CHAPTER 2

ATMOSPHERIC PHYSICS

The science of physics is devoted to finding,defining, and reaching solutions to problems. It is thebasic science that deals with motion, force, and energy.Physics, therefore, not only breeds curiosity of one’senvironment, but it provides a means of acquiringanswers to questions that continue to arise.Atmospheric physics is a branch of physicalmeteorology that deals with a combination of dynamicand thermodynamic processes that account for theexistence of numerous atmospheric conditions.

To understand the weather elements and to analyzemeteorological situations you must know how to applythe fundamental principles of physics. This does notmean that you must be able to understand all of thecomplicated theories of meteorology. It does mean,however, that you should have a working knowledge ofelementary physics. You should learn how to apply therules of physics to understand how the atmosphereworks. This is necessary to perform your duties as anAerographer’s Mate in a creditable manner.

MOTION

LEARNING OBJECTIVE: Describe thelaws of motion and determine how motion isaffected by external forces.

Any general discussion of the principles of physicsmust contain some consideration of the way in whichmass, force, and motion are related. In physics, the lawsof motion state that an object at rest never starts to moveby itself; a push or a pull must be exerted on it by someother object. This also applies to weather. Weather hascomplex motions in the vertical and horizontal planes.To fully understand how and why weather moves, youmust have a basic knowledge of motion and thoseexternal forces that affect motion.

TERMS

In dealing with motion several terms should bedefined before you venture into the study of motion.These terms are inertia, speed, direction, velocity, andacceleration.

Inertia

An object at rest never moves unless something orsomeone moves it. This is a property of all forms ofmatter (solid, liquid, or gas). Inertia, therefore, is theproperty of matter to resist any change in its state of restor motion.

Speed

Speed is the rate at which something moves in agiven amount of time. In meteorology, speed is the termthat is used when only the rate of movement is meant. Ifthe rate of movement of a hurricane is 15 knots, we sayits speed is 15 knots per hour.

Direction

Direction is the line along which something movesor lies. In meteorology, we speak of direction as towardor the direction from which an object is moving. Forexample, northerly winds are winds COMING FROMthe north.

Velocity

Velocity describes both the rate at which a bodymoves and the direction in which it is traveling. If thehurricane, with its speed of 15 knots per hour, isdescribed as moving westward, it now hasvelocity—both a rate and direction of movement.

Acceleration

This term applies to a rate of change of the speedand/or the velocity of matter with time. If a hurricane,which is presently moving at 15 knots, is moving at 18knots 1 hour from now and 21 knots 2 hours from now,it is said to be accelerating at a rate of 3 knots per hour.

LAWS OF MOTION

Everything around us is in motion. Even a bodysupposedly at rest on the surface of Earth is in motionbecause the body is actually moving with the rotation ofEarth; Earth, in turn, is turning in its orbit around theSun. Therefore, the terms rest and motion are relative

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terms. The change in position of any portion of matter ismotion. The atmosphere is a gas and is subject to muchmotion. Temperature, pressure, and density act toproduce the motions of the atmosphere. These motionsare subject to well-defined physical laws. Anexplanation of Newton’s laws of motion can help you tounderstand some of the reasons why the atmospheremoves as it does.

Newton’s First Law

Sir Isaac Newton, a foremost English physicist,formulated three important laws relative to motion. Hisfirst law, the law of inertia, states, every body continuesin its state of rest or uniform motion in a straight lineunless it is compelled to change by applied forces.”Although the atmosphere is a mixture of gases and hasphysical properties peculiar to gases, it still behaves inmany respects as a body when considered in the termsof Newton’s law. There would be no movement of greatquantities of air unless there were forces to cause thatmovement. For instance, air moves from one area toanother because there is a force (or forces) great enoughto change its direction or to overcome its tendency toremain at rest.

Newton’s Second Law

Newton’s second law of motion, force, andacceleration states, “the change of motion of a body isproportional to the applied force and takes place in thedirection of the straight line in which that force isapplied.” In respect to the atmosphere, this means that achange of motion in the atmosphere is determined bythe force acting upon it, and that change takes place inthe direction of that applied force.

From Newton’s second law of motion the followingconclusions can be determined:

1. If different forces are acting upon the samemass, different accelerations are produced that areproportional to the forces.

2. For different masses to acquire equalacceleration by different forces, the forces must beproportional to the masses.

3. Equal forces acting upon different massesproduce different accelerations that are proportional tothe masses.

Newton’s Third Law

Newton’s third law of motion states, “to everyaction there is always opposed an equal reaction; or, themutual actions of two bodies upon each other arealways equal, and directed to contrary parts.” In otherwords forces acting on a body originate in other bodiesthat make up its environment. Any single force is onlyone aspect of a mutual interaction between two bodies.

WORK

Work is done when a force succeeds in overcominga body’s inertia and moving the body in the directionthe force is applied. The formula is

W = F × d

where W is work, F is force and d is the distance moved.The amount of work done is the product of themagnitude of the force and the distance moved.

