Lapse rates and stability, plate FB-ENG-005

What it is

A lapse rate is how fast the temperature falls with height. There are two kinds, and stability is the comparison between them.

The first belongs to the air that stays put: the temperature a balloon measures at each height on a given day. In the standard atmosphere it falls 3.6 °F every 1,000 ft (6.5 °C a km), but the real one changes by the hour.

The second belongs to air that moves. Air that rises expands, and expanding air cools even though it trades no heat with its surroundings. While it is dry it cools 5.4 °F every 1,000 ft (9.8 °C a km), the dry adiabatic rate. Once it is saturated, its vapour condenses as it rises, the condensing releases heat, and it cools more slowly.

Lift a small parcel of air and compare it with the air around it at its new height. If it is colder, it is heavier and sinks back: the air is stable. If it is warmer, it keeps rising: the air is unstable.

What it is not

It is not the temperature itself. Cold air can be unstable and hot air stable; only the rate of change with height matters.

It is not the same at every height. One sounding can be unstable near the ground, stable in an inversion above, and unstable again higher up, and each layer behaves by its own rule.

Lookalikes

The standard atmosphere: A fixed average profile, 3.6 °F per 1,000 ft; a real day departs from it, and the departure is what makes weather.
An inversion: A layer where the temperature rises with height, the most stable air there is.
CAPE: The energy a rising parcel gains over its whole climb; stability here is the rule at each level.

Machine

Three kinds of stability

Fig. A draws every case from one ground temperature, 68 °F (20 °C). When the surrounding air cools more slowly than even the saturated rate, any lifted parcel ends up colder: absolutely stable. When it cools faster than the dry rate, any lifted parcel ends up warmer: absolutely unstable, a state that lasts only near sunbaked ground on a summer afternoon. Between the two adiabats lies conditional instability: stable to dry air, unstable to saturated air. The standard atmosphere's 3.6 °F every 1,000 ft sits in that wedge, and so does most of the real troposphere on most days. Whether storms grow depends on whether something lifts the air far enough to saturate it.

Lifted, and let go

The first equation below puts numbers on it, and Fig. B draws them. A dry parcel lifted 3,000 ft cools to 51.9 °F. In air cooling 3.6 °F every 1,000 ft, the air around it is 57.2 °F, so the parcel is 5.3 °F (2.9 °C) colder and sinks back. It overshoots its old level, is pushed up again, and bobs. The second equation gives the time for one bob, about 10 minutes in the standard lower atmosphere. Wind carrying that bobbing across a ridge draws it out into the standing waves and lens clouds of the mountains, Orographic clouds FB-SKY-035.

In air cooling 6.0 °F every 1,000 ft, the air around the parcel is 50.0 °F, so the parcel is 1.9 °F (1.1 °C) warmer and keeps going. The difference grows as it climbs.

How fast saturated air cools

The saturated rate is not one number. Warm air holds more vapour and releases more heat as it rises, so it cools slowly; cold air holds little and cools almost at the dry rate. Fig. C computes it: at 1,000 mb, 2.3 °F every 1,000 ft (4.2 °C a km) at 68 °F (20 °C), 3.6 °F every 1,000 ft (6.5 °C a km) at freezing, and 4.7 °F every 1,000 ft (8.6 °C a km) at −4 °F (−20 °C). That is why warm, humid air is where the tallest thunderstorms grow, Thunderstorm FB-EVT-001.

A painted sheet of two mountain valleys side by side, heights not to scale. On the left, stable air cooling 3.6 degrees Fahrenheit every 1,000 feet: a parcel at 68 degrees at the ground is lifted to 3,000 feet, cooling at the dry rate, 5.4 degrees every 1,000 feet, to 51.9 degrees, colder than the air around it at 57.2 degrees, and sinks back and bobs about its old level. On the right, unstable air cooling 6.0 degrees every 1,000 feet: the same parcel at 3,000 feet is 51.9 degrees against air at 50.0 degrees, warmer, and keeps rising. — **Fig. B** A parcel lifted, and let go. A parcel at 68 °F lifted 3,000 ft cools to 51.9 °F: colder than stable air, so it sinks back; warmer than unstable air, so it keeps rising.Maximize The drawing, to scale

