Earth is the third planet from the Sun at a distance of about 150 million
km. It has a diameter of about 12,756km, only a few hundred kilometers
larger than that of Venus. The Earth is the only planet in the solar
system known to harbor life. Its large rotation rate and molten nickel-iron
core gives rise to a strong magnetic field that with the atmosphere, shields
us from nearly all of the harmful radiation coming from the Sun and other
stars. The Earth’s atmosphere protects us from meteors, most
of which burn up before reaching the surface.
We have learned a lot about the Earth from space exploration. Explorer
1, the first US satellite discovered that the Earth has an intense radiation
zone, called the Van Allen radiation belts. These radiation belts
are formed from rapidly moving charged particles trapped by the Earth’s
magnetic field in a doughnut-shaped region surrounding the equator. Measurements
made by other satellites showed that the Earth’s magnetic field is
distorted into a tear-drop shape by the solar wind. They also showed
that our thin upper atmosphere is very active, swelling by day and contracting
by night and is strongly affected by solar activity.
Comparative atmospheric science provides a powerful tool
for the understanding of the atmosphere of the Earth and other planets.
It gives a sense of perspective to investigations of the evolution of the
Earth’s atmosphere, global climate change, atmospheric chemistry,
atmospheric convection, and atmospheric dynamics. Our group uses simple
analytical tools to quantitatively study atmospheric circulations and weather
systems on Earth and other planets. We focus on comparative studies of
atmospheric circulations and weather systems ranging from small scale such
as terrestrial dust devils to global scales such as the Earth’s general
circulation (see Figures 1, 2, 3, 4, and 5).
Figure 1. Sketch of the Earth’s general circulation (Courtesy of
Figure 2. Rossby waves at the boundary between polar and mid-latidude
air masses or polar front (Courtesy of The Science of Weather on Suite
Figure 3. Image of hurricane Andrew on 25 August 1992 (Courtesy of NASA/GSFC).
Figure 4. Image of Jupiter clouds showing the Great Red Spot and many
other weather systems (Courtesy of NASA/JPL).
The general circulation describes the basic features of
a planet’s atmosphere (see Figure 1). The Earth’s general circulation
explains the easterly trade winds in tropical and subtropical latitudes,
the westerlies in mid-latitudes, the weaker easterlies near the poles,
the changes in these zonal winds with height, and the meridional circulations
associated with them. In 1735 Hadley proposed that differential solar heating
between the equator and the poles forces the Earth’s general circulation.
It follows from the basic laws of thermodynamics that for a meridional
circulation to do the work that maintains it against friction; warm air
must rise in equatorial regions and sink at higher and colder latitudes.
Conservation of angular momentum causes low level air flowing from mid-latitudes
to the equator to turn towards the west (easterly winds), and upper level
air flowing from the equator to mid-latitudes to turn towards the east
(westerly winds). The westerly winds form an upper level subtropical jet
in mid-latitudes. The descending branch of the meridional circulation transfers
momentum from this westerly jet to lower levels, creating the mid-latitude
westerlies. In steady state, the net torque between the atmosphere and
the surface must be zero. Therefore, the torques produced by the tropical
easterlies must be balanced by that produced by the mid-latitude westerlies.
Traveling mid-latitude cyclones and anticyclones, as well
as other mid-latitude and tropical weather systems are essential features
of the Earth’s general circulation. In 1926 Jeffreys showed that
time-dependent disturbances or weather systems play a fundamental role
in the Earth’s general circulation. He argued that the turbulent
eddy flux produced by these weather systems produces the necessary momentum
transport that maintains the general circulation against viscous friction.
Later Bjerknes pointed that the general circulation is unstable and that
its instability generates weather systems such as the cyclones or baroclinic
waves shown in Figure 2. The hurricane illustrated in Figure 3 is also
an example of weather system generated by instabilities of large scale
circulations. However, the growth of hurricanes is driven by interactions
between the ocean and the atmosphere. Bjerknes’ idea that weather
systems are generated by instabilities of the mean flow gave rise to many
studies of the instability of basic state flows to small perturbations.
