Houze Robert A., Jr. Cloud Dynamics

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5.2 Stratus, Stratocumulus, and SmaU Cumulus in Boundary Layer Heated from Below 169

covered areas. Cellular patterns are also frequently seen in the regions of subtrop-

ical stratocumulus west of continents, especially at locations where the cloud

sheets appear to be breaking up (i.e., reaching the last stage of the life cycle

indicated by Fig. 5.1l).

The cellular patterns seen in oceanic stratocumulus are of two types:

Open

cells

are walls of cloud surrounding open areas. They are envisioned as having

downward motion in the cell center. The cells at the downwind end of the cloud

streets in Fig. 5.21 are of the open type.

Closed cells are rings of open area

surrounding solid cloud. They apparently have upward motion in the cell center.

An example is shown in Fig. 5.22. Between the regions of open and closed cells,

radial arms of cloudiness called

actinae are sometimes found (Fig. 5.23).

A climatology of the occurrence of open and closed cells in the atmosphere is

shown in Fig. 5.24. In the low-cloud fields east of continents, cellular patterns

tend to occur over warm ocean currents, while west of continents they occur over

cool currents. The cellular patterns in any of these regions can occur as open cells,

closed cells, or coexisting open and closed cells. The open cells, however, are

statistically favored over warm water, while the closed cells are preferred over

colder water. These results suggest that open cells, probably often composed of

rings of cumulus and small cumulonimbus, are favored when heating from below

by surface sensible heat flux is dominant (Fig. 5.11b), while closed cells are more

stratiform and favored when radiative cooling from the top of a more continuous

cloud layer is the dominant mechanism responsible for the differential heating

(Fig.

5.lla).

The open and closed cells and actinae all have an intriguing, but possibly

deceptive, similarity to phenomena observed in Rayleigh-Benard convection un-

der laboratory conditions.!" In particular, the atmospheric cells sometimes ap-

pear to be roughly hexagonal. Although Rayleigh's linear theory predicts no par-

ticular horizontal shape, Benard actually observed hexagonal cells, and this tends

to be the preferred geometry of the cells when there is no shear. The hexagonal

case of the classical linear solution is illustrated in Fig. 5.25. The zero vertical

velocity isopleth is a circle with concentrations of upward (or downward) motion

in the center and compensating reverse vertical flow on the hexagonal periphery.

IJ6 For a discussion of the comparisons between laboratory convection and cloud structure, see the

review of Agee (1982).

Figure 5.19 Schematic of secondary roll flow in an Ekman boundary layer with mean wind

hodograph shown. (From Brown, 1983.)

Figure 5.20 Schematic diagram showing characteristics of thermal convection rolls in relation to

the basic flow. Dashed lines indicate the axis of the preferred roll convection. Broad arrow denotes the

phase velocity of the roll convection. (From Asai, 1972.)

Figure 5.21 Detailed view of cloud streets where cold air is flowing off a region of ice over the

Atlantic Ocean near the southern tip of Greenland (upper right). NOAA-7 visible wavelength satellite

photograph made at 1703GMT on 19 February 1984.(Courtesy of University of Dundee, Scotland and

A. Van Delden.)

170 5 Shallow-Layer Clouds

Figure 5.22 Detailed view of closed convection cells over the North Sea. Denmark is in the lower

part of the picture. Norway is in the upper right and the west coast of Scotland is in the upper left to

center. NOAA-9 visible wavelength satellite photograph made at 1703 GMT on

February 1985.

(Courtesy of University of Dundee, Scotland and A. Van Delden.)

Extrema occur on the vertices, and it sometimes appears that the biggest clouds

occur on the vertices of open cells.

One should be cautious in concluding that the hexagonal arrays seen in strato-

cumulus are produced by an exact analog to Rayleigh-Benard convection. As in

the case of bees building a honeycomb, which is also a hexagonal array similar to

that formed by the convection, nature seems to seek a geometrical configuration

in which the amount of fence building between cells is minirnized.!" Although

hexagonal arrays are seen both in laboratory convection and in atmospheric cloud

patterns, it does not necessarily follow that the governing physics are the same in

both cases, any more than the honeycomb and the convection are produced by the

same process. Indeed, there are some major discrepancies between laboratory

convection and atmospheric convection. One such discrepancy is that laboratory

experiments produce closed cells in liquids and open cells in gases, whereas the

137 For a geometrical shape of a given area, a circle has the smallest ratio of perimeter to area. The

polygon that most closely approximates a circle and can also be fitted together into an array of

elements with common boundaries is the hexagon.

