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March-April 2014

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Weather Queries

Q: My daughter, a meteorologist with the National Weather Service in Monterey, California, mentioned recently that an observation she made as an intern at Phoenix's Sky Harbor Airport caused at least a curtailment of flight operations. She recorded a temperature of 122°F on June 26, 1990, and relayed this information to the control tower. Flights were either curtailed or suspended until the temperature fell below 120°F because the density altitude chart only went up to 120°F. What is density altitude, and why is it so important?

Lee Sims
Tucson, Arizona

Density altitude is the pressure altitude corrected for temperature deviations from the standard atmosphere. So says the Glossary of Meteorology, which is published by the American Meteorological Society. For the uninitiated, this definition is unhelpful, so I will elaborate.

The standard atmosphere is a fictitious atmosphere, which nonetheless has many practical applications. In this atmosphere, which contains no water vapor, the sea-level temperature is 15°C, and the temperature deceases with altitude at the constant rate of 6.5°C per km from sea level to 11 km, which is defined to be the top of the troposphere. Pressure altitude is the altitude that corresponds to a given pressure in the standard atmosphere. Commercial aircraft constantly measure pressure. When they are not climbing or descending, they fly on constant pressure surfaces. Their altimeters register the pressure altitude. For example, if the outside air pressure is 301 millibars (mb), that corresponds to an altitude of 30,000 feet in the standard atmosphere, and so the altimeter reads 30,000 feet.

If an aircraft is parked on the tarmac at sea level, and the temperature is 15°C, the density altitude is the same as the pressure altitude (zero feet) because 15°C is the temperature at zero elevation in the standard atmosphere. At Denver International Airport, where the average elevation is about 5,335 feet, the standard-atmosphere has a temperature of 4.4°C and a pressure of 833 mb. Together, the temperature and pressure determine the standard air density: 1.045 kilograms per cubic meter (kg m−3).

The density is all-important for aircraft performance. If the density drops, then, for a given ground speed, the lift of the wings, the thrust provided by spinning propellers, and the mass of oxygen per unit time entering a jet engine all decrease. From a practical standpoint, the lower the air density, the greater the ground speed that is required for takeoff and the longer the takeoff roll. Temperature, pressure, and, to a lesser extent, moisture determine air density. The higher the temperature and dewpoint, and the lower the pressure, the lower is the density. A warm and humid air mass at Denver's elevation will result in low air density.

Figure 1 is a chart for determining density altitude. This chart does not use density explicitly, but density is implied by a pressure measurement (the altimeter setting in inches of mercury) and a temperature measurement. This chart does not include the effect of atmospheric moisture, which is small. For example, find the density altitude for Denver (elevation 5,335 feet) if the airport temperature is 30°C and the altimeter setting is 30.1 inches. Begin with the two columns of numbers at right. The pressure altitude conversion factor for an altimeter setting of 30.1 inches is –165 feet. This number is added to the airport elevation to get 5,170 feet, which is the corrected pressure altitude. Move up the vertical line at 30°C, crossing the diagonal lines of pressure altitude until reaching 5,170 feet. Then move horizontally left to the vertical axis, and read the density altitude value, approximately 8000 feet.

Figure 1: A chart for computing the density altitude, given the altimeter setting, the temperature, and the elevation of the airport. The red lines show a sample determination of density altitude when the altimeter setting is 30.1 inches, the temperature is 30°C, and the airport altitude is 5335 feet. Instructions for using this chart are in the text.

Manufacturers of various aircraft know how they will perform at various density altitudes. To ensure passenger safety, the pilot must be aware of these performance specs.

Figure 2 shows how performance varies with airport temperature and pressure altitude. Suppose the altimeter setting at Denver is just above 29.2 inches, so that the pressure altitude conversion factor is 665 feet (interpolated from the table in Figure 1). Given the field elevation of 5335 feet, the pressure altitude is 6000 feet. Suppose the temperature is 100°F. This is an unlikely combination, in that the altimeter setting will never be this low on a hot summer day, but the red line represents these hypothetical conditions. As noted in the figure caption, an aircraft will require a takeoff roll 3.2 times the distance needed at sea level under standard atmospheric conditions. Moreover, the rate of climb will be only one-quarter of that possible at sea level. No wonder Denver has long runways, four that are 12,000 feet long and one that is 16,000 feet long. On hot summer days, fully loaded jumbo jets departing for foreign destinations use the 16,000-foot runway.

