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# Lapse rate

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 Title: Lapse rate Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Lapse rate

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.

## Contents

• Definition 1
• Mathematical definition 2
• Types of lapse rates 3
• Environmental lapse rate 3.1
• Dry adiabatic lapse rate 3.2
• Saturated adiabatic lapse rate 3.3
• Thermodynamic-based lapse rate 3.4
• Significance in meteorology 4
• References 6

## Definition

A formal definition from the Glossary of Meteorology is:

The decrease of an atmospheric variable with height, the variable being temperature unless otherwise specified.

In the lower regions of the atmosphere (up to altitudes of approximately 12,000 metres (39,000 ft), temperature decreases with altitude at a fairly uniform rate. Because the atmosphere is warmed by convection from Earth's surface, this lapse or reduction in temperature is normal with increasing distance from the conductive source.

Although the actual atmospheric lapse rate varies, under normal atmospheric conditions the average atmospheric lapse rate results in a temperature decrease of 6.4 °C/km (3.5 °F or 1.95 °C/1,000 ft) of altitude above ground level.

The measurable lapse rate is affected by the moisture content of the air (humidity). A dry lapse rate of 10 °C/km (5.5 °F or 3.05 °C/1,000 ft) is often used to calculate temperature changes in air not at 100% relative humidity. A wet lapse rate of 5.5 °C/km (3 °F or 1.68 °C/1,000 ft) is used to calculate the temperature changes in air that is saturated (i.e., air at 100% relative humidity). Although actual lapse rates do not strictly follow these guidelines, they present a model sufficiently accurate to predict temperate changes associated with updrafts and downdrafts. This differential lapse rate (dependent upon both difference in conductive heating and adiabatic expansion or compression) results in the formation of warm downslope winds (e.g., Chinook winds, Santa Ana winds, etc.). The atmospheric lapse rate, combined with adiabatic cooling and heating of air related to the expansion and compression of atmospheric gases, present a unified model explaining the cooling of air as it moves aloft and the heating of air as it descends downslope.

Atmospheric stability can be measured in terms of lapse rates (i.e., the temperature differences associated with vertical movement of air). The atmosphere is considered conditionally unstable where the environmental lapse rate causes a slower decrease in temperature with altitude than the dry adiabatic lapse rate, as long as no latent heat is released (i.e. the saturated adiabatic lapse rate applies). Unconditional instability results when the dry adiabatic lapse rate causes air to cool slower than the environmental lapse rate, so air will continue to rise until it reaches the same temperature as its surroundings. Where the saturated adiabatic lapse rate is greater than the environmental lapse rate, the air cools faster than its environment and thus returns to its original position, irrespective of its moisture content.

Although the atmospheric lapse rate (also known as the environmental lapse rate) is most often used to characterize temperature changes, many properties (e.g. atmospheric pressure) can also be profiled by lapse rates...

## Mathematical definition

In general, a lapse rate is the negative of the rate of temperature change with altitude change, thus:

\gamma = -\frac{dT}{dz}

where \gamma is the lapse rate given in units of temperature divided by units of altitude, T = temperature, and z = altitude.

Note: In some cases, \Gamma or \alpha can be used to represent the adiabatic lapse rate in order to avoid confusion with other terms symbolized by \gamma, such as the specific heat ratio or the psychrometric constant.

## Types of lapse rates

There are two types of lapse rate:

• Environmental lapse rate (ELR) – which refers to the actual change of temperature with altitude for the stationary atmosphere (i.e. the temperature gradient)
• The adiabatic lapse rates – which refer to the change in temperature of a parcel of air as it moves upwards (or downwards) without exchanging heat with its surroundings. There are two adiabatic rates:
• Dry adiabatic lapse rate (DALR)
• Moist (or saturated) adiabatic lapse rate (SALR)

### Environmental lapse rate

The environmental lapse rate (ELR), is the rate of decrease of temperature with altitude in the stationary atmosphere at a given time and location. As an average, the

• Definition, equations and tables of lapse rate from the Planetary Data system.
• National Science Digital Library glossary:
• Lapse Rate
• Environmental lapse rate
• Absolute stable air
• An introduction to lapse rate calculation from first principles from U. Texas