Potter T.D., Colman B.R. (co-chief editors). The handbook of weather, climate, and water: dynamics, climate physical meteorology, weather systems, and measurements

Подождите немного. Документ загружается.

We now deﬁne the dry and moist static energies to be

 c

T  gdzþ lr

and

h  c

T  gdz;

respectively. Notice that the dry static energy is closely related to y and the moist

static energy is closely related to y

. The three energy storage terms involved are the

sensible heat (c

T), the geopotential energy (gz), and the latent heat (L

). It is

now convenient to study the total energy budget of a large-scale atmospheric system

to and assess conversions between kinetic energy and static energy.

REFERENCES

Dutton, J. (1976). The Ceaseless Wind, McGraw-Hill.

Emanuel, K. A. (1994). Atmospheric Convection, Oxford University Press.

Hess, S. L. (1959). Introduction to Theoretical Meteorology, Holt, Reinhardt, and Winston.

Iribarne, J. V., and W. L. Godson (1973). Atmospheric Thermodynamics, D. Reidel Publishing

Co.

Sears, F. W. (1953). Thermodynamics, Addison-Wesley.

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

Academic Press.

236

MOIST THERMODYNAMICS

CHAPTER 17

THERMODYNAMIC ANALYSIS IN

THE ATMOSPHERE

AMANDA S. ADAMS

1 ATMOSPHERIC THERMODYNAMIC DIAGRAMS

Before compu tations were made on computers, atmospheric scientists regularly

employed graphical techniques for evaluating atmospheric processes of all kinds

including radiation processes, dynamical processes, and thermodynamic processes.

Over the last few decades, the use of graphical techniques has almost completely

disappeared with the exception of thermodynamic diagrams and conserved variable

thermodynamic diagrams.

Classical Thermodynamic Diagrams

The thermodynamic diag ram is used to graphically display thermodynamic

processes that occur in the atmosphere. The diagram’s abscissa and ordinate are

designed to represent two of the three state variables, usually a pressure function

on one and a thermodynamic function on another. Any dry atmospheric state may be

plotted. Unfortunately, any moist state cannot be plotted as a unique point since that

must depend on the values of r

, r

, and r

. However, vapor content can be inferred

by plotting dewpoint temperature, and moist processes can be accounted for by

assuming certain characteristics of the moist process such as if the process is

pseudo-adiabatic.

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.

237

There are three characteristics of a thermodynamic diagram that are of paramount

importance. They are:

1. Area is proportional to the energy of a process or the work done by the

process. An important function of a thermodynamic diagram is to ﬁnd the

energy involved in a process. If the diagram is constructed properly, the energy

can be implied, by the area under a curve or the area between two curves

representing a process.

2. Fundamental lines are straight. Keeping the fundamental lines straight aids in

use of the thermodynamic diagram.

3. Angle between isotherms (T) and isentropes (y) are to be as large as possible.

One of the major functions of the thermodynamic diagram is to plot an

observed environmental sounding and then compare its lapse rate to the dry

adiabatic lapse rate. Since small differences are important, the larger the angle

between an isotherm and an isentrope, the more these small differences

stand out.

Over the years there have been several different thermodynamic diagrams

designed. While they all have the same basic function of representing thermody-

namic processes, they have a few fundamental differences. Before these differences

can be discussed, it is important to have an understanding of the variables and lines

found on a thermodyn amic diagram.

Dry Adiabatic Lapse Rate and Dry Adiabats

One of the lines on a thermodynamic diagram, known as the dry adiabat, is repre-

sentative of a constant potential temperature (y). Following along a dry adiabat the

potential temperature will remain constant, while the temperature will cool at the dry

adiabatic lapse rate. The dry adiabatic lapse rate represents the rate at which an

unsaturated parcel will cool as it rises in the atmosphere, assuming the parcel does

not exchange heat or mass with the air around it, hence behaving adiabatically.

The dry adiabatic lapse rate can be derived from a combination of the ﬁrst law

of thermodynamics, the ideal gas law, and the hydrostatic approximation

(see chapters 15 and 16), given by:



Thus the dry adiaba tic lapse rate for an ascending parcel is simply g=c

and is

approximately equal to 9.8



C=km or 9.8 K=km. The dry adiabat lines on a thermo-

dynamic diagram are beneﬁcial in that the user may ascend an unsaturated parcel

along the dry adiabats and simply read off the new temperature.

238 THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

Moist Adiabatic Lapse Rat e and Pseudo-Adiabats

When a parcel is saturated, it does not sufﬁce to use the dry adiabatic lapse rate. A

parcel that is saturated will experience condensation of the water vapor in the parcel.

