Lifted condensation level
Encyclopedia
The lifted condensation level or lifting condensation level (LCL) is formally defined as the height at which the relative humidity
(RH) of an air parcel
will reach 100% when it is cooled by dry adiabatic lifting. The RH of air increases when it is cooled, since the amount of water vapor in the air (i.e., its specific humidity) remains constant, while the saturation vapor pressure decreases almost exponentially with decreasing temperature. If the air parcel is lifting further beyond the LCL, water vapor
in the air parcel will begin condensing
, forming cloud droplets
. (In the real atmosphere, it is usually necessary for air to be slightly supersaturated, normally by around 0.5%, before condensation occurs; this translates into about 10 meters or so of additional lifting above the LCL.) The LCL is a good approximation of the height of the cloud base
which will be observed on days when air is lifted mechanically from the surface to the cloud base (e.g., due to convergence of airmasses).
such as the Skew-T log-P diagram
or the Tephigram
. Nearly all of these formulations make use of the relationship between the LCL and the dew point
, which is the temperature
to which an air parcel needs to be cooled isobarically until its RH just reaches 100%. The LCL and dew point are similar, with one key difference: to find the LCL, an air parcel's pressure
is decreased while it is lifted, causing it to expand, which in turn causes it to cool. To determine the dew point, in contrast, the pressure is kept constant, and the air parcel is cooled by bringing it into contact with a colder body (this is like the condensation you see on the outside of a glass full of a cold drink). Below the LCL, the dew point temperature is less than the actual ("dry bulb") temperature. As an air parcel is lifted, its pressure and temperature decrease. Its dew point temperature also decreases when the pressure is decreased, but not as quickly as its temperature decreases, so that if the pressure is decreased far enough, eventually the air parcel's temperature will be equal to the dew point temperature at that pressure. This point is the LCL; this is graphically depicted in the diagram.
Using this background, the LCL can be found on a standard thermodynamic diagram as follows:
Interestingly, there is actually no exact analytical formula for the LCL, since it is defined by an implicit equation without an exact solution. Normally an iterative procedure is used to determine a highly accurate solution for the LCL (i.e., an altitude is guessed, and the RH for a parcel lifted to that altitude is computed; if it is below 100%, then a higher altitude is taken as the next step in the iteration, or if it is above 100%, then a lower altitude is taken; this is repeated until the desired accuracy for the computed LCL is reached).
There are also many different ways to approximate the LCL, to various degrees of accuracy. The most well known and widely used among these is Espy's
equation, which Espy formulated already in the early 19th century. His equation makes use of the relationship between the LCL and dew point temperature discussed above. In the Earth's atmosphere near the surface, the lapse rate
for dry adiabatic lifting is about 9.8 K/km, and the lapse rate of the dew point is about 1.8 K/km (it varies from about 1.6-1.9 K/km). This gives the slopes of the curves shown in the diagram. The altitude where they intersect can be computed as the ratio between the difference in the initial temperature and initial dew point temperature (T-Td) to the difference in the slopes of the two curves. Since the slopes are the two lapse rates, their difference is about 8 K/km. Inverting this gives 0.125 km/K, or 125 m/K. Recognizing this, Espy pointed out that the LCL can be approximated as:
where h is height of the LCL (in meters), T is temperature in degrees Celsius (or kelvin
s), and Td is dew point temperature (likewise in degrees Celsius or kelvins, whichever is used for T). This formula is accurate to within about 1% for the LCL height under normal atmospheric conditions, but requires knowing the dew point temperature.
Another simple approximation for determining the LCL for moist air makes use of a rule-of-thumb relationship between the "dew point depression" (the temperature difference T-Td) and the RH, which is that the RH decreases by 5% for every degree (Celsius) increase in the dew point depression, starting at RH=100% when T − Td = 0 (for more information, see dew point
). Applying this directly in Espy's formula, however, results in a substantial overestimate of the LCL at lower temperatures. A correction for this is provided by Lawrence's formula:
where T is the temperature at the ground level in degrees Celsius, and RH is the ground level relative humidity in percent. This formula is very simple to use (so that you only need to know T and RH to estimate the LCL, even without a calculator), yet accurate to within about 10% for the LCL height under normal atmospheric conditions, provided RH>50% (it becomes inaccurate for drier air).
