The Mysteries of Mammatus Clouds: Observations and Formation Mechanisms

Abstract

Mammatus clouds are an intriguing enigma of atmospheric fluid dynamics and cloud physics. Most commonly observed on the underside of cumulonimbus anvils, mammatus also occur on the underside of cirrus, cirrocumulus, altocumulus, altostratus, and stratocumulus, as well as in contrails from jet aircraft and pyrocumulus ash clouds from volcanic eruptions. Despite their aesthetic appearance, mammatus have been the subject of few quantitative research studies. Observations of mammatus have been obtained largely through serendipitous opportunities with a single observing system (e.g., aircraft penetrations, visual ob-servations, lidar, radar) or tangential observations from field programs with other objectives. Theories describing mammatus remain untested, as adequate measurements for validation do not exist because of the small distance scales and short time scales of mammatus. Modeling studies of mammatus are virtually nonexistent. As a result, relatively little is known about the environment, formation mechanisms, properties, microphysics, and dynamics of mammatus. This paper presents a review of mammatus clouds that addresses these mysteries. Previous observations of mammatus and proposed formation mechanisms are discussed. These hypothesized mechanisms are anvil subsidence, subcloud evaporation/sublimation, melting, hydrometeor fallout, cloud-base detrainment insta-bility, radiative effects, gravity waves, Kelvin–Helmholtz instability, Rayleigh–Taylor instability, and Ray-leigh–Bénard-like convection. Other issues addressed in this paper include whether mammatus are com-posed of ice or liquid water hydrometeors, why mammatus are smooth, what controls the temporal and spatial scales and organization of individual mammatus lobes, and what are the properties of volcanic ash clouds that produce mammatus? The similarities and differences between mammatus, virga, stalactites, and reticular clouds are also discussed. Finally, because much still remains to be learned, research opportunities are described for using mammatus as a window into the microphysical, turbulent, and dynamical processes occurring on the underside of clouds.

Full text

REVIEW
The Mysteries of Mammatus Clouds: Observations and Formation Mechanisms
DAVID M. SCHULTZ,*,⫹KATHARINE M. KANAK,* JERRY M. STRAKA,#ROBERT J. TRAPP,@
BRENT A. GORDON,&DUSAN S. ZRNIC
´,⫹GEORGE H. BRYAN,** ADAM J. DURANT,⫹⫹
TIMOTHY J. GARRETT,## PETRA M. KLEIN,#AND DOUGLAS K. LILLY@@
*Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma
⫹NOAA/National Severe Storms Laboratory, Norman, Oklahoma
#School of Meteorology, University of Oklahoma, Norman, Oklahoma
@Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana
&NOAA/NWS/NCEP, Camp Springs, Maryland
**National Center for Atmospheric Research, Boulder, Colorado
⫹⫹ Department of Geological/Mining Engineering & Sciences, Michigan Technological University, Houghton, Michigan
##Department of Meteorology, University of Utah, Salt Lake City, Utah
@@University of Nebraska at Kearney, Kearney, Nebraska
(Manuscript received 18 August 2005, in final form 20 January 2006)
ABSTRACT
Mammatus clouds are an intriguing enigma of atmospheric fluid dynamics and cloud physics. Most
commonly observed on the underside of cumulonimbus anvils, mammatus also occur on the underside of
cirrus, cirrocumulus, altocumulus, altostratus, and stratocumulus, as well as in contrails from jet aircraft and
pyrocumulus ash clouds from volcanic eruptions. Despite their aesthetic appearance, mammatus have been
the subject of few quantitative research studies. Observations of mammatus have been obtained largely
through serendipitous opportunities with a single observing system (e.g., aircraft penetrations, visual ob-
servations, lidar, radar) or tangential observations from field programs with other objectives. Theories
describing mammatus remain untested, as adequate measurements for validation do not exist because of the
small distance scales and short time scales of mammatus. Modeling studies of mammatus are virtually
nonexistent. As a result, relatively little is known about the environment, formation mechanisms, properties,
microphysics, and dynamics of mammatus.
This paper presents a review of mammatus clouds that addresses these mysteries. Previous observations
of mammatus and proposed formation mechanisms are discussed. These hypothesized mechanisms are anvil
subsidence, subcloud evaporation/sublimation, melting, hydrometeor fallout, cloud-base detrainment insta-
bility, radiative effects, gravity waves, Kelvin–Helmholtz instability, Rayleigh–Taylor instability, and Ray-
leigh–Bénard-like convection. Other issues addressed in this paper include whether mammatus are com-
posed of ice or liquid water hydrometeors, why mammatus are smooth, what controls the temporal and
spatial scales and organization of individual mammatus lobes, and what are the properties of volcanic ash
clouds that produce mammatus? The similarities and differences between mammatus, virga, stalactites, and
reticular clouds are also discussed. Finally, because much still remains to be learned, research opportunities
are described for using mammatus as a window into the microphysical, turbulent, and dynamical processes
occurring on the underside of clouds.
1. Introduction
The Glossary of Meteorology defines mammatus
clouds (or mamma) as “hanging protuberances, like
pouches, on the undersurface of a cloud” (Glickman
2000, p. 471). The word mammatus is Latin for “having
breasts.” A characteristic of mammatus is their often
smooth, laminar appearance, which makes them some
of the most distinctive clouds in our atmosphere (Figs.
1 and 2). Their aesthetic appearance when illuminated
by the colors of sunset, have made mammatus a popular
subject of photographers and artists. For example, Ged-
zelman (1989) noted that mammatus have appeared in
paintings as early as the 1500s.
Mammatus often occur on the edges and sloping un-
Corresponding author address: Dr. David M. Schultz, NOAA/
National Severe Storms Laboratory/FRDD, Suite 4356, Norman,
OK 73072-7326.
E-mail: david.schultz@noaa.gov
VOLUME 63 JOURNAL OF THE ATMOSPHERIC SCIENCES OCTOBER 2006
© 2006 American Meteorological Society 2409
JAS3758

derside of cumulonimbus (e.g., Fig. 1a) and have been
observed on both the upshear and downshear sides of
the outflow anvil. Although cumulonimbus anvil mam-
matus is the most commonly noted and photographed,
mammatus can occur in other cloud types as well. Ley
(1894, pp. 84–86, 104), who appears to have originated
the term mammatus (Berry et al. 1945, p. 891), identi-
fied two types: cumulonimbus anvil mammatus and cu-
mulostratus (now known as stratocumulus) mammatus
(e.g., Fig. 2e). German meteorologists in the early
FIG. 1. (a) Cumulonimbus anvil mammatus organized into lines, possibly along radiating gravity waves: 5 May
2002, east of Silverton, TX (copyright C. A. Doswell III). (b) Pyrocumulus mammatus associated with the eruption
of Mount Redoubt on 21 Apr 1990 (photo by R. J. Clucas, from the U.S. Geological Survey Digital Data Series,
DDS-039).
2410 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63
Fig 1 live 4/C

twentieth century also recognized that mammatus
clouds could occur in association with altostratus, al-
tocumulus, and cirrus. Scorer (1972) noted that mam-
matus can occur on falling rain or snow below a cloud
base or on streaks of falling ice crystals. Ludlam and
Scorer (1953) observed mammatus-like features as jet-
aircraft condensation trails broke up into pendulous
lumps. Mammatus have even been observed on pyrocu-
FIG. 2. (a) Cumulonimbus anvil mammatus: 25 Mar 2005, Salt Lake City, UT (copyright J.
Steenburgh). (b) Mammatus with ragged edges: 29 Jun 2004, Norman, OK (copyright K.
Kanak and J. Straka). (c) Well-developed cumulonimbus anvil mammatus lobes: 29 May 2004,
near Belleville, KS (copyright V. Doswell). (d) Cumulonimbus anvil mammatus arranged in
lines, showing blue sky between lobes: 8 May 2005, Norman, OK (copyright C. A. Doswell
III). (e) Stratocumulus mammatus: 3 Aug 2003, Ouachita National Forest, OK (copyright D.
Schultz). (f) Mammatus that formed on a cumulonimbus anvil that had all nearly evaporated
except for the leading edge: 2047 CDT 7 Jun 2004, Norman, OK (copyright K. Kanak and J.
Straka). (g) Mammatus exhibiting breaking Kelvin–Helmholtz waves: 2 Aug 1992, Norman,
OK (copyright K. Kanak and J. Straka). (h) Mammatus in the ash cloud from the Mount St.
Helens eruption at 0832 Pacific daylight time (PDT) 18 May 1980: picture taken at about 0900
PDT 18 May 1980, Richland, WA (copyright M. Orgill).
OCTOBER 2006 REVIEW 2411
Fig 2 live 4/C

mulus clouds from volcanic eruptions (e.g., Stith 1995,
p. 911; Figs. 1b and 2h and section 4g in the present
paper). Note the similarities between cumulonimbus
anvil mammatus and pyrocumulus mammatus in terms
of the structures of the mammatus and their locations
on the clouds (cf. Figs. 1a,b). The variety of situations
under which mammatus form led Ley (1894) and Berg
(1938), for example, to argue that these different types
of mammatus are likely formed by different processes.
Not all mammatus look the same, however. Some-
times the surfaces of mammatus are laminar (e.g., Fig.
2a), whereas other times they are ragged (e.g., Fig. 2b).
Sometimes they can penetrate quite deeply from the
cloud base into the subcloud air (e.g., Fig. 2c). Some-
times they can occur on a thin part of the anvil so that
blue sky is seen between the lobes (e.g., Figs. 2d,f).
Because they are not directly related to significant
weather events on the ground and they do not appar-
ently hold insights into forecasting severe convective
storms, mammatus generally have been viewed as no
more than a curiosity in the atmosphere. Consequently,
published research on mammatus is rather limited, and
what literature exists is either highly speculative or se-
verely constrained by the limited nature of the obser-
vations. The majority of observations of mammatus de-
rives from serendipitous measurements using single ob-
serving systems or from field programs with objectives
that exclude studying mammatus. In some cases, al-
though mammatus-like structures may be apparent in
radar data or numerical model output, visual confirma-
tion of mammatus may not even exist. Theories for
mammatus abound, but have rarely been rigorously
tested with observed data. Textbooks at all levels (un-
dergraduate, graduate, general public) parrot these
theories, leading to the further spread of misinforma-
tion. In addition, laboratory experiments and numerical
model simulations of mammatus initialized from ideal-
ized or real-data initial conditions are lacking. As a
result, relatively little is known about the environment,
origin, structure, size, microphysical properties, and dy-
namics of mammatus.
The purpose of this paper is to discuss observations
of mammatus and to critically evaluate existing theo-
ries. In this paper, we choose to broaden our scope to
consider mammatus and mammatus-like structures
whether or not they have been visually identified. Ob-
servations with visual confirmation of mammatus struc-
tures are especially valued because that seems to be the
primary means of identifying these curious cloud struc-
tures, as they have been defined in the past. Further-
more, because the atmosphere often resists being pi-
geonholed into convenient little bins, this paper will
benefit from taking a broader perspective of the fea-
tures on the undersides of clouds.
In section 2, previous observations of mammatus are
reviewed. Particular attention is paid to the shapes,
structures, microphysical compositions, and associa-
tions with different parent clouds. An informed discus-
sion of hypothesized formation mechanisms for mam-
matus is presented in section 3. These theories are
evaluated to the extent possible, in light of the available
observational data. Section 4 contains discussions of
other issues regarding mammatus, including the types
of hydrometeors, their smoothness, and the factors that
control their spatial/temporal scales and organization.
The nature of mammatus formed in pyrocumulus from
volcanic eruptions is also discussed, as are the similari-
ties and differences between mammatus, virga, stalac-
tites, and reticular clouds. Section 5 concludes this pa-
per, addressing the types of observational data and nu-
merical-model experimentation needed to begin to
resolve some of these questions.
2. Observations of mammatus
The literature on mammatus from the first half of the
twentieth century comes mostly from German scientists
and is discussed in section 2a. Later quantitative obser-
vations of mammatus, described in section 2b, are
rather limited, amounting to perhaps a dozen studies
(Table 1). Recently, several studies have presented ob-
servations of cirrus mammatus; these studies are re-
viewed in section 2c. In section 2d, we present data
from a previously unpublished mammatus event, and
we revisit data from another event.
a. Early literature: 1900–48
This period of mammatus research within the Ger-
man literature seems to have been inspired by Osthoff
(1906). His seven-and-a-half-page paper described his
observations of 67 mammatus events over 21 years. He
found that mammatus were 10 times more likely to
occur during the summer than winter, with more than
half of the events occurring during 1400–1700 local
standard time (LST). Almost half (42.6%) of the events
were associated with thunderstorms, squalls, or cumu-
lonimbus, whereas 31.5% were associated with stra-
tocumulus, 24.1% were associated with altocumulus or
middle clouds, and 1.9% were associated with nimbus.
His drawings of mammatus showed the variety of struc-
tures he observed.
Inspired by Osthoff’s work, Wegener (1909) argued
that discontinuities in temperature and wind across the
cloud base would be observed in cumulonimbus anvil
2412 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