Perhaps, the most important of these studies was that of the stability
of zonal flows to small perturbations; that is, studies of baroclinic instability.
Baroclinic instability is favored by large rotation rate, large meridional
temperature gradient, and low static stability. It produces global traveling
waves with 4 to 8 complete cycles encircling the globe in mid-latitudes.
Frequently, weather maps show these weather patterns (see Figure 2). Many
other types of instabilities occur in planetary atmospheres and give rise
to a variety of weather phenomena such as terrestrial hurricanes and polar
lows, the Jovian Great Red Spot and ovals (see Figure 4), and Martian and
terrestrial dust devils and dust storms (see Figures 5 and 6). Our group
studies these planetary weather systems and many interesting physical processes
associated with them, such as electrical activity, non-thermal radiation,
and dust transport in Terrestrial and Martian dust devils and dust storms
(Link to video of a terrestrial dust devil producing non-thermal microwave
Figure 5. Dust devils near the boundary between irrigated and dry fields.
When the wind is light they tend to come in pairs and move over the warmer
terrain, but along the boundary between the two fields (Link to dust devil
movies, including various animations of dust devil formation).
Weather systems range from small scale phenomena such as dust devils to
global circulations such as the Hadley circulation. They are limited by
diffusive processes on the small end of the scale, and by the size of the
planet on the large end. Here, we briefly review these systems with focus
on a non-mathematical description of their basic physics. A detailed mathematical
description of them can be found on the various PowerPoint presentations
linked to the text and the references given on them.
Dust devils are low-pressure, warm-core vortices with typical surface
diameters between 1 and 10 m. Since they receive their vorticity from local
wind shears that can be either due to the convective circulation itself
or due to larger scale phenomena, they rotate either cyclonically or anticyclonically
with equal probability (Williams 1948, Sinclair, 1966; Ryan and Carroll,
1970; Carroll and Ryan, 1970). Dust devils are more frequently observed
in hot desert regions, although they have been observed in colder regions
such as the sub artic (Wegener, 1914; Grant, 1949). To a first approximation,
a dust devil moves with the speed of the ambient wind, typically between
1 and 10 m/s. In general, dust devils slope with height in the wind shear
direction. In environments of high wind speed, dust devil diameters are
biased toward large values. About 55% of the dust devils observed around
Tucson (Arizona) have diameters between 3 and 15 m, and 15% have diameters
larger than 15 m (Sinclair, 1966; 1969; 1973).
In a typical dust devil, near-surface warm air parcels spiral in toward
its center while absorbing heat from the surface. Over deserts, the typical
temperature and pressure perturbation observed within dust devils varies
from 4 to 8 K and from 2.5 to 4.5 hPa (Sinclair, 1973). The vertical velocity
reaches positive peak values in the region of maximum temperature. A weaker
and cooler downdraft, in nearly solid body rotation, is present in the
dust devil core (Sinclair, 1966; 1973; Kaimal and Businger, 1970). The
near-surface vertical velocity reaches peak values of about 15 m/s (Sinclair,
1973; Ives, 1947). Weak thermal updrafts and small dust devils are frequently
observed in the wake of larger dust devils. The low-level tangential velocity
also reaches peak values of about 15 m/s, while the near-surface radial
velocity usually does not exceed 5 m/s. The radial velocity reaches its
peak value outside the region of maximum tangential and vertical velocities
(Sinclair, 1973). Indeed, the radial velocity nearly vanishes in the region
of maximum tangential wind. Moreover, since dust devils are warm-core vortices,
the pressure perturbation and therefore the tangential velocity reach peak
values a few meters above the ground and rapidly decrease with height.
In fact, in typical dust devils they nearly vanish just a few hundred meters
above the surface.
