Temperature and Heat Exchange

The temperature of the air a pilot flies through is the end result of a chain of heat exchanges. The sun heats the Earth's surface; the surface heats the lowest layer of air; wind and rising currents then carry that heat sideways and upwards. Because the chain starts at the ground, temperature normally falls with height, the air is warmest over land in mid-afternoon, and anything that changes the surface, from snow cover to a concrete runway, changes the air above it.

Temperature decides air density and so aircraft performance, sets the freezing level and the icing risk, and drives stability, convection, fog, sea breezes and the diurnal cycle of the surface wind. This article follows the heat from the sun to the thermometer, and ends with the temperature rise an aircraft adds itself through its own speed.

Solar radiation and insolation

The sun's energy arrives as short-wave radiation, with wavelengths of roughly 0.15 to 4 micrometres. The atmosphere is almost transparent to it, so the air is warmed very little as the radiation passes through. Most of what is not reflected is absorbed by the ground and the sea. The solar radiation received at the surface is called insolation, and it is the atmosphere's heat source: the air is heated from below, by the surface, not directly by the sun.

Insolation at a given place depends on:

• the height of the sun: a high sun concentrates its energy on a smaller area and its rays cross less atmosphere;
• the length of the day, which varies with season and latitude;
• cloud, which reflects much of the radiation back to space before it reaches the ground.

Seasons: axial tilt, solstices and equinoxes

The Earth's axis is tilted at about 23½° to the plane of its orbit around the sun. As the Earth travels round its orbit, the latitude at which the sun is directly overhead at noon moves between 23½°N and 23½°S. Those limits are the Tropic of Cancer and the Tropic of Capricorn.

At the equinoxes day and night are of roughly equal length everywhere; at the solstices the difference is greatest. The seasonal change in day length increases with latitude, from long summer days to continuous daylight inside the polar circles, and from short winter days to polar night. The southern hemisphere has its seasons six months out of step with the northern.

Temperature lags behind the sun. Land and sea go on gaining heat after the summer solstice, so in northern temperate latitudes the highest temperatures come in late July or early August, and the lowest in late January or early February. The same seasonal swing moves the thermal equator and the intertropical convergence zone north and south through the year (see global circulation and climate).

Terrestrial radiation and albedo

Every surface radiates according to its temperature. The Earth, much cooler than the sun, emits terrestrial radiation at long wavelengths, roughly 4 to 80 micrometres with a peak near 10 micrometres, by day and by night. Unlike solar radiation, it is readily absorbed by water vapour, carbon dioxide and methane, the greenhouse gases, and that absorption in the lowest layers is what gives the troposphere its fall of temperature with height.

At night, with no insolation, the ground loses heat by terrestrial radiation and cools. Under a clear sky the loss is rapid. Cloud absorbs the outgoing radiation and re-radiates much of it back down, so a cloudy night stays warmer.

Albedo is the fraction of the incoming solar radiation that a surface reflects without absorbing it. Snow reflects around 80 per cent, which is why a snow-covered surface stays cold in bright sunshine; it still radiates its own heat away, so under clear skies it keeps getting colder day by day. Dark, rough surfaces reflect little. Cloud tops also reflect strongly, one reason a cloudy day stays cooler.

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Heat transfer: conduction, convection, advection and latent heat

Once the surface is warm, the heat reaches the air by several routes. The four processes that heat the troposphere are terrestrial radiation, conduction, convection and condensation, and the two most important are terrestrial radiation and convection.

• Conduction is transfer by direct contact, molecule to molecule. Air is a very poor conductor, so conduction warms, or at night cools, only a shallow layer next to the ground.
• Convection is vertical transport by the air itself: air warmed at the surface becomes less dense and rises in thermals, carrying heat upwards, while mechanical turbulence stirs the same heat through the lowest few thousand feet.
• Advection is horizontal transport: the wind carries air of one temperature into a region of another.
• Latent heat moves energy without a change of temperature. Evaporation at the surface absorbs heat; condensation in cloud releases it, often far above and far away from where the water evaporated.