mammatus as a result of the anvil spreading horizon-
tally. Because the anvil outflow and the thunderstorm
environment would not necessarily have the same tem-
perature and horizontal momentum, a thermal inver-
sion and vertical wind discontinuity may be expected.
This argument was supported by future observational
evidence, discussed later in this paper.
Clayton (1911) reported on four different cases of
mammatus sampled by kite soundings at the Harvard
College Astronomical Observatory. Said Clayton
(1911, p. 183), “In every case where the lower surface of
a cloud is mammated, the cloud is found above an in-
verted gradient of temperature.”Hartmann (1920), in
observations of stratus mammatus passing over a
mountaintop observing station, observed a dry layer
underneath the mammatus in association with an inver-
sion and strong wind shear. Further observations of
mammatus by Schneider (1920) from two instrumented
kite ascents showed an inversion of 0.7°–1.5°C at cloud
base. While most authors at this time believed that
mammatus were convex protuberances hanging down
from cloud base, Schmauss (1913) argued, apparently
unconvincingly, that an optical effect due to the illumi-
nation of the underside of the cloud made it difficult to
determine whether mammatus were concave or convex.
Troeger (1921) observed stratus mammatus in asso-
ciation with a 46°halo around the sun. (The 46°halo, or
great halo, is caused by sunlight being refracted
through horizontally falling, pencil-like ice columns
with hexagonal cross sections.) This work later
prompted him to perform a climatology of 100 cases of
mammatus (Troeger 1922), analogous to Osthoff’s.
Troeger (1922) found that mammatus were 2 or 3 times
more likely to occur in summer than winter, compared
to Osthoff’s (1906) 10 times. The editors of Meteorolo-
gische Zeitschrift cautioned that Osthoff (1906) and
Troeger (1922) likely had different definitions of mam-
matus because of Osthoff’s lower frequency of mam-
matus. Like Osthoff (1906), Troeger (1922) also found
an afternoon maximum in occurrence. He proposed
two different mechanisms for mammatus formation.
The first mechanism involved a moist stratus layer mov-
ing over a very dry layer with evaporation of the lower
part of the cloud resulting in mammatus. The second
mechanism occurred in the lower part of fall streaks or
cirrus, where wind shear caused the settling particles to
slow down, recirculate, and form mammatus. Troeger
(1922) appears to have been the first to describe cirrus
mammatus, although Bauman (1927) would later claim
that his observations of cirrus mammatus were the first
reported in the literature. (More discussion on cirrus
mammatus can be found in section 2c.)
Of the mammatus research during the first half of the
twentieth century, that by Berg (1938) was arguably the
most insightful. He discussed three types of mammatus
and attributed each type to a different physical process.
Altostratus mammatus were attributed to waves due to
Kelvin–Helmholtz instability (section 3h) across the in-
version at cloud base. What Berg (1938) considered
cumulonimbus mammatus were fallstreaks. Altocumu-
lus mammatus cumulogenitus (what would be called
cumulonimbus anvil mammatus today) developed
TABLE 1. Previous observational studies of mammatus. Types of observations: A ⫽aircraft, GD ⫽ground-based Doppler radar,
AD ⫽airborne Doppler radar, VD ⫽vertically pointing Doppler radar, R ⫽rawinsonde, L ⫽lidar, P ⫽stereo photogrammetry.
N/A ⫽not available. Height is in km MSL.
Study
Pressure (hPa)
[height (km)]
Temperature
(°C)
Horizontal
scale (km) Environment Obs w(m s
⫺1
)
Hlad (1944) I [1.28] ⫹15 N/A Thunderstorm R N/A
Hlad (1944) II [3.66] ⫹1 N/A Altostratus R N/A
Hlad (1944) III [3.96] ⫺1 N/A Thunderstorm R/A N/A
Clarke (1962) 600 [4] ⫺1to⫺2 0.25–0.75 Cold front R N/A
Warner (1973) [5–6.5] N/A 0.12–1.05
mean 0.35
Hailstorm P ⫺3.1 to ⫺1.2
mean ⫺2.3
Stith (1995) 394 [7.3] ⫺25 2–3 Hailstorm (supercell) A ⫺2.5 to ⫹1.0
Martner (1995) [3–5] ⫹1to⫺11 1.1 Rain shower with anvil VD ⫺3to⫹0.5
mean ⫺0.7
Winstead et al. (2001) 450 [7] ⫺20 1–3 Stratiform anvil between
supercells
AD ⫺2to⫺3
Wang and Sassen (2005) [7.4–8] ⫺37 3–7 Cirrostratus transitioning
to altostratus
L/VD ⫺2to⫹0.5
Jo et al. (2003) and
Kollias et al. (2005)
[5–6] ⬍01–3 Convective anvil VD ⫺5to⫹1.5
This study 4 Aug 1992 [5.4–5.9] ⬍0 0.5–2.0 MCC stratiform region GD/VP 0.0 to ⫺3.5
This study 14–15 Feb 2000 660 [2.97] ⫺1.7 1–2 Pre-cold front GD N/A
OCTOBER 2006 REVIEW 2413

when the overshooting top of a cumulonimbus hit the
tropopause and spread out. Although Berg (1938) rec-
ognized the existence of cirrus mammatus, he did not
discuss it in detail.
Finally, Wagner (1948) suggested that a slowly sub-
siding cloud base would generate instability as the
cloudy air underwent saturated adiabatic descent and
the dry subcloud air underwent dry adiabatic descent.
The result of this steepening lapse rate across the cloud
base may provide impetus for the formation of mam-
matus.
b. Recent observations: 1944–present
Hlad (1944) investigated soundings associated with
three cases of mammatus in southern Texas. Two were
associated with postconvective environments, whereas
the third was associated with a thin altostratus overcast.
On one of the postconvective events, Hlad (1944, p.
331) participated in an aircraft flight through the mam-
matus and described the remarkable experience:
At 13,000 feet [3962 m] we entered the actual mam-
matus cloud deck, although it didn’t appear to be a
cloud deck from a technical standpoint. There were
vast openings where the visibilities were very good,
below we could see trails of very heavy drops, yet
there was no rain striking the plane. The turbulence
was very light in these openings. Seeking an explana-
tion, we went down to 12,000 feet [3658 m] and passed
under the rain trails.
There was no rain striking the plane at this level
either, although looking above us we could see the
large drops. Next we entered this “ball”of rain which
appeared to be suspended in the air. Inside, the rain
drops were very heavy and the turbulence was mod-
erate to heavy. After flying under, over, and through
several of these rain “balls,”the conclusion was
reached that they were the actual “sacks”that gave
the cloud deck above its mammatus appearance.
These rain “sacks”extended as much as 1000 feet [305
m] downward from the main deck and yet no rain fell
from any of those that we passed under.
Hlad (1944) concluded that these rain sacks must be
suspended by strong upward vertical motion (a hypoth-
esis not verified by later observations from others) and
the lower boundary of the sacks were caused by evapo-
ration of the rain drops (evaporation is one possible
mechanism for mammatus, see section 3b).
Clarke (1962) described mammatus on the underside
of a cold-frontal rainband of altocumulus and altostra-
tus associated with virga, employing visual observations
and surface barograms. This field of mammatus was
apparently viewed simultaneously over a 300–500-km-
long region in Australia. The mammatus were orga-
nized into lines believed to be associated with 1.5-hPa
surface pressure perturbations moving at 27 m s
⫺1
.
Richardson numbers less than or approximately equal
to 0.25 in the region of mammatus suggested to Clarke
(1962) that internal gravity waves formed on a low-level
inversion due to forcing from the mammatus circula-
tions.
Warner (1973) employed stereo photogrammetry to
analyze the characteristics of mammatus in a time-lapse
movie of a hailstorm in Alberta. The average lifetime of
14 mammatus lobes was 10 min, the average diameter
of 54 lobes was 350 m, and the mean vertical velocity of
13 lobes was ⫺2.3 m s
⫺1
, with a range of ⫺3.1 to ⫺1.2
ms
⫺1
(Table 1).
Stith (1995) flew through two cumulonimbus mam-
matus lobes over North Dakota using the University of
North Dakota Citation aircraft and particle measuring
systems. Like Hlad (1944), Stith (1995) also noted that
the mammatus were not opaque. Within the lobes, the
hydrometeors were composed mostly of aggregated ice
particles with some rounded ice particles (i.e., frozen
drops). Liquid water was not observed in large quanti-
ties. The main descending portions of the mammatus
lobes were 0.7°C warmer than the ambient air, although
not very turbulent (approximately 0.2–0.3g, just barely
within the range considered light turbulence by pilots).
Vertical air motions measured by the plane were com-
parable to fall speeds for larger ice crystals (⬃2ms
⫺1
),
so these falling particles were likely staying within the
mammatus lobes.
Martner (1995, 1996) used a vertically pointing,
cloud-sensing radar to collect one of the first published,
high-resolution, Doppler radar measurements of cumu-
lonimbus anvil mammatus (Fig. 3a). Descent domi-
nated the region where the mammatus formed (Fig.
3b). The variance of the Doppler spectrum (i.e., spec-
trum width squared) was small within the mammatus
lobe and decreased toward the bottom suggesting that
turbulence was weak and that the hydrometeors were
relatively uniform in fall speed, which would be consis-
tent with aggregated ice particles as their fall speed is
only weakly dependent on size. Martner (1995) also
showed a strong negative correlation between radar re-
flectivity factor and vertical velocity (i.e., high radar
reflectivity factor was associated with downward veloc-
ity), results that would be later confirmed by other stud-
ies (e.g., Jo et al. 2003; Wang and Sassen 2006).
Winstead et al. (2001) obtained airborne Doppler ra-
dar measurements of cumulonimbus anvil mammatus
and found weak turbulent motions within the mamma-
tus and strong turbulence within the anvil. They also
found no decrease in the variance of the Doppler spec-
trum toward the cloud bottom, in contrast to that ob-
2414 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

served by Martner (1995) for the bottom of the mam-
matus and Kollias et al. (2005) for the edges of the
mammatus, suggesting either that turbulence did not
decrease toward the bottom or that the size distribution
of the hydrometeors did not change. Winstead et al.
(2001) documented the first radar cross section of the
internal circulation of a mammatus lobe (Fig. 4). The
internal circulation featured strong descent of several
meters per second in the core and weak ascent around
the edges, although the geometry of the radar scan im-
plied a significant horizontal wind component existed.
Similar observations of the lobe structure of mammatus
at the base of a 6-km-deep layer of cirrus using a cloud-
sensing vertically pointing Doppler radar in Florida
were obtained by Kollias et al. (2005). They found de-
scent of up to ⫺5ms
⫺1
in the mammatus core, decreas-
ing toward the base of and the edges of the mammatus
lobes, and weaker ascent (as much as ⫹1.5 m s
⫺1
) along
the edges, reminiscent of an upside-down cumulus turret.
c. Recent observations of cirrus mammatus
First described by Troeger (1922), Bauman (1927),
and Ludlam (1948), cirrus mammatus were not dis-
cussed much until the advent of ground-based remote
sensing equipment like lidars. Because of the flat, high
cloud base and the small size of the mammatus lobes
(e.g., Figs. 5a and 6), observation of cirrus mammatus
with the naked eye is difficult unless the setting sun
illuminates them (Fig. 5b). In contrast to the smooth
laminar protuberances in most mammatus clouds, cir-
rus mammatus have sharp broken edges (Fig. 6). Wang
and Sassen (2006) argued that two types of cirrus mam-
matus exist: those associated with cirrus uncinus or fall-
streaks (e.g., Scorer 1958; Scorer 1972; Ludlam 1980)
and those associated with cirrostratus or cirrostratus-
altostratus transition clouds. Recent pictures of cirrus
mammatus can be found in Sassen et al. (1995, their
Figs. 11 and 22), Sassen et al. (2001, their Figs. 7, 8, and
15), Quante et al. (2002), and Sassen (2002, his Plates
2.3 and 2.4, and Fig. 2.3). For example, Sassen et al.
(2001) and Sassen (2002) used a vertically pointing lidar
to observe the detailed turbulent structure of cirrus
mammatus and cumulonimbus anvil mammatus (Figs. 6
and 7).
Platt et al. (2002) examined the structure of a field of
cirrus mammatus in decaying tropical convection using
vertically pointing lidars and millimeter-wavelength ra-
dar. Using a lidar radiometer, Platt et al. (2002) found
in-cloud cooling of about 10°C within 1 km of cloud
base, suggesting that sublimation of ice crystals was oc-
curring. Wang and Sassen (2006) arrived at a similar
conclusion by showing smaller linear depolarization ra-
tios along the edges of the mammatus. This observation
FIG. 3. Vertically pointing cloud-sensing (35-GHz) Doppler ra-
dar measurements of (a) reflectivity and (b) mean vertical velocity
on 0556–0624 UTC 2 Aug 1994, north-central Manitoba, Canada.
[Previously published in Martner (1995, 1996). Figure courtesy of
B. Martner].
FIG. 4. Pseudo-RHI plot of (a) reflectivity and (b) radial veloc-
ity for a representative mammatus lobe. This mammatus cloud
was almost directly above the aircraft flight track (Winstead et al.
2001, their Fig. 6).
OCTOBER 2006 REVIEW 2415
Fig 3 live 4/C

suggested smaller ice crystals along the edges, indicat-
ing sublimation of the ice crystals in the dry air sur-
rounding the protuberances.
Wang and Sassen (2006) identified 25 cases of cirrus
mammatus over 9 yr using the high-cloud datasets from
the Facility for Atmospheric Remote Sensing in Salt
Lake City, Utah (Sassen et al. 2001). The horizontal
scale of the cirrus mammatus was 0.5–8.0 km, with a
vertical scale of 0.3–1.1 km below cloud base. Wang and
Sassen (2006) presented a case where both cirrus mam-
matus and cumulonimbus (anvil) mammatus occurred
within the same cloud (Fig. 6). They argued that the
smooth outline of cumulonimbus anvil mammatus was
a result of a hydrometeor fallout front (see section 3d),
which was absent in the coarser-edged cirrus mamma-
tus. Because both types occurred in similar large-scale
environments, Wang and Sassen (2006) argued that the
local microphysical properties and downdraft velocities
must be responsible for the differences, a point re-
turned to later in this paper.
d. Other observed cases
We now present two additional observations of mam-
matus using radar. The first occurrence was collected
from the National Severe Storms Laboratory’s (NSSL)
Cimarron dual-polarization Doppler radar (Zahrai and
FIG. 5. (a) Cloud polarization lidar returned-power displays of cirrus mammatus on 0100–
0230 UTC 10 Sep 1994, Salt Lake City, UT; (b) upward-looking fish-eye lens photo of field of
cirrus mammatus on 0153 UTC 10 Sep 1994 (courtesy of K. Sassen).
2416 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63
Fig 5 live 4/C

Zrnic´1993). The second was collected with one of the
University of Oklahoma Doppler on Wheels (DOW2;
Wurman et al. 1997) during the Intermountain Precipi-
tation Experiment (IPEX; Schultz et al. 2002).
1) CENTRAL OKLAHOMA:4AUGUST 1992
On 4 August 1992, the Cimarron dual-polarization
radar captured the decaying stage of a mesoscale con-
vective complex (MCC) that passed over central Okla-
homa (Gordon 1995; Gordon et al. 1995). The radar
antenna was pointed vertically while the stratiform re-
gion of the MCC passed overhead at 1128–1134 UTC.
Time versus height reflectivity data (Fig. 8a) indicated
the anvil occupied 5.5–7.0 km AGL, below which hung
several perturbations (toward the right-hand side of
Fig. 8a). The appearance of these perturbations on ra-
dar suggests, although we have no visual confirmation,
that these structures were mammatus.
FIG. 6. Cloud polarization lidar returned-power displays of an anvil case on 26 Aug 1998 where mammatus first
developed at cirrus heights and later developed in a dense anvil. The expanded view of the cirrus and anvil
mammatus illustrates the structural differences: cirrus mammatus are relatively narrow and are sharply outlined,
whereas cumulonimbus anvil mammatus are smooth cauliflower-like protuberances (Wang and Sassen 2005, their
Fig. 11).
OCTOBER 2006 REVIEW 2417