In addition to these simple approximations, several much more complex and more accurate approximations have been proposed in the scientific literature, for instance by Bolton (1980) and Inman (1969).
(CCL) results when strong surface heating causes buoyant lifting of surface air and subsequent mixing of the planetary boundary layer
, so that the layer near the surface ends up with a dry adiabatic lapse rate. As the mixing becomes deeper, it will get to the point where the LCL of an air parcel starting at the surface is at the top of the mixed region. When this occurs, then any further solar heating of the surface will cause a cloud to form topping the well-mixed boundary layer, and the level at which this occurs is called the CCL. If the boundary layer starts off with a stable temperature profile (that is, with a lapse rate less than the dry adiabatic lapse rate), then the CCL will be higher than the LCL. In nature, the actual cloud base is often initially somewhere between the LCL and the CCL. If a thunderstorm forms, then as it grows and matures, processes such as increased saturation at lower levels from precipitation and lower surface pressure usually lead to a lowering of the cloud base.
Finally, the LCL can also be considered in relation to the level of free convection
(LFC). A smaller difference between the LCL and LFC (LCL-LFC) is conducive to the rapid formation of thunderstorms. One reason for this is that a parcel requires less work
and time to pass through the layer of convective inhibition
(CIN) to reach its level of free convection
(LFC), after which deep, moist convection
ensues and air parcels buoyantly
rise in the positive area
of a sounding, accumulating convective available potential energy
(CAPE) until reaching the equilibrium level
(EL).
Relative humidity
Relative humidity is a term used to describe the amount of water vapor in a mixture of air and water vapor. It is defined as the partial pressure of water vapor in the air-water mixture, given as a percentage of the saturated vapor pressure under those conditions...
(RH) of an air parcel
Air parcel
In fluid dynamics, within the framework of continuum mechanics, a fluid parcel is a very small amount of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may...
will reach 100% when it is cooled by dry adiabatic lifting. The RH of air increases when it is cooled, since the amount of water vapor in the air (i.e., its specific humidity) remains constant, while the saturation vapor pressure decreases almost exponentially with decreasing temperature. If the air parcel is lifting further beyond the LCL, water vapor
Water vapor
Water vapor or water vapour , also aqueous vapor, is the gas phase of water. It is one state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from the sublimation of ice. Under typical atmospheric conditions, water vapor is continuously...
in the air parcel will begin condensing
Condensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....
, forming cloud droplets
Cloud
A cloud is a visible mass of liquid droplets or frozen crystals made of water and/or various chemicals suspended in the atmosphere above the surface of a planetary body. They are also known as aerosols. Clouds in Earth's atmosphere are studied in the cloud physics branch of meteorology...
. (In the real atmosphere, it is usually necessary for air to be slightly supersaturated, normally by around 0.5%, before condensation occurs; this translates into about 10 meters or so of additional lifting above the LCL.) The LCL is a good approximation of the height of the cloud base
Cloud base
This article refers to meteorology. For the airborne base of the TV series Captain Scarlet and the Mysterons, see Cloudbase.The cloud base is the lowest altitude of the visible portion of the cloud...
which will be observed on days when air is lifted mechanically from the surface to the cloud base (e.g., due to convergence of airmasses).
Determining the LCL
The LCL can be either computed numerically, approximated by various formulas, or determined graphically using standard thermodynamic diagramsThermodynamic diagrams
Thermodynamic diagrams are diagrams used by scientists and engineers to represent the thermodynamic states of a material and the consequences of manipulating this material...
such as the Skew-T log-P diagram
Skew-T log-P diagram
A Skew-T Log-P diagram is one of four thermodynamic diagrams commonly used in weather analysis and forecasting. In 1947, N. Herlofson proposed a modification to the emagram which allows straight, horizontal isobars, and provides for a large angle between isotherms and dry adiabats, similar to that...
or the Tephigram
Tephigram
A tephigram is one of four thermodynamic diagrams commonly used in weather analysis and forecasting. The name evolved from the original name "T-\phi-gram" to describe the axes of temperature and entropy used to create the plot...
