Houze Robert A., Jr. Cloud Dynamics

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10.4 Clouds and Precipitation in the Eyewall

429

NNW

-.5

. .

..-

...

1.0

2.0

3.0

5.0

4.0

8.0

EYE

7.0

-.5

-1

6.0

5.0

4.0

3.0

2.0

1.0

.:>t:.

8.0

(!J

EYE

7.0

6.0

Figure 10.23 Flight-track data of the vertical velocity (m

S-I)

in the eyewall of Hurricane Allen

(1980). (a) Vertical velocity diagnosed from horizontal wind measurements by integrating the

continuity equation. (b) Vertical velocity measured by the inertial navigation equipment of the aircraft.

(From Jorgensen,

1984. Reprinted with permission from the American Meteorological Society.)

strongest peaks were at high levels, which can be observed remotely by radar but

would not be seen at typical flight levels, which are usually below 6 km.

may be

for this reason that the flight level data do not indicate more intense vertical

velocities. Moreover, the model simulations referred to above assume that all of

the condensation is liquid phase. When the model calculations incorporate bulk

RAINBANDS

430

Clouds in Hurricanes

7.5

EYEWALL

7.5

6.0

•

6.0

•

4.5

:t:

....

:t:

3.0

1.5

-10

-5

DOWN

(m 6-

•

-5

DOWN

Figure 10.24 Peak updraft and downdraft speeds measured aboard research aircraft flying through

hurricanes. Each style of point indicates a particular research flight. The value shown by a point is the

maximum draft speed observed on that flight at that altitude. (From Jorgensen

et al., 1985. Reprinted

with permission from the American Meteorological Society.)

ice-phase microphysics (Sec. 3.6.2), peak vertical velocities are

~10

S-I

and

occur at high levels, similar to the Doppler radar data.?"

The Doppler radar data also confirm the radial outflow layer seen in the model

results (cf. Figs. 10.21b,

1O.22b,

and

1O.25b).

The Doppler radar data do not

extend as high as 14 km (the top of the radial outflow layer in the model output).

Thus, Fig.

1O.25b

shows only the lower half of the radial outflow layer. Nonethe-

less, its presence and similarity to the model results are evident.

10.4.3 Vertical Convection in the Eyewall

From the model simulations and flight data, we now have an idea of the magni-

tudes of the in-cloud vertical motions and the upper-level radial outflow that are

important in determining the eyewall cloud structure. We also have gained the

impression that these motions are largely the slantwise momentum-conserving

motion that has adjusted to a state of near neutrality with respect to conditional

symmetric instability. We now extend our discussion of the eyewall cloud dy-

namics by considering whether vertical convection is superimposed on the slant-

wise convection in the real atmosphere (vis

avis the analytic model storm consid-

ered in Sec. 10.3). We previously pointed out that sometimes the eyewall actually

exhibits a vertical structure, suggesting that the vertical convection can some-

times dominate the eyewall dynamics (Fig. 10.12). These cases are undoubtedly

exceptional. Nevertheless, the ambient conditions in which hurricanes occur

really are conditionally unstable, albeit not strongly so. Even when the ambient

278 See Lord et al. (1984).

10.4 Clouds and Precipitation in the

EyewaU

431

(b)

u (rn e-t)

(a)

w (m s-t)

15.0

13.5

12.0

10.5

9.0

7.5

6.0

4.5

3.0

1.5

::I:

C!l

::I: 13.8

11.7

9.6

7.5

5.4

3.3

RADIAL

Figure 10.25 Air motions determined from airborne Doppler radar observations obtained during

aircraft penetration of Hurricane Alicia

(1983). Dotted line shows aircraft flight level. (a) Vertical

velocity and (b) radial velocity (m

S-I).

(From Marks and Houze, 1987. Reproduced with permission

from the American Meteorological Society.)

