Chapter 10 Clouds and Precipitation in Tropical Cyclones

We now move still farther upscale and consider the clouds associated with tropical cyclones.

These clouds are both controlled by and produce feedbacks to the dynamics of the larger scale cyclone.

To see the connection between the clouds and the cyclone, we cannot depend on convective dynamics and hydrostatic reasoning alone.

In this chapter, the dynamics of the clouds in a tropical cyclone are examined in light of (〜に照らして) the dynamics of the tropical cyclone itself.

（節構成）

10.1 DEFINITIONS, CLIMATOLOGY, AND THE SYNOPTIC-SCALE CONTEXTS OF TROPICAL CYCLONES

According to the Glossary of Meteorology,1 a tropical cyclone is any low-pressure system having a closed circulation and originating over a tropical ocean.

table:categorize

peak wind speed (m/s) name

< 17 tropical depression

18-32 tropical storm

33 severe tropical
cyclone

Tropical cyclones originate over oceans.

Their primary energy source is the latent heat of water vapor in the atmospheric boundary layer,

which is released when the air rises out of the boundary layer in deep clouds.

Recall from the C-C equation that

the saturation vapor pressure, (and hence θe of the air near the ocean surface,) increases rapidly with temperature.

Consequently, tropical cyclones nearly always form over regions where the SST exceeds 26.5 °C (Fig. 10.1a)

The free atmosphere over warm oceans is generally slightly conditionally unstable.

In order for deep clouds to form,

the free atmosphere must also have relatively high humidity

to keep developing clouds from being inhibited by entrainment.

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Tropical cyclones form generally between 5° and 20°

They rarely form within 5 of the equator

because the Coriolis force is too weak

for low-level convergence

to be able to generate enough relative vorticity for storm formation.

The strong background positive vorticity helps to trap energy released in clouds

so that it contributes to strengthening of the cyclone.

An especially important factor required for cyclone development is

that the environmental winds must have very little shear to allow the cyclone to develop with vertical coherence.

The climatological presence of strong shear over the South Atlantic,

plus the lack of synoptic precursor disturbances,

accounts for the extremely rare occurrence of tropical cyclones in that region (Fig.10.1)

The above described environmental pre-conditions for tropical cyclogenesis

may be set up by a variety synoptic-scale processes.

Once tropical cyclones form, they tend to be advected by the large scale wind.

Figure 10.1b shows

how the tracks are generally westward at lower latitudes,

where easterlies dominate the large scale flow.

It is also evident that many storms “recurve”(転向) toward the east; that is,

they turn poleward and

then to the east as they move

out of the tropics and into zone of midlatitude westerlies.

Many tropical cyclones

encounter land or colder water and

die out from lack of moisture from a warm sea surface.

Others transition into extratropical cyclones when they interact with midlatitude westerlies.

10.2 CLOUDS INVOLVED IN TROPICAL CYCLOGENESIS

10.2.1 Idealization of the Clouds in an Intensifying Depression

Tropical cyclogenesis is partly a downscale process

as synoptic-scale energy concentrates within a smaller scale vortex.

But it is also partly an upscale process,

with convective-scale dynamics locally adding energy and vorticity

to the developing cyclonic disturbance.

Convective clouds are central to the upscale positive feedback to tropical cyclogenesis,

and they usually take on an especially intense form

in which the beginning of the tropical cyclone development is marked by a “convective burst,”

seen as enhanced cirrus outflow from the convective clouds in satellite imagery.

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Figure 10.2 illustrates conceptually the variety of convective cloud entities

that may exist in the region where a convective burst occurs.

Some of these are individual cumulonimbus towers,

while others take the form of an MCS (Chapter 9),

which contains both deep convective cells and stratiform clouds and precipitation.

The convective entities in Figure 10.2d are depicted within a low-level pre-existing cyclonic circulation,

indicated by the L and the dashed streamline.

Figure 10.2a–c is a simplified depiction of the life cycle of the MCS

as it would occur within an assumed larger scale environment rich in positive vorticity at lower levels.

It is essentially the generic MCS life cycle shown in Figures 9.11 and 9.14,

but with an emphasis on the way vorticity might develop within the MCS.

The MCS begins as one or more isolated deep convective towers (Figure 10.2a).