To determine the size of these mammatus, the fea-
tures were assumed to be advected by the mean wind
speed at that level, and space–time conversion was ap-
plied. Averaging the radial wind at constant ranges
from the radar (i.e., Velocity Azimuth Display or
VAD) produced a mean wind at 6 km AGL of 270°at
15 m s
⫺1
. Consequently, the horizontal diameter of the
perturbations was approximately 500 m. Although the
vertical extent of the perturbations in radar reflectivity
factor was also about 500 m, the circulation, as esti-
mated from the vertical-velocity measurements, was a
little deeper, about 1 km (Fig. 8b), consistent with pre-
vious observations of deeper vertical circulations inside
the cloud associated with some mammatus (e.g., Mart-
ner 1995; Winstead et al. 2001).
The corresponding velocity field (Fig. 8b) shows de-
scent in areas of high reflectivity (greater than 7 dBZ)
and ascent in areas of low reflectivity (less than 7 dBZ),
consistent with previous studies (e.g., Martner 1995; Jo
et al. 2003; Wang and Sassen 2006). The descent ranged
from ⫺1ms
⫺1
to ⫺4.5 m s
⫺1
, whereas the ascent
reached ⫹1ms
⫺1
. The broad region of weak ascent
(⬍⫹lms
⫺1
) below the mammatus (Fig. 8b) is indica-
tive of the slow mesoscale ascent expected within the
MCC (e.g., Houze et al. 1989). Immediately after col-
lecting data with the radar pointing vertically, several
range–height indicators (RHIs) were performed. These
RHIs (not shown) confirm the structures observed dur-
ing the vertically pointing mode.
Spectrum width (Fig. 8c) in the clouds was relatively
low (less than 2 m s
⫺1
), implying little turbulence. In
regions of small reflectivity, noise dominated signal,
producing areas of large spectrum width (3–4ms
⫺1
).
The Norman sounding was released within 20–30 min
of the mammatus event about 41 km southeast of the
Cimarron radar, but only reached about 580 hPa (not
shown). The freezing level was at about 3.6 km MSL
(3.1 km AGL) and a dry subcloud layer was present,
both features typical of many mammatus events. The
band of low correlation coefficient as observed by the
radar at 3.5 km AGL (Fig. 8d) indicated the melting
layer (e.g., Zrnic´et al. 1993; Straka et al. 2000). That
cloud base was 5.0–5.5 km AGL (Fig. 8a) implies the
mammatus were above the freezing level and thus con-
tained primarily ice-phase hydrometeors.
2) NORTHERN UTAH:14–15 FEBRUARY 2000
This mammatus event occurred during IPEX, a field
program designed to improve wintertime quantitative
prediction of precipitation over the Intermountain
West of the United States (Schultz et al. 2002). Known
as the Valentine’s Day windstorm, this cold front was
the focus of IPEX’s fourth intensive observing period
(IOP 4). The microscale structure and evolution of the
front in northern Utah was described by Schultz and
Trapp (2003).
The mammatus were observed on the underside of a
forward-sloping cloud in advance of a surface cold front
FIG. 7. Consecutive ⫾10°elevation angle scans of returned energy collected by the polar-
ization diversity lidar from the Facility for Atmospheric Remote Sensing (FARS) 0225:36–
0228:38 UTC 26 Aug 1998 at a 1.0°s
⫺1
scan rate, showing high-resolution slices through
turbulent cumulonimbus anvil mammatus (Sassen et al. 2001, their Fig. 8).
2418 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

as it moved through northern Utah. The front was char-
acterized by a temperature drop (8°C in 8 min), strong
pressure rise (3 hPa in 30 min), and wind gusting over
40 m s
⫺1
(Schultz and Trapp 2003). An off-duty IPEX
forecaster who was in Big Cottonwood Canyon in the
Wasatch Mountains reported virga and mammatus
draped from a cumulonimbus anvil ahead of the front
around 0100 UTC 15 February (J. Ladue 2000, 2006,
personal communication). He reported, “The mamma-
tus was not as distinct as I see [during severe weather in
the central Great Plains of the United States. In this
case, the mammatus consisted of] stringy virga exten-
sions toward the ground without defined rounded sur-
faces.”These observations of virga in association with
mammatus are similar to those of Clarke (1962).
DOW2 was located 55 km north-northwest from La-
due’s position. An RHI from 0104 UTC 15 February
(Fig. 9a) shows the forward-sloping cloud with lobes of
higher reflectivity underneath, about 1–2 km in hori-
zontal scale.
1
The corresponding radial-velocity field
shows wind-speed minima at the bottoms of the largest
lobes (Fig. 9b). Unfortunately, it was not obvious that
the mammatus could be identified in plan position in-
dicator (PPI) images from DOW2 so that the horizontal
distribution of the mammatus could be determined.
Mobile Cross-Chain Loran Atmospheric Sounding
System (M-CLASS) soundings were released from the
two NSSL mobile laboratories (Rust et al. 1990):
NSSL4 was located at Oasis on the west side of the
Great Salt Lake and NSSL5 was located at Ogden–
Hinckley Airport (OGD). The high vertical resolution
(1 s or about 2–8 m) available with the M-CLASS
soundings provides detail about the environment in
which the mammatus occurred. A sounding was re-
leased from NSSL4 at 2347 UTC 14 February, 15 min
before the surface front passed, through the likely lo-
cation of the mammatus. The profile was characterized
by a dry-adiabatic layer below 680 hPa, an approxi-
mately moist-adiabatic layer above 660 hPa, and a su-
peradiabatic layer 246 m (20.9 hPa) deep below the
cloud (Fig. 10a). The lapse rate was 12.6°Ckm
⫺1
or a
decrease in potential temperature of 0.8 K between
680.7 and 659.8 hPa at temperatures of ⫺2.0 to ⫺5.1°C,
respectively. Berg (1938, his Fig. 2) observed a supera-
diabatic layer under mammatus, and Wagner (1948)
argued that such a superadiabatic layer was important
to the formation of mammatus.
Nearly 90 min later, the sounding from NSSL5 at
1
This cross section of radar reflectivity (Fig. 9a) morphologi-
cally resembles smoke plumes undergoing fumigation, where
stable air within the cloud overrides unstable air below (e.g., Pas-
quill 1962, 181–182).
FIG. 8. Cimarron polarimetric radar data in vertically pointing
mode, 1128:08–1134:40 UTC 4 Aug 1992. (a) Reflectivity (dBZ);
(b) velocity (m s
⫺1
), (c) spectrum width (m s
⫺1
), and (d) correla-
tion coefficient. Height ranges from 1 to 7 km AGL.
OCTOBER 2006 REVIEW 2419
Fig 8 live 4/C

0115 UTC 15 February indicated cloud base was 2.97
km MSL and ⫺1.7°C (Fig. 10b). The cloud base from
the sounding agreed with the height of the mammatus
determined from the RHIs (3.0 km MSL or 1.7 km
AGL on Fig. 9a). This sounding also had a slight su-
peradiabatic layer underneath cloud base (lapse rate of
10.2°Ckm
⫺1
), 49 m thick (4.4 hPa) with a temperature
decrease of 0.5°C and a potential temperature decrease
of only 0.02 K, indicating the deeper superadiabatic
layer observed earlier at NSSL4 had mostly stabilized.
In the inset of Fig. 10b, several superadiabatic layers,
separated by very stable layers, are seen below cloud
base; this pattern is likely indicative of highly turbulent
layers. The RHIs (e.g., Fig. 9a) and soundings (Fig. 10)
indicate that the cloud deck was descending.
e. Summary of observations of mammatus
To summarize, the literature provides some informa-
tion about the characteristics of mammatus clouds.
Mammatus occur in association with a variety of cloud
types: cumulonimbus, altocumulus, altostratus, stra-
tocumulus, and cirrus. Mammatus have even been ob-
served in contrails from jet aircraft and clouds of vol-
canic ash. The horizontal dimensions of individual
mammatus lobes range from 250 m to 8 km, with aver-
age dimensions based on the available observations of
1–3 km. Vertical extent below cloud base ranges from
0.3 to 1.1 km, with most about 0.5 km. Whereas some
studies state the vertical and horizontal scales of motion
within mammatus to be nearly equal, others have sug-
gested or provided evidence that mammatus lobes may
be linked to vertical motions of much greater depth,
perhaps even extending from the top of the cirrus out-
flow anvil to the bottom cloud base of the mammatus
lobes. Mammatus can appear in a local patch over a
small section of cumulonimbus anvil or be spread out
over hundreds of km. The duration of a field of mam-
matus can range from 15 min to as much a few hours.
The life cycle of an individual mammatus lobe is
shorter, however, on the order of 10 min.
Depending on the height of the anvil outflow [re-
ported as low as 1.4 km by Hlad (1944) and as high as
8 km by Wang and Sassen (2006)] and the ambient
stratification, mammatus may be composed of mostly
liquid (e.g., Hlad 1944), mostly ice (e.g., Stith 1995; Kol-
lias et al. 2005), or perhaps a combination of both.
Mammatus in clouds of volcanic ash may challenge the
notion whether moist processes are even required in
some situations. Several studies have noted a negative
correlation between radar reflectivity factor and verti-
cal motion in mammatus fields, indicating that the big-
gest hydrometeors are in the downward-protruding
lobes. Descending air motion in the core of the mam-
matus lobe is typically about ⫺3ms
⫺1
, surrounded by
about ⫹1ms
⫺1
of rising motion.
These observations, however, do not offer a consis-
FIG. 9. RHIs from the Doppler on Wheels (DOW2) at 0104 UTC 15 Feb 2000 along the 117°
azimuth: (a) radar reflectivity factor (dBZ); (b) radial velocity (m s
⫺1
). Solid black line in (b)
represents approximate outline of mammatus in (a).
2420 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63
Fig 9 live 4/C

tent picture of mammatus in some very significant ways.
First, because mammatus have been observed in differ-
ent environments and with different hydrometeors,
multiple formation mechanisms may be acting. Second,
sometimes an inversion is observed at or below cloud
base in association with or in proximity to the mamma-
tus, whereas a subcloud superadiabatic layer is ob-
served in other cases. Still other cases may possess both.
Finally, aircraft penetrations through mammatus may
be smooth or turbulent. Thus, there remains much to
learn about the processes affecting mammatus. The re-
mainder of this paper addresses these and other issues.
3. Mechanisms for formation
A variety of mechanisms have been proposed for
mammatus formation. Unfortunately, the serendipitous
and limited observations of mammatus often lack the
necessary thermodynamic and microphysical data to as-
sess their formation and evolution, let alone adequately
describe their structure. Consequently, rigorous evalu-
ation of these mechanisms can be difficult. In this sec-
tion, hypothesized mechanisms for mammatus are re-
viewed and critically examined. Evidence supporting or
refuting these mechanisms, where available, is pre-
sented.
Unless otherwise indicated, the theories discussed in
this section pertain primarily to cumulonimbus anvil
mammatus (e.g., Fig. 1a). A cumulonimbus anvil forms
when the updraft of a cumulus cloud reaches its equi-
librium level and spreads out. Because the recently
risen air in the anvil is not likely to have the same
temperature, moisture, and momentum as the sur-
rounding environmental air, the base of the anvil is
often characterized by a strong vertical temperature
gradient (either an inversion or a superadiabatic layer),
strong gradient in moisture, and strong wind shear. In
this environment, cumulonimbus anvil mammatus
form.
Some of the following mechanisms overlap. For ex-
ample, several mechanisms destabilize the cloud base
(e.g., the first three sections that follow). Such studies
argue that the creation of a statically unstable layer is
crucial for the formation of mammatus. Indeed, stati-
cally unstable layers exist in several of the recent
soundings that sampled mammatus layers (e.g., Fig. 10
of this paper; Fig. 8 of Stith 1995; Fig. 8 of Winstead et
al. 2001). Despite some overlap, the following processes
are retained as separate discussions, in part because
previous studies have presented them separately.
a. Large-scale anvil subsidence
Large-scale anvil subsidence was first proposed by
Wagner (1948), Ludlam and Scorer (1953), and Scorer
(1958, 1972). This mechanism posits that the dynamics
of the thunderstorm anvil provide a large-scale envi-
ronment favorable for the initiation of mammatus.
FIG. 10. Skew T–log pplot of observed soundings at (a) NSSL4
2347 UTC 14 Feb 2000 and (b) NSSL5 0115 UTC 15 Feb 2000.
Temperature (°C, solid lines), dewpoint temperature (°C, dashed
lines), and winds (one pennant, full barb, and half barb denote 25,
5, and 2.5 m s
⫺1
, respectively). Insets are expanded areas of
soundings showing details of the cloud base and superadiabatic
lapse rates.
OCTOBER 2006 REVIEW 2421

