introduction to tropical cyclones - evans.pdf

Tropical Cyclone Climatology

Introduction

In this section, we open our study of tropical cyclones, one of the most recognizable (and impactful) weather features of the tropics. In this study, we begin with an overview of what tropical cyclones are by presenting the most basic of definitions for a tropical cyclone. Subsequently, the locations in which tropical cyclones form, the paths they take, and the large-scale factors that influence their formation are discussed. This overview will motivate future lectures on tropical cyclone formation and intensity change, enabling us to better understand the physics and dynamics behind why and how tropical cyclones form.

Tropical Cyclone Definitions

As defined by Holland (1993), a tropical cyclone is a non-frontal synoptic-scale low pressure system over tropical or subtropical waters with persistent, organized convection and a closed cyclonic circulation. Tropical cyclones are typically classified by their intensities, with the maximum sustained surface (10-m) wind speed being the most common measure of tropical cyclone intensity. Tropical cyclone classifications include:

A tropical depression is a tropical cyclone with maximum sustained surface winds less than 17.5 m s-1 (34 kt).

A tropical storm is a tropical cyclone with maximum sustained surface wind speeds 17.5-33 m s-1 (34-64 kt). Near Australia and in the Indian Ocean, tropical storms are generically referred to as tropical cyclones.

A hurricane is a tropical cyclone with maximum sustained surface winds in excess of 33 m s-1 (64 kt). In the Western North Pacific, hurricanes are known as typhoons. Near Australia and in the Indian Ocean, hurricanes are known as severe tropical cyclones.

In products issued by the National Hurricane Center, Central Pacific Hurricane Center, and Joint Typhoon Warning Center (e.g., United States-based agencies), the maximum sustained surface wind speed is expressed as the 1-min average wind speed. In products issued by all other agencies, the maximum sustained surface wind speed is expressed as the 10-min average wind speed. The former value is approximately 1.15 times larger than the latter. Thus, care must be taken when comparing tropical cyclone intensities between individual basins.

Within the hurricane classification, there exist several sub-classifications that vary between individual ocean basins. Within the Atlantic and Eastern North Pacific basins, the Saffir-Simpson Hurricane Wind Scale (Schott et al. 2012) is used to classify hurricanes as a function of wind speed and, subsequently, the damage that such winds can inflict. The categories of the Saffir-Simpson Hurricane Wind Scale include:

Saffir-Simpson Hurricane Wind Scale Category Maximum Sustained Wind Speeds

Category 1 64-82 kt

Category 2 83-95 kt

Category 3 96-112 kt

Category 4 113-136 kt

Category 5 >136 kt

Note that category 3 and higher hurricanes are often referred to as major hurricanes. In the Western North Pacific, the Joint Typhoon Warning Center refers to typhoons with maximum sustained wind speeds in excess of 130 kt as super typhoons. The Australian Bureau of Meteorology uses a separate five category scale to express the intensity and expected impacts of tropical cyclones of tropical storm intensity or higher. More details on this classification system may be found on the Bureau of Meteorologys website at http://www.bom.gov.au/cyclone/about/intensity.shtml.

Tropical Cyclone Climatology

On average, approximately 84 tropical cyclones form annually across the globe. Approximately 45, or 54%, of these reach hurricane intensity at some point during their existence. The Western North Pacific is the most active of the worlds ocean basins on average, home to approximately 26 tropical cyclones and 16 typhoons each year. The Eastern North Pacific is the second-most active basin on average, home to approximately 17 tropical cyclones and 9 hurricanes each year. Approximately 10 tropical cyclones occur annually in each of the North Atlantic, Southwest Indian, and Southwest Pacific basins. Slightly more of these tropical cyclones reach hurricane intensity in the North Atlantic as compared to the Southwest Indian and Southwest Pacific. The Southeast Indian basin experiences approximately 7 tropical cyclones and 3 hurricanes per year. The North Indian basin experiences approximately 5 tropical cyclones and 2.5 hurricanes per year. Tropical cyclone activity is rare, though not unprecedented, in the Eastern South Pacific and South Atlantic basins.

Tropical cyclones are seasonal phenomena. Most basins experience peak tropical cyclone activity during the late summer and early fall months. In the Southern Hemisphere, this corresponds to January through March. In the Northern Hemisphere, this corresponds to July through September. Tropical cyclone formation occurs at lower latitudes early in the tropical season, spreads northward thereafter, and only returns to lower latitudes at the very end of the season. Tropical cyclone activity is possible year-round if the conditions which promote tropical cyclone development are present; however, this is most commonly true only in the Western North Pacific basin. The seasonal distribution of tropical cyclone activity is strongly influenced

by the seasonal evolutions of sea surface temperatures and the location/presence of the phenomena that give rise to tropical cyclones.

Tropical cyclones typically form within the deep tropics between 10-20 latitude. To first order, tropical cyclones move in a direction and at a rate of speed approximated by the mean wind over a vertical layer that varies with cyclone intensity. Put more simply, tropical cyclones are typically steered by the flow associated with subtropical anticyclones and mid-latitude troughs. As a result, in the majority of the worlds ocean basins, tropical cyclones move slightly poleward of due west in the deep tropics at a rate of speed of approximately 10-15 kt. Thereafter, as they reach the periphery of the steering subtropical anticyclone, tropical cyclones acquire a significant poleward component of motion. They subsequently accelerate and recurve poleward and eastward into the mid-latitudes. Exceptions occur with tropical cyclones that make landfall or, in the Eastern North Pacific basin, with tropical cyclones that dissipate over the cool waters of the subtropical Eastern North Pacific Ocean. Significant intraseasonal variability in tropical cyclone tracks is largely a function of intraseasonal variability in the large-scale weather pattern across the subtropics and mid-latitudes.

In the following, we consider unique characteristics associated with the climatology of tropical cyclones within each of the ocean basins in which tropical cyclones occur. The exception to this is the North Atlantic basin, which is covered separately within its own section.

Eastern North Pacific

The majority of tropical cyclones in the Eastern North Pacific basin form within a fairly localized region to the west of Central America, where sea surface temperatures are typically well in excess of 29C during the tropical season. It is in this narrow region where the worlds highest frequency of tropical cyclone genesis per unit area occurs. Tropical cyclone formation becomes progressively less likely with westward extent into the Central North Pacific. Tropical cyclone season lasts from June to October, concurrent with the northward shift in sea surface temperatures and ITCZ associated with Northern Hemisphere summer. Tropical cyclone activity peaks in late August. Many tropical cyclones that form in the Eastern North Pacific owe their origins to African easterly waves that did not spawn tropical cyclones in the North Atlantic basin.

Western North Pacific

As compared to the Eastern North Pacific basin, tropical cyclones form over a large area (in terms of both latitudinal and longitudinal extent) across the Western North Pacific. As noted above, tropical cyclones can form throughout the year in the Western North Pacific. However, tropical cyclone activity is maximized between June and November and minimized during February and March. Within the tropical cyclone season, tropical cyclone activity is characterized by successive relatively active and relatively inactive periods with a period of approximately 30-45 days. This implies a potential control on tropical cyclone activity by the

MJO, as briefly alluded to in our earlier lecture on intraseasonal variability. The Western North Pacific is particularly noted for the relatively high frequency of very large and very intense tropical cyclones. The former has origins in the size and characteristics of the disturbances (particularly the monsoon trough) which spawn tropical cyclones in the Western North Pacific; the latter has origins in the relatively large extent of very warm (~30C) sea surface temperatures during the peak of the tropical season.

North Indian Ocean

Although less than 10% of the global tropical cyclones occur in the North Indian Ocean, they are the most deadly. This is because of a number of factors: the shallow waters of the Bay of Bengal promote the development and propagation of large trapped-fetch waves; low, flat coastal terrain promotes the inland spread of waves as they reach the coast; the funneling shape of the coastline promotes the amplification of wave heights over a narrow, focused area; and the presence of a large number of people in a relatively small, third world area promotes heavy casualties from such events. Within the North Indian Ocean, tropical cyclone activity is much more common in the Bay of Bengal than in the Arabian Sea, possibly because of the lack of seedling disturbances and the relatively dry middle tropospheric environment found in the Arabian Sea. Tropical cyclones most commonly form between April and June and October through December when the sea surface temperatures are warm enough to support their formation and while the monsoon is relatively weak. During monsoon season, monsoon depressions (or weak, very large tropical cyclone-like disturbances with no inner core structure) are the preferred mode of cyclone development across the basin.

Southwest Indian Ocean

Tropical cyclone activity is most prevalent in the Southwest Indian Ocean between November and April with maxima in mid-late January and mid-late February. Tropical cyclones in this basin primarily form in two distinct geographic locations: over the open waters of the Indian Ocean between 8-12S latitude and near Madagascar (15-20S) in the far western portion of the basin. Apart from the seasonal variability in sea surface temperatures, activity in this basin and particularly near Madagascar is controlled by seasonal variability in the surface trades. During tropical cyclone season, the typical southeasterly surface trades reverse and acquire a northerly component. It is this reversal that appears to be crucial to tropical cyclone development near Madagascar, although the reasons for this are not entirely clear.