432 10 Clouds in Hurricanes

conditions are neutral for conditional instability, the

air-sea

transfer, boundary-

layer mixing, and hurricane circulation itself create regions of conditional instabil-

ity within the storm as the hurricane develops. Thus, no matter what the case is

regarding the degree of ambient conditional instability, it is reasonable to expect

that some vertical convection occurs when conditioned instability is released and

this convection must be superimposed on the slantwise circulation of the well-

developed storm. The Doppler radar observations in Fig. 10.25a are consistent

with this view in showing discrete bubbles of concentrated rising motion within

the sloping upflow zone.

Model calculations also support this view. We have seen that, when the envi-

ronment is assumed to be conditionally neutral, a model storm can evolve in

which the streamlines in the eyewall become parallel to the

m and

ees

surfaces

(Fig. 10.20). The process of adjustment of the eyewall cloud region to this condi-

tionally symmetric neutral state is indicated by Fig. 10.26, which shows the fields

mand

ees

at three successive times. The mand

ees

lines gradually become more

parallel as time passes. As the storm develops, air in the boundary layer flowing

inward increases its value of

ee, and conditional instability

(dees!

< 0) develops

near the center of the storm in the lower troposphere. Vertical convective motions

take place in response to this instability and, in the process, transport high

upward. This transport produces local maxima of m and hence local areas of

inertial instability, which is released in horizontal accelerations.F? This combina-

279 This process was pointed out by Willoughby et al. (l984a).

Figure 10.26 Results of a two-dimensional nonhydrostatic numerical-model simulation of a

hurricane. Fields of saturation equivalent potential temperature (shaded) and absolute angular

momentum (nondimensional units) are shown for three times. Closed momentum contours have a

value of 3. Shading indicates equivalent potential temperature values of 345-350 K (horizontal lines),

350-360 K (medium shading), and >360 K (heavy shading). (From Rotunno and Emanuel, 1987.

Reprinted with permission from the American Meteorological Society.)

10.4 Clouds and Precipitation in the Eyewall 433

tion of vertical convection in response to conditional instability and horizontal

motion in response to local inertial instability evidently creates a final mixture in

the eyewall region which is neutral to combined vertical and horizontal accelera-

tion (i.e., a conditionally symmetric neutral state rather like that of the simple

analytic model discussed in Sec. 10.3). In the process of achieving this final state,

though, some vertical convection is superimposed on the developing slantwise

circulation.

10.4.4 Downdrafts

As shown in Fig. 10.13, convective downdraft motion is found in the shower of

heavy rain within the eyewall. Although the downdraft motions appear to inter-

rupt the flow of the secondary circulation at low levels in the vicinity of the

eyewall rain maximum, the

peak

downdraft velocities are rather weak:

~2-3

S-I.

Thus,

unlike thunderstorms (Chapter 8) and mesoscale convective systems

(Chapter 9), the eyewall downdrafts probably do not have a strong feedback to the

larger storm circulation. In the mature eyewall, the upward motion appears to be

associated more with

the

frictional convergence of the inwardly spiraling low-

level branch

the secondary circulation than with downdraft-induced conver-

gence.

10.4.5 Eyewall Propagation

The eyewalls of highly symmetric hurricanes are observed to contract; that is, the

eyewall propagates toward the

center

of the storm and thus shrinks in radius. As

the eyewall rainband contracts, the central pressure of the storm decreases. After

1-2

days, the radius

the eyewall reaches its minimum size and dissipates.

replaced by a new eyewall at a radius of 50-100 km and the central pressure of the

storm rises. This process sometimes gives rise to multiple eyewalls. A schematic

representation

a double eyewall structure is shown in Fig. 10.27, and an actual

example is shown in Fig. 10.28.

The

old eyewall is near the storm center, while a

new one is located farther out. As the life cycle of the eyewall band is repeated,

the storm is characterized by a succession of shrinking eyewall rainbands and a

correspondingly pulsating central pressure.

A theoretical explanation of the eyewall propagation has been attained mathe-

matically by considering a point source of heat placed near the radius of maximum

wind in a hurricane-like vortex. The secondary circulation response required to

keep the vortex in gradient wind and hydrostatic balance is then described by the

equations for

the

vortex. One

its characteristics is that temporal increases in

tangential wind are greatest

just

inside

the

radius of maximum wind. This effect

leads to contraction of the zone of maximum wind as the vortex

intensifies.P"

280 This theory of eye wall propagation was put forth by Shapiro and Willoughby (1982). Observa-

tional support for the theory was provided by Willoughby et

at.

