster than the timescale of any dynamical breakdown mechanism which we are investi-

gating. 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 timescale (figures not shown).

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

calculated using

PV = α

(ζ + f

)∂θ

∂z(4)

where α is the specific density and θ is the potential temperature. Between about 60◦ E and 90◦ E

a reversal in the 850 mb zonal wind is apparent between 7◦ N and 18◦ N at t = 0 (Fig. 7a). One

day later at t = 1 d, the region of anomalously low PV associated with the anticyclonic gyre of the

ER wave has taken on a NW-SE tilt. The initiation of the wave-breaking process is evident at this

time, as indicated by the near-vertical slope of the 0.2pvu, 0.15pvu, and 0.10pvu contours on the

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western side of the low-PV ridges at both 50◦ E and 90◦ E in the Northern Hemisphere (NH).

Between t = 0 and t = 3 d, there is a drastic change in the NH PV field as seen in Fig. 7a-d.

At both t = 2 d and t = 3 d, the tongue of anomalously low-PV air in the NH continues to be

stretched in a NW-SE orientation and ejected poleward. Such a feature indicates the continuation

of the wave-breaking process. By t = 3 d, the low-PV air has started to wrap around the NH

cyclonic circulation. A comparison of the ridges of low-PV air near 95◦ E and 58◦ E at t = 0

to those at t = 3 d reveal a significant decrease in the zonal extent of the low-PV ridge, which

provides additional evidence of the wave-breaking process. Closed 0.3pvu contours are evident

at both t = 2 d centered near 83◦ E and 12◦ N and t = 3 d centered near 82◦ E and 12◦ N 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.

Figure 8a-d demonstrates the continued deformation of the ER wave from t = 4 d to t = 7 d. The

tongue of low-PV air continues to be stretched and deformed in a NW-SE orientation. The filament

of low-PV air extending from 92◦ E and 10◦ N to 73◦ E and 20◦ N continues to wrap around the

closed 0.3pvu 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 d, 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 d and t = 7 d, the closed 850 mb PV contour situated near 70◦ E and 15◦ N continues

to intensify and propagate further west and north. By t = 7 d, the intensification of the low-level

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cyclonic circulation is evident, with 850 mb PV values above 0.5pvu at 68◦ E and 16◦ N (Fig. 8d).

Additionally, the horizontal scale of the cyclonic circulation at t = 7 d has decreased substantially

when compared with the horizontal scale of the same cyclonic circulation at earlier times.

Figures 9a-d - 10a-d are the same as Figures 7a-d - 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 d 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 NW-SE 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 d remains attached to the near-equator

zonal band of low-PV air (Fig. 10d). Further, the substantial horizontal scale decrease that was

evident between t = 4 d and t = 7 d is much less apparent in ER-2+BF-1. 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.

From t = 0 to t = 7 d, 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 Fig. 11a-d. At t = 3 d, most of the convection in the NH remains located within the

eastern half of the broad cyclonic circulation extending from about 65◦ E 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 d, 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 anomaly associated with

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this cyclonic circulation with a minimum value near 1009 mb. Thus, by t = 7 d 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.

As was the case in ER-2+BF-2, the broad cyclonic circulation at t = 3 d in ER-2+BF-1 between

about 63◦ E and 83◦ E features convection within its eastern half (Fig. 12a). No distinct sea level

pressure anomaly is associated with this circulation at this time. Between t = 3 d and t = 7 d,

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 d, 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 d in ER-2+BF-1

(Fig. 12d).

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 d to complete. Subsequent to this is a rapid intensi-

fication period, as indicated by the increase in the maximum 850 mb relative vorticity from t = 6 d

to t = 9 d. 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 which was

observed to form in ER-2+BF-2 never forms during the 9 d 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 that some threshold MT intensity coupled with

a sufficiently intense convectively-coupled ER wave is needed for genesis to occur.

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5. Discussion and Future Work

The results show how an ER wave interacting with a MT can cause tropical cyclogenesis. 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, tropical cyclogenesis 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 GFW 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 GFW, 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 tropical

cyclogenesis, 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 vor-

ticity 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. The formation period of this

TC-scale circulation was associated with a concurrent shift in convection from east of the cyclonic

16

circulation to an area co-located 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 non-linear processes crucial to wave-breaking. The timescale 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 signifi-

cance between the location of the critical latitude and the environmental profile of absolute vor-

ticity. 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 vor-

ticity 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 east-

17

erly waves (TD-type waves) become unstable when 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.

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 Enag-

onio 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, i.e. ∂u∂x

< 0. The initial structure of our highly idealized MT was

zonally-uniform, and as result, contained no initial background confluence. Since wave accumu-

lation requires background confluence to decrease the zonal wavelength, wave accumulation was

most likely not the relevant genesis mechanism.

The results 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 tropical cy-

clogenesis. Based on this result, it is hypothesized that the number of TCs is going to be greater

where you have 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

18

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 data set (e.g. Frank and Roundy 2006) of TC

genesis events in which ER waves played a significant role. Additionally, we plan to investigate

both tropical wave activity and MT flow activity under future climate scenarios and relate these

forcings to TC activity.

19

Acknowledgments

Insightful comments from Dr. Matthew Wheeler improved both the ideas expressed herein and the

manuscript itself. The authors would like to 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.