5.2 Stratus, Stratocumulus, and Small Cumulus in Boundary Layer Heated from Below

171

Figure 5.23 Nimbus I satellite imagery of coexisting open and closed cells over the Peru Current

at 1813GMT on 15 September 1964. Radial arms of convective cloudiness, called

actinae, can be seen

between the open- and closed-cell regions. Picture is centered at about

lOoS,

95°W. Each square is

~300

km in dimension. (From Agee, 1982. Reprinted by permission from Kluwer Academic

Publishers.)

atmosphere exhibits both types of structure. Since the atmosphere is a gas, the

appearance of closed cells is somewhat surprising and suggests that at least the

closed cells are not Rayleigh-Benard convection. The most discomforting dis-

crepancy is that the aspect ratio in atmospheric convection is

-10

: 1, whereas the

classical theory predicts ratios

1: 1 (i.e., the atmospheric cells are flatter).

mainly this discrepancy that has led to a search for other explanations for the

behavior of mixed-layer stratus during its breakup stage.

172 5 Shallow-Layer Clouds

Figure

5.24 Global climatology of cellular structure of stratocumulus and small cumulus over

oceans. Shaded areas are regions where closed cells predominate. Hatched areas show where open

cells are more common. Solid streamlines show locations of warm ocean currents. Dashed streamlines

show cold currents. Land masses are blackened. (Adapted from Agee

et al., 1973. Reproduced with

permission from the American Meteorological Society.)

Figure 5.25 Linear solution of the relative vertical velocity field in a hexagonal convection cell.

(From Pellew and Southwell, 1940.)

5.2 Stratus, Stratocumulus, and Small Cumulus in Boundary Layer Heated from Below

173

Stobie Loyer

~IiIIZ=H

--........ z e B

Subcloud Loyer

'-----------------...Lz=o

Figure 5.26 Schematic of a hypothetical mesoscale entrainment instability. A positive buoyancy

fluctuation in the cloud layer rises into the stable layer and becomes adjacent to warmer air. The air

entrained into the thicker cloud is relatively warmer than that where the cloud is thinner. Therefore,

entrainment can reinforce the buoyancy fluctuations. The horizontal lines are lines of constant

8,.

(From Fiedler, 1984. Reprinted with permission from the American Meteorological Society.)

The other explanations that have been attempted revolve around the process of

cloud-top entrainment. We have already noted in discussing the breakup stage of

mixed-layer stratus (Fig. 5.11) that early ideas attempted to relate the stability and

breakup of the stratus to the

!lOe

across the top of the boundary layer; the idea

being that a lower

!lOe

should be conducive to greater entrainment and breakup.

However, these ideas are not confirmed by observations, which indicate a marked

resistance of the stratus to mixing from above, even when the value of

!lOe

is low

enough to suggest instability. A more recent idea is represented schematically in

Fig. 5.26.

was offered to explain the large aspect ratios of cellular convection in

stratocumulus. The basic idea is that an instability of the cloud-topped mixed

layer comes into play whenever one part of the cloud layer is thicker than some

other part and the vertical temperature gradient in the stable layer above the cloud

is sufficiently great.!" According to (5.27), the rate of dilution of the mixed layer

by entrainment is proportional not only to

but also to

!lOe'

If the stability of the

layer above the cloud were very strong, as indicated in Fig. 5.26, the value of

!lOe

across the higher cloud top would be substantially greater than across the lower

cloud top.

is then possible for the dilution of the cloud by entrainment to be

greater over the lower cloud top than over the higher cloud top; that is, there can

be positive feedback leading to the growth of the thicker elements and to the

destruction of the thinner ones. Mixed-layer stratus may thus be unstable under

these conditions, and theoretical calculations suggest that the resulting perturba-

tions grow to a size whose aspect ratio is - 30: 1, in reasonable agreement with

observations. An argument against the applicability of this mechanism is that it

requires a weak inversion at the top of the boundary layer (to get small

as, above

the thick cloud) and a strong stable layer above. These are conditions that are not

normally observed.

138 This hypothesis and the supporting theory were put forth by Fiedler (1984).

174 5 Shallow-Layer Clouds

5.3

Cirriform

Clouds

5.3.1 General Considerations

5.3.1.1 Descriptive Terminology

As we saw in Sec. 1.2.4, upper-tropospheric clouds that exist at temperatures

of about

-20

-85°C

are referred to as cirrus, cirrostratus, and cirrocumulus.

