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unstable parcel lifted to its LCL will typically be cooler than the environment at the

LCL. Further lifting will cause the parcel to cool at a slower rate than the environ-

ment and eventually will become warmer than the environment. To ﬁnd the LCL on

a thermodynamic diagram ﬁrst determine from which level you wish to raise a

parcel. (Typically the LCL is found for a parcel taken from the surface, but in certain

atmospheric conditions, it may be more pertinent for a meteorologist to raise a parcel

from a level other than the surface, especi ally if there is strong convergence at

another level.) Initially the parcel is assumed to have the same temperature and

moisture content (dew-point temperature) as the environment. Starting from the

temperature follow the dry adiabat (constant potential temperature), since the

parcel temperature will change at the dry adiabatic lapse rate until it becomes

saturated. From the dew-point temperature, follow the intersecting line of constant

mixing ratio. The actual grams per kilogram of water vapor in the air is assumed to

not change, so long as the parcel rises the mixing ratio remains constant. Note that

while the actual amount of water vapor remains constant, the relative humidity will

increase. The pressure level at which the mixing ratio value of the parcel intersects

the potential temperature of the parcel is the level at which the parcel is saturated.

This level is the lifting condensation level (Fig. 6).

Level of Free Convection (LFC) In the atmosphere there are many mechan-

isms that may force a parcel to rise, and thus initiate convection. The level of free

convection is the level above which a parcel becomes buoyant and thus will continue

to rise without any addit ional lifting. Typically, the LFC is found at a height above

the LCL. To determine the LFC of a parcel, one need only follow the parcel path

until it crosses the environmental temperature proﬁle (Fig. 6). The path the parcel

will follow is along the dry adiabat until the LCL is reached, and along the pseudo-

adiabat above the LCL. Due to the existence of layers of increased stability (low

Figure 6 Determining the LCL, LFC, and EL of a parcel. See ftp site for color image.

246

THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

lapse rates) in the atmosphere, a parcel may have multiple levels of free convection.

When using the LFC to determine how much lif ting or vertica l motion is needed to

produce free convection, the LFC at the lowest pressure level (highest above the

ground) is typically used.

Equilibrium Level (EL) The equilibrium level is the level at which a parcel

buoyant relative to the environment is no longer buoyant. At the equilibrium level,

the parcel and the environment have the same temperature. If a parcel rises above the

equilibrium level, it will become colder than the environment and thus negatively

buoyant. To determine the EL, follow the parcel path from the LFC until it intersects

the environmental temperature (Fig. 6). Often the equilibrium level will be found

near the beginning of the tropopause. The tropopause is isothermal in nature and

thus very stable. On a sounding with multiple levels of free convection, there will

also be multiple equilibrium levels. In an extremely stable environment, with no

level of free convection, there will also be no equilibrium level. It is noteworthy to

mention that while the equilibrium level represents where a parcel is no longer

positively buoyant, it does not mean the parcel cannot continue rising. Above the

equilibrium level, while the parcel is negatively buoyant, a parcel that reaches this

level will have a certain amount of kinetic energy due to its vertical motion. This

kinetic energy will allow the parcel to continue rising until the energy associated

with the negative buoyancy balances the kinetic energy.

Convective Condensation Level (CCL) The convective condensation level

can be used as a proxy for the level at which the base of convective clouds will

begin. The CCL differs from the LCL in that the LCL assumes some sort of lifting,

and the CCL assumes the parcel is rising due to convection alone. To determine the

convective condensation level on a thermodynamic diagram use the dew-point

temperature and follow the mixing ratio line that intersects that dew-point tempera-

ture until it crosses the environmental temperature (Fig. 7). This represents the level

at which a parcel rising solely due to convection will become saturated and form the

base of a cloud.