Work is measured in the English system by thefoot-pound; that is, if 1 pound of force acts through adistance of 1 foot, it performs 1 foot-pound of work. Inthe metric CGS system, force is measured in dynes,distance is measured in centimeters, and work isdenoted in ergs. An erg is the work done by a force ofone dyne exerted for a distance of one centimeter.Another unit used to measure work is the joule. It issimply 10,000,000 ergs, and is equivalent to just underthree-fourths of a foot-pound.

ENERGY

Energy is defined as the ability to do work. Energyis conservative, meaning it may be neither created nordestroyed. It is defined in two forms—potential energyand kinetic energy. As its name implies, potentialenergy is the amount of energy that MAY BEAVAILABLE to a body due to its position. It isprimarily due to the force of gravity. The higher a bodyis raised above the surface, the greater its POTENTIALenergy. Kinetic energy is the energy available to a bodydue to its motion through a field. The total amount ofenergy a body possesses is the sum of its potential andkinetic energies. The total amount of energy availableto a body determines how much work it canaccomplish.

FORCE

There are two types of forces the AG dealswith—contact force and action at a distance force.Contact force is the force that occurs when pressure is

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put on an object directly through physical contact. Anexample of contact force is the force your hand exertswhen you push your coffee cup across a table. Contactforce may act in several different directions at once aswell. For example, the force exerted by water in a can isequally exerted on the sides and the bottom of the can.In addition, an upward force is transmitted to an objecton the surface of the water. Forces that act throughempty space without contact are known as action at adistance force. An example of this force is gravity.

Vectors

Problems often arise that make it necessary to dealwith one or more forces acting on a body. To solveproblems involving forces, a means of representingforces must be found. True wind speed at sea involvestwo different forces and is obtained through the use ofthe true wind computer. Ground speed and course ofaircraft are computed by adding the vector representingaircraft heading and true air speed to the vectorrepresenting the wind direction and speed. Incomputation of the effective fallout wind and otherradiological fallout problems, the addition of forces isused. From these examples, it is evident that theaddition and subtraction of forces has manyapplications in meteorology.

A force is completely described when itsmagnitude, direction, and point of application aregiven. A vector is a line that represents both magnitudeand direction; therefore, it may be used to describe aforce. The length of the line represents the magnitudeof the force. The direction of the line represents thedirection in which the force is being applied. Thestarting point of the line represents the point ofapplication of the force. (See fig. 2-1.) To represent aforce of 10 pounds or 10 knots of wind acting towarddue east on point A, draw a line 10 units long, starting atpoint A and extending in a direction of 090°.

Composition of Forces

If two or more forces are acting simultaneously at apoint, the same effect can be produced by a single forceof the proper size and direction. This single force,which is equivalent to the action of two or more forces,is called the resultant. Putting component forcestogether to find the resultant force is called compositionof forces. (See fig. 2-2.) The vectors representing theforces must be added to find the resultant. Because avector represents both magnitude and direction, themethod for adding vectors differs from the procedureused for scalar quantities (quantities having onlymagnitude and no direction). To find the resultant forcewhen a force of 5 pounds and a force of 10 pounds areapplied at a right angle to point A, refer to figure 2-2.

The resultant force may be found as follows:Represent the given forces by vectors AB and ACdrawn to a suitable scale. At points B and C drawdashed lines perpendicular to AB and AC, respectively.From point A, draw a line to the point of intersection X,of the dashed lines. Vector AX represents the resultantof the two forces. Thus, when two mutuallyperpendicular forces act on a point, the vectorrepresenting the resultant force is the diagonal of arectangle. The length of AX, if measured on the samescale as that for the two original forces, is the resultantforce; in this case approximately 11.2 pounds. Theangle gives the direction of the resultant force withrespect to the horizontal.

Mathematically, the resultant force ofperpendicular forces can be found by using thePythagorean theorem which deals with the solution ofright triangles. The formula is C2 = a2 + b2. This statesthat the hypotenuse, side “C” (our unknown resultantforce) squared is equal to the sum of side “a” (one of ourknown forces) squared and side “b” (another of ourknown forces) squared.

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N

A

10 LB

AG5f0201

Figure 2-1.—Example of a vector.AG5f0202

C X

5 LB

10 LBBA

Figure 2-2.—Composition of two right angle forces.

If we substitute the known information in figure2-2 we have the following:

C2 = Unknown resultant force

a2 = 5 lb or the known force on one side of ourright triangle, side BX (same as side AC)

b2 = 10 lb or the known force on the other sideof our right triangle, side AB

Setting up the equation we have:

C2 = a2 +

C2 = 52 + 102

C2 = 25 + 100

C2 = 125

C = 125

C = 11.18034

To find the resultant of two forces that are not atright angles, the following graphic method may beused. (See fig. 2-3).

Let AB and AC represent the two forces drawnaccurately to scale. From point C draw a line parallel toAB and from point B draw a line parallel to AC. Thelines intersect at point X. The force AX is the resultantof the two forces AC and AB. Note that the two dashedlines and the two given forces make a parallelogramACXB. Arriving at the resultant in this manner is calledthe parallelogram method. The resultant force anddirection of the resultant is found by measuring thelength of line AX and determining the direction of lineAX from the figure drawn to scale. This method appliesto any two forces acting on a point whether they act atright angles or not. Note that the parallelogrambecomes a rectangle for forces acting at right angles.With a slight modification, the parallelogram method ofaddition applies also to the reverse operation ofsubtraction. Consider the problem of subtracting forceAC from AB. (See fig. 2-4.)