Dust devils have tangential velocity profiles characteristic of a Rankine
vortex. That is, their core is in solid body rotation (the wind speed is
proportional to the distance from its center) and angular momentum is approximately
conserved outside their radius of maximum wind (the wind speed is inversely
proportional to the distance from the dust devil center). To a first approximation,
above the surface the tangential winds are in cyclostrophic balance. However,
since there is a radial inflow of air toward their center, the observed
pressure gradients are larger than those necessary to support cyclostrophic
tangential winds (Sinclair, 1973). Substantial mixing and expansion of
the dust devil vortex occurs near the surface. Warm, near-surface air moves
horizontally toward the low-pressure center until it reaches the dust column.
Then, it rises rapidly. Within the dust column, the radial velocity nearly
vanishes. The presence of dust particles in the dust devil inner core is
suppressed by both a descending motion and centrifugal forces (Sinclair,
There is mounting evidence that dust devils form at the
bottom of convective plumes (Battan, 1958; Sinclair, 1966; Ryan and Carroll,
1970). The radial inflow of near surface warm air into the rising plume
results in the concentration of ambient vorticity and may lead to the establishment
of a weak vortex. As the convective plume rises to higher altitudes, the
pressure depression at its base increases. This low-pressure center near
the surface forces a spiral inflow of warm boundary layer air into the
incipient dust devil. (Surface friction plays an important role in forcing
this near-surface convergence of warm air). When the surface is composed
of loose materials, dust particles might become airborne making the dust
devil visible. However, when loose materials are not present, intense vortices
may exist and not be visible to the observer. The intensity of a dust devil
depends on the depth of the convective plume and the existence of local
wind shears. When a dust devil crosses cold terrain, the dust column is
cut off, and the convective plume quickly dissipates (Sinclair, 1973).
height of the dust column of a dust devil rarely exceeds 1 km.
However, the thermal updraft above dust devils (their invisible part) usually
extends to the top of the convective layer. In the summertime, the convective
boundary layer usually extends to more than 3 km above the ground over
desert regions. Dust devil occurrence increases abruptly from nearly zero
at around 10:00 MST to its maximum value at around 13:00 Local Solar Time
(Sinclair, 1969; Flower, 1936; Williams, 1948). Then, the dust devil activity
slowly decreases as the afternoon progresses. In this study, we present
a simple physical explanation for this distribution and for the potential
intensity of dust devils. In contrast to terrestrial dust devils that have
typical diameters of less than10 m and are seldom higher than a few 100
m (Sinclair, 1973), Martian dust devils have diameters between 100 m and
1 km are up to 10 km tall (Thomas and Gierasch, 1986; Malin et al., 1999).
However, even small terrestrial dust devils can be dangerous to aviation.
There are reports that up to 10% of the accidents with light aircrafts,
sailplanes, helicopters, and blimps are caused by wind gusts associated
with dry convection and dust devils (Spillane and Hess, 1988). Charged
dust particles produce electrical fields in excess of 40,000 V/m in terrestrial
dust devils. Martian dust devils have higher dust content and may produce
even stronger electrical fields. The dust devils observed in the Pathfinder
images have about 700 times the dust content of the local background atmosphere
(Metzger et al., 1999). Thus, electrically charged Martian dust devils and
dust storms are potentially hazards to Landers and will be dangerous to future
astronauts exploring its surface. Indeed, the design of adequate mechanical
and electrical systems for these Landers cannot progress effectively without
a better understanding of Martian dust devils and dust storms. Ancillary
phenomena associated with electrically charged vortices can ionize atmospheric
gases and might have important implications for the chemistry of the Martian
soil and atmosphere (see Figure 7). Electric field gradients of the order
of those observed in terrestrial dust devils (see Figure 8) are expected
in Martian dust devils and dust storms. Atreya et al. (2005) and Delory
et al. (2005) show these electric fields can ionize the Martian atmosphere
and lead to interesting chemical reactions that can produce large quantities
of hydrogen peroxide. This might lead to the settling of “hydrogen peroxide dust" into
the surface of Mars.