Convective Temperature (CT) The convective temperature is the temperature

that must be reached at the surface to form purely convective clouds. If daytime

heating warms the surface to the convective temperature, thermals will begin to rise

and, upon reaching the CCL, be not only saturated but also positively buoyant. The

convective temperature is determined by ﬁrst locating the CCL. The dry adiabat,

which intersects the convective condensation level, is followed down to the surface

(Fig. 7). The temperature at the surface represents the convective temperature. If the

surface is able to warm to the convective temperature, then the LCL and CCL are the

same.

Mixing Condensation Level (MCL) Clouds can form as a result of turbulent

mixing rather than lifting or convection. The height at which a cloud will form due

to mixing can be determined on a thermodynamic diagram and is referred to as the

2 ATMOSPHERIC STATIC STABILITY 247

mixing condensation level (Fig. 8). The MCL is determined on a thermodynamic

diagram by estimating the average water content (mixing ratio) and the average

potential temperature (y) within the layer. The pressure level at which the average

mixing ratio and average potential temperature intersect is the mixing condensation

level. The idea is that in a well-mixed layer the amount of moisture will be constant

with height, as will the potential temperature. This process often occurs in a shallow

strongly capped boundary layer with wind speeds over 10 m=s. The mixing process

that forms the cloud is the same process that allows one to ‘‘see their breath’’ on a

cold day. While the boundary layer may initially be unsaturated throughout, turbu-

lent mixing can redistribute the moisture and result in saturation near the top of the

boundary layer.

Figure 7 Determining the CCL and CT. See ftp site for color image.

Figure 8 Determining the MCL. See ftp site for color image.

248

THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

Diagnosing Stability and Parcel Path

The thermodynamic proﬁle of the atmosphere is indicative of the stability of the

atmosphere. Understanding the stability of various layers of the troposphere is

important in forecasting what processes may occur. To discuss stability, the environ-

ment is compared to a parcel. A parcel can be thought of as an entity of the atmo-

sphere with speciﬁc temperature and moisture content, which is assumed to not

interact with the air around it, and thus undergoes purely adiabatic processes.

With this assumption about a parcel, it is easy to ascertain on a thermodynamic

diagram the temperature a parcel would have as a result of being either raised or

lowered in the atmosphere. This temperature of the parcel at various pressure levels

can be drawn on a thermodynamic diagram and is referred to as the parcel path. In

general, it is assumed that an unsaturated parcel will change temperature at the dry

adiabatic lapse rate, while a saturated parcel will change temperature at the pseudo-

adiabatic (moist) lapse rate, as it moves up or down from its initial location.

Stability is determined by comparing the temperature of a parcel to the tempera-

ture of the environment to which the parcel rises or sinks (Fig. 9). A parcel that is

warmer than the environment is unstable and will rise. A parcel colder than the

environment is stable and will sink. However, it is important to remember that a

parcel will cool as it rises. Therefore, the stability at a single point is not as important

as stability throughout the layer. By comparing the environmental lapse rate to the

lapse rate of the parcel, stability can be determined. A layer is stable if the environ-

mental lapse rate is greater than the parcel’s lapse rate. A layer is unstable if the

environmental lapse rate is less than the parcel’s lapse rate. The lapse rate of the

parcel is dependen t on whether the parcel is unsaturated or saturated. An unsaturated

parcel will cool at the dry adiabatic lapse rate (DALR), of approximately 9.8



C=km

in the troposphere. A saturated parcel will cool at the moist adiabatic lapse rate. The

moist adiabatic lapse rate (MALR) is not constant (hence the use of a thermody-

Figure 9 Using the environmental temperature lapse rate to determine stability. See ftp site

for color image.

2 ATMOSPHERIC STATIC STABILITY 249

namic diagram for ease), but averages about 6



C=km in the troposphere. The moist

adiabatic lapse rate is always less than the dry adiabatic lapse rate. Therefore, if the

environmental lapse rate (ELR) is greater than both the moist and dry adiabatic lapse

rates, the parcel is absolutely stable in that its stabili ty is not dependent on whether

the parcel is unsaturated or saturated. A layer is absolutely unstable when the

environmental lapse rate is less than both the dry and moist adiabatic lapse rates.