. Nearly all of these formulations make use of the relationship between the LCL and the dew point
Dew point
The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water. The condensed water is called dew when it forms on a solid surface. The dew point is a saturation temperature.The dew point is...
, which is the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
to which an air parcel needs to be cooled isobarically until its RH just reaches 100%. The LCL and dew point are similar, with one key difference: to find the LCL, an air parcel's pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
is decreased while it is lifted, causing it to expand, which in turn causes it to cool. To determine the dew point, in contrast, the pressure is kept constant, and the air parcel is cooled by bringing it into contact with a colder body (this is like the condensation you see on the outside of a glass full of a cold drink). Below the LCL, the dew point temperature is less than the actual ("dry bulb") temperature. As an air parcel is lifted, its pressure and temperature decrease. Its dew point temperature also decreases when the pressure is decreased, but not as quickly as its temperature decreases, so that if the pressure is decreased far enough, eventually the air parcel's temperature will be equal to the dew point temperature at that pressure. This point is the LCL; this is graphically depicted in the diagram.
Using this background, the LCL can be found on a standard thermodynamic diagram as follows:
- Start at the initial temperature (T) and pressure of the air parcel and follow the dry adiabatic lapse rate line upward (provided that the RH in the air parcel is less than 100%, otherwise it is already at or above LCL).
- From the initial dew pointDew pointThe dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water. The condensed water is called dew when it forms on a solid surface. The dew point is a saturation temperature.The dew point is...
temperature (Td) of the parcel at its starting pressure, follow the line for the constant equilibrium mixing ratio (or "saturation mixing ratio") upward. - The intersection of these two lines is the LCL.
Interestingly, there is actually no exact analytical formula for the LCL, since it is defined by an implicit equation without an exact solution. Normally an iterative procedure is used to determine a highly accurate solution for the LCL (i.e., an altitude is guessed, and the RH for a parcel lifted to that altitude is computed; if it is below 100%, then a higher altitude is taken as the next step in the iteration, or if it is above 100%, then a lower altitude is taken; this is repeated until the desired accuracy for the computed LCL is reached).
There are also many different ways to approximate the LCL, to various degrees of accuracy. The most well known and widely used among these is Espy's
James Pollard Espy
For the fictional character, see The Magicians of Xanth.James Pollard Espy was a U.S. meteorologist. Espy developed a convection theory of storms, explaining it in 1836 before the American Philosophical Society and in 1840 before the French Académie des Sciences and the British Royal Society...
equation, which Espy formulated already in the early 19th century. His equation makes use of the relationship between the LCL and dew point temperature discussed above. In the Earth's atmosphere near the surface, the lapse rate
Lapse rate
The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is temperature unless specified otherwise. The terminology arises from the word lapse in the sense of a decrease or decline; thus, the lapse rate is the rate of decrease with height and...
for dry adiabatic lifting is about 9.8 K/km, and the lapse rate of the dew point is about 1.8 K/km (it varies from about 1.6-1.9 K/km). This gives the slopes of the curves shown in the diagram. The altitude where they intersect can be computed as the ratio between the difference in the initial temperature and initial dew point temperature (T-Td) to the difference in the slopes of the two curves. Since the slopes are the two lapse rates, their difference is about 8 K/km. Inverting this gives 0.125 km/K, or 125 m/K. Recognizing this, Espy pointed out that the LCL can be approximated as:
where h is height of the LCL (in meters), T is temperature in degrees Celsius (or kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
s), and Td is dew point temperature (likewise in degrees Celsius or kelvins, whichever is used for T). This formula is accurate to within about 1% for the LCL height under normal atmospheric conditions, but requires knowing the dew point temperature.
Another simple approximation for determining the LCL for moist air makes use of a rule-of-thumb relationship between the "dew point depression" (the temperature difference T-Td) and the RH, which is that the RH decreases by 5% for every degree (Celsius) increase in the dew point depression, starting at RH=100% when T − Td = 0 (for more information, see dew point
Dew point
The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water. The condensed water is called dew when it forms on a solid surface. The dew point is a saturation temperature.The dew point is...
