Science Facts

What Is Lapse Rate? – Types, Formula & Application

Lapse Rate

The lapse rate is simply a temperature change rate with altitude and no fixed lapse rate in the real world. Atmospheric pressure decreases with altitude. So as an air parcel is forced to rise, it expands. The expanded parcel cools not from loss of heat energy because energy is dispersed over the larger volume. Temperature changes resulting from pressure changes are called adiabatic. It is a process that does not gain or lose energy from the surrounding environment.

The ability of air to hold water vapor is temperature-dependent. So moisture will condense when air is cooled to the dew point. As condensation begins, latent heat is released. As it rises farther, the air parcel continues to cool by expansion, but it cools at a slower or wet adiabatic rate. The cooling rate decreases as condensation continues because the cooling is partially counteracted by releasing latent heat from what’s in.

What is lapse rate?

A lapse rate is just a rate of change of temperature with altitude. Lapse rates aren’t stationary. The term adiabatic means that there’s no heat lost or gained to the surrounding atmosphere. In the atmosphere, the air parcel is not giving off heat to the surrounding environment, and it’s not receiving heat from the surrounding environment.

  • The temperature, on average, changes about 6.5 degrees per kilometer as change altitude.

Adiabatic processes involve direct energy exchanges. An example is the air’s heating or cooling as it moves across a hot or cold surface. Adiabatic processes do not involve net energy exchange. Heating or cooling is achieved by compression or expansion of the air. Imagine air molecules flying around in a chamber. High temperature means that the molecules have high kinetic energy. They’re flying very fast.

  • When air molecules compress, then they will start flying faster. It means that the air is getting warmer.
  • When air molecules expand, the air molecules will fly at a slower speed, or in other words, the air cools down.

The air pressure decreases with altitude. If an air parcel rises for whatever reason, it will get into a region of lower air pressure. As a result, it will expand and cool.

  • If force work on an air parcel to rise, it will expand and cool.
  • If force work on an air parcel to sink, it will contract and warm.

There are three types of lapse rates. They are:

  1. Dry adiabatic lapse rate.
  2. Wet adiabatic lapse rate.
  3. The environmental lapse rate.

There is no heat added or removed from the system but the observed temperature changes. The gas expands, distributing the energy. It has over a larger area, so therefore the gas itself feels colder. In the same way, the air is denser near the surface of the earth. Thus if a packet of air rises, it cools as it expands into the less dense space above it. The rate at which it cools is called the adiabatic lapse rate.

Lapse rate curve
Lapse rate curve

There are two types of adiabatic lapse rates.

  • Dry adiabatic lapse rate (DALR).
  • Wet adiabatic lapse rate (SALR) or Saturated adiabatic lapse rate.

1. Dry adiabatic lapse rate

The temperature changes with altitude when there is no moisture present in the air parcel or very little moisture in the air parcel. In unsaturated air, as air rises, it cools at 3 degrees centigrade per 1,000 feet. As it cools, it condenses. Eventually, clouds will form. As long as no condensation is involved, a rising air parcel temperature decreases at a fixed rate.

This rate is called the dry adiabatic lapse rate. It is 10 degrees Celsius per 1000 meters. If surface air temperature happens to be 32 degrees Celsius and forces the air to rise to 1,000 meters, the temperature will be 22 degrees Celsius. The force up to 2,000 meters will cool down another 10 degrees, so its temperature is 12 degrees.

The opposite happens when force work on it to come down, it will increase its temperature again at 10 degrees per 1000 meters. If an air parcel is lifted high enough, it will eventually get so cold that it can no longer hold the water vapor. It is the height at which saturation occurs. It is also called the lifting condensation level because further lifting will cause condensation. Condensation means that water vapor gets from the gaseous into the liquid states. We see the formation of clouds.

2. Wet adiabatic lapse rate

The dew point is the term given to the temperature where there is a hundred percent relative humidity. In Layman’s terms is at the temperature that clouds will form as clouds form, the lapse rate changes due to latent heat. As the air condenses, latent heat is released. So as the air cools once it reaches its dew point because of extra heat being released. The rate at which it cools decreases. This reduced rate is the saturated adiabatic lapse rate at 1.5 degrees centigrade per 1,000 feet.

The dewpoint temperature, which depends on the air’s water vapor content, is two degrees Celsius. At 3,000 meters, the air reaches its dew point of 2 degrees Celsius. So any other lifting will cause further condensation in the formation of the cloud. The process of condensation releases energy. Therefore the rate at which the air temperature decreases from the lifting condensation level upward will be less. The air parcel still expands. It still cools down but not so much anymore because energy is released through condensation.

Beyond the lifting condensation level, air parcels cool at the moist adiabatic lapse rate. It is approximately 5 degrees Celsius per 1000 meters. It is also called the saturated or wet adiabatic lapse rate. The real value can be between 4 & 9 degrees Celsius per thousand meters. It depends on the amount of water vapor that condenses during the lifting.

The dry and wet adiabatic lapse rates are values for the temperature decrease of a lifted air parcel. These are not values for temperature decrease with altitude that can be measured by taking temperature readings at different altitudes.