Southeast Indian and Southwest Pacific Ocean Basins

Tropical cyclone activity in these basins preferentially occurs near the northern coast of Australia in three specific regions: the northwest coastline, the Gulf of Carpenteria, and the Coral Sea northeast of Australia. Of these regions, weaker tropical cyclones occur most commonly in the Gulf of Carpenteria while stronger tropical cyclones occur most commonly off of the northwest coast of Australia. Most tropical cyclones in these basins form from disturbances in

the monsoon trough, though some over the eastern reaches of the Southwest Pacific Ocean form from disturbances in the South Pacific Convergence Zone or from equatorial wave forcing. Tropical cyclone season in both basins lasts from December through mid-April with a relative maximum in mid-late February. Tropical cyclone activity is suppressed during the midst of the season while the monsoon is over land. Thus, compared to the North Indian Ocean, tropical cyclones and the monsoon typically co-exist with one another in the Southeast Indian and Southwest Pacific basins.

Other Ocean Basins

As noted above, tropical cyclone activity is rare, though not altogether impossible, in the Eastern South Pacific and South Atlantic basins. Though sea surface temperatures are occasionally supportive of tropical cyclone activity within these basins, strong vertical wind shear and the lack of coherent lower tropospheric disturbances from which tropical cyclones can form inhibit such activity. That said, in a subsequent lecture on the tropical transition process, we will examine the physics and dynamics of a tropical cyclone formation event that occurred within the South Atlantic basin in 2004.

Tropical Cyclone Development in the North Atlantic Basin

Though it was previously thought that the North Atlantic was the only one of the worlds tropical cyclone-supporting ocean basins to not have a monsoon trough, more recent studies have highlighted the presence of a monsoon trough along the western coast of Africa associated with the West African monsoon. That said, though this monsoon trough acts as a locus of cyclonic vertical vorticity and deep-layer moisture, tropical cyclone development in the tropical North Atlantic most often results from African easterly waves. Note also that while the North Atlantic basin is unique amongst the worlds tropical cyclone-supporting ocean basins to have a seasonal mean westerly vertical wind shear, such shear typically reverses in direction (to easterly) prior to individual tropical cyclone developments.

Tropical cyclone season in the Atlantic lasts from June through November, peaking in mid-September. Minor peaks occur in mid-October and, to a lesser extent, late June. Tropical cyclone development is typically confined to tropical latitudes early and late in the season while it expands north and eastward during the middle of the season as sea surface temperatures warm and vertical wind shear lessens. Owing to the relatively large range of latitudes at which tropical cyclones form in the North Atlantic (as well as the Western North Pacific) basin(s), there exist multiple types of disturbances that spawn tropical cyclone development. As noted above, many developments in the tropical North Atlantic occur in conjunction with African easterly waves. Such tropical cyclones form to the south of the African easterly jet and at the southern boundary of the Saharan air layer. A small fraction of tropical cyclones arise from non-easterly wave disturbances in the ITCZ or, in rare instances, the West African monsoon trough. Other disturbances have direct and/or indirect origins with baroclinic systems.

The wide variety of incipient disturbances for tropical cyclone formation in the North Atlantic is captured by the climatology of McTaggart-Cowan et al. (2008). Based off of the evolutions of large-scale forcing for ascent and lower tropospheric thickness prior to tropical cyclone formation, McTaggart-Cowan et al. (2008) developed six unique pathways for tropical cyclone formation in the North Atlantic basin. These pathways include:

Non-baroclinic, accounting for 40% of all tropical cyclone formation events. These are the traditional tropical cyclones, forming most often in the deep tropics from African easterly waves. It is this pathway to genesis that we will examine most closely in subsequent lectures.

Low-level baroclinic, accounting for 13% of all tropical cyclone formation events. These tropical cyclone formation events preferentially occur at low latitudes near the west coast of Africa and in the western Caribbean, both locations where substantial lower tropospheric temperature gradients exist. Near Africa, these are associated with the African easterly jet and Saharan air layer; in the western Caribbean, these are associated with land-sea temperature contrasts.

Transient trough interaction, accounting for 16% of all tropical cyclone formation events. These tropical cyclone formation events preferentially occur early in the tropical cyclone season, when transient mid-latitude troughs impinge upon the still relatively cool sea surface temperatures of the tropics. Most of these developments occur in the Gulf of Mexico or central tropical North Atlantic.

Trough-induced, accounting for only 3% of all tropical cyclone formation events. These tropical cyclone formation events preferentially occur in the Gulf of Mexico or off of the east coast of Florida during the peak of hurricane season. At this time, lower tropospheric temperature gradients are weak but large-scale forcing for ascent can be strong in the presence of a mid-latitude trough.

Weak tropical transition, accounting for 13% of all tropical cyclone events. These tropical cyclone formation events occur in environments of strong large-scale forcing for ascent and medium to large lower tropospheric temperature gradients. Such conditions are most commonly found across the Gulf of Mexico and off of the east coast of Florida throughout the tropical cyclone season, although a relative maximum in such events is noted during June.

Strong tropical transition, accounting for 15% of all tropical cyclone events. Such tropical cyclone formation events most commonly occur late in the season at higher latitudes (at or above 30N) in the western and central North Atlantic basin. These tropical cyclones are most sensitive not to sea surface temperatures but to the relatively cool temperature of

the outflow layer of the cyclone in the upper troposphere. How and why this is the case will be discussed in a subsequent lecture on tropical cyclone intensity change.

In addition to the geographic and seasonal distributions referenced above for the six tropical cyclone development pathways, there exists substantial variability in the peak intensity of tropical cyclones forming along each of these pathways. Trough-induced, weak tropical transition, and strong tropical transition tropical cyclone formations tend to have greater numbers of weaker tropical cyclones and fewer numbers of stronger tropical cyclones as compared to the set of all tropical cyclone formation events. Most of the strongest tropical cyclones are of non-baroclinic or low-level baroclinic origin, although a non-insignificant number of tropical cyclones that develop along the transient trough interaction pathway do go on to become tropical cyclones.

Large-Scale Conditions Necessary for Tropical Cyclone Formation

Gray (1968) highlighted six necessary large-scale conditions for tropical cyclone formation:

Large cyclonic vertical vorticity in the lower troposphere, such as is often associated with the ITCZ, an African easterly wave, or the monsoon trough.

A distance at least several degrees latitude poleward of the equator, such that sufficiently large planetary vorticity is present.

Weak vertical wind shear of the horizontal winds (typically less than ~10 m s-1), so as to promote the development of an upright vortex that is resilient to the infiltration of cool, dry air from the external environment.

Sea surface temperatures exceeding 26C, preferably over a relatively large depth, to provide the necessary heat energy for tropical cyclone development to occur.

Conditional instability through a deep tropospheric layer, so as to promote the development of deep, moist convection in the vicinity of a tropical disturbance.

Large values of relative humidity in the lower and middle troposphere, so as to negate the destructive potential of convectively-generated downdrafts upon the lower tropospheric circulation of a tropical disturbance.

Of these factors, the first three are said to be dynamic parameters whereas the last three are said to be thermodynamic parameters. Each factor is multiplicative, meaning that all must be present in order for tropical cyclone formation to occur. The thermodynamic parameters are slowly varying; indeed, with localized exceptions, the three thermodynamic parameters are all generally favorable for development over a large area throughout the peak of the tropical cyclone season. The same cannot be said for the dynamic parameters, however, and Gray (1968) thus

hypothesized that tropical cyclone activity occurs only during periods in which the dynamic parameters are perturbed to more favorable values above their local climatological means.

Frank (1987) noted that some of Gray (1968)s six environmental parameters are not independent of one another. In the tropics, where horizontal temperature gradients are typically weak, regions of high sea surface temperatures are typically also associated with the presence of conditional instability. From this, Frank (1987) proposed removing the fifth criterion from the Gray (1968) list. Frank (1987) also suggested that the two vorticity-related factors could be combined into a single, more general absolute vorticity criterion and that mean upward vertical motion could be added to the relative humidity criterion so as to better reflect the necessity of deep, moist convective activity to the tropical cyclone formation process. Thus, in the context of Frank (1987), the following four criteria are said to be the necessary conditions for tropical cyclone formation:

Large cyclonic absolute vorticity in the lower troposphere, such as is often found away from the equator in association with the ITCZ, an African easterly wave, or the monsoon trough.

Weak vertical wind shear of the horizontal winds (typically less than ~10 m s-1), so as to promote the development of an upright vortex that is resilient to the infiltration of cool, dry air from the external environment.

Sea surface temperatures exceeding 26C, preferably over a relatively large depth, to provide the necessary heat energy for tropical cyclone development to occur.