The vorticity of the low-level environment is stretched

by convergence at the base of the buoyant convective updrafts and advected upward.

As an individual tower dies off,

it weakens and becomes part of the precipitating stratiform cloud of the MCS.

New towers form adjacent to the stratiform region,

so that at its mature stage of development the MCS has

both convective and stratiform components (Figure 10.2b).

The base of the stratiform cloud deck is in the middle troposphere,

as (理由？) it is mostly composed of the material of the upper portions of convective cells (Figures 9.11 and 9.14).

The vertical profile of heating in the stratiform region leads to

the development of a MCV in midlevels

in association with the stratiform cloud deck, as discussed in Section 9.6.3.

In the case depicted in Figure 10.2,

the stratiform region containing the MCV is composed of the remnants (残り) of convective cells,

which themselves have considerable positive vorticity.

These vortical hot tower remnants add more vorticity to the MCV.

During the middle life cycle state in Figure 10.2b,

the MCS contains vorticity structures both

in the form of convective-scale deep vortical hot towers and

in the form of the wider stratiform-region MCV.

In the late stages of the MCS life cycle,

the hot towers cease forming, but

the stratiform cloud region containing MCV vorticity remains for some hours (Figure 10.2c).

10.2.2 Example of a Vortical Hot Tower

Figure 10.3 shows an example of a vortical hot tower

documented by Doppler radar on an aircraft flying near an MCS

located in the tropical depression

that became Hurricane Ophelia (2005).

The convective cell was exceptionally deep, wide, and intense,

with updrafts of 10–20 m/s
throughout its mid- to upper levels (Figure 10.3a and b).

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The convective cell contained a cyclonic vorticity maximum (at 8 km altitude in Figure 10.3c).

This massive convective updraft was maintained by strong positive buoyancy

(virtual potential temperature perturbation >5 C at 10 km; Figure 10.3a),

probably aided by (手助けされる) latent heat of freezing at higher altitudes.

A layer of strong inflow several kilometers deep fed the convective updraft

(see the isolines of the vertical derivative of the vertical mass flux in Figure 10.3b).

The vorticity field shown in Figure 10.3c shows

both negative and positive vorticity centers near the center of the updraft.

This structure is consistent with

the updraft tilting the environmental horizontal vorticity into the vertical

to produce a vortex couplet in midlevels

(recall Sections 7.4 and 8.5).

For simplicity, this tilting produced couplet is not shown in Figure 10.2a

since the positive member of the tilting produced couplet dominates,

probably because it combines with the positive vorticity of the stretched and upward advected boundary layer vorticity

to produce deep updrafts that are centers of cyclonic rotation.

Numerical experiments suggest that

the negative vorticity anomalies tend to be expelled (追い出される) from the developing tropical cyclone vortex, while

the positive anomalies are retained (維持される).

In Figure 10.3, it can be seen that

stretching of vorticity in the lower portion of the updraft and

the strong vertical motions of the updraft advecting the concentrated vorticity vertically

created a deep convective-scale cyclonic vorticity perturbation—i.e., a vortical hot tower.

10.2.3 Ensemble of Clouds in a Developing Storm

The ensemble of clouds in the intensifying depression

shown in idealized form in Figure 10.2d

is based on real events.

As an example, Figure 10.4 shows

infrared satellite and coastal radar imagery just prior to the tropical depression

that ultimately developed into Hurricane Ophelia (2005).

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A day before the depression reached tropical storm intensity (Figure 10.4a–d),

strong convection was prevalent over a wide area, but

the clouds and precipitation exhibited no structure similar to those of a tropical cyclone.

At the time of Figure 10.4c–d,

the convection seen on radar had grouped into three MCSs ~200 km in horizontal dimension,

each having both active convective cells and areas of stratiform precipitation.

The vortical hot tower cell shown in Figure 10.3 was

in the MCS located northeast of the Melbourne coastal radar.

Thus, the pre-Ophelia depression had a cloud population

containing intense rotational convective cells and MCSs

scattered about in the low-pressure area

as depicted schematically in Figure 10.2d.

By the time of Figure 10.4e–f,

the overall area covered by deep convection in the pre-Ophelia depression

had decreased and

was becoming focused on a single very intense MCS.