20

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24

Table 1: Summary of the relevant parameters for the zonal background flows.

EXP φ1 (◦) φ2 (◦) φ3 (◦) ζ1 (s−1) ζ2 (s−1) u(ymax)

BF-1 4.25 9 12.75 1×10−5 3.21×10−5 -4

BF-2 4.25 9 16.75 2×10−5 4.21×10−5 -9

25

List of Figures

1 Idealized depiction of the near-surface streamlines associated with a MT flow con-

figuration (Figure 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 two-year data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2 An illustration of the wave-breaking process for an idealized wave embedded within

a zonal background flow representative of the shear region of a MT. . . . . . . . . 30

3 The vertical variation of the weighting function γ used to specify the vertical vari-

ation of the background zonal flow. The top of the model lies at approximately

80 mb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 The initial meridional vorticity profile (s−1) for a.) BF-1 and b.) BF-2 and the

initial meridional profile of zonal wind for c.) BF-1 and d.) BF-2. . . . . . . . . . 32

5 Meridional variation of the BF-2 850 mb relative vorticity (s−1) profile averaged

over a 4◦ longitude band at a.) t = 0 and b.) t = 9 d. . . . . . . . . . . . . . . . . . 32

6 The ER-2+BF-2 850 mb wind field and 850 mb z (m) at a.) t = 0 and b.) t = 12 hr.

The continental boundaries are provided for scale only. . . . . . . . . . . . . . . . 33

26

7 The ER-2+BF-2 850 mb wind vectors and 850 mb PV field at a.) t = 0, b.) t = 1 d

, c.) t = 2 d, and d.) t = 3 d plotted over two arbitrary wavelengths of the ER

wave. The PV field is given in units of pvu and 1 pvu=106 K m2 kg−1 s−1. PV

values larger than 0.15pvu 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 GFW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

8 As in 7 except for a.) t = 4 d, b.) t = 5 d , c.) t = 6 d, and d.) t = 7 d. The dark

triangle in d.) indicates the location of genesis. . . . . . . . . . . . . . . . . . . . 35

9 As in 7 except for ER-2+BF-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10 As in 8 except for ER-2+BF-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

11 The ER-2+BF-2 t = 3 d 850 mb wind vectors and a.) 850 mb vertical velocity

(m s−1), b.) sea level pressure field (mb) and the t = 7 d 850 mb wind vectors and

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. . . . . . . . . . . . . . . . 38

12 As in 11 except for ER-2+BF-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

27

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 u − c

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. . . . . . . . . . . . . . . . . . . . . . . . . 41

28

Figure 1: Idealized depiction of the near-surface streamlines associated with a MT flow configura-

tion (Figure 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 two-year data set.

29

Figure 2: An illustration of the wave-breaking process for an idealized wave embedded within a

zonal background flow representative of the shear region of a MT.

30

Figure 3: The vertical variation of the weighting function γ used to specify the vertical variationof the background zonal flow. The top of the model lies at approximately 80 mb.

31

Figure 4: The initial meridional vorticity profile (s−1) for a.) BF-1 and b.) BF-2 and the initialmeridional profile of zonal wind for c.) BF-1 and d.) BF-2.

Figure 5: Meridional variation of the BF-2 850 mb relative vorticity (s−1) profile averaged over a4◦ longitude band at a.) t = 0 and b.) t = 9 d.

32

Figure 6: The ER-2+BF-2 850 mb wind field and 850 mb z (m) at a.) t = 0 and b.) t = 12 hr. Thecontinental boundaries are provided for scale only.

33

Figure 7: The ER-2+BF-2 850 mb wind vectors and 850 mb PV field at a.) t = 0, b.) t = 1 d , c.)t = 2 d, and d.) t = 3 d plotted over two arbitrary wavelengths of the ER wave. The PV field isgiven in units of pvu and 1 pvu=106 K m2 kg−1 s−1. PV values larger than 0.15pvu in magnitudeare shaded. The horizontal dashed line indicates the location of the initial critical latitude assumingan ER wave speed of -2.7 m s−1 from GFW.

34

Figure 8: As in 7 except for a.) t = 4 d, b.) t = 5 d , c.) t = 6 d, and d.) t = 7 d. The dark trianglein d.) indicates the location of genesis.

35

Figure 9: As in 7 except for ER-2+BF-1.

36

Figure 10: As in 8 except for ER-2+BF-1.

37

Figure 11: The ER-2+BF-2 t = 3 d 850 mb wind vectors and a.) 850 mb vertical velocity (m s−1),b.) sea level pressure field (mb) and the t = 7 d 850 mb wind vectors and c.) 850 mb verticalvelocity 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-2simulation. The dark triangle in b.) and d.) indicates the location of genesis.

38

Figure 12: As in 11 except for ER-2+BF-1.

39

Figure 13: Time series of the maximum 850 mb relative vorticity for ER-2+BF-1 (solid black) andER-2+BF-2 (dashed black). The relative vorticity fields were smoothed in the horizontal with anine-point smoothing function prior to identification of the maximum values.

40

Figure 14: The t = 0 meridional profile of absolute vorticity (dashed) centered on the t = 0 850 mbrelative vorticity maximum and the meridional profile of the t = 0 u− c 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 ofthe ER-2 wave in order to identify the critical latitude (star). The shaded box identifies large-scalereversals in the meridional absolute vorticity gradient.

41