First, force AC is reversed in direction giving -AC(dashed line). Then, forces -AC and AB are added bythe parallelogram method, giving the resulting AX,which in this case is the difference between forces ABand AC. A simple check to verify the results consists ofadding AX to AC; the sum or resultant should beidentical with AB.

Application of Vectors and Resultant Forces

The methods presented for computing vectors andresultant forces are the simplest and quickest methodsfor the Aerographer’s Mate. The primary purposes ofusing vectors and resultant forces are for computingradiological fallout patterns and drift calculations forsearch and rescue operations.

REVIEW QUESTIONS

Q2-1. What is the definition of speed?

Q2-2. What is the correct formula for work?

Q2-3. What are the two types forces that AGs dealwith?

MATTER

LEARNING OBJECTIVE: Recognize howpressure, temperature, and density affect theatmosphere. Describe how the gas laws areapplied in meteorology.

Matter is around us in some form everywhere in ourdaily lives—the food we eat, the water we drink, andthe air we breathe. The weather around us, such as hail,rain, invisible water vapor (humidity), etc., are all

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AG5f0203

C

A(R) RESULTANT

B

X

Figure 2-3.—Graphic method of the composition of forces.

C

B

C X

A

AG5f0204

Figure 2-4.—Parallelogram method of subtracting forces.

matter. Matter is present in three forms—solids,liquids, and gases. A good working knowledge of thephysical properties of matter and how matter canchange from one form to another can help youunderstand what is happening in our atmosphere thatproduces the various meteorological occurrences welive with every day.

DEFINITIONS

Matter is anything that occupies space and hasweight. Two basic particles make up the composition ofall matter—the atom and the molecule. The molecule isthe smallest particle into which matter can be dividedwithout destroying its characteristic properties. Inphysics, the molecule is the unit of matter. Moleculesare composed of one or more atoms. The atom is thesmallest particle of an element of matter that can existeither alone or in combination with others of the sameor of another element. The atom and atomic structure isconstantly under study and has revealed a whole newarray of subatomic particles. To date, a new definitionfor atom has not been developed.

A compound is a substance (or matter) formed bycombining two or more elements. Thus, ordinary tablesalt is a compound formed by combining twoelements—sodium and chlorine. Elements andcompounds may exist together without forming newcompounds. Their atoms do not combine. This isknown as a mixture. Air is a familiar mixture. Everysample of air contains several kinds of molecules whichare chiefly molecules of the elements oxygen, nitrogen,and argon, together with the compounds of water vaporand carbon dioxide. Ocean water, too, is anothermixture, made up chiefly of water and salt molecules,with a smaller number of molecules of many othercompounds as well as molecules of several elements.

STATES OF MATTER

Matter is found in all of the following three states:

1. Solid. Solids are substances that have a definitevolume and shape and retain their original shape andvolume after being moved from one container toanother, such as a block of wood or a stone.

2. Liquid. A liquid has a definite volume, becauseit is almost impossible to put it into a smaller space.However, when a liquid is moved from one container toanother, it retains its original volume, but takes on theshape of the container into which it is moved. Forexample, if a glass of water is poured into a largerbucket or pail, the volume remains unchanged. The

liquid occupies a different space and shape in that itconforms to the walls of the container into which it ispoured.

3. Gas. Gases have neither a definite shape nor adefinite volume. Gases not only take on the shape of thecontainer into which they are placed but expand and fillit, no matter what the volume of the container.

Since gases and liquids flow easily, they are bothcalled fluids. Moreover, many of the laws of physicsthat apply to liquids apply equally well to gases.

PHYSICAL PROPERTIES

Since matter is anything that occupies space andhas weight, it can be said that all kinds of matter havecertain properties in common. These properties areinertia, mass, gravitation, weight, volume, and density.These properties are briefly covered in this section andare referred to as the general properties of matter.

Inertia

Inertia of matter is perhaps the most fundamental ofall attributes of matter. It is the tendency of an object tostay at rest if it is in a position of rest, or to continue inmotion if it is moving. Inertia is the property thatrequires energy to start an object moving and to stopthat object once it is moving.

Mass

Mass is the quantity of matter contained in asubstance. Quantity does not vary unless matter isadded to or subtracted from the substance. For example,a sponge can be compressed or allowed to expand backto its original shape and size, but the mass does notchange. The mass remains the same on Earth as on thesun or moon, or at the bottom of a valley or the top of amountain. Only if something is taken away or added toit is the mass changed. Later in the unit its meaning willhave a slightly different connotation.

Gravitation

All bodies attract or pull upon other bodies. In otherwords, all matter has gravitation. One of Newton’s lawsstates that the force of attraction between two bodies isdirectly proportional to the product of their masses andinversely proportional to the square of the distancebetween their two centers. Therefore, a mass has lessgravitational pull on it at the top of a mountain than ithas at sea level because the center is displaced farther

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away from the gravitational pull of the center of Earth.However, the mass remains the same even though thegravitational pull is different. Gravity also varies withlatitude. It is slightly less at the equator than at the polesdue to the equator’s greater distance from the center ofEarth.