Figure 6. Sketch of convective vortices indicating that Martian dust devils
are much larger than terrestrial dust devils and tornadoes (Courtesy NASA/JPL).
Figure 7. Artistic conception of a glowing Martian dust devil. Renno et
al. (2003) suggests that microdischarges (sparks) occurs near the surface,
where sand and dust particles collide with each other. Renno et al. (2004)
showed that the bulk electric field observed in terrestrial dust devils
is consistent with this idea (Link to electrical dust devil movie).
Figure 8. Electric field during the passage of a dust devil. The electric
field gradients observed in terrestrial dust devils are strong enough to
produce glow discharges in the Martian atmosphere (Courtesy of Farrell
In order for a convective vortex such as a dust devil to form, both thermodynamical
processes responsible for maintaining a pressure depression and dynamical
processes capable of producing vorticity must be present. Many dynamical
processes are capable of producing and enhancing vertical vorticity in
convective systems. In particular, the convective plume itself can generate
the vorticity. The vorticity generating processes have been extensively
studied in the atmospheric science literature (Lilly, 1982; Davies-Jones,
1984; Rotunno and Klemp, 1985; Fiedler and Rotunno, 1986; Simpson et al.,
1986; Bluestein et al., 2004). In this review, we focus on the thermodynamics
of the convective process responsible for the maintenance of the pressure
depression within convective vortices.
It follows from theoretical models (see Renno et al., 1998) that the intensity
of dust devils depends on the surface air temperature increase from the local
environment towards the center of the vortex. The daytime surface air temperature
over a desert is regulated mainly by sensible heat flux from the ground into
the surface air. The sensible heat flux, in turn, is proportional to the difference
between the ground temperature and the surface air temperature (see the bulk
aerodynamic formula). Therefore, the ground temperature provides an upper bound
(through the second law of thermodynamics) for the temperature at the center
of a dust devil (assuming an equal mass contribution from warmer and colder
air parcels, strong mixing near the surface reduces the difference between
the center air temperature and the ground temperature to about 50% of its maximum
Large increases in air temperature are likely to occur when air parcels
sitting over relatively cold terrain move towards warmer surfaces. Therefore,
dust devils are more likely to form in regions of larger horizontal temperature
gradients (within the dust devil inflow region, about 100 m) than in regions
of smaller temperature gradients. This idea is supported by the observation
of a local maximum of dust devil occurrence near dry washes (Sinclair,
1966) and over dry fields downwind of irrigated fields (personal communication
by Gary Osoba, 1997). Moreover, it is supported by the occasional observation
of dust devils in the French countryside, during the summer, over warm
fields with cooler surroundings (Georgii, 1952). Obviously, we are making
the hypothesis that the observation of larger dust devil occurrence near
dry washes is due to temperature contrasts between areas of sandy soil
and areas covered by vegetation, which frequently occur around dry washes.
However, a large quantity of dust near dry washes would potentially make
visible dust devils that would elsewhere be invisible. Our hypothesis is
supported by observations that dust devil occurrence is not as frequent
in plain deserts covered by loose materials as it is near dry washes (Link
to PowerPoint presentation on a theory for convective vortices).
Dust devils and waterspouts are not only of exceptional natural beauty, but
also of great scientific interest. They are of particular meteorological
interest because they might be thermodynamically similar to tornadoes and
hurricanes, the most destructives storms observed on Earth. Therefore, the
theoretical understanding of these smaller and weaker convective vortices
has the potential to further our understanding of their larger and violent
cousins. Since dust devils and waterspouts are relatively frequent, small,
and weak, they allow safer and more efficient in situ measurements. Convective
vortices are all low-pressure warm-core vortices with radius of maximum wind
varying between about 1 m (dust devils) and 25km (hurricanes). Here, we focus
on the study of waterspouts, which cover a wide range of sizes and intensities
(see Figures 9 and 10).