The various forms taken by these clouds, as seen by an observer on the ground,

were shown in Figs. 1.15-1.17. In addition to these forms, the tops of deep

precipitating cloud systems seen by satellite (Figs. 1.27-1.30) typically

occur

these high altitudes. Strong wind shear aloft can displace these upper cloud layers,

producing long streamers of high cloud extending great distances downshear from

the parent phenomenon. These streamers of cloud are extensive partly because

ice particles, with their low-saturation vapor pressure, are slow to sublimate and

partly because they are not necessarily inactive debris of the parent phenomena,

but rather can be continually regenerated by their own cloud dynamics (see Sees.

5.2.2-5.2.4). Henceforth, we will refer to all high-level clouds as

cirriform clouds,

whether they occur atop a major precipitating cloud system or as separate cloud

entities.

5.3.1.2 Microphysical, Kinematic, and Radiative

Characteristics

Cirriform clouds consist primarily of ice particles, although some embedded

convective elements may contain supercooled water for a few minutes at a time.

Aircraft observations of the composition of cirriforrn

clouds"

show ice contents

in cirriform clouds to be in the range 0.001-0.25 g m

with values of 0.01-0.1 g

being typical. The sizes of the particles range from 50 to 1000 /Lm. The most

commonly reported crystal habits are columns, bullets, bullet-rosettes, and

plates. Aggregates of crystals are also seen in cirrus.

140 The vertical air motions in

cirriform clouds are typically

0.1-0.2

m s

-1,

except in floccus and uncinus ele-

ments, where the vertical velocity is

-1-2

S-I.141

As in fog and stratus, radiation interacts strongly with the dynamics of cirri-

form clouds.

The

radiation is, however, more complicated than in fog and stratus

because the particles are complex, do not scatter isotropically, and are often

present in very low concentrations. A detailed treatment of the radiative transfer

in cirriform cloud is beyond the scope of this text, and extensive treatments of

these topics already exist.

142 The radiative transfer equations can be solved under

139 Summarized in Table I of Liou (1986).

140 See Heymsfield and Knight (1988).

141 See Heymsfield (l975b, 1977) and Gultepe and Heymsfield (1988).

142 See, for example, the book by Liou (1980) and the review articles by Stephens (1984) and Liou

(1986).

5.3 Cirriform Clouds

175

various sets of assumptions. The example results shown in Fig. 5.27 assume that

the crystals are columns and use empirical information on optical depth, contribu-

tion of scattering to optical depth, and the normalized scattering phase function.

With these factors taken into account, the heating of air as a result of the diver-

gence of net radiative flux through cirriform cloud of various depths has been

estimated.!" Heating by solar radiation is felt through the cloud layer, while

infrared wavelengths produce a destabilizing effect by cooling the cloud top and

warming the base of the cloud.

5.3

.1.3 Climatology

In any global satellite picture (e.g., frontispiece), many of the photographed

cloud tops are

cirriform.l" Climatologies showing the global extent and distribu-

tion of cirriform cloud have been constructed from both satellite observations

(dashed curve in Fig. 5.28) and visual observations of the state of the sky (solid

curve in Fig. 5.28). Both types of climatology indicate maxima of cirriform cloud

in the tropics and midlatitudes and minima in the subtropics. These curves tend to

mirror the global distribution of precipitation (dotted curve in Fig. 5.28), indicat-

ing that most cirriform cloud is of the type that has its origin in the upper layers of

deep, precipitating cloud

systems.l"

5.3.1.4 Approach to Studying the Dynamics

A common form of cirriform cloud is a small convective entity described as

consisting of a dense

head

and a long fibrous tail (or fallstreak) of falling snow.

This form is seen in both cirrus uncinus (Fig. 1.15c) and cirrus spissatus with virga

(Fig. 1.16). The uncinus or floccus elements may occur either alone or as convec-

tive elements embedded in a widespread layer of cirriform cloud. In examining the

dynamics of cirriform clouds, we will first examine (in Sec. 5.3.2) the dynamics of

the basic uncinus or floccus element.