Figure 2: The Koch chart for calculating the take-off distance factor and the climb rate factor from the airport temperature and pressure altitude. The red line, connecting an airport temperature of 100°F with an airport pressure altitude of 6,000 feet, passes through a take-off distance factor of 3.2 and a climb rate factor of 0.25. This means that the takeoff roll will take 3.2 times the runway length that would be required at sea level, and the climb rate will be only 0.25 of that at sea level, given a standard atmosphere.

Another example of flights being cancelled because of high temperatures (and high values of density altitude) occurred recently. On Saturday, June 29, 2013, The New York Times reported that, as the temperature hit 119°F in Phoenix, Arizona, the fourth highest temperature ever recorded there, US Airways cancelled 18 of its regional flights. The manufacturer of the smaller jets that fly the shorter routes provides performance specifications only up to 118°F, and an airline spokesman said there was no way to know for sure how long a runway pilots would need to take off safely.


Q: Many times here in Ahmedabad, India, I see bright lightning flashes but don't hear thunder, and many times I see rather dim lightning flashes but do hear thunder. Why is this?

Kaushal Acharya
Ahmedabad, Gujarat, India

Lightning occurs when an electrical current passes through a channel of air one to two centimeters in diameter. The current heats the air within milliseconds to about 30,000°C, causing explosive expansion and a shock wave. Just a few meters from the channel, the shock wave converts to an acoustic (sound) wave, which then travels away from the channel in all directions at the speed of sound. Thunder from different parts of the channel reaches your ears at different times depending on the distance between you and all parts of the channel, which can easily be several kilometers long. That's why thunder may rumble for many seconds after the initial boom. If lightning is frequent, one or more flashes per second, the rumbling may be continuous.

A second cause of thunder generates mainly infrasound—acoustic waves at frequencies below 20 Hertz (Hz)—which cannot be heard. This is associated with the sudden contraction of a large volume within the thunderstorm immediately after lightning removes charge from that volume. Infrasonic thunder won't be discussed here.

Several factors determine whether you hear the thunder or not.

The amount and duration of the current: A typical cloud-to-ground (CG) stroke lowers negative charge to the ground. A typical peak current is 30,000 amperes lasting 70-80 microseconds. Higher currents that flow longer generate more heating and more acoustic energy. For example, positive CG strokes can carry several times more current than a negative CG stroke, and so the acoustic energy generated is correspondingly greater. In-cloud (IC) strokes seldom generate as much acoustic energy as CG strokes.

Distance from the source: The intensity of sound drops quickly with distance from the source according to an inverse square law. For example, thunder one kilometer from the lightning channel will seem four times louder than thunder two kilometers from the lightning channel. For this reason alone, the audible range of thunder is seldom greater than 25 km.

Orientation of the lightning channel with respect to the line of sight: Most of the acoustic energy generated by a lightning stroke is directed roughly perpendicular to the channel. For this reason, you will hear louder thunder if your line of sight is perpendicular to the channel than if it is parallel. In the latter case, you may hear little thunder at all.

Refraction of sound waves due to horizontal temperature stratification: The speed of sound c in still, dry air depends upon the temperature T as follows:

where T is expressed in degrees Celsius, and c and 331.3 are in meters per second (m s−1). The higher the temperature, the greater the speed of sound. Thus, if a sound wave passes through layers of air at different temperatures, its propagation speed changes and it refracts (bends) much the same as a ray of light refracts as it passes from air to water. In the case of sound, the bending is gradual, but it can be enough to influence strongly how far from the lightning stroke thunder will be audible.

Figure 1 illustrates the usual situation during thunderstorm activity, in which temperature decreases with altitude. A point source of sound (for example, a short segment of a lightning channel a kilometer above ground) emits acoustic waves. As the sound waves travel through the atmosphere, they encounter temperature changes, and so they bend upward. The lower curved arrows indicate where the sound waves are tangent to the ground. Beyond this point, the waves curve back upward into the atmosphere and so no thunder can be heard by an observer in the “shadow” zone.