In the case of an absolutely unstable layer, both dry and saturated parcels will be

unstable relative to the environment and will rise. An absolutely unstable layer is

rarely observed in a sounding because when a layer is absolutely unstable it will

instantly overturn and mix the air in the layer. If an absolutely unstable layer is

plotted on a thermodynamic diagram, it is likely that the observation is an error, with

the possi ble exception being when it is plotted in the lowest 50 m near the surface.

When the environmental lapse rate is less than the dry adiabatic lapse rate, but

greater than the moist adiabatic lapse rate, the atmosphere in that layer is condition-

ally unstable. In a conditionally unstable environment a saturated parcel will be

unstable, while an unsaturated parcel is stable. The average environmental lapse

rate of the troposphere is conditionally unstable:

DALR > MALR > ELR Absolutely stable

DALR > ELR > MALR Conditionally unstable

ELR > DALR > MA LR Absolutely unstable

As mentioned previously in this chapter, one of the beneﬁts of a thermodynamic

diagram is that area is proportional to energy. By comparing the parcel path to the

environmental temperature proﬁle on one of these diagrams, the convective available

potential energy (CAPE) and convective inhibition (CIN) can be ascertained

(Fig. 10). The equation for CAPE is found by integrating from the LFC to the EL

to determine the area where the parcel is positively buoyant:

CAPE ¼ g

LFC

parcel

 y

env

If a parcel reaches the LFC, the maximum updraft speed that could develop can

be estimated by converting the convective available potential energy into kinetic

energy. This gives an equation for the updraft speed of

w ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ



CAPE

The CIN represents the area from the surface to the LFC where the parcel is

colder than the environment. Whereas the CAPE provides an idea of how much

energy is available once the LFC is reached, the CIN gives an approximation of how

much energy must be expended to lift a parcel to the LFC. CAPE and CIN play an

important role in determining the possibility for severe weather to occur. Convective

inhibition is important for severe weather because it allows CAPE above the bound-

250 THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

ary layer to build. Convective inhibition also keeps parcels from freely rising every-

where, and thus the convection will be more focused along a speciﬁc forcing

mechanism when signiﬁcant CIN is present. Large values of CAPE are conducive

to severe weather because the more CAPE the more energy a potential storm will

have.

Inversions

When the environmental lapse rate is such that the temperat ure actually increases

with height, the layer in which this oc curs is called an inversion. An inversion is a

very stable layer. The high stability of an inversion can act to ‘‘cap’’ a layer of the

atmosphere, preventing parcels from rising above the inversion. Inversions can form

as a result of several different processes. While the environmental temperature

proﬁle is the same for different types of inversions, the environmental dew-point

proﬁle will appear different depending on the processes involved.

Subsidence Inversion The most distinct characteristic of a subsidence inver-

sion (Fig. 11) is the dryness of the inversion. A subsidence inversion occurs as the

result of widespread sinking air. The air aloft is initially cooler, and thus has less

water vapor. As the air sinks, compressional heating warms it, but no additional

water vapor is added. The dew-point temperature will decrease throughout the

inversion, with the driest air at the top of the inversion. A subsidence inversion

will commonly occur due to the position of the jet streak, causi ng wide-scale

subsidence.

Figure 10 Path of parcel rising from the surface is denoted by the arrows. See ftp site for

color image.

2 ATMOSPHERIC STATIC STABILITY 251

Radiational Inversion Strong radiational cooling can act to form an inversion.

The dew-point temperature in this inversion will typically follow the slope of the

temperature proﬁle. However, the dew-point temperature proﬁle does not have to

follow the temperature proﬁle slope in the case of a radiational inversion. See Figure

12. An inversion formed by radiational cooling is typically deduced by where in the

vertical the inversion occurs. Nighttime cooling of Earth’s surface will for m an

inversion near the surfa ce visible on morning soundings. A radiational inversion

can also be observed at the top of a cloud layer due to the cloud top cooling.