In the next several hours,

this mesoscale precipitation area

radically changed its shape and

took on the structure of a tropical storm (Figure 10.4g and h).

The radar echo exhibited

an incipient (初期の) eyewall and

a well defined principal rainband extending from south to east to north of the storm center.

Details of principal rainbands will be discussed in Section 10.7.3.

10.2.4 Cloud Feedback in Cyclogenesis

Figure 10.2d depicts an idealized scenario

in which a population of clouds occurs in a region

where large scale conditions have dictated (命令される) the presence of a pre-existing low-level weak cyclonic circulation.

The cloud population within this region consists of a combination of:

isolated deep convective cells with cyclonic vorticity maxima in the updrafts, as in Figure 10.2a;

one or more mature MCSs with both cyclonically rotating convective cells and MCVs, as in Figure 10.2b; and

older MCSs with residual MCVs, as in Figure 10.2c.

Each of the clouds contains significant vorticity perturbations

in the form of convective-scale vortical hot towers and/or stratiform-region MCVs.

These in-cloud vorticity perturbations can feed back positively to the larger scale cyclonic vorticity.

The deep convection generates potential vorticity.

Collectively (集団的に), the clouds accumulate and distribute vorticity

derived from the boundary layer and low levels of the free environment

throughout a deep layer.

By these means, they help organize the preexisting weaker synoptic-scale cyclonic circulation into a tropical storm.

The background positive vorticity helps to reduce the Rossby radius (Section 2.8),

thus keeping the effect of the clouds locally confined

so they can contribute to cyclogenesis.

Tropical cyclogenesis is not just a question of strengthening the pre-existing vortex.

The vortex must reorganize to become a tropical cyclone.

An important question is how a cloud population

such as that depicted conceptually in Figure 10.2d, or shown by example in Figure 10.4,

helps convert a pre-existing benign (穏やかな) synoptic-scale cyclonic circulation

to a structure having the specific configuration of a tropical cyclone.

One of the distinctive features of a tropical cyclone is

a narrow annulus (輪,環) of maximum wind at some distance (usually between 10 and 100 km) from the storm center.

and it is kept in near thermal wind balance by a strong secondary circulation,

which in turn produces an eyewall cloud.

Outside the eyewall, precipitation occurs in mesoscale spiral rainbands.

These cloud and precipitation features of the mature tropical cyclone will be discussed in detail in subsequent sections of this chapter.

As a cyclonic disturbance reaches tropical storm strength,

it also changes

its structure by developing an RMW and

incipient (初期の) eye, eyewall, and rainbands.

An important question then is:

how does the cloud population (depicted in Figure 10.2d) help

convert the pre-existing cyclonic circulation to a cyclonic disturbance

exhibiting an RMW, eye, eyewall, and rainbands?

One idea about how this conversion occurs is that

the convective and mesoscale vorticity perturbations contained within the members of the cloud population,

as depicted in Figure 10.2d,

are eventually sheared apart by the radial gradient of the vortex wind and

mixed into the mean flow around the low

Model calculations indicate that

axisymmetrization may distribute subsynoptic-scale vorticity perturbations,

such as those contained in the vortical hot towers and MCVs,

into a ring of high vorticity at a specific distance from the storm center,

giving the enhanced low-pressure system an RMW and thus a structure like that of a tropical cyclone.

While axisymmetrization must play a role, we also observe that

the tropical cyclone center can occur suddenly within a particular member of the cloud population

rather than as a collective smearing (にじむ) of the effects of the whole population around the pre-existing low

(e.g., Figure 10.4h).

This behavior has not been fully explained; however, there may be a stochastic aspect to the process.

As the larger depression

gathers strength from all the ongoing convective activity and

gradually takes on tropical storm structure in its wind field,

the probability increases

that one of the MCSs with rotational convective cells and/or MCV will occur in the ideal spot

(presumably the exact center of the depression)

where the MCS’s cloud structure interacts with the vortex center

to metamorphose into a structure that has an incipient eye, eyewall, and rainbands.

10.3 OVERVIEW OF THE MATURE TROPICAL CYCLONE

10.3.1 Visible Clouds

The clouds in a mature tropical cyclone are dominated

by upper-level cirrus and cirrostratus spiraling anticyclonically outward.