When cloudy anvil air flows horizontally over a layer of
unsaturated air, a vertical moisture gradient exists.
Sinking of the cloud deck and the unsaturated air below
occurs, perhaps because of the compensating down-
drafts associated with the main thunderstorm updraft
(e.g., Ludlam and Scorer 1953), the descent of hydrom-
eteors through the cloud (e.g., Wagner 1948; Martner
1995; Platt et al. 2002), or the cloud deck having
reached its level of neutral buoyancy. [Descending an-
vils have been described by Lilly (1988), Martner
(1995), Platt et al. (2002), Knight et al. (2004), and
Wang and Sassen (2006).] As the air sinks, the cloudy
layer warms at the moist-adiabatic lapse rate, while the
unsaturated air below warms at the dry-adiabatic lapse
rate. The difference in lapse rates results in greater
warming in the subcloud air than in the cloudy air and
a consequent steepening of the local lapse rate at the
cloudy–clear-air interface. Convective overturning at
the base of the anvil may then result, in which the satu-
rated air falls in drop-like formations resembling mam-
matus lobes (e.g., Ludlam and Scorer 1953).
Observational support for this mechanism comes
from Imai (1957). Using a 3.2-cm radar in Japan, Imai
(1957) documented a thunderstorm with a subsiding
anvil and a horizontal cellular pattern of mammatus
clouds. Reflectivity images (his Fig. 11) show an anvil
underside with mammatus-like features remarkably
similar to that presented more recently (e.g., Martner
1995; Winstead et al. 2001; section 2d of the present
paper). The anvil descended from 11 to 8 km over
about 3 h. The anvil descent speed of 0.4 m s
⫺1
was
similar to the terminal velocity for frozen 0.7-mm ice
needles, suggesting some validity to Wagner’s (1948)
hypothesis. (The size and shape of the hydrometeors at
the top of the anvil cannot be assumed to be the same
as those at the bottom, however.)
Although a plausible mechanism, there are several
problems with large-scale subsidence as the sole mecha-
nism for mammatus production. First, some previous
observations of mammatus do not show subsidence of
the cloud base. For example, the 4 August 1992 event
discussed in section 2d(l) exhibited weak ascent in the
region below the mammatus, which is consistent with
the conceptual model of mesoscale ascent above the
melting level within mesoscale convective systems (e.g.,
Houze et al. 1989). Second, care must be taken in in-
terpreting some mammatus cases where a descending
anvil is believed to occur. Specifically, if a mammatus
event is observed on a sloped undersurface of a cloud
deck from a time series of radar reflectivity from a
vertically pointing radar [e.g., Martner 1995; Kollias et
al. 2005; section 2d(l) of the present paper], then deter-
mining whether a horizontal cloud base descended over
time or whether a sloped cloud base [e.g., Warner 1973;
section 2d(2) of the present paper] translated over the
radar cannot be determined without additional infor-
mation. Finally, separating the fall speed of the hy-
drometeors from the vertical air motions is not easy,
thereby preventing a clean interpretation of the mean-
ing of these radar-derived vertical motions. In any case,
the data needed to adequately test the hypothesis that
anvil subsidence produces an instability responsible for
mammatus formation, even for a specific case, is lack-
ing.
b. Subcloud evaporation/sublimation
Subcloud evaporation or sublimation is the most
commonly cited mechanism to explain mammatus for-
mation, originating from Troeger (1922), Letzmann
(1930), Hlad (1944), Ludlam (1948), and Scorer (1958).
Ice crystals, snow aggregates, liquid water droplets, or
mixtures of these hydrometeors fall from cloud base
into subsaturated air and begin to sublime and evapo-
rate. Cooling just below cloud base provides the impe-
tus for saturated descent in mammatus-like lobes. This
process, if it occurs over a large portion of the cloud
base, can result in a lowering of the anvil cloud base
over time (see section 3a). At the point where the de-
scending lobe is no longer buoyant with respect to the
ambient air, the lobe, or edges of the lobe, may return
upward and create a rounded shape to the mammatus
cloud.
Three pieces of evidence support subcloud evapora-
tion/sublimation as a viable hypothesis for mammatus
formation. First, several radar-based studies imply that
the decreasing particle size and the narrowing size dis-
tribution near the bottom of radar-observed mammatus
lobes indicate evaporation/sublimation is occurring
within the mammatus lobes (e.g., Martner 1995; Kollias
et al. 2005; Wang and Sassen 2006). Aircraft penetra-
tions by Heymsfield (1986) also found that evaporation
was occurring underneath a cumulonimbus anvil in a
region where mammatus was forming.
Second, Letzmann (1930) hypothesized that the cool-
ing due to evaporation of water droplets below cloud
base, in conjunction with the warming due to descent of
the cumulonimbus anvil, may be responsible for the
commonly observed inversion at the base of the mam-
matus (e.g., Clayton 1911; Hartmann 1920; Schneider
1920).
Finally, the prevalence of a subcloud dry layer in
many soundings near mammatus (e.g., Clayton 1911;
Schneider 1920; Berg 1938; Hlad 1944; Wagner 1948;
Winstead et al. 2001; Wang and Sassen 2006; Fig. 10a of
the present paper; K. M. Kanak and J. M. Straka, un-
2422 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

published research results) suggests evaporation near
cloud base is likely. For example, soundings through
mammatus sometimes show a superadiabatic layer un-
derneath the mammatus (e.g., Fig. 2 in Berg 1938; Fig.
10 in the present paper). Superadiabatic layers in the
free atmosphere can result from strong evaporation,
cooling the air just below cloud base more quickly than
turbulence can eliminate the instability. Hodge (1956)
noted similar superadiabatic layers at the tops of clouds
where evaporative cooling was occurring. Such supera-
diabatic layers are more common than perhaps previ-
ously recognized. For example, Slonaker et al. (1996)
constructed a climatology of superadiabatic layers at
least 50 hPa above the surface in 73 497 soundings from
the U.S. Midwest for 1983–87. They found 60% of the
soundings had at least one superadiabatic layer, al-
though most of these layers were only a few degrees in
magnitude and existed over a shallow depth. Slonaker
et al. (1996, their Table 9) identified where these layers
occurred relative to clouds and found that 7.5% of the
layers with superadiabatic lapse rates existed below
cloud base. Precipitation falling onto temperature sen-
sors approaching clouds may also explain some sub-
cloud superadiabatic lapse rates. Section 4.3.2 of the
Federal Meteorological Handbook 3 (http://www.ofcm.
gov/fmh3/text/chapter4.htm) states that superadiabatic
layers “shall be categorized as valid if the decrease in
potential temperature in the layer does not exceed 1.0
K. If the lapse rate exceeds this value, the temperature
data in the layer are not realistic. Data shall be deleted
if the potential temperature decreases by more than 1.0
K over any stratum or interval. If the temperature re-
verts back to the original trend, the data should be
carefully examined to determine if the shift is real or
erroneous. If the observer suspects it is erroneous those
data shall be flagged as doubtful.”In both cases in Fig.
10, the superadiabatic layers are valid by these criteria.
Despite strong evidence in support of evaporative
cooling as a mechanism for some mammatus, there are
three reasons why it may not be operating in all cases.
First, the presence of evaporation does not always pro-
duce mammatus (Heymsfield 1986). Second, Stith
(1995) argued that, because the temperature inside a
mammatus lobe was 0.7°C higher than that outside,
evaporative cooling could not be responsible, at least at
the mature stage of this one mammatus lobe. Expecting
the inside of a mammatus lobe to be warmer or cooler
does not appear to be a rigorous test for the evapora-
tive cooling hypothesis, however. For example, initial
inhomogeneities in evaporative cooling at cloud base
may manifest themselves as the early stages of mam-
matus, drawing the cloudy air downward underneath
the maxima of cooling. Once the mammatus lobes ma-
ture and become large, evaporative cooling becomes
greatest at the edge of the mammatus, not inside the
mammatus. Thus, in the mature stage, we speculate that
moist-adiabatic descent and warming may be occurring
within the mammatus lobe, whereas evaporative cool-
ing may be occurring along the edges where descent
(and adiabatic warming) is less, also.
Third, Martner (1995), Winstead et al. (2001), and
section 2d(l) of the present paper documented reflec-
tivity and velocity structures extending from the mam-
matus bases up to 1 km or so into the convective cloud.
That the vertical velocities at heights above the mam-
matus bases were greater than those within the mam-
matus lobes suggests that evaporation at cloud base was
not the main driving force for these downward motions.
On the other hand, Platt et al. (2002) presented lidar
data of tropical cirrus clouds with mammatus. Calcula-
tions of cooling rates based on their data yielded cool-
ing to at least 1 km above cloud base. Thus, evaporative
cooling may act on scales much deeper than just at the
cloudy–clear-air interface.
c. Melting
Like sublimation and evaporation, cooling due to
melting near cloud base may be responsible for mam-
matus formation. Knight et al. (2004) found that the
descent of an anvil below the freezing level appeared to
be associated with the formation of mammatus. They
proposed a mechanism, first suggested by Findeisen
(1940), that explains the formation of convective clouds
beneath and within nimbostratus generated through the
agency of the melting level. As falling precipitation
melts, release of latent heat deepens the isothermal
layer at 0°C (e.g., Findeisen 1940; Stewart 1984; Bosart
and Sanders 1991; Kain et al. 2000), steepening the
lapse rate underneath. Eventually, saturation is reached
in the layer below the melting level and convection can
result. If cloud base were to occur near the freezing
level, the formation of mammatus is possible.
This hypothesis is supported by two other observa-
tions. First, like Knight et al. (2004), Imai (1957, his Fig.
15) showed the close association between mammatus
and the location of the radar bright band where melting
occurs (e.g., Byers and Coons 1947). Second, Table 1
shows that five of the eight (63%) noncirrus mammatus
events in the literature for which temperatures were
available occurred at temperatures within a few degrees
of freezing. This observation would appear to be rather
strong evidence for the viability of this mechanism. On
the other hand, not all mammatus, including cirrus
mammatus, occur near the melting layer [e.g., section
2d(1)], thus melting may not be the sole mechanism by
which all mammatus form.
OCTOBER 2006 REVIEW 2423

d. Local-scale hydrometeor fallout
Local inhomogeneities in hydrometeor mass can lead
to inhomogeneities in vertical air motion, which can
lead to inhomogeneities in the descent of hydromete-
ors. When coupled with the hydrodynamic effects of
frictional drag around the edge of such a precipitation
shaft, the scale of the downdraft expands, and mamma-
tus-like perturbations may result (Scorer 1958). Al-
though anvils are observed to subside possibly due to
this effect (section 3a), this fallout mechanism does not
require thermodynamic instability, which is essential to
some other proposed mechanisms for mammatus.
As hydrometeors descend in lobes, sublimation and
evaporation occur, eventually limiting the mass of hy-
drometeors causing the descent, which may limit the
depth of descent. Once the mammatus lobe forms, it
also forms a baroclinic zone owing to temperature gra-
dients from the sublimation/evaporation and mass gra-
dients from the presence of hydrometeors. Around the
lobe, shear and curvature vorticity are present. The cur-
vature vorticity would lead to the upward motions
around the lobes, providing the observed ascending re-
turn flow (e.g., Fig. 4).
Supporting evidence for this mechanism comes from
three sources. First, some studies have shown that
variations of reflectivity in mammatus are negatively
correlated with Doppler vertical velocity variations
(e.g., Martner 1995; Jo et al. 2003; Wang and Sassen
2006). Thus, the descent in mammatus would appear to
be strongly related to the fall speeds of the hydromete-
ors. In addition, the magnitudes of the vertical motions
at the bottom of the mammatus are often comparable
to the terminal velocity of the constituent hydromete-
ors (e.g., Stith 1995). Other evidence suggests that a
cloud layer may fall faster than its constituent hydro-
meteors (Clark and List 1971).
Second, Heymsfield (1986) used in situ measure-
ments of a Colorado thunderstorm anvil and found that
aggregation of hydrometeors was a likely process
within anvils and that the maximum particle size should
increase with distance downwind of the updraft core.
For storms in which this is true, mammatus located
adjacent or very near the updraft core may be made up
of generally smaller particles. Heymsfield (1986) added
that falling aggregates lower the anvil base and modify
the relative humidity below cloud base. He also ob-
served that the particle spectrum broadened toward
cloud base where mammatus existed. The broad spec-
trum at cloud base may allow differential fallout
speeds, which might be conducive to forming lobe
structures through the mechanism described above.
Third, Stith (1995) found a warm anomaly inside de-
scending mammatus lobes relative to the ambient air.
Thus, if the air inside the mammatus lobe is not nega-
tively buoyant due to temperature, the air must be
negatively buoyant due to the mass of hydrometeors or
through nonhydrostatic effects in order to be respon-
sible for the observed descending motion inside mam-
matus lobes.
A weakness in the hydrometeor fallout mechanism is
that vertical motions inside the mammatus lobes can be
larger than the fall speeds of hydrometeors, especially
when those are small ice crystals with slow fall speeds
(e.g., Martner 1995; Jo et al. 2003). Thus, the size or
composition (ice/water) of the hydrometeors cannot be
primarily responsible for the mammatus, and some
other dynamic effect must be occurring. Furthermore, if
fallout were a feasible mechanism, all clouds might
have mammatus.
e. Cloud-base detrainment instability
Emanuel (1981; 1994, 220–221) presented a mixing
theory to explain mammatus called cloud-base detrain-
ment instability (CDI). CDI is analogous to cloud-top
entrainment instability (e.g., Deardorff 1980; Randall
1980), but applied at the anvil cloud base. CDI is similar
to, but differs from, subcloud evaporation/sublimation
(section 3b) and hydrometeor fallout (section 3d) in the
following manner. In subcloud evaporation/sublimation
and hydrometeor fallout, condensed water is intro-
duced to the dry subcloud air by precipitation (Ludlam
and Scorer 1953), whereas, for CDI, condensed water is
introduced to the dry subcloud air by mixing (Emanuel
1981). CDI typically occurs under differential horizon-
tal advection of cloudy air over clear air, as in the case
of cumulonimbus anvils.
The condition for CDI is that the liquid-water static
energy of the subcloud air be higher than that of the
cloudy air. Consider a cloudy–clear-air interface with
this stratification. If a parcel of cloudy air is mixed
down into the subcloud air and all the liquid water is
evaporated, the resulting air parcel becomes negatively
buoyant and accelerates downward. Instability is opti-
mized by a moderate level of relative humidity in the
subcloud layer. If the subcloud environment is too
moist, evaporation takes place too slowly to overcome
adiabatic warming; if it is too dry, evaporative cooling
of the hydrometeors quickly occurs and penetration of
the thermal will not be very deep. Fernandez (1982)
suggested that CDI may be responsible for local-scale
initiation of downdrafts in tropical squall lines, al-
though the scale of the downdrafts would need to be
hundreds of meters, smaller than the typical scale of
mammatus (e.g., Table 1) in order to be effective.
Emanuel (1981) further hypothesized that CDI could
2424 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