Figure 11 Subsidence inversion. See ftp site for color image.

Figure 12 Radiation inversion. See ftp site for color image.

252

THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

Frontal Inversion In the case of a frontal inversion the dew-point temperature

will generally increase with height through the inversion (Djuric, 1994) (Fig. 13).

Along a frontal boundary warm, less dense, air will override the colder denser air at

the surface. This results in the air aloft being warmer than the surface, and this is

depicted in the environmental temperature proﬁle as an inversion. A frontal inversion

is differentiated from a radiational inversion in that it is typically much deeper than a

radiational inversion. Also, meteorologists with many tool s at their disposal will be

able to determine the location of the front with surface and upper air analyses.

Inversions, even shallow ones, can play an important role in thermodynamic

processes. The height of the LFC, the amount of CAPE, and the amount of convec-

tive inhibition a sounding possesses is very dependent on the strength and height of

any inversions. The processes involved in the creation of an inversion are also

important to the stability of the atmosphere. While a frontal inversion is representa-

tive of a stable layer, a trained meteorologist may infer that there is lifting in advance

of the front, which could force convection.

BIBLIOGRAPHY

Bohren, C. F., and Albrecht, B. A. (1998). Atmospheric Thermodynamics, Oxford University

Press, New York, NY.

Djuric’, D. (1994). Weather Analysis, Prentice Hall Inc., Englewood Cliffs, New Jersey.

Emanuel, Kerry A. (1994) Atmospheric Convection, Oxford University Press, New York, NY.

Hess, Seymour L., (1959) Introduction to Theoretical Meteorology, Krieger Publishing

Company, Malabar, FL.

Glossary of Meteorology, (2nd ed.) (2000). American Meteorological Society, Boston, MA.

Wallace, J. M., and P. V. Hobbs (1977). Atmospheric Science An Introductory Survey,

Academic, San Diego, CA.

Figure 13 Frontal inversion. See ftp site for color image.

BIBLIOGRAPHY 253

CHAPTER 18

MICROPHYSICAL PROCESSES

IN THE ATMOSPHERE

ROBERT M. RAUBER

1 INTRODUCTION

Viewed from space, the most distinct features of Earth are its clouds. Most of the

world’s clouds form within rising air currents forced by atmospheric circulations that

can be local or extend over thousands of kilometers. Clouds and fogs also form when

air cools to saturation either from radiative cooling or from conduction of heat from

atmosphere to Earth’s surface. Clouds can also develop as air masses with different

thermal and moisture properties mix together. In all cases, clouds have direct inﬂu-

ence on atmospheric motions through latent heat exchange, absor ption and scatter-

ing of solar and terrestrial radia tive energy, and redistribution of water vapor. They

modulate Earth’s climate, reducing the amount of solar radiation reaching Earth and

trapping terrestrial radiation. Particle scavenging, chemical reactions, and precipita-

tion processes within clouds continuously alter the trace gas and aerosol compo sition

of the atmosphere. Clouds are an important component of Earth’s hydrological cycle.

Clouds are broadly classiﬁed according to their altitude, the strength, orientation,

and extent of their updrafts, their visual shape, and whether or not they are preci-

pitating. The internationally accepted cloud classiﬁcat ion ﬁrst proposed by Pharma-

cist Luke Howard in 1803 identiﬁes four broad categories: cumulus (clouds with

vertical development), stratus (layer clouds), cirrus (high, ﬁbrous clouds), and

nimbus (precipitating clouds), and numerous secondary categories. For example,

clouds forming at the crest of waves generated by airﬂow over mountains are

called altocumulus lenticularis because they are often lens shaped. Excellent

Handbook of Weather, Climate, and Water: Dynamics, Climate, Physical Meteorology, Weather Systems,

and Measurements, Edited by Thomas D. Potter and Bradley R. Colman.

ISBN 0-471-21490-6 # 2003 John Wiley & Sons, Inc.

255