As water vapor condenses the process releases latent heat. This release of latent heat

keeps the parcel from cooling at the dry adiabatic lapse rate. The parcel cools at a

slower rate, which is dependent on temperature. This reduced rate of temperature

decrease has a slope approximately parallel to the moist adiabat and exactly parallel

to a line of constant equivalent potential temperature. The term pseudo-adiabat is

often used to describe the moi st adiabat on a thermodynamic diagram. The moist

adiabat on a thermodynamic diagram ignores the contribution by ice, which is more

difﬁcult to represent because freezing and melting do not typically occur in equili-

brium as does condensation. In a pseudo-adiabatic process the liquid water that

condenses is assumed to be immediately removed by idealized instantaneous preci-

pitation. Thus the word pseudo-adiabat is used since the line on a thermodynamic

diagram is not truly moist adiabatic. If ice is neglected, an expression for the moist

adiabatic lapse rate can be derived in a manner similar to the dry adiabatic lapse rate,

by using the ﬁrst law for moist adiabatic hydrostatic ascent. The moist adiabatic

lapse rate can never be greater than the dry adiabatic lapse rate. At very cold

temperatures, around 40



C, the moist adiabatic lapse rate will approach the dry

adiabatic lapse rate. In the lower troposphere the moist adiabatic lapse rate may be as

small as 5.5



C=km. The equation for the moist adiabatic lapse rate is given as:



1 þ

Types of Thermodynami c Diagrams

There are several different thermodynamic diag rams. All the diagrams serve the

same basic function; however, there are differences among these diagrams that

should be understood before choosing a diagram. The emagram was named by

Refsdal as an abbreviation for ‘‘energy per unit mass diagram’’ (Hess, 1959). The

emagram uses temperat ure along the abscissa and the log of press ure along the

ordinate. The isobars (lines of constant pressure) and the isotherms (lines of

constant temperature) are straight and at a right angle to each other. With pres-

sure plotted on a logarithmic scale, the diagram is terminated at 400 mb, well

before the tropopause.

On the tephigram one coordinate is the natural log of potential temperature (y)

and the other is temperature. Thus, on a tephigram an isobar is a logarithmic curve

sloping upward to the right. The slope decreases with increasing temperature. In the

range of meteorological observations, the isobars are only gently sloped. When using

the tephigram, the diagram is usually rotated so that the isobars are horizontal with

decreasing pressure upward. The pseudo-adiaba ts are quite curved, but lines of

1 ATMOSPHERIC THERMODYNAMIC DIAGRAMS 239

constant saturation mixing ratio tend to be straight. The angle between the isotherms

and isent ropes is 90



, making this type of thermodynamic diagram particularly good

for looking at variations in stability of an environmental sounding.

The skew T–log P diagram is now the most commonly used thermodynamic

diagram in the meteorological community (Fig. 1). This diagram ﬁrst suggested by

Herlofson in 1947 was intended as a way to increase the angle between the

isotherms and isentropes on an emagram (Hess, 1959). The isobars are plotted

on a log scale, similar to the emagram. The isotherms slope upward to the right at



to the isobars. This angle of the isotherms is what gives this diagram its name,

since the temperature is skewed to the right. The isentropes are skewed to the left,

at approximately a 45



angle to the isobars. However, the isentropes are not

perfectly straight, although they remain nearly straight in the meteorological

range typically used. With both the isotherms and isentropes (dry adiabats) at

approximately 45



to the isobars, the angle between the isotherms and isentropes

is close to 90



. The pseudo-adiabats are distinctly curved on this diagram. In order

for the pseudo-adiabats to be straight, the energy–area proportionality of the

diagram would need to be sacriﬁced.

The Stu

ve diagram is another type of thermodynamic diagram. The Stu

diagram has pressure in mb along the x axis and temperature along the y axis.

This coordinate system allows the dry adiabats (ise ntropes) to be straight lines.

However, this diagram does not have area proportional to energy. The uses of the

Stu

ve diagram are limited when compared to the uses of energy conservation ther-

modynamic diagrams. This diagram is still occasionally used in the meteorological

community, but because of familiarity rather than usefulness.

The characteristics of the thermodynamic diagrams discussed is summarized in

the following table:

Figure 1 Skew T–log P diagram. See ftp site for color image.

240

THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

Attribute Emagram Tephigram Skew T–log P Stu¨ve

Area a energy Yes Yes Yes No

T vs. y angle 45



Almost 90



p Straight Gently curved Straight Straight

T Straight Straight Straight Straight

y Gently curved Straight Gently curved Straight

Curved Curved Curved Curved

Gently curved Straight Straight Straight

With multiple thermodynamic diagrams available it may seem overwhelming to a

new user to determine the appropriate diagram for the task. The skew T–log P

diagram and tephigram are the most commonly used thermodynamic diagrams.