(1982).

Figure 10.27 Schematic illustration of

radar reflectivity in a Northern Hemisphere

tropical cyclone with a double eyewall.

(From Willoughby, 1988. Commonwealth

of Australia copyright reproduced by per-

mission.)

!Wi!

>20

dBZ

•

>32dBZ

Figure 10.28 Example of double-eyewall structure. The plot is a composite of radar reflectivity

from Hurricane David (1979). The darker the shading the higher the reflectivity. The size of the

horizontal area of ocean enclosed by the box is 240 km x 240 km. The storm is centered at 16.34°N,

65.18°W. (From Houze and Hobbs, 1982.)

10.4 Clouds and Precipitation in the Eyewall 435

(a)

::c

I I

400

(km)

300

200

DISTANCE DOWNBAND

100

CONSTANT

ALTITUDE

CONTOURS

3km

4.6km

6.1 km

---

7.6km

•••••.•••••

Xf~~mWZl

(b)

220·

RADAR

210·

200·

Figure 10.29 Hurricane rainband observed by a ground-based radar at North Truro,

Massachusetts, as Hurricane Esther (1961)moved northward over the Atlantic Ocean just off the coast

of the United States. (a) Vertical cross section showing returned power at a sequence of gain settings

(numbered

1-7). The horizontal axis is along the axis of the rainband. Only the most intense echoes are

seen at the highest gain setting, but the intensity has not been corrected for range from the radar. An

hypothesized ice particle trajectory is indicated. (b) Horizontal projection of the hypothesized ice

particle trajectory is superimposed on the plan view of the radar echo at several altitudes. For the 3-km

level, the location

ofthe

intense echo core is shown in addition to the overall echo outline. (From Atlas

et al., 1963.)

436 10 Clouds in Hurricanes

10.5 Rainbands

The rainbands, which are found outside the eyewall, are of more than one type. A

rainband can be purely stratiform when a plume of ice particles from somewhere

along the eyewall falls through the

ooe

level after spiraling outward at upper levels

(Fig. 10.14). Other rainbands appear to be distinct from the eyewall. These rain-

bands are labeled as

principal and secondary rainbands in the nomenclature of

Fig. 10.3 and are represented as the convective phenomena occurring in region III

of the theoretical model sketched in Fig. 10.15.

(a)

x 2

:::::::::;w.::

CONVECTIVE

SCALE

MESOSCALE

'$44

K-__

-;'44

5 25

~4K

c=:::::»

=:=>w'::~:::::"~b

(hil~

;~/{~/'

;'44

I(, '.' .....•• ~:.

;'54

......

~~..

100 110

RADIAL DISTANCE FROM STORM CENTER (km)

-24

-96

-72

-48

-24

0 24

72 96 120

DISTANCE

EAST

FROM

STORM

CENTER

(km)

120...-..:.......,--,..",.....-:::II"".,.,.'""T""-,--,..--------,

III

to)

III

Figure 10.30 Hurricane rainband observed by aircraft penetration of Hurricane Floyd (1981). (a)

Vertical cross section with horizontal axis along the aircraft track, which was across the axis of the

rainband. The track is shown in (b), which is a horizontal projection of the data. In both panels,

contours show radar reflectivity in dBZ, temperatures refer to values of equivalent potential

temperature, and arrows indicate airflow (on either the convective scale or mesoscale, as indicated by

the style of arrow). (From Barnes

et al., 1983. Reprinted with permission from the American

Meteorological Society.)

10.5 Rainbands 437

Analyses of features that appear to have been principal rainbands are repre-

sented in Figs. 10.29 and to.30. In the first example, a vertical cross section in the

along-band direction is presented (Fig. to.29a). Convective radar echo was seen

on the upwind end of the rainband, while stratiform precipitation with a bright

band at the melting level (Sec. 6.1.2) was seen downwind. Precipitation trajecto-

ries of the type we have seen in the eye wall (Fig. to. 13)and in mesoscale convec-

tive systems (Figs. 6.12 and 9.13) were inferred, where ice particles detrained

from the upper levels of the convective towers are advected downwind while

slowly falling, producing the bright band when they finally fall through the

O°C

level.