Large values of relative humidity in the lower and middle troposphere in association with mean ascent, so as to negate the destructive potential of convectively-generated downdrafts upon the lower tropospheric circulation of a tropical disturbance

In addition to the aforementioned requisite factors for tropical cyclone formation, the following characteristics have been shown by observational studies to be important to the tropical cyclone formation process:

The presence of a pre-existing, convectively-active disturbance, such as an African easterly wave, monsoon trough, or other similar disturbance.

The transformation of the disturbances initially cold-core thermal structure into that of a tropospheric-deep warm-core thermal structure. Precisely how this occurs is detailed in a subsequent section on tropical cyclone formation.

The accumulation (increase, spin-up, etc.) of lower tropospheric cyclonic relative vorticity on the synoptic-scale in the presence of the disturbance.

Weak vertical wind shear of the horizontal winds in the environment of the disturbance (typically less than ~10 m s-1), so as to promote the development of an upright vortex that is resilient to the infiltration of cool, dry air from the external environment.

The development of curved banding features associated with active convection, often a signature of intensifying rotation found in association with the disturbance.

The presence of synoptic-scale upper tropospheric divergence, so as to promote lower tropospheric convergence and tropospheric-deep ascent in the environment of the disturbance.

It should be noted that, as with the Gray (1968) and Frank (1987) conditions, these are all necessary but insufficient conditions for tropical cyclone development. Furthermore, missing from the above discussion are considerations of precisely how the tropical cyclone vortex develops, the role that deep, moist convection and its organization play in the tropical cyclone formation process, and the precise energetics of the tropical cyclone. The physics and dynamics of these processes are discussed in subsequent lectures on tropical cyclone formation.

References

Elsberry, R. L., 1995: Tropical cyclone motion. Global Perspectives on Tropical Cyclones, R. L. Elsberry (ed.). World Meteorological Organization, Geneva, Switzerland, Report No. TCP-38. [Available online at http://derecho.math.uwm.edu/classes/TropMet/GPTC/tcmotion.pdf].

Frank, W. M., 1987: Tropical cyclone formation. Chapter 3, A Global View of Tropical Cyclones. Office of Naval Research, Arlington, Virginia, 53-90.

Gray, W. M., 1968: Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev., 96, 669-700.

Holland, G. J., 1993: Ready Reckoner. Chapter 9, Global Guide to Tropical Cyclone Forecasting, WMO/TC-No. 560.

McBride, J. L., 1995: Tropical cyclone formation. Global Perspectives on Tropical Cyclones, R. L. Elsberry (ed.). World Meteorological Organization, Geneva, Switzerland, Report No. TCP-38. [Available online at http://derecho.math.uwm.edu/classes/TropMet/GPTC/tcclimo.pdf].

McTaggart-Cowan, R., G. D. Deane, L. F. Bosart, C. A. Davis, and T. J. Galarneau, Jr., 2008: Climatology of tropical cyclogenesis in the North Atlantic (1948-2004). Mon. Wea. Rev., 136, 1284-1304.

Schott, T., and coauthors, 2012: The Saffir-Simpson hurricane wind scale. [Available online at http://www.nhc.noaa.gov/pdf/sshws.pdf].

Tropical Cyclone Formation, Page 1

Tropical Cyclone Formation

Introduction

Previously, we discussed large-scale (or climatological) conditions believed to be

necessary for tropical cyclone development to occur. Now, we focus on describing two physical

processes: the development of the tropical cyclone vortex and the acquisition of a warm-core

thermal structure by an initially cold-core incipient disturbance. Thus, we define tropical cyclone

formation as the initial development of a tropical cyclone. In subsequent lectures, we will discuss

processes that influence the intensity of an existing tropical cyclone, focusing upon both external

and internal influences upon tropical cyclone intensity.

Observational Perspective on Tropical Cyclone Formation

Presuming that a pre-existing synoptic-scale tropical disturbance of some form (e.g.,

African easterly wave, monsoon trough, the ITCZ, or an equatorial wave) exists in an

environment conducive to tropical cyclone development (e.g., as described in the lecture on

tropical cyclone climatology), the tropical cyclone formation, or tropical cyclogenesis, process

can broadly be described as a two stage process (Zehr 1992). In the first stage, deep, moist

convection is triggered by persistent lower tropospheric convergence associated with the pre-

existing disturbance in a modestly unstable environment. Over a period of several hours, such

convection grows upscale, resulting in the formation of a mesoscale convective system (MCS).

Middle tropospheric warming via latent heat release and lower tropospheric cooling via

the generation of evaporatively-driven downdrafts accompany the MCS. This thermal structure

promotes greater packing of isentropes in the vertical in the middle troposphere. Relating this to

potential vorticity, this is associated with high potential vorticity in the middle troposphere, thus

highlighting the development of a middle tropospheric mesoscale convective vortex (MCV) in

the vicinity of the pre-existing disturbance.

The generation of evaporatively-driven downdrafts acts to stabilize the boundary layer

and weaken the large-scale boundary layer convergence driving the deep, moist convection. Over

time, these processes result in the erosion of the MCS, though not before significant moistening

of the middle troposphere has occurred. The end result of the first stage of tropical cyclogenesis

is thus a middle tropospheric MCV devoid of most if not all deep, moist convective activity. The

middle tropospheric is moister but the boundary layer is cooler and drier than prior to the onset

of the first stage of development. In all, this first stage encompasses a time period of

approximately 12-24 hr.

Prior to the onset of the second stage of tropical cyclone development, the boundary

layer must be sufficiently warmed and/or moistened so as to permit the renewed development of

deep, moist convection. Over warm oceans, this is typically accomplished by the flux of latent

heat energy from the underlying surface into the boundary layer. As this occurs, the environment


in the vicinity of the MCV can again support deep, moist convection. Such convective activity is

triggered by forcing for ascent triggered by balanced lifting associated with the MCV and/or

large-scale convergence associated with the MCV or remnant tropical disturbance. The

redevelopment of convection signals the onset of the second stage of tropical cyclone

development, a series of processes that, over the span of approximately 12-24 hr, can lead to the

development of a tropical cyclone.

This round of deep, moist convective activity differs from that in the first stage of tropical

cyclone development in two important ways. First, the presence of the MCV increases the

inertial stability (related to the absolute vorticity), thereby reducing the Rossby radius of

deformation, itself approximated by the ratio of the static stability to the inertial stability.

Reducing the Rossby radius of deformation acts to laterally constrain the radial extent of the

heating associated with the convection, the implications of which will be discussed shortly. Note

that we are not yet ascribing such heating to a particular physical process; rather, we are merely

stating that it occurs in environments of deep, moist convection.

Second, the middle troposphere is significantly moister as compared to the first stage of

tropical cyclone development. This mitigates the intensity and development of evaporatively-

driven downdrafts. If the middle troposphere is entirely saturated, assuming minimal water

loading in regions of active precipitation, then downdraft activity is entirely suppressed. In such

an environment, the atmospheric lapse rate is typically said to be moist neutral, describing a

situation in which parcels are neutrally buoyant to vertical parcel displacements. Such conditions

have been found in observational and numerical modeling studies to be favorable for the efficient

development of a cyclonic circulation within the boundary layer, such as is associated with a

tropical cyclone. Note, however, that we are not yet describing precisely how this cyclonic

circulation forms.

In a quiescent environment, or one that is altogether favorable for tropical cyclogenesis,

this observational perspective elucidates the basic physical characteristics and applicable time

scale(s) of the tropical cyclogenesis process quite nicely. However, as noted above, it does not

address the two fundamental questions associated with precisely how tropical cyclogenesis

occurs. Namely, it does not provide insight into how the tropical cyclone vortex is constructed

within the boundary layer, nor does it provide insight into whether the tropical cyclone warm

core is a response of convective heating or some other thermodynamic process. To address these

questions, we must turn to other resources.

The Development of the Tropical Cyclone Vortex

The development of the tropical cyclone vortex is fundamentally dependent upon the role

of the middle tropospheric MCV in the lower tropospheric vortex development process. There

are two theories that attempt to address this issue. The first emphasizes the downward

development or penetration of a middle tropospheric MCV into the boundary layer (Bister and


Emanuel 1997; Ritchie and Holland 1997) whereas the second emphasizes the development and

eventual organization of deep, moist convective towers within the embryonic environment

provided by the middle tropospheric MCV (Montgomery et al. 2006). The former has been

studied extensively from observational and numerical modeling perspectives whereas the latter

has largely only been studied extensively using numerical model simulations. We now turn to

describing the salient physical and dynamical processes associated with each of these two

theories.