Their strength lies in the angle between the isentropes and isotherms. The tephigram

is most widely used by tropical meteorologists because of the ability of the tephi-

gram to show small changes in stability. In the tropics convective potential may be

modiﬁed by only small changes in the vertical stability of the environment, and the

tephigram best captures small changes in the environmental lapse rate. The skew T–

log P diagram is the most commonly used thermodynamic diagram in the midlati-

tudes. The straight isobars and the straight up verti cal temperature proﬁle make the

diagram intuitively easy to comprehend. The ultimate decision of which diagram to

use relies on the familiarity of the diagram to the user. While a summer air mass in

the middle latitudes may best show instability on a tephigram, a meteorologist may

prefer to use the familiar skew T–log P diagram.

2 ATMOSPHERIC STATIC STABILITY AND APPLICATIONS OF

THERMODYNAMIC DIAGRAMS TO THE ATMOSPHERE

Early atmospher ic scientists sent up kites with thermometers attached to acquire an

understanding of the vertical proﬁle (atmospheric sounding) of the atmosphere.

Today, atmospheric scientists use balloons rather than kites and radiosondes rather

than thermometers in an effort to understand the vertical structure of the atmosphere.

Radiosondes collect temperature, moisture, wind speed, and wind direction at

various pressure levels in the atmosphere. The data gained from radiosondes,

when displayed on a thermodynamic diagram, provide forecasters and scientiﬁc

investigators with infor mation that can be used to diagno se not only the current

state of the atmosphere but also the recent history of the local atmospher e and the

likelihood of future evolution. An air mass originating over a land mass wi ll have

inherently different characteristics to its ther modynamic proﬁle than an air mass

originating over the oceans. An air mass inﬂuenced by motions associated with an

approaching weather system will acquire characteristics associated with those circu-

lations. A trained meteorologist can read an atmospheric sounding plotted on a

thermodynamic diagram like a book, revealing the detailed recent history of the

air mass.

2 ATMOSPHERIC STATIC STABILITY 241

Radiosondes are launched twice daily around the world, at 0000 Universal Time,

Coordinated (UTC), also known as Greenwich Mean Time (GMT) or Zulu time (Z),

and 1200 UTC. While the data from radiosondes are available only twice daily, when

the data is plotted on a thermodynamic diagram, they can be used to study potential

changes in the atmosphere. Thermodynamic diagrams can be used to examine the

potential warmth of the atmosphere near the surface during the day, the potential

cooling of temperature at night, and the potential for fog. The potential for cloudiness

can be found due to the movements induced by approaching or withdrawing weather

systems or by the development of unstable rising air parcels. When the vertical

thermodynamic structure is combined with the vertical wind stru cture, information

on the structure, and severity of possible cumulus clouds can be ascertained. The

sounding can also describe the potential for local circulations such as sea breezes,

lake effect snow, downslope windstorms, and upslope clouds and precipitation.

An atmospheric sounding plotted on a thermodynamic diagram is one of the most

powerful diagnostic tools available to meteorologists. The applications of the ther-

modynamic diagrams are far too many to be adequately c overed in this discussion.

This discussion will focus on some of the basic interpretive concepts that can be

applied generally to atmospheric soundings plotted on thermodynamic diagrams.

Environmental Structure of the Atmosphere

The sounding plotted on a thermodynamic diagram represents a particular atmo-

spheric state. The state may be observed by radiosonde, satellite derived, or fore-

casted by a computer atmospheric numerical model. The data plotted on the diagram

represent the temperature and dew-point temperature at various pressure levels

throughout the atmosphere. Individual observations are plotted, and then the

points are connected forming the dew point and temperature curves. The dew-

point temperature is always less than or equal to the temperature for any given

pressure level. The plotted curves represent the environmental temperature and

dew-point temperature, as a function of pressure.

The environmental temperature and dew-point temperature curves will divulge

much information to a well-trained observer who can deduce where the sounding is

from, as well as identify air masses and the processes involved in their formation.

Air masses originate from speciﬁc source regions and carry the characteristics of that

source region.