Figure 2 illustrates the opposite situation: an inversion, in which the temperature increases with height. In this case, the curvature of sound waves is downward. From those parts of the lightning channel lying within the inversion, sound could reach the ground at distances beyond the normal limit of audibility.

Figure 1: Propagation of acoustic waves from a source above ground when temperature decreases with altitude. Sound waves curve upward, creating a shadow zone, where the sound cannot be heard

Figure 2: Same as Figure 1, but with temperature increasing with altitude. If the source of sound is a segment of the lightning channel, an inversion can make thunder from this source audible at greater distances than normal.

Refraction of sound waves due to wind shear: Familiar sounds such as traffic noise are commonly heard more readily downwind from the source than upwind. This is true even when temperature is constant with altitude. It cannot be that the wind carries the sound away, because sound travels at more than 300 m s−1, whereas wind speeds are almost always less than 100 m s−2, even in the jet stream, and always much less at the ground. Vertical wind shear, a change in wind speed or direction with altitude, is responsible for this common experience. If the leading edge of an acoustic wave, initially vertical, travels in an environment where the wind speed increases with altitude, its upper portion will outpace its lower portion so that the wave front will tilt forward and the propagation direction will incline downward. This is another form of refraction. In an environment favorable for severe thunderstorms, the wind speed increases rapidly with altitude, and the refraction of sound waves traveling downwind can match or exceed the refraction caused by temperature decreasing with altitude. Conversely, sound waves traveling upwind in the same sheared environment will bend upward, causing shadow zones on the ground. For this reason, thunder from an approaching storm is more easily heard than from a receding one.

Atmospheric attenuation by water vapor and hydrometeors: As noted earlier, distance from the lightning stroke strongly determines whether you hear thunder and how loud it is. But atmospheric attenuation (damping) of the acoustic signal can also be significant. It occurs because of water vapor and any liquid or solid water particles (hydrometeors) in the air between you and the stroke. The higher the vapor content of the air and the greater the concentration of cloud particles and precipitation, the greater the attenuation. The acoustic spectrum of thunder covers frequencies from less than 1 Hz to 500 Hz. As noted before, the lower limit of audibility is near 20 Hz. CG strokes have a spectral peak near 100 Hz, while both IC and CG strokes have a peak in the infrasonic part of the spectrum. Higher frequencies attenuate more readily than lower frequencies so that, at distances greater than a few kilometers, it is unusual to hear frequencies above 100 Hz.

Wind noise: The acoustic spectrum of wind overlaps that of thunder, so, if strong winds accompany the storm, the roar of the wind passing through trees and around structures may mask or drown out the sound of thunder.

Several times I have witnessed the passage of severe squall lines accompanied by frequent lightning—almost constant flickering—but I heard surprisingly little thunder. The wind roared, but even during lulls between gusts, thunder was barely audible. Why? Severe storms have very strong updrafts, which tend to transport charge centers to high altitudes, above 30,000 feet. With charge centers more distant from the ground than in ordinary thunderstorms, CG discharges are less frequent. Moreover, the breakdown potential (the voltage difference between charge centers necessary to initiate a discharge) is much less at high altitudes than near the ground so that in-cloud discharges near the top of the storm are likely to carry less current and result in the release of less acoustic energy. This energy may be strongly attenuated by heavy precipitation between the thunderstorm anvil, where the lightning occurs, and the ground. Finally, vertical wind shear can bend the acoustic waves upward, away from the ground.

In summary, it is very difficult to determine what combination of factors makes thunder from a given lightning stroke audible or not. New Lightning Mapping Arrays (LMAs) deployed at a number of locations in the United States enable the three-dimensional location of points along a lightning channel. Coupled with an array of acoustic sensors on the ground, these LMAs will enable a more quantitative examination of the sounds heard during a long, low rumble of thunder.

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, 530 Walnut Street, Suite 850, Philadelphia, PA 19106.

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