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January-February 2012

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Weather Queries

What is going on in the attached image (see image below)? The picture was taken on April 28, 2011, in Tucson, Arizona.

John T. Alden
Tucson, Arizona

You've photographed a dense patch of cirrus cloud, composed entirely of ice crystals. You could view this cloud as a very high-altitude shower, occurring at temperatures far below freezing, probably below −30°C (−22°F). The balloon sounding (rawinsonde) taken late on the afternoon of April 28 in Tucson indicates a steep lapse rate (rapid decrease of temperature with altitude) in the high troposphere. The relative humidity is less than 20 percent at all altitudes below 6100 meters and does not exceed 30 percent between there and the tropopause at 10,800 meters. It is a little surprising to see any clouds in an atmosphere apparently this dry, but a localized patch of air with greater moisture content must have existed in the high troposphere for this cloud to form at all.

Shallow convection clearly occurred in a layer of atmosphere just below the tropopause, where the lapse rate was steep. The temperature was probably near −30°C near the base of this layer and −52°C at the top, at the tropopause. The ice crystals in the thickest part of the cloud grew large enough that their fall speed exceeded the updraft speed. These crystals fell out of the main cloud, creating the long, beard-shaped streamer. The crystals eventually evaporated in the drier air below.

Caption: Ice crystal shower falling from a dense patch of cirrus and evaporating into the drier air below.

The Phoenix Valley at the western foot of the Superstition Mountains (away from the city lights) is a great location for stargazing. A bright star, Arcturus, will often not scintillate for a solid minute of watching, and Saturn's image is rock steady at high power in mid-evening. My astronomer friends and I agree that the quality of viewing is remarkable, so high that it might occur in the Portland, Oregon, area only twice a year. Can you explain why?

Wolf H. Fahrenbach
Gold Canyon, Arizona

First, let's dispose of the obvious. Portland is cloudier than Phoenix. The percent of possible sunshine for the year is the ratio of the number of hours the sun actually shines at the ground to the number of hours it could shine if the sky is always clear. For Phoenix, the annual average is 85 percent; for Portland, it is 48 percent. (Daytime cloudiness is highly correlated with nighttime cloudiness.) But the greater frequency of clear sky in Phoenix by no means explains the superior viewing conditions there.

Scintillation refers to the apparent inconstancy of light from a star. It inspired “Twinkle, Twinkle, Little Star.” When point sources of light twinkle, the cause is high-frequency variability in atmospheric refraction—momentary bending of light rays out of the (nearly) straight-line path between the observer and the light source.

The index of refraction is the ratio of the speed of light in a vacuum to that in some medium, such as air or water. The closer the index of refraction is to unity, the less the light rays bend when they pass from a vacuum into a medium. In air, the index of refraction is slightly greater than one; a typical value is 1.000293. Light from a star entering the atmosphere thus bends very slightly from a straight-line path, but very predictably if the atmosphere is at rest.

Unfortunately for astronomers, turbulence is ever-present in the atmosphere, with random fluctuations in wind speed and air density at spatial scales ranging from millimeters to many meters.

The density of the air depends on temperature and pressure and, to a lesser extent, on the moisture content. Small variations in these parameters are ubiquitous. They cause corresponding variations in air density, and these in turn cause variations in the index of refraction. When the wind carries “pockets” of air having slightly different indices of refraction across the viewing path between the observer and a star, the bending of light rays, though slight, becomes inconstant, resulting in abrupt changes, many per second, in the intensity of light received by the eye.

Most scintillation is caused by turbulence on scales of a few centimeters to a few tens of centimeters. The longer the pathway of starlight through the atmosphere, the greater the likelihood of scintillation. Thus viewing stars in the vertical direction is likely to be more satisfying than viewing them near the horizon; the scintillation is less distracting.

Light enters the eye through an aperture (opening) called the pupil. When the eyes are night-adapted, the pupil is roughly five millimeters wide. The distance from the Earth to stars (excluding the sun) is so great that stars can be considered to be point sources of light. Thus the pathway taken through the atmosphere by starlight that enters the eye is essentially cylindrical and hardly wider than a pencil. If the atmosphere is turbulent, the probability of softball-sized anomalies in the index of refraction crossing this pathway is high. Scintillation is likely. When viewing through a telescope, however, scintillation is less likely, at least for apertures up to about 20 cm. The pathway taken by starlight is now many centimeters wide (instead of five millimeters), and so the telescope has a better chance of gathering starlight slightly bent out of the normal pathway than the eye does, and some of the scintillation is averaged out of the image seen with the telescope.

Stargazing is best on clear nights when atmospheric turbulence is at a minimum. That occurs when the atmosphere is stably stratified, that is, when vertical motions are suppressed and when winds aloft are light. Vertical wind shear, the variation of wind speed or direction with altitude, is undesirable because strong shear generates turbulence. Vertical wind shear is invariably associated with the jet stream—a ribbon of high-speed air that blows between 25,000 and 40,000 feet at mid-latitudes. The jet stream determines the mid-latitude storm track. It meanders north and south throughout the year, but its mean position is near 40°N in the winter, when it is strongest, and close to the Canadian border during the summer, when it is weakest.