How much a surface warms depends on its specific heat capacity, the heat needed to raise the temperature of a unit mass by one degree. Water has a specific heat of unity (one calorie per gram per degree Celsius), high compared with rock or soil. Land also concentrates the heat in a thin surface layer, whereas sunlight penetrates the sea and waves mix it downwards. Land therefore heats and cools much faster than the sea. Bare rock, dry sand, tarmac and concrete runways get hotter by day than woods, grass, lakes and wet soil, and a concrete surface can be up to about 4 °C warmer than the grass beside it.

This land and sea contrast drives the sea breeze by day and the land breeze by night (see local winds). On a continental scale it drives the monsoons: in winter the sea stays warmer than the rapidly cooling land, so air flows from land to sea, and in summer the flow reverses.

Warm and cold air advection

Warm air advection occurs when the wind brings warmer air into an area, cold air advection when it brings colder air. Advection changes temperature at a place without any change in local heating, so it can make the temperature rise overnight or fall in the middle of the day.

The effect on the weather depends on the surface the air crosses:

The first case explains why convection-type cloud can form over the sea, where surface heating alone could not produce it. The second explains the sea fogs of coasts swept by warm, moist air, which may persist all day in a steady wind (see fog and fronts).

Diurnal variation of temperature

The diurnal variation of temperature is the daily cycle of surface air temperature. Over land on a clear day with light wind:

• The maximum occurs at about 1500 local time. Insolation peaks at noon, but the surface goes on gaining more heat than it loses until mid-afternoon.
• The minimum occurs at about 30 minutes after sunrise, when the sun first begins to replace the heat lost overnight.
• In temperate latitudes the temperature typically swings about ±6 °C either side of the daily mean, a range of roughly 12 °C.

Cloud and wind both reduce the range. By day cloud reflects insolation and lowers the maximum; by night it returns terrestrial radiation and raises the minimum. Wind mixes the surface air with the air above, spreading the heating by day and the cooling by night through a deeper layer. Over the open sea the diurnal variation is generally less than 1 °C.

The cycle drives much of the day's weather: thermal turbulence and cumulus by afternoon, the sea breeze, radiation fog and temperature inversions at night, and a surface wind that in the northern hemisphere veers and strengthens by day and backs and eases at night. Density altitude is also highest in the afternoon, when take-off performance is poorest.

Measuring air temperature

Surface air temperature is measured in the shade in a Stevenson screen, a white louvred box on legs that holds the thermometers about 4 ft (1.2 m) above the ground. The louvres let air circulate freely while protecting the instruments from direct sunshine, wind and precipitation. The screen typically holds a dry-bulb thermometer, a wet-bulb thermometer for humidity, and a thermograph, a recording thermometer that traces temperature continuously on a chart, as the barograph does for pressure.

METARs report temperature and dew point in whole degrees Celsius, with M for minus: M03/M04 is −3 °C with a dew point of −4 °C. US METARs add a remark group with both values to a tenth of a degree. Upper-air temperatures come from radiosonde ascents, made mainly at 0000 and 1200 UTC, and from aircraft reports.

On charts, an isotherm is a line joining places of equal temperature. The height of the 0 °C isotherm is the freezing level, and an inversion can produce more than one.

Kinetic heating and ram rise

An aircraft's own speed heats the air it measures. The static air temperature (SAT), also called the outside air temperature, is the temperature of the undisturbed air. When air is brought to rest in a temperature probe it is compressed adiabatically, and to a lesser extent heated by friction, so the probe reads more. The increase is the ram rise, and the total air temperature (TAT) is SAT plus the full ram rise.

A quick rule gives the ram rise in degrees Celsius as the square of the true airspeed in hundreds of knots:

A probe senses only a fraction of the theoretical rise, its recovery factor, typically 0.95 to 0.98 for modern TAT probes. The air data computer applies it and the Mach number to recover SAT from TAT, using SAT = TAT / (1 + 0.2 × Kr × M²) with temperatures in kelvin. At high subsonic cruise the difference is large: with SAT −55 °C, TAT can be near −25 °C.

The same kinetic heating warms the airframe skin by about the same amount. Kinetic heating that lifts the skin above 0 °C can keep ice off, but heating that leaves it just below freezing may make icing worse.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.