3. Environmental lapse rate (ELR)

The temperature within the troposphere layer decreases with altitude. ELR is also an ambient lapse rate. Similar to the other lapse rates, it expresses in temperature difference per 1000 meter altitude difference. The environmental lapse rate varies with time and place. It depends strongly on surface temperatures. Solar radiation causes surface heating during the day. This generally leads to high temperatures near the surface and a high environmental lapse rate in the lower atmosphere.

Terrestrial radiation causes surface cooling during the night, which typically results in a low environmental lapse rate. When the new surface air is colder than the upper air, then it is a temperature inversion. The horizontal transport of air is advection. It is another factor that influences the environmental lapse rate. Advection of cold or warm air at different levels, such as varying wind direction with altitude, causes changes in the environmental lapse rate.

Adiabatic cooling occurs when air expands because it is lifted. 4 principle mechanisms can initiate an air parcel’s lifting.

  • Orographic lifting.
  • Frontal lifting.
  • Convergence lifting.
  • Convection lifting.

Orographic lifting

Orographic uplift occurs when mountains act as barriers to the flow of air. Air ascends the mountain slope causes adiabatic cooling. This often generates clouds. Many of the rule’s rainiest places are located on windward mountain slopes. When air reaches the leeward side of the mountain, much of the moisture has been lost. Air descends warms adiabatically, and condensation and precipitation are not likely.

The results are rain shadow deserts such as the Great Basin desert in the western United States and the Patagonia Desert in Argentina. The rising air on the mountain range’s windward side first dry adiabatically and later wet adiabatically. The sinking air on the leeward side of the mountain range warms only dry adiabatically. The results are warm downslope winds on the leeward side, such as the chinook winds in the Rocky Mountains or the Alps’ fern winds.

Frontal lifting: A front is a line where cold and warm air masses collide. It causes the lifting of warm air, which is called frontal lifting.

Convergence lifting: A low-pressure center, also called a cyclone, always causes air to converge. Horizontal convergence always causes air to rise.

Convection lifting: Convection occurs when air is lifted as the result of heating near the surface. It is localized over fairly limited areas and can result in localized thundershowers.

Two forces are working on an air parcel.

  • Gravitational force.
  • Buoyancy force.

Gravitational force tries to pull it down to the earth’s surface. Buoyancy force tries to pull it upward. It is simply the result of higher air pressure near the ground, low air pressure in the upper atmosphere. As a result, air should be moving upward. These two forces are at an equilibrium. There is no reason for an air parcel to rise or sink. However, their changes when the density of the air parcel changes.

  • If an air parcel has a higher density than its surrounding air, it will sink towards the Earth’s surface.
  • If the air parcel density is lower than the surrounding air, then it will rise.

Lapse rate formula: The temperature difference, Δ temp = Δ elevation × lapse rate

Lapse rate = Δ temp/Δ elevation.

What determines the density of air? The answer is simple. It’s the temperature: Lower temperature higher density, higher temperature lower density. An air parcel warmer than its surroundings will rise an air parcel that is colder than its surroundings will sink.

Lapse rate problems & solutions

Problem 1: The environmental lapse rate is 3.8 °F/1000ft. If the ground temperature is 68 °F, what will the temperature be at 5400ft?

Solution: The temperature difference, Δ temp = Δ elevation × lapse rate

Δ temp = 5400 ft (3.8 °F/1000ft) = 20.5 °F.

Temperature at 5400 ft = 68 °F – 20.5 = 47.5 °F.

Problem 2: A ballon of classroom air is 70 F. If the ballon is brought to the top of the Sandia Mountains in Albuquerque, what will the air temperature inside the balloon be? Assume adiabatic cooling.

Solution: The temperature difference, Δ temp = Δ elevation × lapse rate

Δ temp = 5400 ft (5.4 °F/1000ft) = 29.2 °F.

Temperature at 5400 ft = 70 °F – 29.2 °F = 40.8 °F.

Application of lapse rate

Lapse rate help to determine the temperature variation with altitude or how actual temperatures vary altitude. It is used frequently in atmospheric sciences and studying other earth processes like magma’s movement through the crust. Cloud formation, weather news, storm/disaster alarm all depend on the lapse rate calculation.

  • If an air parcel is displayed vertically, it will change its temperature due to its size.
  • An air parcel with more than the surrounding air will rise due to its lesser density.
  • An air parcel that is colder than the surrounding air will sink to do its increased density.

That’s just some basic physical processes in the atmosphere. Stable air is a term given to air that returns to its original position after it’s displaced either up or down. Simultaneously, unstable air is a term given to the air that moves in the replaced direction. So if it’s lighter and continues to move, it’ll be unstable and promote unstable weather conditions.


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Sources:

Jacobson, Mark Zachary. Fundamentals of Atmospheric Modeling (2nd ed.). Cambridge University Press. ISBN 978-0-521-83970-9.
Ahrens, C. Donald. Meteorology Today (8th ed.). Brooks/Cole Publishing. ISBN 978-0-495-01162-0.
Todd S. Glickman (June 2000). Glossary of Meteorology (2nd ed.). American Meteorological Society, Boston.
Salomons, Erik M. (2001). Computational Atmospheric Acoustics (1st ed.). Kluwer Academic Publishers.

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