Weight

The weight of an object is a measure of itsgravitational attraction. The weight depends upon themass or quantity that it contains and the amount ofgravitational attraction Earth has for it. Weight is aforce, and as such it should be expressed in units offorce. Since gravity varies with latitude and heightabove sea level, so must weight vary with the samefactors. Therefore, a body weighs more at the polesthan at the equator and more at sea level than atop amountain. In a comparison of mass and weight, massremains constant no matter where it is, but weightvaries with latitude and height above sea level.

Volume

Volume is the measure of the amount of space thatmatter occupies. The volume of rectangular objects isfound directly by obtaining the product of their length,width, and depth. For determining the volume of liquidsand gases, special graduated containers are used.

Density

The mass of a unit volume of a substance or massper unit volume is called density. Usually we speak ofsubstances being heavier or lighter than another whencomparing equal volumes of the two substances.

Since density is a derived quantity, the density of anobject can be computed by dividing its mass (or weight)by its volume. The formula for determining the densityof a substance is

DM

V(or D M V)= = = ÷

where D stands for density, M for mass, and V forvolume.

From this formula, it is obvious that with massremaining unchanged, an increase in volume causes adecrease in density. A decrease in volume causes anincrease in density.

The density of gases is derived from the same basicformula as the density of a solid. Pressure and

temperature also affect the density of gases. This effectis discussed later in this unit under Gas Laws.

CHANGES OF STATE

A change of state (or change of phase) of asubstance describes the change of a substance from asolid to a liquid, liquid to a vapor (or gas), vapor to aliquid, liquid to a solid, solid to vapor, or vapor to asolid. In meteorology you are concerned primarily withthe change of state of water in the air. Water is present inthe atmosphere in any or all of the three states (solid,liquid, and vapor) and changes back and forth from onestate to another. The mere presence of water isimportant, but the change of state of that water in the airis significant because it directly affects the weather.The solid state of water is in the form of ice or icecrystals. The liquid state of water is in the form ofraindrops, clouds, and fogs. The vapor state of water isin the form of unseen gases (water vapor) in the air.

Heat Energy

Energy is involved in the various changes of statethat occur in the atmosphere. This energy is primarily inthe form of heat. Each of the changes of state processeseither uses heat from the atmosphere or releases heatinto the atmosphere. The heat used by a substance inchanging its state is referred to as the latent heat and isusually stated in calories.

The calorie is a unit of heat energy. It is the amountof heat required to raise the temperature of 1 gram ofwater 1°C. A closer look at some of the major changesof state of the atmosphere helps to clarify latent heat.Refer to figure 2-5 during the following discussions.

Liquid to Solid and Vice Versa

Fusion is the change of state from a solid to a liquidat the same temperature. The number of gram caloriesof heat necessary to change 1 gram of a substance fromthe solid to the liquid state is known as the latent heat offusion. To change 1 gram of ice to 1 gram of water at aconstant temperature and pressure requires roughly 80calories of heat. This is called the latent heat of fusion.Fusion uses heat. The source of this heat is thesurrounding air.

The opposite of fusion is freezing—a liquidchanges into a solid. Since it requires 80 calories tochange 1 gram of ice to 1 gram of water, this sameamount of heat is released into the air when 1 gram ofwater is changed to ice.

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Liquid to Gas and Vice Versa

Water undergoes the process of evaporation whenchanging from the liquid to a gaseous state. Accordingto the molecular theory of matter, all matter consists ofmolecules in motion. The molecules in a bottled liquidare restricted in their motion by the walls of thecontainer. However, on a free surface exposed to theatmosphere, the motion of the molecules in the liquid isrestricted by the weight of the atmosphere or, moreprecisely, by the atmospheric pressure. If the speed ofthe liquid molecules is sufficiently high, they escapefrom the surface of the liquid into the atmosphere. Asthe temperature of the liquid is increased, the speed ofthe molecules is increased, and the rate at which themolecules escape from the surface also increases.Evaporation takes place only from the free or exposedsurface of a substance.

During the process of evaporation, heat is released.This heat is absorbed by the water that has vaporized.The amount absorbed is approximately 539 calories pergram of water at a temperature of 100°C. On the otherhand, the amount is 597.3 calories, if the evaporationtakes place at a water temperature of 0°C. This energyis required to keep the molecules in the vapor state and

is called the latent heat of vaporization. Since the waterneeds to absorb heat in order to vaporize, heat must besupplied or else evaporation cannot take place. The airprovides this heat. For this reason, evaporation is said tobe a cooling process, because by supplying the heat forvaporization, the temperature of the surrounding air islowered.

Condensation is the opposite of evaporationbecause water vapor undergoes a change in state fromgas back to liquid. However, a condition of saturationmust exist before condensation can occur. That is, theair must contain all the water vapor it can hold (100percent relative humidity) before any of it can condensefrom the atmosphere. In the process of condensation,the heat that was absorbed in evaporation by the watervapor is released from the water vapor into the air and iscalled the latent heat of condensation. As you mightexpect, condensation warms the surrounding air.