Downward MCV Penetration

Much of the following discussion follows from Bister and Emanuel (1997), though it

should be noted that the results of Ritchie and Holland (1997) are largely consistent with their

findings. Utilizing a combination of observational analysis, numerical model simulations, and

theory, Bister and Emanuel (1997) suggest that tropical cyclone development occurs in response

to the downward development of a middle tropospheric MCV into the boundary layer. This

process can be briefly summarized as follows. A middle tropospheric MCV forms in the

stratiform rain region of an MCS associated with a pre-existing tropical disturbance. Evaporation

of rain in the environment of the MCV increases lower tropospheric relative humidity and leads

to a downdraft that advects the vortex downward into the boundary layer. Subsequently, deep,

moist convection redevelops, leading to the increase of cyclonic vertical vorticity in the lower

troposphere via vorticity tilting and stretching processes.

Bister and Emanuel (1997) argue that the initial cold-core structure of the MCV is crucial

to the subsequent development of a tropical cyclone as such a structure reduces the value of

boundary layer equivalent potential temperature necessary for deep, moist convection to occur.

Furthermore, increased lower to middle tropospheric relative humidity associated with

evaporative moistening associated with initial convective activity mitigates evaporatively-driven

downdrafts associated with subsequent convective activity. As the cold-core structure of the

MCV implies relatively cool boundary layer conditions, such a structure in and of itself further

mitigates against the deleterious impacts of downdraft activity upon the near-surface profiles of

convergence and vertical vorticity. Finally, the boundary layer gradually warms and moistens as

the MCV's circulation penetrates into the boundary layer. This enhances fluxes of latent heat

energy from the underlying ocean surface, allowing the boundary layer value of equivalent

potential temperature to rise to the reduced level necessary for deep, moist convection to

redevelop.

The downward development or advection of the cyclonic circulation of the MCV takes as

long as it takes air to descend through the layer of evaporational cooling. This downward

extension mechanism thus requires precipitation to last sufficiently long, whether in one or more

episodes, so as to moisten/humidify the entire lower to middle troposphere (i.e., the entire layer

of evaporational cooling). The relevant time scale for such activity can be as short as a few hours

or as long as a couple of days. It should also be noted that the downward development process,


and thus tropical cyclogenesis as a whole, is significantly hindered by relative flow through the

MCV. This is most often attributable to vertical wind shear, which forces the vortex to become

tilted vertically and is often associated with the import of dry air into the vortex's circulation. As

a result, the relative flow through the MCV and associated precipitation system must be small so

as to promote a humid, upright vortex core favorable for subsequent tropical cyclone

development.

Convective Tower-Driven Development

Much of the following discussion follows from Montgomery et al. (2006) and Dunkerton

et al. (2009). It should be noted that the results of multiple recent numerical modeling and

observational analyses provide evidence to support the simulation- and theory-driven hypotheses

of both Montgomery et al. (2006) and Dunkerton et al. (2009). Utilizing output from high-

resolution idealized numerical simulations of tropical cyclogenesis, Montgomery et al. (2006)

suggest that tropical cyclone development occurs in response to cycles of deep, moist convective

activity, termed vortical hot towers, and the gradual upscale growth of cyclonic vertical vorticity

from the cloud-scale to the vortex-scale. Such development is said to occur in the unstable,

cyclonic vorticity-rich environment of the middle tropospheric MCV embryo, colloquially

referred to as the "pouch" (e.g., Dunkerton et al. 2009). While the MCV plays an important role

in focusing deep, moist convection within a laterally-confined region, its downward development

is de-emphasized in this paradigm in favor of the upscale growth of tropospheric-deep towers of

cyclonic vertical vorticity.

Specifically, within the pouch environment, cloud-scale cumulonimbus towers possessing

intense cyclonic vertical vorticity in their cores emerge as the preferred coherent convective

structures. Such cyclonic vertical vorticity is generated through two processes. Initial cyclonic

vertical vorticity, particularly in the lower troposphere, is generated through the tilting of

horizontal vorticity associated with the vertical wind shear of the horizontal wind. This is most

generally associated with the cold-core structure of the middle tropospheric MCV. Thereafter,

cyclonic vertical vorticity is amplified through the stretching of both the MCV-scale and

convective tower-scale vertical vorticity. These convective towers exhibit lifetimes on the order

of 1 h. Repeated cycles of convective tower activity act to overcome the adverse effects of

evaporatively-driven downdraft activity by reducing the amount of available buoyancy,

humidifying the middle and upper troposphere, and merging with neighboring convective

towers. Such merger processes act to increase the horizontal scale of the vortices associated with

the convective towers.

While each individual convective tower is short-lived, the aggregate of towers about the

pouch mimic a quasi-steady heating rate on the scale of the middle tropospheric MCV. For

thermal wind balance to be maintained, a thermally-direct circulation with lower and middle

tropospheric convergence, tropospheric-deep ascent, and upper tropospheric divergence must

develop in response to this heating. Over a period of 6 h or greater, the convergence associated


with this circulation converges the convective tower-generated near-surface and MCV-associated

middle to upper troposphere cyclonic vertical vorticity, building the tropospheric-deep tropical

cyclone vortex. Such development typically occurs near what is colloquially known as the

"sweet spot," or intersection of the wave's critical latitude (i.e., the latitude at which the

horizontal velocity vanishes) and trough axis as viewed within a reference frame moving with

the developing disturbance (Dunkerton et al. 2009).

Summary

As noted by Dunkerton et al. (2009), the downward MCV penetration and convective-

tower driven development paradigms are not necessarily at odds with one another. Both

paradigms emphasize the presence of a middle tropospheric MCV and a role of deep, moist

convective activity toward building the lower tropospheric tropical cyclone vortex. They differ in

the spatiotemporal scales emphasized within each paradigm. The downward MCV penetration

paradigm emphasizes processes occurring on the meso- and larger scales of the middle

tropospheric MCV. Conversely, the convective tower paradigm emphasizes processes on the

cloud scale and, subsequently, the upscale growth of the vortices resulting from such processes

to larger scales. Depending on the spatial and temporal scales that one uses in a budgetary

analysis of tropical cyclogenesis, support for both paradigms can be obtained. Therefore, it is

possible that both paradigms may be at least partially correct or, conversely, may be entirely

incorrect! in their depictions of tropical cyclogenesis. This emphasizes the need for further

research into the tropical cyclogenesis process.

Independent of how the near-surface tropical cyclone vortex is built, neither theory is

meant to address the underlying energetics of tropical cyclone development. In other words,

these theories are not meant to be used to elucidate the source of the heating that drives tropical

cyclones. This problem is addressed in the following section.

The Development of the Tropical Cyclone Warm Core

Tropical cyclones are driven by heating, particularly heating found in the middle to upper

troposphere and constrained to near the center of the cyclone by sufficiently strong rotational

forces. From thickness arguments, heating maximized in the middle to upper troposphere will

result in lower pressure beneath the level of peak heating. When constrained to near the center of

the cyclone, the strong, localized heating can result in a strong area of low pressure at the

surface. Precisely how this is manifest will be discussed in the context of the Sawyer-Eliassen

non-linear secondary circulation model in future lectures on tropical cyclone structure and

intensity change. Before delving into such material, however, we wish to describe the source for

such heating, or in other words, is such heating associated with latent heat release within deep,

moist convection or is it merely transported to the middle and upper troposphere by convective

updrafts?


The currently-accepted theory for the source of this heating and, by extension, the

development of the tropical cyclone warm core is given by the non-linear wind-induced surface

heat exchange (WISHE) theory of Emanuel (1986) and subsequent works. In the presence of a

pre-existing tropical disturbance over a sufficiently warm ocean surface, WISHE states that

latent heat release in the free troposphere is governed by the evaporation of moisture from the

underlying ocean surface as determined primarily by the magnitude of the surface winds. In

other words, latent heat energy used to fuel the tropical cyclone and build the tropical cyclone

warm core is obtained from the underlying surface and not through convective heating processes.

The tropical cyclone warm core is constructed aloft as updrafts within deep, moist convection

carry this latent heat energy from the boundary layer to the middle and upper troposphere.

Several assumptions are implicit to WISHE theory. First, the inner core environment of

the developing tropical cyclone vortex must be nearly saturated (i.e., nearly moist neutral) so that

evaporatively-generated downdrafts do not import low equivalent potential temperature into the

boundary layer. As previously discussed, this occurs via moistening processes associated with

cyclic convective activity in the early stages of the tropical cyclogenesis process. Similarly, the

atmosphere is assumed to be neutrally stratified along angular momentum surfaces. Within the

inner core of a developing or mature tropical cyclone, such surfaces are generally vertically-

oriented with a slight outward tilt. Therefore, this assumption is equivalent to saying that there is

no slantwise instability present. There may be a small amount of upright, or traditional,

instability present within the environment (i.e., slightly departing from moist neutrality),

however. Third, WISHE assumes that deep, moist convection is ongoing and acts to mix air in

the vertical direction. Fourth, and perhaps key, WISHE assumes that deep, moist convection

does not impact temperature in the absence of surface fluxes. Therefore, surface fluxes are

critical to the development of the tropical cyclone warm core. Without them, not only would the

tropical cyclone warm core not be able to develop, but the boundary layer would never be able to

recover sufficiently so as to permit deep, moist convective development in the pre-genesis

period!