Golden (1968, 1971, 1973, 1974a, b, 1977), Leverson et al. (1977), Simpson
et al. (1986), and Wakimoto and Lew (1993) describe the characteristics
of waterspouts in detail. Here we briefly review some of their findings.
Hundreds of waterspouts are observed each summer around the Florida Keys,
and a small number over the open oceans. Waterspouts usually have surface
diameters between 5 and 75 m. Like their smaller cousins, dust devils,
they receive their vorticity from local wind shear. Therefore, they rotate
either cyclonically or anticyclonically (Golden, 1974a; Schwiesow, 1981).
Near the surface, air parcels absorb heat from the surface as they spiral
in toward the waterspout and become warmer and moister than the ambient
air. The temperature and pressure perturbations observed within waterspouts
vary from 0.2 to 2.5 K and from 10 to 90 hPa (Golden, 1974a; Leverson et
al., 1977). The vertical velocity reaches positive peak values of about
10 m/s in the region of highest temperature. In the waterspout there is
solid-body rotation and a weak forced downdraft in its core (Golden, 1974a).
A more intense rain-cooled downdraft is frequently observed near the waterspout.
A waterspout's low level tangential velocity can reach peak values of about
80 m/s (Golden, 1974a, Schwiesow, 1981).
To a first approximation, the tangential winds of waterspouts are in cyclostrophic
balance. However, since near the surface there is a radial inflow of air
toward their center, the observed pressure gradients are slightly larger
than those necessary to support the cyclostrophic tangential winds. Like
dust devils, waterspouts have tangential velocity profiles characteristic
of a Rankine vortex. That is, near their center the tangential velocity
is proportional to the radius; from there it decreases inversely proportional
to it. Waterspouts usually form under convective clouds deeper than about
4 km (Golden, 1974a). They usually originate in regions of horizontal wind
shear between updrafts and downdrafts (Golden, 1974a; Hess and Spillane,
1990). Moreover, the observations suggest that the existence of these local
horizontal shear lines (vertical vorticity) separating the updrafts from
the downdrafts is a necessary, but not sufficient condition for waterspout
formation (Simpson et al., 1986). It is important to point out that these
shear lines can be generated by the convective system itself (see Simpson
et al., 1991).
Golden (1974a) identified the dark spot as the initial stage of a waterspout
formation –the dark spot is caused by wind stress on the ocean surface.
Initially, air parcels moving toward the convective plume absorb sensible
and latent heat from the ocean while the vortex intensifies. During the
dark spot stage, the vortex tangential windspeed reaches approximately
10 m/s. The plume's intensification, in turn, produces an increase in the
surface heat flux. This positive feedback continues unabated until the
vortex reaches the maximum potential intensity predicted by thermodynamics
or until it is disrupted by other means. Golden (1974a, b) observed that
the majority of waterspouts do not evolve past this first stage. He suggests
that this occurs because the incipient vortices are disrupted by either
cool outflows from nearby showers or downdrafts from the parent cloud.
It has been suggested by Golden that the source of vorticity for the waterspout
vortex is the wind shear between the warm updraft inflow and the rain-cooled
downdraft outflow. This idea is supported by the observations that waterspouts
generally form over warm waters, close to their boundary with colder waters
(Golden, 1974b; Peterson, 1978; Simpson et al., 1986). However, frequently
a rain-cooled downdraft outflow cuts off the source of warm air, and the
waterspout decays. Golden (1974a) observes that most waterspouts do not
intensify past the spray ring stage, which corresponds to a tangential
windspeed of about 20 m/s. These vortices are classified by Golden as weak
waterspouts. Renno and Bluestein (2001) propose that most waterspouts do
not intensify past the weak stage because the spray evaporation provides
a negative feedback by cooling the updraft air. In cases where the convective
heat engine is potentially powerful, however, the condensation funnel may
reach down the surface shortly after the spray ring forms. The saturation
of the near-surface air then nullifies the negative feedback by suppressing
the spray evaporation. These waterspouts are then capable of intensifying
until they either reach their full potential intensity or until they are
destroyed by some other mechanism. The idea that most waterspouts do not
intensify past the weak stage because of sea spray evaporation is supported
by the following observations: (i) The evaporation of water can potentially
cool the air down to its wet-bulb temperature; (ii) The convective updrafts
are at most a few degrees K warmer than the ambient air; (iii) Over the
tropical oceans the wet bulb temperature of the near-surface air is, in
general, a few degrees K lower than its temperature.