proceed rapidly enough in cirrus clouds to generate
mammatus-like perturbations.
CDI implies a steep lapse rate under the cloud and an
inversion at cloud base (Emanuel 1981) as observed in
numerous cases of mammatus (e.g., Clayton 1911; Hart-
mann 1920; Schneider 1920; our Fig. 10a). On the other
hand, CDI does not explain why mammatus only ap-
pears locally on some regions of the anvil and not over
the entire anvil region (e.g., Fig. 1a). CDI also fails to
explain how the mixing initiates, which is required to
obtain the instability. Perhaps a second mechanism, like
Kelvin–Helmholtz instability, is required to mix the air
before CDI can ensue. According to K. Emanuel (2005,
personal communication), CDI is almost linear, and so
its release is expected to occur spontaneously.
f. Radiative effects
Mammatus are observed most frequently in the af-
ternoon and early evening (e.g., Osthoff 1906; Troeger
1922), perhaps due to adequate illumination of the un-
derside of cumulonimbus clouds that can only occur
when the sun angle is low. Although most cumulonim-
bus occur during this time because of daytime heating,
the prevalence of mammatus late in the day may also
suggest that radiative processes may play some role in
mammatus formation. For example, after the initial tur-
bulence in the anvil outflow is largely dissipated, a ra-
diative–convective mixed layer may form (Lilly 1988).
The cloud top is almost certain to be radiatively warmer
than its upper environment (i.e., space), whereas the
bottom is probably cooler than its radiative environ-
ment (i.e., ground surface). Under these conditions, the
anvil cloud may act somewhat like a stratocumulus
layer, except convection is driven on both top and bot-
tom. Plank et al. (1955) also suggested longwave radia-
tion from cloud top might destabilize the cloud layer
and lead to instabilities at cloud top. If so, radiative
processes could result in deep vertical motions within
the anvil. In this scenario, the mammatus at cloud base
may be the visible manifestation of the convection pen-
etrating downward from the top of the cloud layer.
Based on radiative-cooling estimates of Ackerman et
al. (1988), Lilly (1988) estimated a characteristic verti-
cal velocity scale for this downward convection of about
2ms
⫺1
, small compared to the storm updraft, but quite
similar to the vertical motions within mammatus lobes
(Table 1).
Radiatively cooled thermals expand as they descend.
Similarity theory shows that the diameter of such ther-
mals expands at a rate of about 50% of the cloud depth
(e.g., Rogers and Yau 1989, 54–55). Thus, a mammatus
lobe diameter of 1–3 km corresponds to a depth of
penetration of 2–6 km, which is a typical depth of the
cloud anvil.
How does the rate of radiational cooling compare to
that from evaporation/sublimation? Consider a hypoth-
esis whereby mammatus is driven by the evaporation of
1gkg
⫺1
of liquid precipitation. Complete evaporation
would correspond to 2.5 K of cooling, as calculated
from L
␷
w/c
p
, where L
␷
is the latent heat of vaporization,
wis the liquid water content, and c
p
is the specific heat
of air. Of course, evaporation is not instantaneous. As-
suming the precipitate falls order 1 m s
⫺1
into a dry
layer with 60% relative humidity, evaporation is order
10% km
⫺1
(Pruppacher and Klett 1997, p. 543). In
other words, the evaporative cooling rate is order 1 K
h
⫺1
. For snow, cooling should be of a similar order of
magnitude. In contrast, cloud-top radiative cooling
could be well in excess of5Kh
⫺1
(e.g., Garrett et al.
2005) and is in the right place (cloud top, not cloud
base) to stimulate the observed deep penetrative down-
drafts. Thus radiative cooling can have similar, if not
greater, potential for forcing negatively buoyant ther-
mals.
Furthermore, observations by Garrett et al. (2005)
showed that cloud radiative heating in optically thick,
tropical cloud anvils can be concentrated within 100 m
of cloud base, because terrestrial longwave radiation
cannot penetrate deep into optically thick clouds. Con-
sequently, a layer near the lowest part of the cloud
becomes destabilized (Garrett et al. 2006). This type of
radiative destabilization is more consistent with obser-
vations that show descending lobes originating within
the cloud near cloud base [e.g., Martner 1995; Winstead
et al. 2001; section 2d(1) of the present paper]. The
necessary precondition for this destabilization to occur
is that the cloud is sufficiently optically dense (either
small particles or large water contents) to be nearly
opaque to longwave radiation in the lowest 100 m or so.
Specifically, to create longwave radiative contrasts, the
absorption optical depth should be greater than unity,
in which case the visible optical depth is greater than
about 2, sufficient to nearly obscure the direct radiation
beam from sources behind the cloud. Because clouds of
volcanic ash are moist and optically thick (Fig. 1b, sec-
tion 4g), this condition is likely satisfied for these situ-
ations. This argument raises the question: are mamma-
tus ever seen extending from optically thin clouds? If
so, then alternative mechanisms, such as evaporation,
are required to produce the mammatus because long-
wave radiation is likely not playing an important role.
Indeed, Fig. 2d shows blue sky between the mammatus
lobes indicating that mammatus can occur in the ab-
sence of thick clouds. Two caveats to the above obser-
vation need to be made. First, what the thickness of the
OCTOBER 2006 REVIEW 2425

cloud was at the time any hypothesized downward pen-
etrating thermal was initiated through radiative cooling
is unknown. Second, the cloud may be thinner around
the mammatus because of the descent of cloudy air
from around the downward-penetrating lobe and the
recirculation of drier air upward.
g. Gravity waves
Gravity waves are ubiquitous in the atmosphere. As
such, it is perhaps not surprising that they have been
implicated as mechanisms for mammatus formation.
Gravity waves excited as thunderstorm updrafts im-
pinge on the tropopause can result in wave phenomena
at upper levels (e.g., Hung et al. 1979; Balachandran
1980; Fovell et al. 1992; Alexander et al. 1995; Beres et
al. 2002), or gravity waves can result from the imposi-
tion of thermal forcing in the midtroposphere (e.g.,
Yang and Houze 1995; Pandya and Durran 1996).
Clarke (1962; discussed in section 2b), Gossard and
Sweezy (1974), and Winstead et al. (2001) observed
wavelike patterns in cases associated with mammatus
and attributed them to gravity waves.
Similar to the surface pressure oscillations observed
by Clarke (1962), Gossard and Sweezy (1974) observed
waves with surface observations and a radar sounder at
San Diego, California. Waves were evident from the
sounder at 500–750 m AGL, with a spectacular display
of mammatus at middle levels (2–7 km) throughout the
observation period. These waves were associated with
significant wind shear at 1–4 km. The shear was strong-
est within and above a nearly dry-adiabatic layer, where
the directional shear was nearly 180°. A nearly adia-
batic layer existed, across which the significant speed
shear was observed, as was the case for Clarke (1962).
Gossard and Sweezy (1974) calculated a Richardson
number less than 0.25 at 2 km AGL. Although Kelvin–
Helmholtz instability may have been being released,
Gossard and Sweezy (1974) interpreted their results in
the context of gravity waves. Proximity soundings
showed conditional instability above the shear layer so
that shear-induced waves could have resulted in the
release of conditional instability that could then have
been manifest as mammatus clouds. The presence of
the shear and a similar sounding do not always imply
the presence of mammatus, however (e.g., Gossard and
Sweezy 1974; Gossard 1975).
Winstead et al. (2001) identified wave patterns in a
mammatus-bearing cloud with 4–7-km wavelength and
vertical velocity minima of ⫺10 m s
⫺1
. Vertical velocity
perturbations of similar scale were also found in the
clear air below the anvil, indicative of downward-
propagating waves. The lines of mammatus were ap-
proximately oriented perpendicular to the mean wind
direction,
2
and the sounding through the mammatus
possessed exceptionally strong shear across the cloud
base (Winstead et al. 2001, their Fig. 7).
Yang and Houze (1995) and Pandya and Durran
(1996) used two-dimensional idealized simulations of
convective systems with 1-km horizontal resolution to
show gravity waves on the underside of the trailing
stratiform regions. These gravity waves modulated the
cloud base in a manner that looked like mammatus,
although clearly of much larger scale. Ooyama’s (2001)
two-dimensional idealized simulation of a convective
updraft impinging on a stable layer excited gravity
waves in a spreading canopy. He described the horizon-
tal rotation of cloud at the outer edge of the spreading
canopy as mammatus-like protrusions, although there
may be some debate about the exact nature of these
protrusions. Indeed, still photos (Fig. 1a) and time-
lapse movies (D. Dowell 2005, personal communica-
tion) of cumulonimbus sometimes show mammatus
forming at the leading edge of the spreading anvil.
As for some previous mechanisms (e.g., sections 3e,
f), one argument that works against gravity waves being
responsible for mammatus is why mammatus would oc-
cur on a localized section of cumulonimbus anvil when
gravity waves would be traveling radially away from the
updraft over a larger horizontal distance. Furthermore,
the scale and lobed shape of the mammatus do not
match the pattern of vertical motions in a gravity wave.
For example, Kollias et al. (2005, their Fig. 1) showed
gravity waves within the depth of the cloud, but they
were at a much different scale than that of the mam-
matus. Gravity waves may organize mammatus lobes,
as perhaps seen in Fig. 1a, but likely do not generate the
mammatus themselves.
h. Kelvin–Helmholtz instability
Kelvin–Helmholtz instability can occur within a sta-
bly stratified fluid with strong vertical wind shear (e.g.,
Chandrasekhar 1961, his chapter 11). If the shear across
the interface exceeds a critical Richardson number rela-
tive to the stratification, then distinctive Kelvin–
Helmholtz waves can form. Although early researchers
recognized that mammatus often occurred in conjunc-
tion with strong wind shear (e.g., Wegener 1909; Hart-
mann 1920; Troeger 1922), Berg (1938) was the first to
2
There is a discrepancy between the text on p. 161 and the
figure caption of Fig. 3 in Winstead et al. (2001) (N. Winstead
2005, personal communication). The text should read, “The
dashed lines in Fig. 3 indicate an orientation approximately per-
pendicular to the mean wind direction, though other orientations
may also be envisioned.”
2426 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

suggest that mammatus may be a result of the release of
Kelvin–Helmholtz instability.
Strong evidence for an association between the re-
lease of Kelvin–Helmholtz instability and mammatus
clouds comes from radar observations of a tropical cu-
mulonimbus anvil by Petre and Verlinde (2004). They
observed Kelvin–Helmholtz waves that descended to
cloud base, occurring at the same time as the formation
of mammatus clouds observed by Jo et al. (2003) and
Kollias et al. (2005). Therefore, in at least one case,
wave-induced vertical motions inside clouds appear to
be associated with mammatus clouds, perhaps the most
convincing evidence published to date.
Despite this evidence for the association of mamma-
tus with Kelvin–Helmholtz instability, several questions
arise. First, why don’t mammatus look more like the
organized rows of Kelvin–Helmholtz billows? Second,
why isn’t the nonlinear wave-breaking stage (Fig. 2g)
apparent more frequently? Perhaps such wave breaking
is not visible because the billows are in-cloud and not
visible. In the case presented in Fig. 2g, the mammatus
could have been formed due to other mechanisms, but
began to break once the mammatus extended into a
region of stronger shear. Whether the shear resulted in
the release of Kelvin–Helmholtz instability that caused
the mammatus or the mammatus revealed the existence
of the shear layer is not known for this case. Finally,
Kelvin–Helmholtz instability requires a statically stable
atmosphere, so mammatus forming in regions of static
instability are not likely to be due to Kelvin–Helmholtz
instability.
Finally, although some aircraft penetrations through
mammatus have been turbulent (e.g., Hlad 1944), oth-
ers have not been (e.g., Stith 1995). Doppler spectrum
width measurements by Kollias et al. (2005) indicate
that the mammatus is the most turbulent region of the
cloud, whereas Winstead et al. (2001) found that the
mammatus was not very turbulent at all, although the
environment was quite turbulent. It may be that if
Kelvin–Helmholtz instability were responsible for
mammatus, the billows may only be developing and,
thus, not have become turbulent with breaking waves.
Consequently, care must be taken in attributing
Kelvin–Helmholtz instability to mammatus.
i. Rayleigh–Taylor instability
Rayleigh–Taylor instability was proposed as a
mechanism for mammatus by Agee (1975). This insta-
bility, as classically defined (e.g., Rayleigh 1883; Taylor
1950), occurs on the interface between two incompress-
ible fluids when denser fluid lies overtop a less-dense
fluid (e.g., Chandrasekhar 1961, his chapter 10; Sharp
1984). Because Rayleigh–Taylor instability is an inter-
facial instability, it cannot be applied to continuously
stratified atmospheric flows.
For the sake of argument, however, if Rayleigh–
Taylor instability were applicable to clouds, the cloud
could be considered one fluid and the subsaturated air
below cloud the other fluid. Simple calculations reveal
the magnitude of the effect that would be required to
produce Rayleigh–Taylor instability. Assuming density
increases with height, the necessary criterion for Ray-
leigh–Taylor instability, a subsaturated atmosphere
would have to have a lapse rate exceeding 32°Ckm
⫺1
,
the autoconvective lapse rate (Glickman 2000, p. 64).
Such a lapse rate is hard to imagine in the free atmo-
sphere. Alternatively, density may increase with height
because of precipitation loading. For a saturated atmo-
sphere with a lapse rate of 7°Ckm
⫺1
, the hydrometeor
mixing ratio (liquid and/or ice) would need to increase
at a rate of ⬃100gkg
⫺1
km
⫺1
. For a 10-m-deep layer at
cloud base, the hydrometeor mixing ratio need increase
only about1gkg
⫺1
. Such a change in the hydrometeor
mixing ratio is possible across a hydrometeor front, sug-
gesting that Rayleigh–Taylor instability might be acting
along the cloudy–clear-air interface, or across the inter-
face of an ash cloud (see section 4g).
Any fluid that has density increasing with height,
however, will be statically unstable (i.e., N
2
⬍0, where
Nis the Brunt–Väisäläfrequency). Thus, even if an
interfacial instability (and an interface) exists, buoyant
instability of the entire layer exists. Indeed, Rayleigh
(1883) showed that the interfacial instability is simply
the limiting case of the layer depth going to zero (i.e.,
an infinitely thin transition between two fluids). As
noted earlier, to invoke an explanation requiring a dis-
continuous fluid seems artificial in the context of
clouds. Therefore, mammatus formation does not seem
likely to be associated with Rayleigh–Taylor instability.
j. Rayleigh–Bénard-like convection and the
Schaefer and Day mechanism
Mammatus have been referred to as “upside-down
convection”with sinking cold-air plumes instead of ris-
ing warm-air plumes (e.g., Schlatter 1985), and has been
hypothesized to occur because of cellular convection
(e.g., Ludlam 1948; Schaefer and Day 1981). Specifi-
cally, Rayleigh–Bénard convection arises from the cre-
ation of static instability through the heating of the
lower boundary (or cooling of an upper boundary) of
an initially quiescent homogeneous fluid. In the case of
mammatus, however, the geometry is reversed with the
lower boundary (cloud base) cooled by differential
adiabatic cooling due to vertical motion (section 3a),
evaporation (section 3b), or mixing (section 3e). Be-
cause this cooling is not occurring on a flat boundary,
OCTOBER 2006 REVIEW 2427

