On December 6, 2010, I saw an unusual “comet tail” cloud over Phoenix, Arizona, at about 8:30 a.m. and had to grab a camera and take pictures, as I've never seen anything like this before. The head of the “comet” was to the west and the tail to the east. The sky was partly cloudy, with cirrocumulus and altocumulus mostly to the south of this cloud. The upper altitude winds must have been blowing at high speed, because this cloud moved quickly across the sky, elongating as it went. I wonder if high-flying aircraft had anything to with this cloud's formation, because 30 minutes later I saw a similar cloud in the same part of the sky. It, too, moved east while, at the same time, the first cloud I had seen was still visible over the eastern horizon.
Caption: A plume of cirrus emanating from a supercooled cloud, likely caused when an aircraft penetrated the supercooled cloud and generated ice crystals spontaneously.
You are probably right in suggesting that aircraft contributed to the formation of this unusual cloud. How this might happen makes for an interesting story. I checked the upper air weather charts, and the temperature and moisture profiles at the closest rawinsonde station, Tucson, about 115 miles southeast of Phoenix. All profiles were available at 5:00 a.m. local time on December 6, 2010. There was a moist layer in the atmosphere above an altitude of about 7,100 meters (23,300 feet). At the base of the moist layer, the temperature was −20.5°C, the dewpoint was −26.5°C, and the wind was blowing from 256° (west-southwest) at 63 knots.
From these data and your photos, one of which is shown here, the evidence is strong that a cloud of tiny supercooled droplets existed near the base of the moist layer. Supercooled droplets (liquid at subfreezing temperatures) are common in stratiform clouds from 0°C down to −20°C, but ice crystals become more common as the temperature falls still lower. By −40°C, all cloud particles are ice. Why should this be so?
Ice nuclei are microscopically tiny solid particles in the atmosphere, upon which vapor can condense to form an ice crystal. Ice nuclei play another role. If they come in contact with supercooled droplets, they can cause freezing. Different ice nuclei cause freezing at different temperatures. Thus, an ice nucleus that becomes active at −15°C would not cause a cloud droplet to freeze if the air temperature were −10°, but it certainly would if the temperature were −20°C. An ice crystal itself is the perfect ice nucleus. If it touches a supercooled droplet at any temperature below 0°, the droplet will freeze. At a temperature of −40°C, water droplets freeze spontaneously, and the presence or absence of ice nuclei becomes irrelevant. Below −40°C, only ice crystals exist, and these make up cirrus clouds.
Ice nuclei are almost always in short supply. There are many more supercooled droplets than ice nuclei, and this accounts for the fact that liquid cloud droplets abound at subfreezing temperatures. Because more ice nuclei become active as the temperature drops, the probability of finding ice crystals in a supercooled cloud rises at the same time.
Following the evidence, suppose the existence of a thin, supercooled cloud at a temperature between −20°C and −25°C. A propeller-driven plane or a jet taking off from Phoenix pokes through this cloud layer. What happens? Aerodynamic calculations indicate that the average pressure difference between the upper and lower surfaces of the wing of a jet aircraft is about 50 millibars. As air passes roughly two meters above the wing, the pressure drops, and this sudden expansion of the air causes cooling of more than 20°C. For a split second, the air temperature experienced by supercooled water droplets is less than −40°C, and they freeze instantly. Similarly, the cooling behind the tips of propellers can be even more than that over the wing of a jet aircraft, with the same result: production of ice particles.
The disturbed air warms up after the aircraft passes through, but the ice crystals persist. Why? The supercooled droplets and the vapor in the cloud were probably near an equilibrium state before the passage of the aircraft, which is to say that about the same number of water molecules were entering the vapor state from the surface of the droplets as were arriving on the surface and condensing from the air. Under this condition, the water molecules in the air exert what is called an equilibrium vapor pressure. At, say, −21°C, the equilibrium vapor pressure in a supercooled water droplet cloud is 1.16 millibars. If passage of an aircraft suddenly creates ice crystals, the situation changes. The equilibrium vapor pressure for an ice crystal is only 0.94 millibars, but the vapor pressure in the supercooled cloud is 1.16 mb. The pressure difference causes water vapor to migrate toward the ice crystal, spurring growth. The loss of water molecules in the transition from vapor to ice lowers the vapor pressure in the cloud to below the equilibrium value for the supercooled droplets so that they begin to evaporate. This process leads to the growth of ice crystals at the expense of water droplets. Explained first by Tor Bergeron and W. Findeisen in the 1930s, this process bears their name.
Because of the plentiful supply of vapor in the supercooled cloud, the ice crystals continue to grow. An ice crystal contacting a droplet will cause it to freeze and may collect it as well. The crystals usually become large enough to fall out of the cloud. If they fall to an altitude where the wind is different from that in the cloud (vertical shear), they may be swept into spreading, fibrous streamers, as in the photograph. Eventually, the streamers evaporate in drier air below the supercooled cloud, but they often persist for 30 minutes or more.
