# Saturated Adiabatic Lapse Rate

## Description

The lapse rate is defined as the rate at which atmospheric temperature decreases with increase in altitude. The terminology arises from the word lapse in the sense of a decrease or decline. While most often applied to Earth’s troposphere, the concept can be extended to any gravitationally supported parcel of gas.

When the air is saturated with water vapour (at its dew point), the moist adiabatic lapse rate (MALR) or saturated adiabatic lapse rate (SALR) applies. This lapse rate varies strongly with temperature. A typical value is around 5 °C/km (2.7 °F/1,000 ft) (1.5 °C/1,000 ft).

The reason for the difference between the dry and moist adiabatic lapse rate values is that latent heat is released when water condenses, thus decreasing the rate of temperature drop as altitude increases. This heat release process is an important source of energy in the development of thunderstorms. An unsaturated parcel of air of given temperature, altitude and moisture content below that of the corresponding dew point cools at the dry adiabatic lapse rate as altitude increases until the dew point line for the given moisture content is intersected. As the water vapour then starts condensing the air parcel subsequently cools at the slower moist adiabatic lapse rate if the altitude increases further.

The saturated adiabatic lapse rate is given approximately by this equation from the glossary of the American Meteorology Society as shown here.

## Variables

Γ_{w} | wet adiabatic lapse rate (K/m) |

g | Standard gravity |

H_{v} | heat of vaporization of water (2501000 J/kg) (J/kg) |

r | mixing ratio of the mass of water vapour to the mass of dry air (dimensionless) |

R_{sd} | specific gas constant of dry air (287 J*kg^−1 K^−1) (J/(kg*K)) |

T | temperature of the saturated air (K) |

c_{pd} | specific heat of dry air at constant pressure (1003.5 J*kg^−1 K^−1) (J/(kg*K)) |

R_{sw} | specific gas constant of water vapour (461.5 J*kg^−1 K^−1) (J/(kg*K)) |