It should be noted that surface fluxes, whether of sensible or latent heat energy, are

dependent upon the wind speed. To first order, at sub-hurricane intensities, surface flux

magnitudes increase as wind speed increases. (We will consider the impact of surface fluxes on

continued tropical cyclone development in a subsequent lecture.) As a result of this dependence,

WISHE can be viewed as a non-linear feedback loop. The weak winds associated with a pre-

existing tropical disturbance act to induce weak surface latent (and sensible) heat fluxes. Such

fluxes slowly warm and moisten the boundary layer, enabling it to recover from earlier cooling

associated with evaporatively-driven downdrafts. Deep, moist convection acts to transport this

heat and moisture energy vertically to the upper troposphere, where it is accumulated beneath the

tropopause. The radial extent of this heat accumulation is controlled by the radial extent of the

pre-existing disturbance and accompanying middle tropospheric MCV (i.e., by the Rossby radius

of deformation).


As noted above, heating released aloft acts to lower the pressure at levels beneath and

raise the pressure at levels above that of the peak heating. In time, the wind fields respond to this

forcing upon the mass (pressure) field, resulting in an increase in the magnitude of the cyclonic

surface winds of the vortex. This acceleration in the surface wind speed acts to enhance the

magnitude of the surface heat fluxes. Enhanced heat energy is carried aloft by deep, moist

convection, resulting in a further increase of the temperature aloft. This results in an enhanced

response in the mass and, subsequently, wind fields above and below the level of peak heating.

The feedback loop continues from here through at least the tropical cyclogenesis process and,

perhaps, through the entirety of the tropical cyclone lifecycle. The net result of these processes is

two-fold. First, a substantial warm anomaly constrained to the inner core of the tropical cyclone

develops in the middle to upper troposphere. Second, a strong near-surface cyclone and modest

anticyclone at the level of the tropopause develop. These are both characteristics of warm-core

cyclones.

The feedback loop associated with the WISHE paradigm describes the Carnot cycle

approximation to the secondary circulation of a tropical cyclone. This representation of the

tropical cyclone secondary circulation is comprised by the four branches of the secondary

circulation itself. First, there is isothermal inflow toward the center of the cyclone in the lower

troposphere. Typically, the temperature of inflowing parcels is approximately 1C less than the

local sea surface temperature, a necessary requirement for the flux of heat and moisture energy

from the underlying surface. Second, moist adiabatic ascent occurs near the center of the

cyclone. Moist adiabatic ascent implies the conservation of equivalent potential temperature.

Indeed, equivalent potential temperature is nearly constant in the vertical within the inner core of

tropical cyclones. Such moist adiabatic ascent transports latent heat energy to the middle and

upper troposphere. Compared to larger radii, where ascent is not entirely moist adiabatic, the net

result is a warm anomaly within the inner core of the cyclone. Third, there is moist adiabatic

outflow away from the center of the cyclone near the tropopause. Finally, there is descent at

large radii from the center of the cyclone. As parcels quickly become subsaturated upon descent,

whether forced or unforced in nature, such descent is predominantly dry adiabatic in nature. This

implies that the parcels approximately conserve potential temperature as they descend to the

boundary layer.

Also tied to WISHE and the Carnot cycle approximation is the concept of a maximum

potential intensity, or MPI, of tropical cyclones. We will consider MPI more closely in a

subsequent lecture on tropical cyclone intensity change.

References

Bister, M., and K. A. Emanuel, 1997: The genesis of Hurricane Guillermo: TEXMEX

analyses and a modeling study. Mon. Wea. Rev., 125, 2662-2682.


Dunkerton, T. J., M. T. Montgomery, and Z. Wang, 2009: Tropical cyclogenesis in a

tropical wave critical layer: easterly waves. Atmos. Chem. Phys., 9, 5587-5646.

Emanuel, K., 1986: An air-sea interaction theory for tropical cyclones. Part I: steady-state

maintenance. J. Atmos. Sci., 43, 585-605.

McBride, J. L., 1995: Tropical cyclone formation. Global Perspectives on Tropical

Cyclones, R. L. Elsberry (ed.). World Meteorological Organization, Geneva, Switzerland,

Report No. TCP-38. [Available online at

http://derecho.math.uwm.edu/classes/TropMet/GPTC/tcclimo.pdf].

Montgomery, M. T., M. E. Nicholls, T. A. Cram, and A. B. Saunders, 2006: A vortical

hot tower route to tropical cyclogenesis. J. Atmos. Sci., 63, 355-386.

Ritchie, E. A., and G. J. Holland, 1997: Scale interactions during the formation of

Typhoon Irving. Mon. Wea. Rev., 125, 1377-1396.

Zehr, R. M., 1992: Tropical cyclogenesis in the western North Pacific. NOAA Technical

Report NESDIS 61, U.S. Dept. of Commerce, Washington, DC, 181pp.

Tropical Cyclone Intensity Change, Page 1

Tropical Cyclone Intensity Change

Introduction

To this point, we have discussed the dynamics and thermodynamics of the tropical cyclogenesis process. Now, we wish to consider what impacts the intensity of the tropical cyclone after it has formed. In so doing, we will consider a wide array of factors, both positive and negative, that are known to exert a significant control on the intensity of the tropical cyclone. Some of these, such as vertical wind shear and dry air intrusion, are well-known. Others, like trough interaction, are less well-known but nevertheless important to the study of tropical cyclone intensity change.

Maximum Potential Intensity

The idea that a tropical cyclone can be approximated as a Carnot cycle enables us to determine a relationship for the maximum potential intensity (MPI) of a tropical cyclone. For a system in which dissipative heating is included, we first define an efficiency :

(1) o

os

TTT

=

Ts is the surface temperature whereas To is the temperature at the outflow layer just below the tropopause. For a difference of 75 K between Ts (~300 K/27C) and To (~225 K/-48C), the efficiency of the system is on the order of 0.33. Efficiencies of 0.3-0.5 are common in the environments of most tropical cyclones. Though higher efficiencies are possible for greater differences between Ts and To, such conditions are often not realized in the nearly saturated environments of tropical cyclones unless the tropopause is substantially elevated as compared to normal.

The rate of input of available potential energy from the underlying surface can be expressed as:

(2) ( ) saosk TkkVCG = *

where Ck is the enthalpy transfer coefficient, Vs is the surface wind speed, ko* is the enthalpy of the ocean surface, and ka is the enthalpy of boundary layer air near the ocean surface. For G to be positive, the enthalpy of the ocean surface must be higher than the enthalpy of the boundary layer near the ocean surface. This describes the scenario in which enthalpy is being transferred from the ocean's surface to the boundary layer near the ocean's surface. The rate of input of available potential energy increases linearly as a function of the maximum sustained surface wind speed.

The rate of dissipation can be expressed as:


(3) 3sd VCD =

where Cd is the drag, or momentum transfer coefficient. The rate of dissipation increases exponentially with the maximum sustained surface wind speed.

Typically, the input of available potential energy from the underlying surface exceeds dissipation. The maximum potential intensity of a tropical cyclone is reached when the rate of dissipation becomes equal to the input of available potential energy, a condition that becomes reached at high wind speeds. Thus, setting G equal to D and solving for Vs, we obtain an expression for the maximum possible sustained surface wind speed of a tropical cyclone:

(4) ( )aosd

ks kkTC

CV = *2

The maximum sustained wind speed is a function of:

1. The enthalpy and momentum transfer coefficients, themselves a function of wind speed.

2. The sea surface and outflow layer temperatures, primarily as viewed in the context of efficiency.

3. The transfer (e.g., surface flux) of enthalpy from the underlying ocean into the boundary layer.

Factors (2) and (3) vary with environmental conditions; factor (1) varies as a function of the intensity of the tropical cyclone itself. With respect to (1), note that the ratio between Ck and Cd increases linearly with wind speed at low wind speeds but levels off (i.e., begins to remain constant with increasing wind speed) near 30 m s-1.

Of particular interest is factor (2), involving both the surface and outflow layer temperatures. This has important implications for variability of tropical cyclone activity in a warming environment (e.g., even if sea surface temperatures increase, increases in the outflow layer temperature will counteract the otherwise-expected increase in MPI) and for tropical cyclone activity at higher latitudes (as will be discussed in greater detail in our lectures on tropical transition).

If we assume cyclostrophic balance, a fair assumption at hurricane-force wind speeds, we can obtain a relationship for the lowest-possible sea level pressure of a tropical cyclone:

(5)

=

sd

smc TR

Vpp2

exp2

where pc is the pressure at the center of the tropical cyclone, pm is the pressure at the radius of maximum winds, and Rd is the dry air gas constant. A similar expression may be derived using


gradient or even geostrophic balance; however, as we are typically interested in the maximum possible intensity for a given tropical cyclone, cyclostrophic balance is typically the most appropriate choice.