Rayleigh–Bénard convection cannot be occurring in the
strictest sense, so we say the convection is Rayleigh–
Bénard-like convection and refer to the more general
term cellular convection.
Schaefer and Day (1981, p. 136) proposed a mecha-
nism for mammatus in which Rayleigh–Bénard-like
convection plays a central role. They argue:
In a short time the cloudy air reaches the same
temperature as the cloud-free air because of radiation
and mixing. Because some of the cloudy air above is
now at the same temperature, it is unstable because of
the aggregate weight of the cloud droplets. However,
because it has no nearby boundaries, the falling air
divides into a polygonal array of downward-moving
parcels of air called Bénard Cells. Because such
downward movement must have upward compensa-
tion of cloud-free air, the undersurface of the cloud
soon becomes a mass of pendules.
Whether the cloudy air and cloud-free air reach ther-
mal equilibrium is debatable (e.g., Stith 1995). Cer-
tainly, soundings where mammatus are present (e.g.,
Fig. 10) can show strong temperature gradients across
cloud base. Taken as a whole, Schaefer and Day’s
(1981) proposed mechanism seems weak and unsub-
stantiated.
4. Discussion
In sections 2 and 3, we discussed previous observa-
tions of mammatus and proposed mechanisms for their
formation, respectively. In this section, other questions
concerning the composition, character, size, and orga-
nization of mammatus are discussed.
a. Are mammatus composed of ice crystals or
liquid water droplets?
Scorer (1958) argued that mammatus are more likely
to be seen in snow showers because the reduction in
visibility is greater than rain, similar to the arguments
about whether virga was associated with melting snow
or evaporating rain (i.e., Fraser and Bohren 1992, 1993;
Sassen and Krueger 1993). Table 1 shows the tempera-
ture at which mammatus was observed for eight events
where temperature could be determined. Except for
one event [case I in Hlad (1944), where the temperature
was about ⫹15°C], temperatures were all very near or
below freezing (⫹1°to ⫺25°C), suggesting that mam-
matus is often associated with at least some ice. Cer-
tainly, cirrus mammatus (section 2c) is composed en-
tirely of ice crystals.
Microphysical observations inside mammatus, how-
ever, are inconsistent. Aircraft penetrations of mamma-
tus in Hlad’s (1944) case III showed that rain was heavy
inside the mammatus. In contrast, Stith (1995) found
aggregated ice particles with insignificant liquid water
amounts inside mammatus. The mammatus in Mart-
ner’s (1995) and our cases (e.g., Figs. 8 and 9a) occurred
above the radar bright band, also suggesting ice was a
component. Clough and Franks (1991) showed that the
sublimation of snow and falling ice hydrometeors oc-
curs more rapidly and over a shorter distance than liq-
uid water, suggesting some preference for frozen hy-
drometeors in mammatus. Thus, mammatus are likely
to be mostly ice, although some may occur with liquid
water.
In the case of mammatus in jet contrails, liquid water
contents are very low (about 1–10 mg m
⫺3
), so it is
unlikely that precipitation-sized particles are involved.
Observations of hydrometeors in contrails confirm rela-
tively small particle sizes (1–10
␮
m; Schröder et al.
2000), much smaller than precipitation-sized hydrom-
eteors. Thus, mechanisms that require precipitation can
likely be eliminated from consideration for mammatus
in contrails.
b. Why are mammatus generally smooth and
laminar?
Regardless of whether mammatus are composed of
ice crystals or liquid water, why the edges of the mam-
matus usually have smooth laminar shapes remains an
intriguing question. Emanuel (1981) attributed the
smoothness of mammatus to mammatus lobes having
undershot their equilibrium levels. At the leading edge
of such lobes, a layer of strong static stability would be
observed that might account for their laminar appear-
ance. Stith (1995) observed a warm anomaly inside the
mammatus of 0.7°C, suggesting that the strong static
stability at their leading edge helps maintain the integ-
rity of the individual lobes in agreement with Eman-
uel’s (1981) hypothesis.
Second, Ludlam (1980) hypothesized that, with a uni-
formly sized hydrometeor distribution, the precipita-
tion falls at the same rate as the downdraft and holds
together. Stith (1995) measured the fall speed of ice
particles in mammatus being similar to the downdraft,
supporting this hypothesis. Further support comes from
the observation that the descent associated with mam-
matus is rarely as large as the fall speed of rain drops
(⬃5ms
⫺1
) and that most observations of mammatus
occur at temperatures near or colder than freezing
(Table 1).
A third hypothesis (e.g., Scorer 1972; Schlatter 1985)
is that a range in ice crystal sizes results in more rapid
evaporation of the smallest ones first, mostly around
the edges of the mammatus. With the larger crystals
2428 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

inside the mammatus lobe and the hydrometeor con-
centration small enough, there appears to be a some-
what opaque, but smooth, outline to the cloud. Thus,
there is a lower limit to the size of a protuberance that
will be visible. This contrasts to the cumulus turrets that
form at the top of the cloud, with their large liquid
water contents, small hydrometeors, and sharp, fractal
edges. Thus, mammatus is not upside-down convection.
Convective overturning at the base of the anvil (sec-
tion 3e) results in cloudy air being drawn into the clear
air below cloud base, and clear air being drawn upward
into the anvil cloud deck. This vertical entrainment pro-
cess as part of mammatus formation (e.g., Scorer 1972)
can explain why mammatus sometimes appear more
lumpy and cauliflower-shaped. Sometimes mammatus
may appear semitransparent with double outlines.
Scorer (1972) attributes this to the edge of the hydrom-
eteor fallout being ahead of the cold descending ther-
mal plume. Evaporation of the hydrometeors adds this
cooled air to the descending plume, but, because the
hydrometeors are falling into more stable air, the shape
of the descending plume is relatively smooth.
c. What controls the spatial and temporal scales of
mammatus?
Most mammatus have a typical horizontal dimension
of 1–3 km in diameter (Table 1). Several observations
of much smaller mean diameters of less than 1 km are
also possible (e.g., Clarke 1962; Warner 1973). Why
mammatus seem to occur with this particular narrow
range of scales is unknown. The mechanism(s) respon-
sible for the mammatus likely plays a controlling factor
in the resulting scale. For example, in section 3f, a re-
lationship between the size of negatively buoyant
downdrafts from cloud-top cooling and the size of
mammatus lobes can be derived. Clearly, a more com-
prehensive understanding of the mechanism(s) that
produce mammatus is required in order to understand
the factors affecting the size of the mammatus.
Another important clue to understanding mammatus
is their temporal scale, which is on the order of 10 min
(e.g., Warner 1973). Given that mammatus have a
length scale of about 1 km and a velocity scale of about
1ms
⫺1
, scaling arguments suggest a time scale of about
15 min. This argument is independent of the processes
that cause mammatus, but it introduces new questions
such as what dictates the length scale (discussed above)
and what dictates the velocity scale. Dictates on the
velocity scale are likely related to the mechanism,
which may be associated with the buoyancy of the in-
dividual mammatus lobes, for example.
An alternative estimate of the temporal scale can be
derived from the buoyancy period 2
␲
/N. For typical
atmospheric stabilities, a period of about 10 min results.
This value, although perhaps a coincidence, is highly
dependent upon the choice of N. Specifically, for neu-
tral layers (N⫽0), the buoyancy period would go to
infinity, indicating that gravity waves could not be re-
sponsible for the mammatus and some other mecha-
nism must be implicated. If Nis found to affect the time
scale of the mammatus, then mammatus being driven
by buoyancy is a possibility. If not, then mechanisms
not associated with buoyancy are required (e.g., pre-
cipitation mechanisms).
d. What controls how mammatus are organized?
In a field of mammatus, the individual mammatus
lobes can be organized in several ways. Sometimes
mammatus can be organized into lines (e.g., Figs. 1a
and 2d,f). For example, Warner (1973, his Fig. 1) and
Winstead et al. (2001, their Fig. 3) suggested linear or-
ganization in their cases. In contrast, Imai (1957, his
Fig. 17) reported cellular mammatus in a dissipating
Japanese thunderstorm. At other times, mammatus ap-
pear to have no organized pattern (Ludlam and Scorer
1953, p. 321; Figs. 2a,c,e of the present paper) and form
in clusters of unequal-sized lobes.
Linear organization to the mammatus lobes suggests
that a wavelike process may be responsible. The pos-
sible role of gravity waves has already been discussed in
section 3g. Another process that can lead to linear or-
ganization is shear in the presence of static instability.
Consider mammatus forming in a region with both
unstable stratification and vertical wind shear. If the
Richardson number is less than 0, mammatus may ex-
tend deep below cloud base, appear with a smooth
leading edge, and align in rows parallel to the local
shear vector. In this case, the bands align parallel to the
local shear vector, as in horizontal convective rolls in
the planetary boundary layer. This mechanism was first
proposed by Jeffreys (1928), first explained by Kuo
(1963), and demonstrated rigorously by Asai (1970a,b).
In contrast, if the Richardson number is greater than
zero but less than ⬃0.25, then Kelvin–Helmholtz insta-
bility could occur, and mammatus would align in rows
perpendicular to the local shear vector, as shown by
Asai (1970b) for horizontal convective rolls in shear. A
spectrum of intermediate morphologies may exist, be-
ing a function of the relationship between buoyancy
and shear.
Less organization to the mammatus lobes may sug-
gest a form of cellular convection akin to Rayleigh–
Bénard convection (section 3j). Although mammatus
may occur through cellular convection, better under-
OCTOBER 2006 REVIEW 2429

standing is needed before the validity of this process
can be assessed. Furthermore, a rigorous observational
examination of this mechanism is lacking because hori-
zontal maps of a field of mammatus lobes and their
organization over time do not exist.
e. What is the relationship between mammatus,
stalactites, and virga?
Pendulous extensions from the cloud base observed
by radar bear remarkable similarity to mammatus.
Plank et al. (1955) referred to them as precipitans; At-
las (1955), Douglas et al. (1957), Imai (1957), and Platt
et al. (2002), among others, referred to them as stalac-
tites.Atlas (1955) and Harris (1977) used the terms
stalactites and mammatus interchangeably, and Imai
(1957) said that stalactites are mammatus. They stated
that these stalactites were associated with snow falling
into dry air, evaporating, cooling, and overturning the
subcloud air.
Harris (1977) presented theoretical models based on
radar data to study the structures associated with the
sublimation of ice particles at the base of clouds, par-
ticularly mammatus and stalactite structures. In con-
trast to other studies, he reported that the cloud layer
ascended. He stated that mammatus could be gener-
ated by cellular motions at cloud top that can be 1.5 km
deep and 600–900 m in horizontal spacing. In this case
of the modulation of precipitation at cloud top, wind
shear reduced the duration of the stalactites.
Virga is defined as streaks of rain or ice crystals that
fall from a cloud but evaporate before reaching the
ground, although there is some debate about whether
virga is associated with evaporating rain or melting
snow (i.e., Fraser and Bohren 1992, 1993; Sassen and
Krueger 1993). Hlad (1944), Aufm Kampe and Weick-
mann (1957), and Clarke (1962) suggested that virga
may be created when mammatus lobes “burst”open:
Might the formation of virga from mammatus occur
when an equilibrium level for the downward-
accelerating parcel no longer exists and the restoring
force is not strong enough to recirculate the cloudy air
upward? The relationship between mammatus and
virga, if any, is unclear.
f. What is the relationship between mammatus and
reticular clouds?
Another unusual cloud phenomenon is reticular
clouds (Kanak and Straka 2002), which, like mamma-
tus, are similarly not well understood. Reticular is an
adjective defined as, “resembling a net; having veins,
fibers, or lines crossing”(Webster’s New Collegiate Dic-
tionary, s.v. “reticulate”). In reticular features, the
cloud peripheries outline a netlike pattern made visible
by cloud condensation and have a cloud-free core (Fig.
11b). Ludlam and Scorer (1953) use reticular to con-
trast with the case of a typical convective cell in which
upward motion in the center is coincident with cloudy
air. In contrast to the downward protuberances of
cloudy air in mammatus (Fig. 11a), reticular clouds
have upward protuberances of clear air (Fig. 11b).
Given that only one sounding has been collected in the
vicinity of reticular clouds (Kanak and Straka 2002), we
do not really know what the characteristic differences
in the thermodynamic environment, if any, are between
mammatus and reticular clouds.
g. What are the properties of volcanic ash clouds
that produce mammatus?
As previously shown, mammatus can form in volca-
nic ash clouds. Only a few eruptions have documented
such structures, however: Mount St. Helens on 18 May
1980 (e.g., Fig. 2h), Mount St. Augustine on 27–31
March 1986 (eruption pictures available online at http://
www.prattmuseum.org/kachemak/forces/volcano.
html), and Mount Redoubt on 21 April 1990 (Fig. 1b).
To understand possible mechanisms for such mamma-
tus, measurements of the character of the ash clouds are
required. A few research datasets have been described
in the literature. For example, Hobbs et al. (1991, their
FIG. 11. Mammatus vs reticular clouds. Two-dimensional sketch
of possible (a) mammatus and (b) reticular vertical cloud struc-
ture.
2430 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

Plate 1a) observed ash veils using airborne lidar in the
ash plumes of the Redoubt eruptions in 1990. These ash
veils were reminiscent of mammatus observed with ra-
dar (e.g., Plank et al. 1955; Imai 1957; Platt et al. 2002).
In addition, the characteristics of pyrocumulus from in
situ aircraft observations at Mount St. Helens have
been described by Hobbs et al. (1981, 1982). They
found large amounts of water (Hobbs et al. 1982), con-
sistent with the large, wet, loosely aggregated ash that
formed in the cloud [what Hobbs et al. (1981) termed
volcanic hail]. Such results are consistent with the con-
clusion of Rose et al. (2003) who found that the major-
ity of the particle mass from the Hekla, Iceland, 26–27
February 2000 eruption was ice nucleated on the sur-
face of ash particles.
Remote sensing has shown that ice is an important
component of volcanic clouds (Rose et al. 2004), but
amounts vary markedly. Ice, which is thought to coat
ash nuclei, dominates some volcanic clouds, as in the 19
September 1994 Rabaul Caldera eruption, Papua New
Guinea (Rose et al. 1995) and the 2000 Hekla (Rose et
al. 2003) eruptions. In contrast, in cases like the 17
September 1992 Mount Spurr eruption (Rose et al.
2001) and the 19 February 2001 eruption of Cleveland
Volcano, Alaska (Gu et al. 2005), ash seems to domi-
nate over ice during most of the life of the volcanic
cloud. Finally, neither ice nor ash dominates in other
volcanic clouds, such as those from the 15 June 1991
eruption of Mount Pinatubo, Luzon, Philippines (Guo
et al. 2004) and March–April 1982 eruptions of El
Chichón (Schneider et al. 1999). Once in the atmo-
sphere, the mass of ice in volcanic clouds declines
quickly, especially in the dry stratosphere. In the Hekla
eruption, the total mass of ice decreased because of
sublimation by an order of magnitude within 24 h (2 Tg
to ⬍0.2 Tg; Rose et al. 2003). A. Durant (2006, unpub-
lished manuscript) has shown that, in the early stages of
the September 1992 Spurr cloud, ice must have been
abundant with at least 0.2 g kg
⫺1
in the cloud 3.7 h after
emplacement at ⫺62°C and 191 hPa. After only a few
hours, the same Spurr cloud contained mainly ash, ap-
parently also because of rapid sublimation (Rose et al.
2001). Overall, the role of ice must be very important in
all volcanic clouds, although some clouds dry markedly
within hours (Rose et al. 2004).
Given the abundant ice often found in volcanic
clouds, the role of subcloud sublimation could be quite
important to mammatus formation. Indeed, soundings
taken near the eruptions discussed above (Mount St.
Helens, Mount St. Augustine, and Redoubt) all possess
dry subcloud layers (not shown), similar to soundings
near cumulonimbus mammatus (e.g., Clayton 1911;
Schneider 1920; Berg 1938; Hlad 1944; Wagner 1948;
Winstead et al. 2001; Wang and Sassen 2006; Kanak
and Straka 2006; Fig. 10a of the present paper). There-
fore, given the varying amounts of ice versus ash, the
relative importance of sublimation versus particulate
loading and fallout in creating mammatus in volcanic
clouds remains unclear.
5. Conclusions
Serendipity has long been recognized as a driving
factor in the advancement of science (e.g., Blanchard
1996, and references within). Nearly all observations of
mammatus to date have resulted from serendipitous
encounters with these clouds. Even idealized modeling
simulations specifically designed to address mammatus
have not been performed. This article presents a review
of previous studies of mammatus, performs a critical
analysis of proposed mechanisms, and raises additional
unanswered questions about mammatus. Clearly, there
is much that remains to be learned. Below we highlight
just a few issues from this paper.
Most previous studies in the literature (especially the
latter half of the twentieth century) discussed cumulon-
imbus anvil mammatus. Although cumulonimbus anvil
mammatus is perhaps the most photogenic and impres-
sive of the mammatus displays, mammatus can form in
cirrus, cirrocumulus, altocumulus, altostratus, stratocu-
mulus, contrails, and volcanic ash clouds.
Nearly all the observations of mammatus described
in this paper are snapshots of just a few lobes at best—
no studies have mapped out the horizontal distribution
of the mammatus field, describing the evolution of
mammatus over time. Observations of the environment
before their formation and after their dissipation are
not available. Yet, like other atmospheric phenomena,
mammatus likely proceeds through some life cycle,
which remains uncaptured with our current observa-
tions and models. For example, whereas some have hy-
pothesized that mammatus may evolve into virga, many
other observations show that this does not occur. Nev-
ertheless, no study has carefully examined the evolu-
tion of a mammatus field. Could the existing observa-
tions reviewed in this paper be better put into context if
they were placed within a mammatus lifecycle concep-
tual model? Modeling experiments would seem to be
required to offer testable hypotheses in this regard.
Many mechanisms have been proposed in the previ-
ous literature and are summarized in section 3. Some of
these mechanisms cannot be acting at the same time.
For example, gravity waves and Kelvin–Helmholtz in-
stability require stable stratification; thus, several ob-
servations pointing to the importance of statically un-
OCTOBER 2006 REVIEW 2431