One other striking feature, not illustrated in the photo, can develop if the supercooled cloud is thin enough and the ice crystal production caused by the passing aircraft is great enough. The change of phase from liquid to ice is a source of heating. For every gram of liquid converted to ice, 334 joules of energy are released into the air, potentially heating it enough to make it buoyant. A gentle updraft may form where ice crystal production is largest, and a compensating downdraft may form on its periphery. This downdraft, in turn, causes warming that can evaporate supercooled droplets in an oval region surrounding the updraft, creating a hole in the original cloud, with a dense web of ice crystals in the middle. Apparently the original supercooled cloud photographed by Jim Barton was too thick for this to happen.
Andrew Heymsfield (National Center for Atmospheric Research, Boulder, Colorado) and several of his colleagues have studied holes in clouds. They've written a nicely illustrated article in the June 2010, issue of the Bulletin of the American Meteorological Society called “Aircraft-Induced Hole Punch and Canal Clouds: Inadvertent Cloud Seeding.” Heymsfield has just submitted a second closely related article to Science. It should be published sometime this year. I thank him for consulting with me on this article.
A satellite image of Hurricane Alex (June 2010) made me think it was a huge storm. Clouds associated with Alex stretched all the way to the Gulf Coast. Is a large storm like this comparable to an ice skater with her arms stretched out? If the storm remains large, will the wind speeds not increase too much? On the other hand, if the storm contracts, will the winds increase, similar to the skater spinning faster if she pulls her arms in?
I've included a visible image of Alex from the U.S. GOES East satellite that I think was acquired about the time you posed your question. The image shows most of the western Gulf of Mexico, with the U.S. shoreline from Texas to Florida near the top and the Yucatan Peninsula of Mexico at the bottom. At this time (3:33 p.m. CDT), Alex was just a tropical storm, off the west coast of the Yucatan Peninsula (red arrow). Note the heavy clouds, many of them containing thunderstorms, from Yucatan to the Florida coast. Alex moved slowly northwest, becoming a hurricane on the evening of June 29 and continuing to intensify until landfall as a Category 2 storm on the Mexican coast well south of Brownsville, Texas, in late evening on June 30.
Caption: GOES East visible image of Tropical Storm Alex acquired at 1533 CDT, 28 June 2010. The red arrow points to the center of circulation. The yellow arc shows that the circulation around Alex extends well to the north of the heavy convection surrounding Alex's center. The blue Xs indicate areas of convection probably not incorporated in Alex's circulation.
The circulation around Alex covers a large area. One can see circular striations in the clouds north of the main convective activity (mass of bright white clouds) that surrounds the storm center, especially the northeast quadrant. The yellow arc shows where to look. Alex does not have a well-defined eye; the center of circulation is not cloud-free, as it would be in a more intense tropical storm. The large complex of bright convective clouds in the central Gulf and another patch of convective clouds well south of the Florida Panhandle (blue X's) are probably not part of Alex's circulation, but they may contribute to the impression that the circulation covers a very large area.
With the foregoing as background, the size of a hurricane's circulation is not correlated with the hurricane intensity, measured either by minimum atmospheric pressure in the eye or by maximum wind speed. Hurricane Andrew, a Category 5 storm that devastated parts of Florida south of Miami on August 24, 1992, is often cited as a very intense but small hurricane. Gale-force winds extended only about 90 miles out from the center.
In a well-developed hurricane and far enough above the ocean surface that frictional forces are not important, the wind speed ν satisfies approximately the following relationship:
r is the distance from the center of the hurricane where an estimate of wind speed is desired. f = 2Ω sin ϕ is the Coriolis parameter, which takes into account the rotation rate of the earth Ω: one complete rotation in 24 hours or 7.29 × 10−5 radians per second. ϕ is the latitude. ρ is the air density, at sea level, roughly 1.2 kilograms per cubic meter. is a partial derivative. It measures how quickly the pressure rises in a direction pointing away from the center of the hurricane. For example, suppose the pressure increases 15 millibars in 10 km as one moves radially outward from the eye of the hurricane. Expressed in metric (MKS) units, this is a pressure gradient of 1,500 Pascals per 10,000 meters. If you want to use this equation for some back-of-the-envelope calculations, be sure to use consistent units such as MKS.
The pressure gradient essentially determines the wind speed, but the radius of maximum wind (which is the same as the radius of maximum pressure gradient), varies from hurricane to hurricane.
There is a correlation between minimum pressure in the eye and the peak wind observed in the hurricane, but only because the total pressure drop from the periphery to the center of the hurricane is greater for hurricanes with lower minimum pressure, and thus the potential for stronger pressure gradients is greater.
It is also true that a contraction of the diameter of the eye is usually a signal of hurricane intensification. In this case, the analogy with an ice skater pulling her arms in and spinning faster may be appropriate. As the radius of rotation of the eye wall contracts, conservation of angular momentum results in increasing wind speeds in the eye wall.
Weatherwise Contributing Editor THOMAS SCHLATTER is a retired meteorologist and volunteer at NOAA's Earth System Research Laboratory in Boulder, Colorado. Submit queries to the author at firstname.lastname@example.org, or by mail in care of Weatherwise, Taylor & Francis, 325 Chestnut St., Suite 800, Philadelphia, PA 19106.