281

The analysis shown in Fig. 10.30 presents a vertical cross section in the across-

band direction. In this cross section we again see both convective and stratiform

structure in the radar echo. A sloping convective cell is surrounded by stratiform

echo characterized again by a radar bright band. The cell slopes radially outward

with height, in the same sense as the eyewall convection. Inward flowing bound-

ary-layer air of high

ii. rises out of the boundary, then reverses its radial direction

and flows radially outward along a slantwise path as it continues to rise. This

slantwise upward motion in relation to the sloping radar echo maximum is similar

to the slantwise motion in the eyewall (Fig. to.13). Also similar to the eyewall,

downdraft motion occurs in the sloping precipitation echo core. Whereas in the

case of the eyewall the downdraft appears to

playa

minor role in the dynamics,

the downdraft in the rainband is significant.

transports low-s, air from the

midlevel environment into the boundary layer. This type of downdraft is evidently

the primary mechanism by which negative flux of (). occurs at the top of the

boundary layer in region III of the theoretical model hurricane (Sec. to.3, Fig.

10.15). After entering the boundary layer as the downdraft spreads out below

cloud, the

low-s, air flows on toward the center of the storm.

281 Atlas et al. (1963), from whose paper Fig. 10.29is taken, appears to have been the first to suggest

this type of stratiform precipitation mechanism, which is now recognized to be prevalent in many types

of mesoscale precipitation systems.

Chapter

11 Precipitating Clouds in

Extratropical Cyclones

...

notwithstanding the repeated fall of rain which has fallen almost

constantly since

...

November last.

"282

The primary cloud and precipitation producers in middle latitudes are extratropi-

cal cyclones. As noted in Sec. 1.3.3, these storms include both large-scale frontal

cyclones and smaller polar lows (Figs. 1.29 and 1.30). These weather systems all

contain arctic or polar air and, in this way, differ markedly from the hurricanes

considered in Chapter 10, which are low-level cyclonic circulations of purely

tropical air. Unlike the tropics, where the thermal contrasts are small over large

horizontal distances, extratropicallatitudes are characterized by zones of strong

horizontal temperature contrast, referred to as

baroclinic zones. These zones are

usually associated with an upper-level

jet

stream, since, according to the thermal-

wind relation (Sec. 2.2.5), the wind speed increases with height in a zone of strong

thermal contrast. Under certain conditions, a baroclinic

jet

is unstable and,

perturbed in certain ways, a synoptic-scale baroclinic wave can develop. An

important characteristic of this wave is its tendency to take the form of a closed

cyclonic disturbance at low levels. The process of forming the cyclone is called

cyclogenesis. The developing cyclone, which is the product of the cyclogenesis, is

characterized, in turn, by

frontogenesis, which is the process in which the air-

streams of contrasting thermal properties within the cyclone come together in

such a way that the temperature gradients and cloud-producing vertical circula-

tions in the lower troposphere are concentrated on small scales.

The end product of baroclinic wave development is manifested in a variety of

types of extratropical cyclones. The largest members of the spectrum of storms

that result from this process are large frontal cyclones, such as the large cloud

system shown in Fig. 1.29. In these storms, cyclogenesis produces a major low-

pressure center on the surface weather map, and long fronts form and account for

the extensive cloud bands extending outward from the storm center. Polar lows

are smaller extratropical cyclones that occur poleward of major frontal cyclones.

They are connected with the flow of cold polar or arctic air over a warm ocean

282 From the journal entry of Captain Meriwether Lewis on 23 March 1806 after the expeditionary

party of Lewis and Captain William Clark, dispatched to the west coast of North America by President

Thomas Jefferson, had wintered on the Oregon coast. The explorers had suffered the precipitation of

one extratropical cyclone after another and were evidently feeling weary as a result of the long rainy

period-just

as do many modern residents of the Pacific Northwest coast at the end of winter.

438