stable layers tends to diminish the possible importance
of these mechanisms. As another example, linear orga-
nization perpendicular to the shear vector supports
Kelvin–Helmholtz instability, whereas linear organiza-
tion parallel to the shear vector supports static instabil-
ity, and organization radially from a heat source (i.e., a
cumulonimbus cloud) supports gravity waves. Signifi-
cantly, the observed variety of mammatus may indicate
that more than one mechanism is responsible.
Proposed mammatus mechanisms must be able to
explain the following observed characteristics of mam-
matus. First, the lifetime of a mammatus lobe is about
10 min, although few quantitative observations of this
lifetime exist. Second, the size of mammatus lobes is
typically 1–3 km. Third, the temperature of the cloud
base relative to the surface temperature can be used to
ascertain the role of radiative processes on the under-
side of the cloud. Specifically, if mammatus are ever
observed with cloud-base temperature close to the sur-
face temperature, then strong radiative-heating gradi-
ents near cloud base probably are not responsible for
the mammatus. Fourth, the optical thickness of the
clouds may also have some relevance in distinguishing
between different mechanisms. For example, if mam-
matus is observed in optically thin clouds, radiative ef-
fects are probably negligible. Fifth, the temperature at
cloud base can also be used to ascertain the relevance
of evaporative cooling. The magnitude of cooling is
tightly constrained by the saturation mixing ratio,
which decreases exponentially with temperature. Sixth,
the cloud-top brightness temperature from satellite
relative to that of the atmosphere above provides a
constraint on the amount of radiative cooling at cloud
top. Seventh, if mammatus are merely a manifestation
of upside-down convection, then a description is
needed of why cumulus turrets differ in appearance
from mammatus lobes. Last, observations of the tem-
perature at which mammatus occur, along with hy-
drometeor composition inside mammatus lobes, could
provide the critical observations to discriminate among
several of the proposed mechanisms.
For example, cirrus mammatus are highly con-
strained on several levels. Because they exist at cold
temperatures, the capacity for condensation/evapora-
tion to affect local temperature is small, eliminating
most of the latent-heat based mechanisms from consid-
eration. In addition, given the small hydrometeor size
in cirrus, fall speeds do not approach several m s
⫺1
,
eliminating the fallout mechanism. Wang and Sassen
(2006) found that wind shears were relatively weak
across the cloud bases of 25 cases of cirrus mammatus,
eliminating shear instabilities. Thus, remaining viable
mechanisms include radiative effects and gravity waves.
Several studies have shown convincing evidence that
mammatus may be more than just appendages hanging
down from cloud base. These appendages are the vis-
ible manifestations of motions inside the cloud, motions
that may reach to the cloud top. What are the processes
that are associated with the deep circulations present in
mammatus? What role do mammatus serve in the at-
mosphere? What balance are they trying to restore?
To address these issues, additional specialized mea-
surements of mammatus are needed. One way to obtain
such measurements would be to organize a mammatus
field program (may we suggest the name MAMMEX?),
arguing that mammatus are the visible manifestation of
poorly understood processes, like entrainment or mi-
crophysical effects. Alternatively, during field opera-
tions already occurring on different phenomena, col-
lecting data on mammatus serendipitously as part of
that larger research effort may be possible. Hopefully,
datasets can be collected that provide complete micro-
physical, thermodynamic, and dynamic documentation
of such mammatus. In particular, observations of the
premammatus environment, hydrometeor type and
concentration, thermodynamic measurements of the
environment and the mammatus lobes, horizontal dis-
tribution of mammatus lobes, and evolution of the field
of mammatus would be helpful to answer some of the
questions in this paper.
Modeling studies of clouds using a hierarchy of mod-
els with increasing complexity from two-dimensional
idealized models to three-dimensional real-data simu-
lations could be performed to examine the structure
and evolution of mammatus. Surprisingly, no modeling
studies designed specifically to investigate mammatus
exist. This deficiency could be attributable to two rea-
sons. First, resolution needs to be quite high because
mammatus have a typical spatial scale of about 1 km.
Thus, grid spacings on the order of 100 m are required.
For example, Grabowski et al. (1998) found mamma-
tus-like circulations in a two-dimensional cloud-model
simulation with a horizontal grid spacing of 200 m, but
not in one with 2-km grid spacing. Second, most ideal-
ized cloud simulations often use very moist soundings,
not the dry subcloud air typically found in environ-
ments favoring mammatus. Well-designed numerical
experiments could explore the sensitivities of the mam-
matus formation and structure to the thermodynamic
and cloud microphysical conditions. By suggesting
these experiments, we hope to inspire others to begin to
think about the interesting scientific questions about
mammatus needing to be explored.
Although mammatus clouds may not pose any sig-
nificant weather threat, except perhaps for turbulence
affecting aviation, their photogenic characteristics and
2432 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

their very occurrence raises many interesting scientific
questions that challenge our conventional views of
clouds and hydrometeors. As our review has shown,
further studies of mammatus could help provide in-
sights into the turbulent, microphysical, and dynamical
processes occurring at the base of clouds. Mammatus
also may give us additional information about anvil dy-
namics in cumulonimbus clouds. Because a dedicated
field program to take measurements of mammatus may
be a while in coming, serendipitous observations of
mammatus during field programs, as in the past, as well
as numerical modeling experimentation, may provide
the key pieces of evidence to accept or refute some of
the issues discussed in this paper.
Acknowledgments. We have benefited considerably
from discussions with and comments from Ernest Agee,
Will Cantrell, Charles Doswell, Larry Dunn, Kerry
Emanuel, Frédéric Fabry, Robert Fovell, John Horel,
Charles Knight, Alex Kostinski, Steven Krueger, James
Ladue, Steve Nesbitt, William Rose, Richard Rotunno,
Jason Shafer, Raymond Shaw, and Edward Zipser. Jeff
Stith and two anonymous reviewers provided com-
ments that improved the manuscript. A comprehensive
search of the literature by Katherine Day, formerly of
the NOAA Library in Boulder, was helpful in identi-
fying articles that our initial survey did not discover.
Photos of mammatus other than those by the authors
are published with the permission of Charles Doswell
(Figs. 1a and 2d), James Steenburgh (Fig. 2a), Vickie
Doswell (Fig. 2b), and Montie Orgill (Fig. 2h). Figure
1b was taken by R. J. Clucas, and is in the public do-
main. Thanks to Brooks Martner for providing Fig. 3,
Ken Sassen for providing Figs. 5 and 7, and Likun
Wang for providing Fig. 6. Thanks to David Dowell for
sharing his time-lapse movies of mammatus clouds.
Much of the work on the IPEX case in section 2d(2),
and the early work on this manuscript, was performed
during fall 2002 while Schultz was visiting the Depart-
ment of Meteorology at the University of Utah; their
support is gratefully acknowledged. Funding for
Schultz and Kanak was provided by NOAA/Office of
Oceanic and Atmospheric Research under NOAA–
University of Oklahoma Cooperative Agreement
NA17RJ1227, Department of Commerce. Funding was
also provided for Kanak by NSF Grant ATM-0135510
and for Straka by NSF Grant ATM-0340639.
REFERENCES
Ackerman, T. P., K.-N. Liou, F. P. J. Valero, and L. Pfister, 1988:
Heating rates in tropical anvils. J. Atmos. Sci., 45, 1606–1623.
Agee, E. M., 1975: Some inferences of eddy viscosity associated
with instabilities in the atmosphere. J. Atmos. Sci., 32, 642–646.
Alexander, M. J., J. R. Holton, and D. R. Durran, 1995: The grav-
ity wave response above deep convection in a squall line
simulation. J. Atmos. Sci., 52, 2212–2226.
Asai, T., 1970a: Three-dimensional features of thermal convection
in a plane Couette flow. J. Meteor. Soc. Japan, 48, 18–29.
——, 1970b: Stability of a plane parallel flow with variable vertical
shear and unstable stratification. J. Meteor. Soc. Japan, 48,
129–139.
Atlas, D., 1955: The origin of “stalactites”in precipitation echoes.
Proc. Fifth Radar Weather Conf., Asbury Park, NJ, U.S.
Army Signal Corps, 321–326.
Aufm Kampe, H. J., and H. K. Weickmann, 1957: Physics of
clouds. Meteorological Research Reviews: Summaries of
Progress from 1951 to 1955, Meteor. Monogr., No. 18, Amer.
Meteor. Soc., 182–225.
Balachandran, N. K., 1980: Gravity waves from thunderstorms.
Mon. Wea. Rev., 108, 804–816.
Bauman, G., 1927: Mammato-Formation an Cirren (Mammatus
formation on cirrus). Meteor. Z., 44, 420.
Beres, J. H., M. J. Alexander, and J. R. Holton, 2002: Effects of
tropospheric wind shear on the spectrum of convectively gen-
erated gravity waves. J. Atmos. Sci., 59, 1805–1824.
Berg, H., 1938: Mammatusbildungen (Mammatus developments).
Meteor. Z., 55, 283–287.
Berry, F. A., Jr., E. Bollay, and N. R. Beers, 1945: Handbook of
Meteorology. McGraw-Hill, 1068 pp.
Blanchard, D. C., 1996: Serendipity, scientific discovery, and Proj-
ect Cirrus. Bull. Amer. Meteor. Soc., 77, 1279–1286.
Bosart, L. F., and F. Sanders, 1991: An early-season coastal storm:
Conceptual success and model failure. Mon. Wea. Rev., 119,
2831–2851.
Byers, H. R., and R. D. Coons, 1947: The “bright line”in radar
cloud echoes and its probable explanation. J. Meteor., 4, 75–
81.
Chandrasekhar, S., 1961: Hydrodynamic and Hydromagnetic Sta-
bility. Oxford University Press, 654 pp.
Clark, T. L., and R. List, 1971: Dynamics of a falling particle zone.
J. Atmos. Sci., 28, 718–727.
Clarke, R. H., 1962: Pressure oscillations and fallout down-
draughts. Quart. J. Roy. Meteor. Soc., 88, 459–469.
Clayton, H. H., 1911: A study of clouds with data from kites.
Annal. Astron. Observatory Harvard Coll., 68, 170–192.
Clough, S. A., and R. A. A. Franks, 1991: The evaporation of
frontal and other stratiform precipitation. Quart. J. Roy. Me-
teor. Soc., 117, 1057–1080.
Deardorff, J. W., 1980: Cloud top entrainment instability. J. At-
mos. Sci., 37, 131–147.
Douglas, R. H., K. L. S. Gunn, and J. S. Marshall, 1957: Pattern in
the vertical of snow generation. J. Meteor., 14, 95–114.
Emanuel, K. A., 1981: A similarity theory for unsaturated down-
drafts within clouds. J. Atmos. Sci., 38, 1541–1557.
——, 1994: Atmospheric Convection. Oxford University Press, 580
pp.
Fernandez, W., 1982: A review of downdrafts at the rear of tropi-
cal squall lines. Bull. Amer. Meteor. Soc., 63, 1285–1293.
Findeisen, W., 1940: Die Entstehung der 0°-Isothermie und die
Fraktocumulus-Bildung unter Nimbostratus (The origin of
0°C isothermal layers and of fractocumulus beneath nimbos-
tratus). Meteor. Z., 57, 49–54.
Fovell, R., D. Durran, and J. R. Holton, 1992: Numerical simula-
tions of convectively generated stratospheric gravity waves. J.
Atmos. Sci., 49, 1427–1442.
OCTOBER 2006 REVIEW 2433