A painted sheet in a watercolour border: a chart, to scale, of how fast saturated air cools as it rises against its temperature from minus 40 to 86 degrees Fahrenheit. The dry rate, 5.4 degrees Fahrenheit every 1,000 feet (9.8 degrees Celsius a kilometre), and the standard atmosphere, 3.6 degrees (6.5 degrees Celsius a kilometre), drawn across. The saturated rate at 1,000 millibars falls from near the dry rate in the coldest air to 1.9 degrees at 86 degrees Fahrenheit, marked at 4.7 degrees at minus 4, 3.6 at 32 and 2.3 at 68; the rate at 500 millibars, drawn dashed from minus 40 to 32 degrees, a little slower at each temperature. — **Fig. C** How fast saturated air cools. The saturated rate against temperature: 2.3 °F per 1,000 ft at 68 °F, 3.6 at freezing, 4.7 at -4 °F, nearing the dry 5.4 in the coldest air.Maximize The drawing, to scale

Drawings

Each figure drawn as an engineering sheet, its parts numbered, to print at 11 by 17.

Fig. A, the drawing Three kinds of stability. Temperature against height to 10,000 ft, from 68 °F at the ground, with the dry and saturated adiabats and three kinds of surrounding air TO SCALEMaximize The sheet, SVG, 11 by 17 The painting

The dry adiabat
The saturated adiabat
Stable air, cooling slower than both
Conditionally unstable air, between them
Unstable air, cooling faster than both
Between the adiabats, stable to dry air, unstable to saturated air

Fig. B, the drawing A parcel lifted, and let go. A dry parcel lifted 3,000 ft through stable air and through unstable air, the temperatures worked from the lapse rates; not to scale across HEIGHT NTSMaximize The sheet, SVG, 11 by 17 The painting

The parcel at the ground
Lifted into stable air, colder than its surroundings
It sinks back and bobs
Lifted into unstable air, warmer than its surroundings
It keeps rising

Fig. C, the drawing How fast saturated air cools. The saturated adiabatic lapse rate against temperature at 1,000 and 500 mb, computed from its definition, with the dry rate and the standard atmosphere's TO SCALEMaximize The sheet, SVG, 11 by 17 The painting

The dry rate
The standard atmosphere's rate
The saturated rate at 1,000 mb
The saturated rate at 500 mb

Ingredients

Air that rises expands and cools, and air that sinks is squeezed and warms, without trading heat with its surroundings
Water vapour that condenses as saturated air rises, releasing heat that slows its cooling
The temperature of the surrounding air at each height, which the sun, the ground, fronts and sinking air all change

Scales

time: minutes for a parcel to bob or rise; hours for the sun or a front to change the lapse rate
horizontal: from one thermal a few hundred feet (100 m) across to a whole air mass
vertical: the lowest few thousand feet on a sunny afternoon to the whole troposphere
orlanski: meso

Equations

A lifted parcel against its surroundings

T_{parcel} - T_{env} = (\Gamma_{env} - \Gamma_{parcel})\,\Delta z

$T_{parcel} - T_{env}$: how much warmer the parcel is than the air around it after the lift, °F
$\Gamma_{env}$: how fast the surrounding air cools with height, °F per 1,000 ft
$\Gamma_{parcel}$: how fast the parcel cools as it rises, 5.4 °F per 1,000 ft (9.8 °C per km) while it is dry
$\Delta z$: how far the parcel is lifted, in thousands of feet

Assumes The parcel method; the parcel trades no heat with its surroundings and does not disturb them. A parcel warmer than its surroundings is buoyant and rises; a colder one sinks.

Working form A dry parcel lifted 3,000 ft through air cooling 3.6 °F per 1,000 ft ends 5.3 °F (2.9 °C) colder than its surroundings, and sinks back. Through air cooling 6.0 °F per 1,000 ft it ends 1.9 °F (1.1 °C) warmer, and keeps rising.