In the visible image of Hurricane Katrina (2005) in Figure 10.5a,

the rough tops of convective clouds penetrate through the smooth cirrus outflow.

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located in the middle of the spiraling cloud pattern

A zoomed-in satellite view of the eye in Figure 10.5b shows that

the cloud top surrounding the eye slopes downward and inward toward the ocean surface.

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Seen from an aircraft flying inside the eye (Figure 10.5c),

the cloud surface

bounding the eye region and sloping at an angle of about 45

gives an observer on the plane

the impression of being inside a giant circular sports stadium

with the grandstand (スタンド席) banking (堤で囲む, 傾斜させる？) upward and outward.

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This huge sloping cloudbank, called the eyewall, is highlighted

by the sunlight on the east side of the eye in all three panels of Figure 10.5.

The ocean surface is not visible in Figure 10.5b and c

but rather is obscured by low stratus or stratocumulus clouds.

This low cloud cover is common in the eye of a strong tropical cyclone.

The dynamics of clouds in the eye and eyewall regions will be discussed further in Sections 10.4–10.6.

10.3.2 Three-Dimensional Wind Field

The visible cloud pattern seen in Figure 10.5 is determined mainly

by the wind and thermodynamic structure of the cyclone.

An example of the low-level wind field in a tropical cyclone (Gloria 1985) is shown in Figure 10.6a–b.

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The winds were constructed from rawinsonde, dropsonde, and aircraft Doppler radar measurements.

（GPSゾンデが無かった時代）

In Figure 10.6a,

the wind data have been filtered to remove wavelengths less than about 150 km near the center of the storm and 440 km in the outer portions of the figure.

This view emphasizes the large scale flow pattern in which the storm is embedded.

In Figure 10.6b,

the analysis retains wavelengths down to about 16 km in the center of the figure and down to about 44 km in the outer part of the figure.

In this higher resolution analysis, the tropical cyclone vortex itself is highlighted.

The streamlines show boundary-layer air spiraling inward toward the center of the storm.

The shaded isotachs (Figure 10.6b) show the roughly annular zone

corresponding to RMW at ~20 km (0.18 latitude) from the storm center.

The air parcels spiraling inward at 900 hPa tend to increase their angular momentum,

and the RMW occurs where the radial inflow rate abruptly slows down.

Radial convergence, increased tangential wind speed, and sudden upward turning of the air current occur

at this location and produce the eyewall cloud.

Inside the RMW is the eye,

where the wind speeds drop off almost immediately to nearly zero, and

the vertical air motion is downward,

producing the eye of the storm by suppressing clouds,

except for the low-level stratus capping the mixed layer (Figure 10.5).

The dynamics of the eye are discussed further in Section 10.5.

The 200 hPa wind pattern (Figure 10.6c and d) illustrates that

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although the tropical cyclone’s outflow is strong, it is generally asymmetric.

In this case, the outflow is concentrated in a channel northeast of the storm center.

The depth of the cyclone core is also apparent;

even at this high altitude,

the flow is cyclonic near the storm center

but changes to anticyclonic 〜100 km from the storm center.

Details of the cyclonic flow near the center of the storm are illustrated by the higher resolution analysis in Figure 10.6d.

余談

熱帯は200と850(900)を見る。上昇流が対流圏を貫いて、下層収束・上昇発散という第一傾圧モード（あってる？）が卓越するためでしょう

中緯度で500を見るのは、等価順圧的な構造が卓越するからだと思っている

Vertical cross sections of the broad scale mean radial (u) and tangential (v) components of the wind of a tropical cyclone are shown in Figure 10.7a and b,

which are composites of data collected in many storms.

Most evident in the radial wind field (Figure 10.7a) is

the increase in the inward directed component at low levels as one approaches the storm center.

Strong radial outflow is evident at the top of the storm, at about the 200-hPa level.

An important feature missed by these old, low resolution composite observations is

the occurrence of a shallow radial outflow layer at the top of the boundary layer,

which is related to the fact that the strong winds near the center of the vortex become supergradient.

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The strongest tangential wind field (Figure 10.7b), defining the RMW, is at ~500 m above the surface.

The strong convergence in the eyewall at low levels and the strong outflow aloft

must be balanced by strong upward motion.

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The broad scale pattern of vertical motion in a tropical cyclone is shown in Figure 10.7c.