As may be inferred from the above, MPI theory does not provide a pathway by which tropical cyclones intensify. Rather, in the context of WISHE theory, it provides insight as to the maximum intensity a given tropical cyclone can reach in a perfectly ideal, quiescent environment. Note the vast majority of storms do not reach their MPI. Departures from the aforementioned ideal environment, such as manifest via physical processes such as dry air intrusion, vertical wind shear, interaction with land, and/or cooler sea surface temperatures, are the primary causes behind this failure to reach the MPI. A small percentage of storms on the order of 1% or less reach and/or exceed their MPI. Given that the MPI is supposed to provide a maximum possible intensity, how can this be?

For some tropical cyclones, the impacts of asymmetric forcing unaccounted for by MPI theory are the culprit. Examples of asymmetric forcing are manifest via radial momentum flux sources such as mid-latitude troughs and vortex Rossby waves. We will discuss these phenomena in more detail in this and subsequent lectures. For other tropical cyclones, the evolving energetics of tropical cyclones undergoing extratropical transition are the culprit. As a tropical cyclone undergoes extratropical transition, it begins to draw energy from the vertically-sheared midlatitude flow (e.g., the conversion of available potential energy to kinetic energy) rather than from the underlying oceanic surface. This typically allows a tropical cyclone to maintain its intensity, particularly in terms of the minimum sea level pressure of the cyclone, even as surface fluxes wane as the tropical cyclone moves over sub-critical sea surface temperatures (with no accompanying change in outflow layer temperature).

Three charts related to MPI are included within the lecture materials. The first of these charts depicts the minimum-possible sea level pressure as a function of surface and outflow temperatures. Holding surface temperature constant, values of sea level pressure decrease for decreasing outflow temperature (i.e., increasing the efficiency of the system). The second of these charts depicts the maximum-possible surface wind speed as a function of surface and outflow temperatures. Holding surface temperature constant, values of maximum surface wind speed increase for decreasing outflow temperature. The third chart utilizes the climatological atmospheric and oceanic conditions for September to construct spatial maps of the climatological minimum-possible sea level pressure. MPI is at a maximum across the Western North Pacific warm pool north of Indonesia, near the southern Mexican coastline in the Eastern North Pacific, and across the central Gulf of Mexico in the North Atlantic. It decays rapidly away from the tropics.

Global maps of daily MPI values are available online at http://wxmaps.org/pix/hurpot.html.


The Importance of WISHE at Higher Wind Speeds

Traditionally, WISHE has been viewed as an "exponential instability," meaning that as a tropical cyclone becomes more intense, the magnitude of the wind-induced heat and moisture fluxes increases, subsequently leading to the non-linear intensification of the tropical cyclone. However, recent work by Montgomery et al. (2009), though still the subject of much heated debate within the tropical cyclone community, challenges this viewpoint. In the Montgomery et al. (2009) work, they demonstrate that an intense tropical cyclone develops even when the surface latent heat flux is capped at less than 150 W m-2, approximately equal to the trade wind value associated with the easterly 5-10 m s-1 trades flowing across a sufficiently warm oceanic surface. They argue that while surface fluxes remain important prior to tropical cyclogenesis (to enable boundary layer equivalent potential temperature to rise sufficiently to permit convective redevelopment), the exponential instability associated with WISHE does not drive the subsequent intensification of the tropical cyclone.

Instead, Montgomery et al. (2009) pose that local buoyancy within individual convective towers serves as the energy source for deep, moist convection and, by extension, the tropical cyclone itself. In this framework, cyclonic vertical vorticity is generated within these towers and subsequently grows upscale through vortex merger and filamentation processes. The resultant upward cascade of energy, rather than the vertical lofting of increasingly large heat and moisture fluxes, leads to the intensification of the tropical cyclone. It should be noted that such convective processes occur within all tropical cyclones and thus, in and of itself, such a condition does not disprove WISHE theory. Rather, Montgomery et al. (2009) argue that the development of an intense tropical cyclone despite capped surface latent heat fluxes is what acts to disprove WISHE theory. As many in the community remain skeptical of the Montgomery et al. (2009) claims, however, more research is necessary to precisely identify and isolate the intensification mechanism(s) for tropical cyclones.

Oceanic Upwelling and Localized Oceanic Eddies

The cyclonic circulation associated with a tropical cyclone acts to upwell water from beneath the ocean's surface. The magnitude of this upwelling is a function of the structure of the cyclone's wind field. Typically, stronger, larger tropical cyclones result in greater upwelling compared to their weaker, smaller counterparts. As a tropical cyclone typically moves at a rate of speed of 2-3 m s-1 or greater, the overall magnitude of such upwelling is generally weak ( 1C cooling of the sea surface temperature). Thus, to first order, upwelling is generally only significant for slow-moving or stationary tropical cyclones. Examples of upwelling exerting a substantial influence on the intensity of a nearly-stationary tropical cyclone include Hurricanes Roxanne (1995) and Ophelia (2005), both in the North Atlantic basin.

A notable exception to this statement is found with tropical cyclones that follow closely in the path of an earlier tropical cyclone. For an eighteen-year composite of Northern


Hemisphere tropical cyclones, Hart et al. (2007) demonstrate that the sea surface temperature in the wake of a tropical cyclone remains below normal for approximately one month after its passage. The greatest impacts are felt within ten days after tropical cyclone passage. Thus, in situations where a tropical cyclone follows a similar path to that a preceding tropical cyclone, its intensity may be limited to some extent by the upwelling of cool water induced by the preceding tropical cyclone.

Conversely, localized oceanic warm eddies can exert a positive influence on tropical cyclone intensity. Such eddies are common within the Gulf of Mexico and are associated with the Loop Current that extends from the Caribbean Sea northward into the Gulf of Mexico. These eddies are characterized by locally warm water over a large depth and an above-normal sea surface height anomaly. As a result, they provide a substantial source of heat energy to fuel a tropical cyclone. There may also be a contribution to tropical cyclone intensity from the mesoscale baroclinic zone (i.e., temperature gradient) that develops on the periphery of the warm eddy. Regardless, some of the most intense tropical cyclones in the Gulf of Mexico in recent years, including both Hurricanes Katrina and Rita in 2005, passed over or near such a warm eddy during a period of rapid intensification. Global maps of real-time oceanic heat content and sea surface height anomalies are available online at http://www.aoml.noaa.gov/phod/cyclone/data/.

Ventilation of the Tropical Cyclone Inner Core

The ventilation of a tropical cyclone's inner core refers to the dynamic and thermodynamic impacts of vertical wind shear upon the tropical cyclone (Tang and Emanuel 2010). The dynamic component deals with how the tropical cyclone vortex interacts with the environmental vertical wind shear. Implicit to this is the tilt of the vortex due to differential vorticity advection by the vertically-sheared background flow and the resulting asymmetric structure (e.g., Jones 1995). The thermodynamic component concentrates on the impact upon a tropical cyclone's intensity resulting from the import of low entropy air (i.e., low equivalent potential temperature air) from the ambient environment into the tropical cyclone's inner core. Two ways exist by which low entropy air can infiltrate the tropical cyclone inner core:

1. The lower tropospheric ingestion of low entropy air resulting from downdrafts formed in response to the interaction of the tropical cyclone with vertical wind shear (Riemer et al. 2010).

2. The direct middle tropospheric import of low entropy air into the tropical cyclone's inner core.

Dynamical Effects of Vertical Wind Shear

Dynamically, vertical wind shear acts to vertically tilt the circulation of the tropical cyclone. At the onset of the vertical wind shear, this results in the tilt of the vortex in the downshear direction. For westerly vertical wind shear, the upper tropospheric vortex will be


tilted to the east of the lower tropospheric vortex. The opposite is true for easterly vertical wind shear. However, after a very short period of time (on the order of one hour), the situation becomes much more complex. In this discussion, we will highlight the resultant mutual rotation of the upper and lower tropospheric vortices; the development of asymmetries in the environment of the tropical cyclone and their role in modulating its vertical tilt; and the sensitivity in these processes to the structure of the vertical wind shear and, in particular, the vortex itself.

As noted above, vertical wind shear initially acts to tilt the vortex downshear in the vertical. This results in the misalignment of the lower tropospheric and upper tropospheric vortices. From potential vorticity arguments, the lower tropospheric vortex can induce a cyclonic circulation at higher levels whereas the upper tropospheric vortex can induce a cyclonic circulation at lower levels. The strength of these circulations at any given level decays with increasing distance from the inducing vortex and is a function of the Rossby penetration depth. For a rapidly rotating vortex, the Rossby penetration depth can be expressed as in Jones (2004) and references therein:

(6) ( )

N

Lfrvf

H

T

R

2/12

+

+=

where f is the Coriolis parameter, vT is the tangential wind, r is the radius, is the vertical component of the relative vorticity, L is the horizontal length scale of the vortex, and N is the square root of the static stability. Therefore, a stronger and/or larger vortex, larger Coriolis parameter, or reduced static stability all result in a larger Rossby penetration depth. As might be expected, a larger Rossby penetration depth implies a larger depth over which a given vortex may induce a meaningful circulation. Note that diabatic processes, such as associated with deep, moist convection, generally act to locally reduce the static stability and increase the rotation, thereby acting to increase the Rossby penetration depth.