The buoyancy frequency

N = \sqrt{\frac{g}{T}\,(\Gamma_d - \Gamma_{env})}, \qquad \text{period} = \frac{2\pi}{N}

$N$: how fast a nudged parcel bobs in stable air, per second
$g$: gravity, 9.81 m s⁻²
$T$: the temperature of the air, K
$\Gamma_d$: the dry adiabatic lapse rate, 9.8 K per km
$\Gamma_{env}$: the lapse rate of the surrounding air, K per km

Assumes Dry air, small displacements; in unstable air the root has no real value and the parcel does not bob, it runs away.

Working form In the standard lower atmosphere, 59 °F (15 °C) and cooling 3.6 °F per 1,000 ft (6.5 °C per km), a nudged parcel bobs up and down once about every 10 minutes.

Signatures

sounding: the temperature line leaning left of the dry adiabat near the ground on a hot afternoon; an inversion; warming with height; as a lid; conditional instability through most of the troposphere most days
surface: strong gusts and dust devils under a superadiabatic layer; still air; fog and trapped smoke under an inversion
satellite: flat layer clouds in stable air; cumulus towers in unstable air
radar: steady; widespread rain from lifted stable air; scattered cells from unstable air

Numbers

Quantity	Value, and the kind of number it is
Lapse rate	The rate at which an atmospheric variable, usually temperature, decreases with heightStandard, Glossary of Meteorology
Dry adiabatic lapse rate	5.4 °F per 1,000 ft (9.8 °C per km)Standard, Glossary of Meteorology
Saturated adiabatic lapse rate at 1,000 mb	2.3 °F per 1,000 ft (4.2 °C per km) at 68 °F (20 °C); 3.6 °F per 1,000 ft (6.5 °C per km) at 32 °F (0 °C); 4.7 °F per 1,000 ft (8.6 °C per km) at −4 °F (−20 °C)This site, Glossary of Meteorology
The standard atmosphere	3.6 °F per 1,000 ft (6.5 °C per km) from the ground to 36,000 ft (11 km)Standard, U.S. Standard Atmosphere
Absolutely stable	The air cools more slowly than the saturated adiabatic rateStandard, Glossary of Meteorology
Conditionally unstable	The air cools faster than the saturated rate but more slowly than the dry rate: stable to dry air, unstable to saturated airStandard, Glossary of Meteorology
Absolutely unstable	The air cools faster than the dry adiabatic rateStandard, Glossary of Meteorology

How the station sees it

A surface station sees the bottom of the column. On a sunny afternoon its temperature climbs until the lowest layer cools faster than the dry rate, and then the air turns over: gusts, cumulus, dust devils. On a clear, calm night its temperature falls below the air a few hundred feet up, an inversion, and fog, frost and smoke collect under it. Road weather stations on mountain passes show the inversion directly when the pass reads warmer than the valley below.

The full profile comes from weather balloons, plotted on the skew T chart that forecasters read stability from, How to read a skew T FB-STN-003.

Airport weather stations: the temperature at the bottom of the column, which the afternoon sun raises until the lowest layer turns unstable
Road weather stations: the air in the valleys and on the passes, where an inversion shows as the pass warmer than the valley

On the radar

Hail core height, live radar analysis: How far above the freezing level each storm holds its heaviest echo, 50 dBZ, in thousands of feet.
Forecast temperature map: The temperature ahead across the lower 48, Alaska, Hawaii and Puerto Rico, hour by hour to seven days.

How it is warned

Stability is not warned. It is the setting a forecaster reads first each morning, because it decides whether the day brings flat cloud and steady rain or towers, hail and tornadoes, and what an air quality alert will do under an inversion.

Sources

American Meteorological Society. Glossary of Meteorology.
NOAA, NASA and the U.S. Air Force. U.S. Standard Atmosphere, 1976.
Wallace, J. M. and P. V. Hobbs. Atmospheric Science, An Introductory Survey, 2nd ed. (2006).

Definition after the Glossary of Meteorology. Plate FB-ENG-005, revision 1, 2026-09-25. The number is permanent; cite it.

Lapse rates and stability