Arctic Air Mass Air masses that originate near one of the poles have a nearly

isothermal temperature proﬁle. In the polar regions, the main process driving the

temperature proﬁle is radiational cooling. Light winds allow very little vertical

mixing of the air. When coupled with the lack of solar radiation for much of the

year, radiational cooling of the surface is the remaining process. Initially the air near

Earth’s surface cools faster. The rate at which energy is emitted is dependent on

temperature to the fourth power (Stefan–Boltzmann equation), and therefore the

warmer air above will then cool faster than the colder air at the surface. This results

in the atmosphere moving toward a constant temperature, and this result is

242 THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

observable on a skew-T diagram by the isothermal proﬁle that begins at the surface

(Fig. 2). The tropopause is found at a much lower height near the poles. An arctic

sounding will illustrate the low tropopause. Both maritime and continental arctic air

masses will have an isothermal temperature proﬁle; the difference is found in the

degree of saturation of the air.

Marine Tropical Air Mass In a marine tropical environment (Fig. 3) the

temperature proﬁle is nearly moist adiabatic (parallels the pseudo-adiabats).

The air in this region is close to saturation near the surface and thus very humid.

Above the planetary boundary layer, the air is dominated by sinking motion between

cumulus clouds and will tend to be dry except for some moisture mixed from the

cumulus clouds. Since saturated air parcels in cumulus updrafts force much of the

sinking motion outside clouds, the temperature proﬁle closely parallels the pseudo-

adiabat. A dry air maximum resulting from the sinking around 700 mb characterizes

the dew-point proﬁle of a marine tropical environment. Below 700 mb surface

moisture mixes upward driven by solar heating and solar-powered surface evapora-

tion. The dry air maximum is the feature that truly distinguishes the maritime

tropical air mass from other air masses.

Well-Mixed Air Mass Perhaps one of the easiest air masses to identify is one

that is well mixed (Fig. 4). If a layer of the atmosphere has sufﬁcient turbulence, the

layer wi ll become well mixed with the moisture and potential temperature evenly

distributed.

The temperature proﬁle will take on the slope of the adiabatic lapse rate and the

dew-point temperature will follow a constant mixing ratio value. Mixing ratio is a

measure of the actual amount of water vapor in the air, and in an environment with a

Figure 2 Characteristic arctic air mass. See ftp site for color image.

2 ATMOSPHERIC STATIC STABILITY 243

lot of turbulent mixing the water vapor will become evenly distributed. Well-mixed

layers generally form in a capped boundary layer. However, a well-mixed layer may

form in the boundary layer of one region and then be advected into another region.

If the region that the well-mixed layer is advected into is at a lower elevation, the

well-mixed layer may ride over the existing boundary layer, resulting in an elevated

mixed layer. This is commonly observed in the Great Plains of the United States,

where a well-mixed layer is advected off the Mexican Plateau or Rocky Mountains,

over the boundary layer of the Plains, which is very moist due to ﬂow from the Gulf

of Mexico.

Figure 3 Marine tropical air mass. See ftp site for color image.

Figure 4 Well-mixed layer in the atmosphere. See ftp site for color image.

244

THERMODYNAMIC ANALYSIS IN THE ATMOSPHERE

Deep Convection Layers of the atmosphere that include clouds are identiﬁable

because the temperature and dew-point temperatures will be close together indicat-

ing the air is saturated. In the case of deep convection (Fig. 5), the dew-point

temperature and temperature, within the updraft, are so close together that they

are almost indisti nguishable from each other. They are close together throughout a

deep layer of the atmosphere, typically the surface up to the tropopause. The

temperature proﬁle of the environment will closely parallel the moist adiabat in

the case of deep convection. In deep convection, where the atmosphere is basically

saturated throughout, all rising parcels will cool at the moist adiabatic lapse rate.

Critical Levels on a Thermodynamic Diagram

The information on a thermodynamic diag ram may be used not only to determine

where air masses originated from but to also determine what processes the atmo-

sphere may undergo. There are many different critical levels that can be diagnosed

from a sounding plotted on a thermodynamic diagram. A thermodynamic diagram

may be used to determine where a parcel will become either saturated and=or buoy-

ant. The level at which the parcel becomes saturated depends on not only the

moisture content but the processes the atmosphere is u ndergoing, for this reason

there are multiple condens ation levels dependent on the process occurring.

Lifting Condensation Level (LCL) This is the pressure level at which a parcel

lifted dry adiabatically will become saturated. This level is impor tant for two

reasons. First, since the parcel becomes saturated at this point, it represents the

height of cloud base. Second, since the parcel is saturated, if it continues to rise

above this level, the parcel will cool at the moist adiabatic lapse rate. In a condi-

tionally unstable atmosphere, a parcel is unstable only if saturated. A conditionally

Figure 5 Deep convection. See ftp site for color image.

2 ATMOSPHERIC STATIC STABILITY 245