Solid to Gas and Vice Versa

Sublimation is the change of state from a soliddirectly to a vapor or vice versa at the sametemperature. In physics and chemistry, sublimation isregarded as the change of state from solid to vapor only,

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FREEZING

FREEZING

CONDENSA IT ONCOOLING

COOLING

MELTING EVAPORATIONHEATING

HEATINGMELTING

COOLING & CONDENSATION

HEATING & EVAPORATION

SUBLIMATION

SUBLIMATION

1 gm

ICE 0 C

1 gm

ICE 0 C

1 gm

ICE -10 C

1 gm

ICE 0 C

1 gmINVISIBLE

WATER VAPOR100 C

1 gmINVISIBLE

WATER VAPOR100 C

1 gmWATER

0 C

1 gmWATER

0 C

1 gmINVISIBLE

WATER VAPOR0 C

TOTAL CALORIESADDED TO

THE AIR

727

723

677

TOTAL CALORIESTAKEN FROM

THE AIR

727

723

677

80 597 50

4 80 100+539

677

NOTE:1. EVAPORATION COOLS AIR.2. CONDENSATION HEATS.3. CALORIES SHOWN TO NEAREST

WHOLE FIGURES.

1 gmINVISIBLE

WATER VAPOR0 C

AG5f0205

Figure 2-5.—Thermal history of 1 gram of ice during changes of state.

but meteorologists do not make this distinction. Theheat of sublimation equals the heat of fusion plus theheat of vaporization for a substance. The caloriesrequired for water to sublime are: 80 + 597.3 = 677.3, ifthe vapor has a temperature of 0°C.

In the sublimation process of vapor passing directlyinto the solid form without going through the liquidphase, the calories released are the same as those for thesublimation of a solid to a gas. Sublimation of watervapor to ice frequently takes place in the atmospherewhen supercooled water vapor crystallizes directly intoice crystals and forms cirriform clouds.

REVIEW QUESTIONS

Q2-4. What are the two basic particles that make upthe composition of matter?

Q2-5. What is the correct formula for density?

Q2-6. What is fusion?

GAS LAWS

LEARNING OBJECTIVE: Recognize howpressure, temperature, and density affect theatmosphere and describe how the gas laws areapplied in meteorology.

Since the atmosphere is a mixture of gases, itsbehavior is governed by well-defined laws.Understanding the gas laws enables you to see that thebehavior of any gas depends upon the variations intemperature, pressure, and density.

To assist in comparing different gases and inmeasuring changes of gases it is necessary to have astandard or constant to measure these changes against.The standard used for gases are: a pressure of 760millimeters of mercury (1,013.25 mb) and atemperature of 0°C. These figures are sometimesreferred to as Standard Temperature and Pressure(STP).

KINETIC THEORY OF GASES

The Kinetic theory of gases refers to the motions ofgases. Gases consist of molecules that have no inherenttendency to stay in one place as do the molecules of asolid. Instead, the molecules of gas, since they aresmaller than the space between them, are free to moveabout. The motion is in straight lines until the linescollide with each other or with other obstructions,making their overall motion random. When a gas isenclosed, its pressure depends on the number of times

the molecules strike the surrounding walls. The numberof blows that the molecules strike per second againstthe walls remains constant as long as the temperatureand the volume remain constant.

If the volume (the space occupied by the gas) isdecreased, the number of blows against the wall isincreased, thereby increasing the pressure if thetemperature remains constant. Temperature is ameasure of the molecular activity of the gas moleculesand a measure of the internal energy of a gas. When thetemperature is increased, there is a correspondingincrease in the speed of the molecules; they strike thewalls at a faster rate, thereby increasing the pressureprovided the volume remains constant. Therefore,there is a close relationship of volume, pressure, anddensity of gases.

BOYLE’S LAW

Boyle’s law states that the volume of a gas isinversely proportional to its pressure, provided thetemperature remains constant. This means that if thevolume is halved, the pressure is doubled. An exampleof Boyle’s law is a tire pump. As the volume of thepump’s cylinder is decreased by pushing the handledown, the pressure at the nozzle is increased. Anotherway of putting it is, as you increase the pressure in thecylinder by pushing down the handle, you also decreasethe volume of the cylinder.

The formula for Boyle’s law is as follows:

VP = V’P’V = initial volumeP = initial pressureV’ = new volumeP’ = new pressure

For example, assume 20 cm3 of gas has a pressureof 1,000 mb. If the pressure is increased to 1,015 mband the temperature remains constant, what will be thenew volume? Applying the formula, we have

V = 20 cm3

P = 1000 mbV’ = Unknown in cm3

P’ = 1015 mbV • P = V’ • P’20 • 1,000 = V’ • 1,01520,000 = V’ • 1,015

V’ =20 000

1015

,

,V’ = 19.71 cm3

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Boyle’s law does not consider changes intemperature. Since our atmosphere is constantlychanging temperature at one point or another,temperature must be considered in any practicalapplication and understanding of gas laws.