Figure 9. A waterspouts near a shear-line. Note the near surface air spiraling
in towards the waterspout (Courtesy of NOAA).
Figure 10. Waterspout of tornadic intensity near the coast of Australia
Tornadoes and waterspouts are produced by either, non-rotating thunderstorms
in the presence of low-level ``gyratory wind fields’’ (Wakimoto
and Wilson, 1989), or under rotating severe thunderstorms. The most intense
and long-lived tornadoes form under these rotating thunderstorms known as
supercells. This special type of thunderstorm forms in the presence of strong
ambient windshear (changes in windspeed and/or direction with height). Data
from radar and numerical simulations show that intense tornadoes are associated
with regions of large reflectivity that travel to the right of the winds
of the cloud-bearing layer. Rotation is deduced from surface observations
and the presence of a ``hook’’ echo.
The idea that strong, long-lived, tornadoes are produced by a special
type of thunderstorm called ``supercell’’ was first proposed
by Browning (1964). His idea was that longevity is achieved by a special
airflow pattern that allows the updraft to unload its rain without disrupting
the storm’s updraft inflow. This airflow is consistent with the preferential
growth of right moving thunderstorms. Tornadoes form at the storms’ micro
front (the boundary between warm updraft and cold downdraft air masses).
Klemp and Wilhelmson (1978a, b) used numerical modeling to show that the
supercell flow structure is acquired during the cell splitting. Indeed,
they showed that a curved hodograph (horizontal component of the wind plotted
as a function of height) favors the growth of right moving supercell thunderstorms.
Figure 11. Numerical simulation of a severe thunderstorm with a tornado.
The larger grey surface depicts the thunderstorm cloud. The colored contour
lines represent rapidly rising or sinking air that is associated with the
storm (Courtesy of Wicker and Wilhelmson).
Figure 12. Numerical simulation of a line of non-severe thunderstorms
with tornadoes. The deep convective clouds are rendered in a cyan color.
The tornadic circulations having high values of vertical vorticity are
represented by the yellow isosurfaces. The blue surface at the model domain
base depicts the surface outflow boundary (Courtesy of Wicker and Wilhelmson).
Dust storms frequently occur over deserts and regions of dry soil, where dust
and sand are loosely bound to the surface. Saltation is the mechanism by
which dust is lifted from a planet's surface (Bagnold, 1941). By way of this
mechanism, sand grains move in a skipping motion that propels dust particles
a few microns in diameter into the air. Bagnold's study allows the computation
of the minimum friction windspeed necessary to initiate saltation. On Earth,
free-stream windspeeds of about 10 m/s are sufficient to produce saltation,
while on Mars windspeeds in excess of 40 m/s are necessary. During saltation,
grains of sand lofted into the air fall back to the ground, but smaller particles
remain suspended in the air for a week or more and can be swept thousands
of kilometers downwind. Dust from the Sahara desert regularly crosses the
Atlantic Ocean, causing bright red sunrises and sunsets in Miami, traveling
as far as the Caribbean and the Amazon basin. Airborne dust particles can
be dangerous to aviation and automobiles and they alter the climate by intercepting
sunlight. Thus, it is important to understand the processes that cause dust
storms on Earth and other planets.
Figure 13. Dust storm during the spring of 1999 (Courtesy of NOAA).
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