). Applying this directly in Espy's formula, however, results in a substantial overestimate of the LCL at lower temperatures. A correction for this is provided by Lawrence's formula:
where T is the temperature at the ground level in degrees Celsius, and RH is the ground level relative humidity in percent. This formula is very simple to use (so that you only need to know T and RH to estimate the LCL, even without a calculator), yet accurate to within about 10% for the LCL height under normal atmospheric conditions, provided RH>50% (it becomes inaccurate for drier air).
In addition to these simple approximations, several much more complex and more accurate approximations have been proposed in the scientific literature, for instance by Bolton (1980) and Inman (1969).
Relation with CCL
The convective condensation levelConvective condensation level
The convective condensation level represents the height where an air parcel becomes saturated when lifted adiabatically to achieve buoyant ascent. It marks where cloud base begins when air is heated from below to the convective temperature, without mechanical lift...
(CCL) results when strong surface heating causes buoyant lifting of surface air and subsequent mixing of the planetary boundary layer
Planetary boundary layer
The planetary boundary layer , also known as the atmospheric boundary layer , is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface forcing in an hour or less...
, so that the layer near the surface ends up with a dry adiabatic lapse rate. As the mixing becomes deeper, it will get to the point where the LCL of an air parcel starting at the surface is at the top of the mixed region. When this occurs, then any further solar heating of the surface will cause a cloud to form topping the well-mixed boundary layer, and the level at which this occurs is called the CCL. If the boundary layer starts off with a stable temperature profile (that is, with a lapse rate less than the dry adiabatic lapse rate), then the CCL will be higher than the LCL. In nature, the actual cloud base is often initially somewhere between the LCL and the CCL. If a thunderstorm forms, then as it grows and matures, processes such as increased saturation at lower levels from precipitation and lower surface pressure usually lead to a lowering of the cloud base.
Finally, the LCL can also be considered in relation to the level of free convection
Level of free convection
The level of free convection is the altitude in the atmosphere where the temperature of the environment decreases faster than the moist adiabatic lapse rate of a saturated air parcel at the same level....
(LFC). A smaller difference between the LCL and LFC (LCL-LFC) is conducive to the rapid formation of thunderstorms. One reason for this is that a parcel requires less work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...
and time to pass through the layer of convective inhibition
Convective inhibition
Convective inhibition is a numerical measure in meteorology that indicates the amount of energy that will prevent an air parcel from rising from the surface to the level of free convection....
(CIN) to reach its level of free convection
Level of free convection
The level of free convection is the altitude in the atmosphere where the temperature of the environment decreases faster than the moist adiabatic lapse rate of a saturated air parcel at the same level....
(LFC), after which deep, moist convection
Atmospheric convection
Atmospheric convection is the result of a parcel-environment instability, or temperature difference, layer in the atmosphere. Different lapse rates within dry and moist air lead to instability. Mixing of air during the day which expands the height of the planetary boundary layer leads to...
ensues and air parcels buoyantly
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
rise in the positive area
Free convective layer
In atmospheric sciences, the free convective layer is the layer of conditional or potential instability in the troposphere. It is a layer of positive buoyancy and is the layer where deep, moist convection can occur. On an atmospheric sounding, it is the layer between the level of free...
of a sounding, accumulating convective available potential energy
Convective available potential energy
In meteorology, convective available potential energy , sometimes, simply, available potential energy , is the amount of energy a parcel of air would have if lifted a certain distance vertically through the atmosphere...
(CAPE) until reaching the equilibrium level
Equilibrium level
In meteorology, the equilibrium level , or level of neutral buoyancy , or limit of convection , is the height at which a rising parcel of air is at a temperature of equal warmth to it....
(EL).
Related Reading
- Bohren, C.F., and B. Albrecht, Atmospheric Thermodynamics, Oxford University Press, 1998. ISBN 0-19-509904-4
- M K Yau and R.R. Rogers, Short Course in Cloud Physics, Third Edition, published by Butterworth-Heinemann, January 1, 1989, 304 pages. EAN 9780750632157 ISBN 0-7506-3215-1
External links
- LCL tutorial
- SKEW-T: A LOOK AT SBLCL
- Lifting condensation level (LCL) (Glossary of Meteorology)