CHARLES’ LAW

In the section on the kinetic theory of gases, it wasexplained that the temperature of a gas is a measure ofthe average speed of the molecules of the gas. It wasalso shown that the pressure the gas exerts is a measureof the number of times per second that the moleculesstrike the walls of the container and the speed at whichthey strike it. Therefore, if the temperature of a gas in aclosed container is raised, the speed of the moleculeswithin the gas increases. This causes the molecules tostrike the sides of the container more often per secondand with more force because they are moving faster.Thus, by increasing the temperature, the pressure isincreased.

Charles’ law states if the volume of an enclosed gasremains constant, the pressure is directly proportionalto the absolute temperature. Therefore, if the absolutetemperature is doubled, the pressure is doubled; if theabsolute temperature is halved, the pressure is halved.Experiments show that the volume increases by 1/273for a 1°C rise in temperature. (Remember, 0°C is equalto 273°K.) An example of Charles’ law is a bottle ofsoda or beer. When the soda or beer is cold, very littlepressure is released when the bottle is opened. When awarm soda or beer is opened, it often results in enoughpressure buildup in the bottle to squirt soda or beer outof the top. Sometimes, warm soda or beer explodesspontaneously when exposed to too much direct heatsuch as sunlight.

The formulas for Charles’ law are as follows:

VT’ = V’T, where pressure is assumed to beconstant, and

PT’ = P’T, where volume is constant

V = initial volumeT = initial temperature (absolute)V’ = new volumeT’ = new temperature (absolute)

For example, assume that 10 cm3 of a gas has atemperature of 200° absolute. If the temperature isincreased to 300° absolute, what will be the newvolume? Applying the formula, we have

V = 10 cm3

T = 200°KV’ = Unknown in cm3

T’ = 300°K10 • 300 = V’ • 2003000 = V’ • 200

V’ =3000

200V’ = 15 cm3

The same type relationship can be computed byapplying T’ (new temperature) and P’ (new pressure)using the formula PT’ = P’T where the volume isassumed to remain constant.

UNIVERSAL GAS LAW

The universal gas law is a combination of Boyle’slaw and Charles’ law. It states that the product of theinitial pressure, initial volume, and new temperature(absolute scale) of an enclosed gas is equal to theproduct of the new pressure, new volume, and initialtemperature. The formula is as follows:

PVT’ = P’V’T

P = initial pressureV = initial volumeT = initial temperature (absolute)P’ = new pressureV = new volume (absolute)T = new temperature (absolute)

For example, assume the pressure of a 500 cm3

volume of gas is 600 mb and the temperature is 30°C(303 absolute). If the temperature is increased to 45°C(318° absolute) and the volume is decreased to 250cm3, what will be the new pressure of the volume?Applying the formula, we have

P = 600 mbV = 500 cm3

T = 303°KP’ = Unknown pressure in mbV’ = 250 cm3

T’ = 318°K600 • 500 • 318 = P’ • 250 • 30395,400,000 = P’75,750

P’ =95 400 000

75 750

, ,

,P’ = 1,259.4 mb

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EQUATION OF STATE

The equation of state is a general gas law forfinding pressure, temperature, or density of a dry gas.Rather than using volume, this formula uses what iscalled gas constant. A gas constant is a molecularweight assigned to various gases. Actually, air does nothave a molecular weight because it is a mixture of gasesand there is no such thing as an air molecule. However,it is possible to assign a so-called molecular weight todry air that makes the equation of state work. The gasconstant for air is 2,870 and for water vapor it is 1,800when the pressure is expressed in millibars and thedensity is expressed in metric tons per cubic meter. Thegas constant may be expressed differently dependingon the system of units used.

The following formula is an expression of theequation of state:

P = ρRT

P = pressure in millibarsρ = density (Greek letter rho)R = specific gas constantT = temperature (absolute)

The key to this formula is the equal sign thatseparates the two sides of the formula. This equal signmeans that the same value exists on both sides; bothsides of the equation are equal. If the left side of theequation (pressure) changes, a corresponding changemust occur on the right side (either in the density ortemperature) to make the equation equal again.Therefore, an increase of the total value on one side ofthe Equation of State must be accompanied by anincrease of the total value on the other side. The same istrue of any decrease on either side.

NOTE: Since R is a constant it will always remainunchanged in any computation.

The right side of the equation can balance out anychange in either density or temperature without havinga change on the left side (pressure). If, for example, anincrease in temperature is made on the right side, theequation may be kept in balance by decreasing density.This works for any value in the equation of state.

From this relationship, we can draw the followingconclusions:

1. A change in pressure, density (mass orvolume), or temperature requires a change in one orboth of the others.

2. With the temperature remaining constant, anincrease in density results in an increase in atmosphericpressure. Conversely, a decrease in density results in adecrease in pressure.

NOTE: Such a change could occur as a result of achange in the water vapor content.

3. With an increase in temperature, the pressureand/or density must change. In the free atmosphere, atemperature increase frequently results in expansion ofthe air to such an extent that the decrease in densityoutweighs the temperature increase, and the pressureactually decreases. Likewise, a temperature increaseallows an increase in moisture, which in turn decreasesdensity (mass of moist air is less than that of dry air).Couple this with expansion resulting from thetemperature increase and almost invariably, the finalresult is a decrease in pressure.