The circulations associated with the vertical reflections of the upper and lower tropospheric circulations act against the vertical wind shear in two ways. First, the flow associated with these circulations is also vertically sheared, with stronger winds found near the level of the PV anomaly and decaying away from there. This can either add to or oppose the environmental vertical wind shear. Similarly, the circulations induced by these vortices act to influence the motion of the other vortex. This mutual rotation of the vortices can also bring them into configurations in which the environmental vertical wind shear can act to either reduce or further enhance the tilt of the vortex.

Vertical wind shear acts to destroy thermal wind balance in the environment of the vortex. In order for balance to be restored, a transverse (i.e., vertical) circulation must develop, the strength of which is directly proportional to the strength of the vortex. From quasi-


geostrophic omega arguments, differential cyclonic vorticity advection leads to ascent while differential anticyclonic vorticity advection leads to descent. Thus, ascent occurs downshear while descent occurs upshear. Vertical motions subsequently force the development of potential temperature anomalies via vertical advection, with a cold anomaly forming at the location of ascent and a warm anomaly forming at the location of descent. If potential temperature is (approximately) conserved, vortex-relative flow through these anomalies forces ascent 90 downstream of the warm anomaly and descent 90 upstream of the cold anomaly.

From continuity considerations, the forced vertical motions are associated with divergence and convergence. In regions of ascent, there is lower level convergence and upper level divergence. The inverse is true in regions of descent. The cross-vortex flow from the location of divergence to the location of convergence is noted to counteract the vertical shear within the inner core of the vortex. Thus, the tilt of the inner core of the vortex is typically observed to be less than that of the outer core of the vortex. The subsequent interaction of the outer core of the vortex with the vertically-sheared flow results in the development of large-scale asymmetries at large radii from the center of the vortex (Jones 2000a) that may also act to counterbalance the environmental vertical wind shear.

In the analytical framework of Jones (1995), the 90 out-of-phase relationship between vertical motion and potential temperature anomalies develops within the first six hours of the imposition of vertical wind shear. This relationship is noted to remain robust after the first six hours even as the anomalies and upper and lower tropospheric vortices continue to rotate cyclonically about the middle tropospheric vortex (which, to first order, propagates with the middle tropospheric flow). However, in observed tropical cyclones, the region of ascent is typically found in the downshear-left quadrant (i.e., to the left of the shear vector) of the cyclone. This implies that an approximate steady-state solution for vortex tilt and mutual rotation exists that is not addressed in the framework of Jones (1995).

The resiliency of a tropical cyclone to vertical wind shear also depends in large part upon the radial structure of the tropical cyclone's tangential wind profile, as highlighted by Reasor et al. (2004) and Mallen et al. (2005). Tropical cyclones in which the tangential wind profile only decays gradually with increasing radius away from the inner core of the storm are better able to resist the deleterious effects of vertical wind shear. The reasoning behind this relates to vortex Rossby wave theory, whereby Rossby waves about the vortex at some critical radius from the center act to counteract the vertical wind shear. While the dynamics of vortex Rossby waves are beyond the scope of this course, Reasor et al. (2004) argue that the vortex Rossby wave paradigm provides a more complete framework by which vortex resiliency to vertical wind shear can be understood than does the Jones (1995) framework. This is particularly true in terms of addressing the reduction of vortex tilt and the aforementioned approximate steady-state structure of the tropical cyclone under persistent vertical wind shear.


To summarize, we present a hypothetical thought experiment. By itself, the imposition across the tropical cyclone of a 10 m s-1 tropospheric-deep vertical wind shear leads to the horizontal displacement of the lower and upper tropospheric circulation centers by 864 km over one day. As this is generally not observed, other processes must counteract this tilt. As described above, the frameworks of Jones (1995, 2000a,b) and Reasor et al. (2004) describe physical mechanisms by which this shear-induced tilt is (generally) reduced. The precise details of this reduction in the tilt of the vortex depend most significantly upon the radial structure of the vortex and the Rossby penetration depth.

Note that the studies considered to this point are all studies of tropical cyclone-like vortices in dry dynamical frameworks. It is true that a tropical cyclone-like vortex can be maintained for some time in a dry, vertically-sheared environment (e.g., Jones 2004). However, as observed tropical cyclones are, to first order, thermodynamically-driven heat engines, it is also important to consider the effects of vertical wind shear upon the thermodynamics of a tropical cyclone. This is the focus of the next section.

Thermodynamic Effects of Ventilation and Vertical Wind Shear

Thermodynamically, the general impact of low entropy air upon the intensity of a tropical cyclone can be viewed in terms of the Carnot heat engine analog to the tropical cyclone (Tang and Emanuel 2010). The import of low entropy air into the inner core of the tropical cyclone, whether in the lower or middle troposphere, results in a local decrease in the entropy along the ascending branch of the Carnot heat engine. Over a sufficient length of time, convective motions act to spread this low entropy air through a deep, slantwise layer within the inner core. This weakens the differential in entropy (or, alternatively, equivalent potential temperature) between the eyewall and ambient environment, reducing the amount of energy available to the tropical cyclone. Concurrently, the implied loss of buoyancy corresponds to a decrease in the height of the outflow layer and an increase of the temperature at the outflow layer. As the efficiency of the tropical cyclone heat engine is a function of the difference between the surface and outflow layer temperatures, this results in a reduction of the efficiency of the tropical cyclone.

Mechanically forcing low entropy air into the tropical cyclone's inner core in the middle troposphere is more deleterious upon the intensity of a tropical cyclone than is importing low entropy air into the tropical cyclone's inner core in the lower troposphere. In contrast to the lower troposphere, where entropy may partially be restored via surface fluxes from the underlying ocean, no such recovery is possible in the middle troposphere. As a result, tropical cyclones are substantially less resilient to the direct import of low entropy air (most commonly associated with colder, drier environmental air) via vertical wind shear in the middle troposphere than they are to the import of low entropy air along the radially inflowing branch of its secondary circulation in the lower troposphere.


The precise impact of ventilation upon the intensity of the tropical cyclone depends in part upon a substantial number of factors. Three such factors are highlighted by Tang and Emanuel (2010). These include:

1. How low is the entropy of the air that is imported into the inner core?

2. How strong is the import of the low entropy air into the inner core?

3. How favorable is the ambient environment (e.g., warmth of the sea surface)?

Lower entropy air, stronger import, and marginal or unfavorable ambient thermodynamic conditions have a more substantial deleterious impact upon the intensity of the tropical cyclone. As shown by Tang and Emanuel (2010), this impact can lead to a nearly 60% reduction in the maximum attainable intensity of a given tropical cyclone. If the magnitude of the ventilation is sufficiently large, tropical cyclone dissipation and/or mitigation are also possible. Conversely, only slightly reduced entropy air, weaker import, and favorable ambient thermodynamic conditions may lead to little if any deleterious impact upon the intensity of the tropical cyclone.

Riemer and Montgomery (2011) suggest that the impact of ventilation upon the intensity of a tropical cyclone also depends in large part upon the strength of the tropical cyclone, as manifest by the magnitude of its tangential winds. The strong inertial (or rotational) constraint exerted on a fluid in a region of strong rotation acts to dampen the rate at which asymmetric flows impinge upon the vortex. As a result, as the intensity and/or size of the tropical cyclone increases, the magnitude of the vertical wind shear that is necessary for the interaction of both the eyewall and outer rain bands with environmental air (whether drier or not) also increases. Furthermore, they suggest that the ability of dry environmental air to enter into the circulation and impact the intensity of a tropical cyclone is dependent upon its location with respect to the vortex and the direction of the vertical wind shear. For easterly vertical wind shear, the lower tropospheric storm-relative flow in the environment of the vortex is westerly. This would act to advect the dry air away from the vortex. Conversely, for westerly vertical wind shear, the lower tropospheric storm-relative flow in the environment of the vortex is easterly. This would act to import the dry air into the circulation of the tropical cyclone.

Trough Interaction

The interaction of a tropical cyclone with an upper tropospheric trough can lead to both strengthening and weakening of a tropical cyclone. The strong vertical wind shear associated with such a trough can result in the weakening of the tropical cyclone via the mechanisms described above. This is particularly true for upper tropospheric troughs of large horizontal scale (i.e., bigger than that of a tropical cyclone).