Aside from the differences in cloudiness, why should astronomical viewing conditions be better in Phoenix than in Portland? Primarily because of latitude. Near 45°N, Portland comes under the influence of the jet stream far more often than Phoenix, near 33°N. For most of the year, atmospheric turbulence is thus much more likely over Portland than Phoenix.

I thank Andrew Planck and William Knoche for help in answering this question.

How do you calculate the dewpoint mathematically using the wet- and dry-bulb temperatures?

Gerry Clink
Moore, Oklahoma

The dewpoint is the temperature to which air must be cooled at constant pressure and constant water vapor content for saturation to occur. In practice, this is the temperature as measured on a grassy surface on a still, clear night, when dew first forms. It is an absolute measure of the amount of moisture in the air. Together with temperature, it is used to estimate the cloud base on a summer afternoon, levels in the atmosphere where layered clouds occur, the potential for thunderstorms, and the amount of rain that might fall.

The wet-bulb temperature is the lowest temperature to which air can be cooled by evaporating water into it at constant pressure. In practice, this temperature is determined by covering the bulb of an ordinary thermometer with a wet cloth and then whirling it vigorously through the air to see how low the temperature falls before the cloth dries out. Unless the air is saturated, the wet-bulb temperature is always higher than the dew point temperature. The wet-bulb temperature is a forecast tool, useful on days when high-based showers or thunderstorms produce rain that falls through dry air below the cloud base. The evaporation of rain into the dry air causes cooling (in the limit, down to the wet-bulb temperature), and the amount of cooling is a measure of downdraft strength and the speed of the outflow winds from the shower or thunderstorm.

The dry-bulb temperature is just the ordinary air temperature. It got its name because of an instrument called a sling psychrometer (see image below), a small metal frame holding two thermometers and attached to a handle by a bearing or a loose chain. A wet cloth, for example, a narrow sleeve of muslin, is attached to one of the thermometer bulbs to measure the wet-bulb temperature. Because the bulb of the other thermometer is dry, the latter measures the dry-bulb temperature, which is just the air temperature. The weather observer whirls the psychrometer by hand to provide the ventilation that evaporates water on the cloth. This should take less than a minute.

With this background, here are formulas for computing dew point from the wet- and dry-bulb temperatures. The first formula is called the psychrometric equation. It calculates the vapor pressure e from the total air pressure p (as measured by a barometer), the dry-bulb temperature Ta, and the wet-bulb temperature Tw.

Because this equation contains a temperature difference, units of Celsius or Kelvin temperature are both okay. For a reason that will soon become apparent, Celsius is preferred.

cpd = 1005 J kg−1 K−1 (joules per kilogram per degree Kelvin) is the specific heat capacity of dry air at 0°C at constant pressure. cpd varies slightly with temperature but is considered a constant here.

∊ = Rd/Rv = 0.622 is the ratio of gas constants for dry air and water vapor (dimensionless).

lv = 2.501 × 106 J kg−1 is the enthalpy of vaporization of water at 0°C—a measure of the energy required when a measured amount of water changes phase from liquid to vapor. lv varies slightly with temperature but is considered a constant here. The quantity

is often called the psychrometric constant. At sea level, where the standard pressure is 1013.25 millibars (mb), its value is approximately 0.65 mb per degree Celsius.

The first term in the psychrometric equation is an as-yet undefined function es for saturation vapor pressure. It depends only on temperature, which controls the maximum vapor pressure possible in air. In 1980, David Bolton suggested a formula for es that is still popular today. It has the dual advantages of simplicity and accuracy.

where exp(x) means ex and e = 2.71828. es0 = 6.1121 mb is the saturation vapor pressure at 0°C.

When using Bolton's formula, the temperature must be in degrees Celsius, which explains an earlier suggestion that one use Celsius degrees in the psychrometric formula. To get the first term in the psychrometric equation, just substitute Tw for T in Bolton's equation. By design, es(Tw) is in millibars. For consistency, p must also be in millibars in the psychrometric equation so that the vapor pressure e is correctly calculated in millibars.

One step remains: to calculate the dew point from the vapor pressure e. The definition of dewpoint given earlier suggests that, if we invert Bolton's equation and solve for temperature and then plug in e for the vapor pressure but assume that it is the saturation vapor pressure, we'll obtain the dew point temperature Td.

The inverse of Bolton's equation is

where “ln” means natural logarithm. If we assume that the vapor pressure e obtained from the psychrometric equation is a saturation vapor pressure and use it in the above formula, the result will be the dewpoint temperature, T = Td.

These equations are not difficult to program. In fact, equations like this lie behind Web calculators that do the work for you. You can test these equations against results from the Web, for example, at When I specified an air temperature of 30°C, a wet-bulb temperature of 20°C, and a pressure of 1000 mb, this Web site gave me a dewpoint of 14.6°C. When I used the equations above with the same input and a hand calculator, which I don't recommend, I obtained a dewpoint of 14.9°C. Since I don't know which formulas the Web site used, I consider this reasonably close.

Caption: A sling psychrometer. This particular version is used to obtain wet- and dry-bulb temperatures at wildfire sites, where in situ measurements of moisture are vital. Courtesy of the National Weather Service Office, Denver, Colorado.

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, or by mail in care of Weatherwise, Taylor & Francis, 325 Chestnut St., Suite 800, Philadelphia, PA 19106.

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