At first glance, it may appear that pressureincreases with an increase in temperature. Earlier,however, it was noted that this occurs when volume (thegas constant) remains constant. This condition wouldbe unlikely to occur in the free atmosphere becausetemperature increases are associated with densitydecreases, or vice versa. The entire concept of theequation of state is based upon changes in densityrather than changes in temperature.

HYDROSTATIC EQUATION

The hydrostatic equation incorporates pressure,temperature, density, and altitude. These are the factorsthat meteorologists must also deal with in any practicalapplication of gas laws. The hydrostatic equation,therefore, has many applications in dealing withatmospheric pressure and density in both the horizontaland vertical planes. The hydrostatic equation itself willbe used in future units and lessons to explain pressuregradients and vertical structure of pressure centers.Since the equation deals with pressure, temperature,and density, it is briefly discussed here.

The hypsometric formula is based on thehydrostatic equation and is used for either determiningthe thickness between two pressure levels or reducingthe pressure observed at a given level to that at someother level. The hypsometric formula states that thedifference in pressure between two points in theatmosphere, one above the other, is equal to the weightof the air column between the two points. There are twovariables that must be considered when applying thisformula to the atmosphere. They are temperature anddensity.

2-10

From Charles’ law we learned that when thetemperature increases, the volume increases and thedensity decreases. Therefore, the thickness of a layer ofair is greater when the temperature increases. To findthe height of a pressure surface in the atmosphere (suchas in working up an adiabatic chart), these two variables(temperature and density) must be taken intoconsideration. By working upward through theatmosphere, the height of that pressure surface can becomputed by adding thicknesses together. A good toolfor determining height and thickness of layers is theSkew-T Log P diagram, located in AWS/TR-79/006.

Since there are occasions when Skew-Ts are notavailable, a simplified version of the hypsometricformula is presented here. This formula for computingthe thickness of a layer is accurate within 2 percent;therefore, it is suitable for all calculations that theAerographer’s Mate would make on a daily basis.

The thickness of a layer can be determined by thefollowing formula:

Z = (49,080 + 107t) • Po P

Po P

−+

Z = altitude difference in feet (unknownthickness of layer)

49,080 = A constant (representing gravitation andheight of the D-mb level above thesurface)

107 = A constant (representing density andmean virtual temperature)

t = mean temperature in degrees Fahrenheit

Po = pressure at the bottom point of the layer

P = pressure at the top point of the layer

For example, let us assume that a layer of airbetween 800 and 700 millibars has a mean temperatureof 30°F. Applying the formula, we have

Z = (49,080 + 107 × 30) • 800 700

800 700

−+

Z = (49,080 + 3,210) • 100

1 500,

Z = (52,290) • 1

15

Z = 3,486 feet (1,063 meters)(1 meter = 3.28 feet)

REVIEW QUESTIONS

Q2-7. What three things does the behavior of gasesdepend on?

Q2-8. According to Boyle's Law, how is volume andpressure related?

Q2-9. According to Charles' Law, how istemperature and pressure related?

Q2-10. What is the formula for the Universal GasLaw?

ATMOSPHERIC ENERGY

LEARNING OBJECTIVE: Describe theadiabatic process and determine how stabilityand instability affect the atmosphere.

There are two basic kinds of atmospheric energyimportant to AGs—kinetic and potential. Kineticenergy is energy that performs work due to presentmotion while potential energy is energy that is storedfor later action. Kinetic energy is discussed first inrelation to its effect on the behavior of gases.

According to the kinetic theory of gases, thetemperature of a gas is dependent upon the rate at whichthe molecules are moving about and is proportional tothe kinetic energy of the moving molecules. The kineticenergy of the moving molecules of a gas is the internalenergy of the gas; it follows that an increase intemperature is accompanied by an increase in theinternal energy of the gas. Likewise, an increase in theinternal energy results in an increase in the temperatureof the gas. This relationship, between heat and energy,is called thermodynamics.

An increase in the temperature of a gas or in itsinternal energy can be produced by the addition of heator by performing work on the gas. A combination ofthese can also produce an increase in temperature orinternal energy. This is in accordance with the first lawof thermodynamics.

FIRST LAW OF THERMODYNAMICS

This law states that the quantity of energy suppliedto any system in the form of heat is equal to work doneby the system plus the change in internal energy of thesystem. In the application of the first law ofthermodynamics to a gas, it may be said that the twomain forms of energy are internal energy and workenergy. Internal energy is manifested as sensible heat orsimply temperature. Work energy is manifested aspressure changes in the gas. In other words, work is

2-11

required to increase the pressure of a gas and work isdone by the gas when the pressure diminishes. Itfollows that if internal energy (heat) is added to asimple gas, this energy must show up as an increase ineither temperature or pressure, or both. Also, if work isperformed on the gas, the work energy must show up asan increase in either pressure or temperature, or both.

An example of the thermodynamic process is amanual tire pump. The pump is a cylinder enclosed by apiston. In accordance with the first law ofthermodynamics, any increase in the pressure exertedby the piston as you push down on the handle results inwork being done on the air. As a consequence, eitherthe temperature and pressure must be increased or theheat equivalent of this work must be transmitted to thesurrounding bodies. In the case of a tire pump, the workdone by the force on the piston is changed into anincrease in the temperature and the pressure in the air. Italso results in some increase in the temperature of thesurrounding body by conduction.

