Earth

Atmospheric Circulations

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 Video Productions).

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 101).

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 radiation).

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

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

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, 1966; 1973).

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).

The 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 and Delory).

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 possible value).

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).

Waterspouts

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 (Photographer unknown).

Tornadoes

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

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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