The overall cloud and precipitation amounts are determined by this vertical mass transport,

which on average is upward over the region located within 400 km of the storm center.

However, this large scale mean vertical motion pattern

does not have the spatial resolution to provide much insight into cloud structures,

nor does it show the downward motion in the eye.

To see these details, specialized aircraft observations are required.

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10.3.3 Equivalent Potential Temperature and Angular Momentum in Relation to the Eye and Eyewall

In the large scale environment, far from the center of a tropical cyclone,

the typical sounding shows that

stratification of equivalent potential temperature θe is dominated by potential instability

(decrease of θebar with height; recall Section 2.9.1)

in the lower troposphere,

with θebar reaching a minimum at about the 650-hPa level.

The overbar is used here to signify a mean-variable field,

for which turbulent and convective fluctuations have been averaged out.

Above that level, the air is potentially stable.

The pattern of θebar changes markedly (著しく)

as one proceeds inward toward the center of a tropical cyclone

The typical pattern of θebar within a tropical cyclone is indicated by the example in Figure 10.8a.

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In the low levels,

the values of θebar increase steadily (着実に) to a maximum in the eye of the storm.

In the vicinity of the eyewall (10–40 km from the storm center),

the gradient of θebar is maximum, and

the isotherms of θebar rise nearly vertically through the lower troposphere,

then flare (広がる) outward as they extend into the upper troposphere.

Above the boundary layer, where θebar is nearly conserved following a parcel,

hese contours reflect the flow of air upward and outward in the eyewall.

In the very center of the storm, θebar decreases strongly with height.

The center of low θe at 500 hPa is evidence of subsidence concentrated in the eye of the storm.

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The vertical circulation of the tropical cyclone in relation to θebar

is illustrated qualitatively in Figure 10.8b,

where the low-level radial flow is depicted as converging into the center of the storm

(consistent with Figure 10.7a)

in the boundary layer below cloud base.

As it flows inward,

turbulence produces a well mixed boundary layer of high θebar.

When this air enters cloud in the eyewall zone,

it ascends to the upper troposphere approximately along the lines of constant θebar.

The θebar lines also reflect a concentrated descent of air in the eye of the storm,

which will be discussed further in Section 10.4.

Early meteorologists reasoned out

the dynamical necessity of the funnel-like shape of the outward sloping flow lines in the eyewall region

simply from hydrostatic balance.

Assuming a vanishing pressure gradient at some high level, one concludes that

the strong pressure gradient in a tropical cyclone must be associated with

an outward slope of the boundary of the core of warm air in the center of the storm.

Another argument was that

in a warm core storm

in which the radial pressure gradient decreases upward,

rising rings of air move outward

in order for the centrifugal and Coriolis forces (corresponding to their initial angular momentum)

to balance the weaker pressure gradients aloft.

This reasoning foreshadowed today’s view of the inner region of the storm,

which expresses the eyewall circulation

in terms of parcels of air rising out of the boundary layer and

subsequently conserving both angular momentum and θe

as they ascend in the free atmosphere.

Above the boundary layer,

where frictional effects are small,

the angular momentum m (defined in (2.35)) about the central axis of the storm

is approximately conserved following a parcel,

as is θe.

The isopleths of mbar and θebar therefore tend to be congruent (一致する),

implying that above the boundary layer the eyewall cloud is in a state of approximate conditional symmetric neutrality.

symmetric instability 縦にも横にも安定だけど斜めは不安定なやつ。

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cf. 傾圧不安定の図 Vallis 2nd.より

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Although the outward spreading of the mbar and θebar lines

is consistent with the theory of a balanced vortex and

is a typically observed characteristic of tropical cyclones,

there are nonetheless observations and model simulations that indicate that

vertical locally buoyant convection is often embedded in an eyewall cloud,

modifies its structure, and

may affect the intensity of the tropical cyclone.

To fully examine the eye and eyewall dynamics,

Sections 10.4 and 10.5 will discuss

how the basic or mean structure of the eye and eyewall cloud

can be thought of in terms of the slantwise conditionally symmetrically neutral component of motion

in a thermal wind balanced tropical cyclone vortex.

Section 10.6 will then examine

the buoyancy driven vertical drafts superimposed on the eyewall cloud.