Conversely, however, there are two pathways by which an upper tropospheric trough may lead to the intensification of a tropical cyclone (Hanley et al. 2001). The first pathway is


associated with quasi-geostrophic forcing for large-scale ascent that accompanies such features. As such forcing spreads over a tropical cyclone, stronger ascent is promoted within the inner core of the tropical cyclone. From mass conservation arguments, this is associated with enhanced divergent outflow and convergent inflow into the tropical cyclone. If the vertical wind shear (or cross-cyclone flow) associated with the upper tropospheric trough is relatively weak ( 10 m s-1) in the environment of the tropical cyclone, the resultant enhancement to the tropical cyclone's secondary circulation promotes its intensification. Conversely, if the vertical wind shear is relatively strong ( 15 m s-1), its deleterious effects upon the intensity of the cyclone dominate and the cyclone weakens.

The second pathway is associated with the superposition of the cyclonic potential vorticity anomalies associated with the upper tropospheric trough and the tropical cyclone. If the upper tropospheric potential vorticity anomaly is of similar horizontal scale to that of the tropical cyclone, the magnitude of the vertical wind shear is relatively weak. In such a scenario, as the upper tropospheric anomaly approaches the tropical cyclone, the superposition and interaction of the two distinct anomalies is favorable for the deepening of the tropical cyclone. With time, however, the anomaly associated with the upper tropospheric trough weakens, presumably as a result of stronger diabatic heating that takes place with the tropical cyclone at lower altitudes.

Hanley et al. (2001) suggest that trough interaction is more often favorable than unfavorable to tropical cyclone intensification. Specifically, over a ten year sample of storms across the North Atlantic basin, they suggest that 78% of cases fitting into the second pathway and 61% of cases fitting into the first pathway led to the intensification of the tropical cyclone. These percentages are likely at the high end of expectations, however, given that they excluded tropical cyclones near land and/or over sub-26C waters (e.g., likely undergoing extratropical transition). The precise dynamics of how the aforementioned forcing can result in the strengthening of the tropical cyclone's secondary and, subsequently, primary circulation(s) will be explored in the forthcoming lecture on tropical cyclone structure.

References

Emanuel, K., 1986: An air-sea interaction theory for tropical cyclones. Part I: steady-state maintenance. J. Atmos. Sci., 43, 585-605.

Hanley, D., J. Molinari, and D. Keyser, 2001: A composite study of the interactions between tropical cyclones and upper-tropospheric troughs. Mon. Wea. Rev., 129, 25702584.

Hart, R., R. Maue, and M. Watson, 2007: Estimating the atmospheric and SST memory of tropical cyclones through MPI anomaly evolution. Mon. Wea. Rev., 135, 3990-4005.

Jones, S. C., 1995: The evolution of vortices in vertical shear. Part I: Initially barotropic vortices. Quart. J. Roy. Meteor. Soc., 121, 821-851.


Jones, S. C., 2000a: The evolution of vortices in vertical shear. Part II: Large-scale asymmetries. Quart. J. Roy. Meteor. Soc., 126, 3137-3159.

Jones, S. C., 2000b: The evolution of vortices in vertical shear. Part III: Baroclinic vortices. Quart. J. Roy. Meteor. Soc., 126, 3161-3185.

Jones, S. C., 2004: On the ability of dry tropical-cyclone-like vortices to withstand vertical shear. J. Atmos. Sci., 61, 114-119.

Mallen, K. J., M. T. Montgomery, and B. Wang, 2005: Reexamining the near-core radial structure of the tropical cyclone primary circulation: implications for vortex resiliency. J. Atmos. Sci., 62, 408-425.

Montgomery, M. T., V. S. Nguyen, J. Persing, and R. K. Smith, 2009: Do tropical cyclones intensify by WISHE? Quart. J. Roy. Meteor. Soc., 135 (644), 1697-1714.

Reasor, P. D., M. T. Montgomery, and L. D. Grasso, 2004: A new look at the problem of tropical cyclones in vertical shear flow: vortex resiliency. J. Atmos. Sci., 61, 3-22.

Riemer, M., and M. T. Montgomery, 2011: Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear. Atmos. Chem. Phys., 11, 9395-9414.

Riemer, M., M. T. Montgomery, and M. E. Nicholls, 2010: A new paradigm for intensity modification of tropical cyclones: thermodynamic impact of vertical wind shear on the inflow layer. Atmos. Chem. Phys., 10, 3163-3188.

Tang, B., and K. Emanuel, 2010: Midlevel ventilation's constraint on tropical cyclone intensity. J. Atmos. Sci., 67, 1817-1830.

Tropical Cyclone Structure, Page 1

Tropical Cyclone Structure

Introduction

To this point in the semester, we have only briefly touched upon the salient structural features of a tropical cyclone. Now, however, it is worth describing these in greater detail. Included in this are structural aspects of both the primary (horizontal) and secondary (vertical) circulations and the axisymmetric and asymmetric structure of a tropical cyclone. We begin by introducing the basic structure of a tropical cyclone, using that as a launching point for exploring the tropical cyclone secondary circulation and asymmetric structure in greater detail.

Tropical Cyclone Structure: Overview

Tropical cyclones, as areas of low pressure, are characterized by cyclonic tangential and inflowing radial winds. The cyclonic winds associated with a tropical cyclone can extend out to over 1000 km from its center in the lower troposphere; this radial extent decays with increasing height. Tropical cyclones are warm core features, meaning that their intensity (as measured by the magnitude of the cyclonic tangential wind) decreases with increasing height. A tropical cyclone is most intense just above the top of the boundary layer, where frictional dissipation is minimized, and weakest in the upper troposphere, where the winds become anticyclonic and evacuate mass outward. Radial inflow is typically maximized within the boundary layer with weaker inflow observed into the middle troposphere. The radial inflow rapidly decelerates upon reaching the eyewall of the tropical cyclone. The resultant convergence leads to ascending motion over a deep vertical layer within the eyewall. Compensatory descent for such strong ascent occurs in a concentrated manner within the eye and in a diffuse manner at radii larger than the radius of maximum winds.

The warm core structure of a tropical cyclone can be viewed as the hydrostatic response to a radially-constrained warm potential temperature anomaly near the center of the tropical cyclone. This warm anomaly primarily results from latent heat energy extracted from the underlying surface that is released in the upper troposphere by convective updrafts. A small but non-negligible contribution to this warm anomaly is also observed from subsidence warming within the eye.

In a planar view, a mature tropical cyclone is characterized by a nearly cloud-free region near its center, termed the eye. The minimum sea level pressure of the cyclone is found at the center of the eye. For weaker tropical cyclones without eye features, the minimum sea level pressure is typically found at the location of the greatest vertically-integrated potential temperature (i.e., where the warm anomaly associated with the tropical cyclone is strongest). The primary eyewall is found at the outermost radius of the eye. Here, intense convection and modestly strong updrafts (~5-10 m s-1) are often found. The eyewall is often the location of the radius of maximum winds, or the radius at which the wind field associated with the tropical cyclone is at its most intense. On average, the eyewall and radius of maximum winds are

Tropical Cyclone Structure, Page 2

typically found approximately 35 km from the center of the tropical cyclone; however, much smaller and much larger radii have been observed.

The eyewall region of a tropical cyclone is characterized by a local maximum in equivalent potential temperature. Isosurfaces of equivalent potential temperature are nearly vertical within the eyewall, implying that equivalent potential temperature is nearly constant with increasing height. Above the level of non-divergence, these surfaces flare radially outward. A local minimum in equivalent potential temperature is found in the middle to upper troposphere within the eye itself, reflecting drying associated with the aforementioned concentrated descent into the eye.

The eyewall and radius of maximum winds within a mature tropical cyclone slope outward with increasing height at an angle approaching 45. This implies that the outward displacement of the eyewall in the upper troposphere is approximately equivalent to its height above the sea surface. The physical reasoning behind this sloping structure lies with the conservation of angular momentum and the warm core structure of the tropical cyclone. As air parcels ascend within the eyewall, angular momentum is approximately conserved. Recall that angular momentum is both a function of the radius from the center of rotation (r) as well as the tangential wind speed (v), i.e.,

(1) 2

2frrvm +=

Thus, since v decreases with increasing height with a warm-core cyclone, r must increase for m to remain constant.

A moat region, or region of predominantly stratiform precipitation, is found radially outward of the eyewall. Continuing radially outward from the moat region, mature tropical cyclones often possess secondary eyewalls. Most generically, secondary eyewalls form in response to the accumulation of heat energy, angular momentum, and vertical vorticity at some critical radius. The precise dynamics behind secondary eyewall formation remain unclear, however. Kossin and Sitkowski (2009) suggest that secondary eyewall formation is associated with high values of maximum potential intensity, small values of vertical wind shear, weak upper tropospheric zonal winds, a deep layer of underlying warm water, and high middle to upper tropospheric relative humidity. In other words, the factors that promote tropical cyclone intensification also tend to promote secondary eyewall formation.

The formation of a secondary eyewall temporarily halts the intensification of a tropical cyclone. The formation of a secondary eyewall effectively cuts off radial inflow into the inner eyewall. As the secondary eyewall matures and begins to contract, or move inward toward the center of the cyclone, compensating descent acts to erode the inner eyewall and clear out the moat region. After approximately 1-2

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