We have also noted that cirriform cloud comprises the upper portions of deep

precipitating cloud systems and that layers of cirriform cloud extend downwind of

the deep cloud systems where the upper portion of such a deep cloud spreads into

the environment. As an example of this process, we consider in Sec. 5.3.3 the

dynamics of the ice-cloud layer produced by a cumulonimbus cloud (such as

illustrated in Fig. 1.5).

143 See Liou (1986).

144 Actually, the area covered by cirriform cloud is even greater than that apparent in satellite

images, as much cirriform cloud is too thin to be seen in satellite imagery and is barely evident to the

naked eye. The existence of such thin cirriform cloud is indicated by sensitive aircraft instruments and

certain ground-based remote-sensing devices.

145 The high percent cloud cover by cirrus indicated by the visual observation in high latitudes does

not contradict this conclusion, since the precipitation totals at high latitudes must be low because of

the small surface areas encompassed by high-latitude circles and the low surface temperatures.

176 5 Shallow-Layer Clouds

Infrared

Solar

-6 -4 -2 0 2 4 -6 -4 -2 0 2 4 6 8

HEATING I COOLING RATES

(OC

I day)

0 0

::l

I-

Figure 5.27 Heating of air as a result of the divergence of net radiative flux in atmospheres with

cirriform cloud of thicknesses 0, 0.1, I, and 3 km (dotted boxes). The base of the cirriform cloud is

placed at 8 km. Standard atmospheric conditions were assumed. The mean ice content of the cloud

layer was 0.13 g m

and the cosine of the solar zenith angle was 0.5. Upper panel is for the solar flux.

Lower panel is for the infrared. (Adapted from Liou, 1986. Reproduced with permission from the

American Meteorological Society.)

r-----------------,..----------------,

200

precipitation'

. /

',A

• / " satellite

. ,

.£.

100

ii:

a..

90N

9~0":;:"S-------:!=-------.L-------I..-----L--------l,,--------l

5.3 Cirriform Clouds 177

In Sec. 5.3.4 we will examine the dynamics of a thin layer of cirriform cloud in

which convective elements are embedded and which forms apart from a source

cloud such as a cumulonimbus.

5.3.2 Cirrus Uncinus

Cirrus uncinus (Fig. 1.15c) and cirrus spissatus with virga (Fig. 1.16)have much in

common in appearance, with the spissatus being more pronounced. The similarity

of appearance suggests that the two forms are dynamically similar, at least qualita-

tively, and that what is learned about one is probably applicable to the other. An

empirical model of a cirrus uncinus element has been developed and is shown in

Figs. 5.29-5.31.

146

According to this model, the head of the uncinus element

146 This empirical model of cirrus uncinus was constructed by Heymsfield (l975b) on the basis of

aircraft and Doppler radar observations.

is consistent with earlier work by Japanese investigators

(Yagi

et al., 1968; Yagi, 1969; Harimaya, 1968).

Wind direction

0.3·1

1·2

Cloud Becomes Visible

Nucleation Level

Updrafl Begins Here

Figure 5.29 Empirical model of a cirrus uncinus element under positive wind shear conditions.

(Adapted from Heymsfield, 1975b. Reproduced with permission from the American Meteorological

Society.)

(a)

NEGATIVE

SHEAR

IN HEAD

Figure 5.30 Empirical model of a cirrus

uncinus element. (a) Wind shear opposite to that

in Fig. 5.29. (b) No wind shear. (From

Heymsfield, 1975b. Reprinted with permission

from the American Meteorological Society.)

Wind

direction

(b)

NO SHEAR

IN HEAD

_ Wind direction

NEW

TURRETS

(

STABLE

LAYER

DRY

ADIABATIC

LAYER

STABLE

LAYER

.Positive Wind Shear

EVAPORATIVE

COOLING

REGION

(b)

-W-D

Convergence

Divergence

(c)

Postive Wind Shear

- Wind direction

Negative Wind Shear

- Wind direction

STABLE

LAYER

DRY

ADIABATIC

LAYER

STABLE

LAYER

DRY

ADIABATIC

LAYER

Figure 5.31 How new cirrus uncinus elements may be generated by older elements. (a) Cooling by

evaporation causes turbulence in the stable layer, which in turn perturbs the unstable layer above; (b)

because of the shear in the environment, horizontal momentum transported downward in the

downdraft produces convergence at the bottom of the unstable layer on one side of the downdraft; (c)

opposite shear to that in (b) produces shear on the other side of the downdraft. (From Heymsfield,

1975b. Reprinted with permission from the American Meteorological Society.)