Fraser, A. B., and C. F. Bohren, 1992: Is virga rain that evaporates
before reaching the ground? Mon. Wea. Rev., 120, 1565–1571.
——, and ——, 1993: Viewing the vagaries and verities of virga.
Mon. Wea. Rev., 121, 2429–2430.
Garrett, T. J., and Coauthors, 2005: Evolution of a Florida cirrus
anvil. J. Atmos. Sci., 62, 2352–2372.
——, M. A. Zulauf, and S. K. Krueger, 2006: Effects of cirrus near
the troposphere on anvil cirrus dynamics. Geophys. Res.
Lett., 33, L17804, doi:10.1029/2006GL027071.
Gedzelman, S. D., 1989: Cloud classification before Luke How-
ard. Bull. Amer. Meteor. Soc., 70, 381–395.
Glickman, T. S., Ed., 2000: Glossary of Meteorology. 2d ed. Amer.
Meteor. Soc., 855 pp.
Gordon, B. A., 1995: Structure of precipitation fields in the strati-
form region of mesoscale convective systems as observed by
polarimetric radar. M.S. thesis, School of Meteorology, Uni-
versity of Oklahoma, 104 pp. [Available from School of Me-
teorology, University of Oklahoma, 100 East Boyd St., Suite
1310, Norman, OK 73019.]
——, D. S. Zrnic´, and J. Straka, 1995: Observations of mammata
with polarimetric Doppler radar. Preprints, 27th Conf. on
Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 461–463.
Gossard, E. E., 1975: Reply. J. Atmos. Sci., 32, 639–642.
——, and W. B. Sweezy, 1974: Dispersion and spectra of gravity
waves in the atmosphere. J. Atmos. Sci., 31, 1540–1548.
Grabowski, W. W., X. Wu, M. W. Moncrieff, and W. D. Hall,
1998: Cloud-resolving modeling of cloud systems during
Phase III of GATE. Part II: Effects of resolution and the
third spatial dimension. J. Atmos. Sci., 55, 3264–3282.
Gu, Y., W. I. Rose, D. J. Schneider, G. J. S. Bluth, and I. M.
Watson, 2005: Advantageous GOES IR results for ash map-
ping at high latitudes: Cleveland eruptions 2001. Geophys.
Res. Lett., 32, L02305, doi: 10.1029/2004GL021651.
Guo, S., W. I. Rose, G. J. S. Bluth, and I. M. Watson, 2004: Par-
ticles in the great Pinatubo volcanic cloud of June 1991: The
role of ice. Geochem. Geophys. Geosyst., 5, Q05003,
doi:10.1029/2003GC000655.
Harris, F. I., 1977: The effects of evaporation at the base of ice
precipitation layers: Theory and radar observations. J. At-
mos. Sci., 34, 651–672.
Hartmann, W., 1920: Über die Entstehung von Mamato-Formen
(About the origin of mammatusforms). Meteor. Z., 37, 216–
220.
Heymsfield, A. J., 1986: Ice particle evolution in the anvil of a
severe thunderstorm during CCOPE. J. Atmos. Sci., 43, 2463–
2478.
Hlad, C. J., Jr., 1944: Stability-tendency and mammatocumulus
clouds. Bull. Amer. Meteor. Soc., 25, 327–331.
Hobbs, P. V., L. F. Radke, M. W. Eltgroth, and D. A. Hegg, 1981:
Airborne studies of the emissions from the volcanic eruptions
of Mount St. Helens. Science, 211, 816–818.
——, J. P. Tuell, D. A. Hegg, L. F. Radke, and M. W. Eltgroth,
1982: Particles and gases in the emissions from the 1980–1981
volcanic eruptions of Mt. St. Helens. J. Geophys. Res., 87,
11 062–11 086.
——, L. F. Radke, J. H. Lyons, R. J. Ferek, D. J. Coffman, and
T. J. Casadevall, 1991: Airborne measurements of particle
and gas emissions from the 1990 volcanic eruptions of Mount
Redoubt. J. Geophys. Res., 96, 18 735–18 752.
Hodge, M. W., 1956: Superadiabatic lapse rates of temperature in
radiosonde observations. Mon. Wea. Rev., 84, 103–106.
Houze, R. A., Jr., S. A. Rutledge, M. I. Biggerstaff, and B. F.
Smull, 1989: Interpretation of Doppler weather radar dis-
plays of midlatitude mesoscale convective systems. Bull.
Amer. Meteor. Soc., 70, 608–619.
Hung, R. J., T. Phan, and R. E. Smith, 1979: Case studies of grav-
ity waves associated with isolated tornadic storms on 13 Janu-
ary 1976. J. Appl. Meteor., 18, 460–466.
Imai, I., 1957: Radar study of a dissipating thunderstorm. Pap.
Meteor. Geophys., 8, 81–97.
Jeffreys, H., 1928: Some cases of instability in fluid motion. Proc.
Roy. Soc. London, 118A, 195–208.
Jo, I., B. A. Albrecht, and P. Kollias, 2003: 94-GHz Doppler
radar observations of mammatus in tropical anvils during
CRYSTAL-FACE. Preprints, 31st Int. Conf. on Radar Me-
teorology, Seattle, WA, Amer. Meteor. Soc., 197–199.
Kain, J. S., S. M. Goss, and M. E. Baldwin, 2000: The melting
effect as a factor in precipitation-type forecasting. Wea. Fore-
casting, 15, 700–714.
Kanak, K. M., and J. M. Straka, 2002: An unusual reticular cloud
formation. Mon. Wea. Rev., 130, 416–421.
——, and ——, 2006: An idealized numerical simulation of mam-
matus-like clouds. Atmos. Sci. Lett., 7, 2–8.
Knight, C. A., L. J. Miller, and W. D. Hall, 2004: Deep convection
and “first echoes”within anvil precipitation. Mon. Wea. Rev.,
132, 1877–1890.
Kollias, P., I. Jo, and B. A. Albrecht, 2005: High-resolution ob-
servations of mammatus in tropical anvils. Mon. Wea. Rev.,
133, 2105–2112.
Kuo, H. L., 1963: Perturbations of plane Couette flow in stratified
fluid and origin of cloud streets. Phys. Fluids, 6, 195–211.
Letzmann, J., 1930: Cumulus-Pulsationen (Cumulus pulsations).
Meteor. Z., 47, 236–238.
Ley, W. C., 1894: Cloudland. Edward Stanford, 208 pp.
Lilly, D. K., 1988: Cirrus outflow dynamics. J. Atmos. Sci., 45,
1594–1605.
Ludlam, F. H., 1948: The forms of ice clouds. Quart. J. Roy. Me-
teor. Soc., 74, 39–56.
——, 1980: Clouds and Storms, the Behavior of Water in the At-
mosphere. Pennsylvania State University Press, 405 pp.
——, and R. S. Scorer, 1953: Convection in the atmosphere.
Quart. J. Roy. Meteor. Soc., 79, 317–341.
Martner, B. E., 1995: Doppler radar observations of mammatus.
Mon. Wea. Rev., 123, 3115–3121.
——, 1996: An intimate look at clouds. Weatherwise, 49 (3), 20–23.
Ooyama, K. V., 2001: A dynamic and thermodynamic foundation
for modeling the moist atmosphere with parameterized mi-
crophysics. J. Atmos. Sci., 58, 2073–2102.
Osthoff, H., 1906: Der Mammato-Cumulus (The mammatocumu-
lus). Meteor. Z., 23, 401–408.
Pandya, R. E., and D. R. Durran, 1996: The influence of convec-
tively generated thermal forcing on the mesoscale circulation
around squall lines. J. Atmos. Sci., 53, 2924–2951.
Pasquill, F., 1962: Atmospheric Diffusion: The Dispersion of
Windborne Material from Industrial and Other Sources. Van
Nostrand, 297 pp.
Petre, J. M., and J. Verlinde, 2004: Cloud radar observations of
Kelvin–Helmholtz instability in a Florida anvil. Mon. Wea.
Rev., 132, 2520–2523.
Plank, V. G., D. Atlas, and W. H. Paulsen, 1955: The nature and
detectability of clouds and precipitation as determined by
1.25-centimeter radar. J. Meteor., 12, 358–378.
Platt, C. M. R., R. T. Austin, S. A. Young, and A. J. Heymsfield,
2002: LIRAD observations of tropical cirrus clouds in
MCTEX. Part II: Optical properties and base cooling in dis-
sipating storm anvil clouds. J. Atmos. Sci., 59, 3163–3177.
2434 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63

Pruppacher, H. R., and J. D. Klett, 1997: Microphysics of Clouds
and Precipitation. 2d ed. Kluwer Academic, 348 pp.
Quante, M., G. Teschke, M. Zhariy, P. Maaß, and K. Sassen, 2002:
Extraction and analysis of structural features in cloud radar
and lidar data using wavelet based methods. Proc. European
Radar Conf., Delft, Netherlands, Eur. Meteor. Soc., 95–103.
Randall, D. A., 1980: Conditional instability of the first kind up-
side-down. J. Atmos. Sci., 37, 125–130.
Rayleigh, L., 1883: Investigation of the character of the equilib-
rium of an incompressible heavy fluid of variable density.
Proc. London Math. Soc., 14, 170–177.
Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud
Physics. 3d ed. Pergamon Press, 293 pp.
Rose, W. I., and Coauthors, 1995: Ice in the 1994 Rabaul eruption
cloud: Implications for volcano hazard and atmospheric ef-
fects. Nature, 375, 477–479.
——, G. J. S. Bluth, D. J. Schneider, G. G. J. Ernst, C. M. Riley,
and R. G. McGimsey, 2001: Observations of 1992 Crater
Peak/Spurr volcanic clouds in their first few days of atmo-
spheric residence. J. Geol., 109, 677–694.
——, and Coauthors, 2003: The February–March 2000 eruption of
Hekla, Iceland from a satellite perspective. Volcanism and
the Earth’s Atmosphere, Geophys. Monogr., No. 139, Amer.
Geophys. Union, 107–132.
——, G. J. S. Bluth, and I. M. Watson, 2004: Ice in volcanic clouds:
When and where? Proc. Second Int. Conf. on Volcanic Ash
and Aviation Safety, OFCM, Washington, DC, 27–33.
Rust, W. D., R. Davies-Jones, D. W. Burgess, R. A. Maddox,
L. C. Showell, T. C. Marshall, and D. K. Lauritsen, 1990:
Testing a mobile version of a cross-chain loran atmospheric
sounding system (M-CLASS). Bull. Amer. Meteor. Soc., 71,
173–180.
Sassen, K., 2002: Cirrus clouds: A modern perspective. Cirrus. D.
K. Lynch et al., Eds., Oxford University Press, 11–40 (text),
458–468 (figures).
——, and S. K. Krueger, 1993: Toward an empirical definition of
virga: Comments on “Is virga rain that evaporates before
reaching the ground?”Mon. Wea. Rev., 121, 2426–2428.
——, and Coauthors, 1995: The 5–6 December 1991 FIRE IFO II
jet stream cirrus case study: Possible influences of volcanic
aerosols. J. Atmos. Sci., 52, 97–123.
——, J. M. Comstock, Z. Wang, and G. G. Mace, 2001: Cloud and
aerosol research capabilities at FARS: The Facility for At-
mospheric Remote Sensing. Bull. Amer. Meteor. Soc., 82,
1119–1138.
Schaefer, V. J., and J. A. Day, 1981: A Field Guide to the Atmo-
sphere. Houghton Mifflin Co., 359 pp.
Schlatter, T., 1985: Mammatus clouds, sheltered thermometers.
Weatherwise, 38, 216–217.
Schmauss, A., 1913: Der Mammatocumulus—Ein Beleuchtungs-
effekt? (The mammatocumulus—An illumination effect?)
Meteor. Z., 30, 188–189.
Schneider, D. J., W. I. Rose, L. R. Coke, G. J. S. Bluth, I. E.
Sprod, and A. J. Krueger, 1999: Early evolution of a strato-
spheric volcanic eruption cloud as observed with TOMS and
AVHRR. J. Geophys. Res., 104, 4037–4050.
Schneider, K., 1920: Die Inversion an der Basis von Stratus Mam-
matus (The inversion at the base of stratus mammatus). Me-
teor. Z., 37, 137–139.
Schröder, F., and Coauthors, 2000: On the transition of contrails
into cirrus clouds. J. Atmos. Sci., 57, 464–480.
Schultz, D. M., and R. J. Trapp, 2003: Nonclassical cold-frontal
structure caused by dry subcloud air in northern Utah during
the Intermountain Precipitation Experiment (IPEX). Mon.
Wea. Rev., 131, 2222–2246.
——, and Coauthors, 2002: Understanding Utah winter storms:
The Intermountain Precipitation Experiment. Bull. Amer.
Meteor. Soc., 83, 189–210.
Scorer, R. S., 1958: The dynamics of mamma. Sci. Prog., 46, 75–82.
——, 1972: Clouds of the World. Stackpole Books, 176 pp.
Sharp, D. H., 1984: An overview of Rayleigh–Taylor instability.
Physica D, 12, 3–18.
Slonaker, R. L., B. E. Schwartz, and W. J. Emery, 1996: Occur-
rence of nonsurface superadiabatic lapse rates within RAOB
data. Wea. Forecasting, 11, 350–359.
Stewart, R. E., 1984: Deep 0°C isothermal layers within precipi-
tation bands over southern Ontario. J. Geophys. Res., 89,
2567–2572.
Stith, J. L., 1995: In situ measurements and observations of cumu-
lonimbus mamma. Mon. Wea. Rev., 123, 907–914.
Straka, J. M., D. S. Zrnic´, and A. V. Ryzhkov, 2000: Bulk hydrom-
eteor classification and quantification using polarimetric ra-
dar data: Synthesis of relations. J. Appl. Meteor., 39, 1341–
1372.
Taylor, G., 1950: The instability of liquid surfaces when acceler-
ated in a direction perpendicular to their planes. Proc. Roy.
Soc. London, A201, 192–196.
Troeger, H., 1921: Sonnenring und Stratus Mammatus (Sun ring
and stratus mammatus). Das Wetter, 38, 190.
——, 1922: Die Häufigkeit der Mammatus-Formen (The fre-
quency of the mammatus). Meteor. Z., 39, 122–123.
Wagner, F., 1948: Mammatusform als Anzeichen für Absinkbe-
wegung in Wolkenluft (The shape of mammatus as an indi-
cator for subsidence in cloudy air). Ann. Meteor., 1, 336–340.
Wang, L., and K. Sassen, 2006: Cirrus mammatus properties de-
rived from an extended remote sensing dataset. J. Atmos.
Sci., 63, 712–725.
Warner, C., 1973: Measurements of mamma. Weather, 28, 394–
397.
Wegener, A., 1909: Zur Entstehung des Cumulus Mammatus
(About the formation of cumulus mammatus). Meteor. Z., 26,
473–474.
Winstead, N. S., J. Verlinde, S. T. Arthur, F. Jaskiewicz, M.
Jensen, N. Miles, and D. Nicosia, 2001: High-resolution air-
borne radar observations of mammatus. Mon. Wea. Rev., 129,
159–166.
Wurman, J., J. Straka, E. Rasmussen, M. Randall, and A. Zahrai,
1997: Design and deployment of a portable, pencil-beam,
pulsed, 3-cm Doppler radar. J. Atmos. Oceanic Technol., 14,
1502–1512.
Yang, M.-J., and R. A. Houze Jr., 1995: Multicell squall-line struc-
ture as a manifestation of vertically trapped gravity waves.
Mon. Wea. Rev., 123, 641–661.
Zahrai, A., and D. S. Zrnic´, 1993: The 10-cm-wavelength polari-
metric weather radar at NOAA’s National Severe Storms
Laboratory. J. Atmos. Oceanic Technol., 10, 649–662.
Zrnic´, D. S., N. Balakrishnan, C. L. Ziegler, V. N. Bringi, K. Ay-
din, and T. Matejka, 1993: Polarimetric signatures in the
stratiform region of a mesoscale convective system. J. Appl.
Meteor., 32, 678–693.
OCTOBER 2006 REVIEW 2435