If the surrounding body is considered to beinsulated so it is not heated, there is no heat transferred.Therefore, the air must utilize this additional energy asan increase in temperature and pressure. This occurs inthe adiabatic process.

THE ADIABATIC PROCESS

The adiabatic process is the process by which a gas,such as air, is heated or cooled, without heat beingadded to or taken away from the gas, but rather byexpansion and compression. In the atmosphere,adiabatic and nonadiabatic processes are taking placecontinuously. The air near the ground is receiving heatfrom or giving heat to the ground. These arenonadiabatic processes. However, in the freeatmosphere somewhat removed from Earth’s surface,the short-period processes are adiabatic. When a parcelof air is lifted in the free atmosphere, pressuredecreases. To equalize this pressure, the parcel mustexpand. In expanding, it is doing work. In doing work,it uses heat. This results in a lowering of temperature aswell as a decrease in the pressure and density. When aparcel of air descends in the free atmosphere, pressureincreases. To equalize the pressure, the parcel mustcontract. In doing this, work is done on the parcel. Thiswork energy, which is being added to the parcel, showsup as an increase in temperature. The pressure anddensity increase in this case also.

Terms

In discussing the adiabatic process several termsare used that you should understand.

LAPSE RATE.—In general, lapse rate is the rateof decrease in the value of any meteorological elementwith elevation. However, it is usually restricted to therate of decrease of temperature with elevation; thus, thelapse rate of the temperature is synonymous with thevertical temperature gradient. The temperature lapserate is usually positive, which means that thetemperature decreases with elevation.

INVERSION.—Inversions describe theatmospheric conditions when the temperature increaseswith altitude, rather than decreases as it usually does.Inversions result from the selective absorption ofEarth’s radiation by the water vapor in the air, and alsofrom the sinking, or subsidence, of air, which results inits compression and, therefore, heating. Either effectalone may cause an inversion; combined, the inversionis stronger.

When air is subsiding (sinking), the compressed airheats. This frequently produces a subsidence inversion.When subsidence occurs above a surface inversion, thesurface inversion is intensified. Such occurrences arecommon in wintertime high-pressure systems. The airin the inversion layer is very stable, and the cold airabove the inversion acts as a lid trapping fog, smoke,and haze beneath it. Poor visibility in the lower levels ofthe atmosphere results, especially near industrial areas.Such conditions frequently persist for days, notably inthe Great Basin region of the western United States. Aninversion is a frequent occurrence (especially at night)in the Tropics and in the Polar regions. For nightconditions all over the world, polar and tropical regionsincluded, it may be said that low- level inversions arethe rule rather than the exception.

ISOTHERMAL.—In the isothermal lapse rate, nocooling or warming is noted and the rate is neutral withheight—no change in temperature with height.

Adiabatic Heating and Cooling

Air is made up of a mixture of gases that is subjectto adiabatic heating when it is compressed andadiabatic cooling when it is expanded. As a result, airrises seeking a level where the pressure of the body ofair is equal to the pressure of the air that surrounds it.There are other ways air can be lifted, such as throughthe thermodynamic processes of a thunderstorm ormechanically, such as having colder, denser air move

2-12

under it or by lifting as it flows up over a mountainslope.

As the air rises, the pressure decreases whichallows the parcel of air to expand. This continues until itreaches an altitude where the pressure and density areequal to its own. As it expands, it cools through athermodynamic process in which there is no transfer ofheat or mass across the boundaries of the system inwhich it operates (adiabatic process). As air rises, itcools because it expands by moving to an altitudewhere pressure and density is less. This is calledadiabatic cooling. When the process is reversed and airis forced downward, it is compressed, causing it to heat.This is called adiabatic heating, (See fig. 2-6.)

Remember, in an adiabatic process an increase intemperature is due only to COMPRESSION when theair sinks or subsides. A decrease in temperature is due

only to EXPANSION when air rises, as with convectivecurrents or air going over mountains. There is noaddition or subtraction of heat involved. The changes intemperature are due to the conversion of energy fromone form to another.

STABILITY AND INSTABILITY

The atmosphere has a tendency to resist verticalmotion. This is known as stability. The normal flow ofair tends to be horizontal. If this flow is disturbed, astable atmosphere resists any upward or downwarddisplacement and tends to return quickly to normalhorizontal flow. An unstable atmosphere, on the otherhand, allows these upward and downward disturbancesto grow, resulting in rough (turbulent) air. An exampleis the towering thunderstorm that grows as a result of alarge intense vertical air current.

2-13

AG5f0206

MOIST AIR BEING LIFTEDBY COLD FRONT.

AS THE LIFTED AIR EXPANDS,IT COOLS ADIABATICALLY.

COLD FRONT

WHEN AIR RISES IN ALTITUDE,IT EXPANDS AND COOLS AT ITSADIABATIC LAPSE RATE.

ADIABATICCOOLING

WHEN AIR DESCENDS IN ALTITUDE,IT COMPRESSES AND HEATS AT ITSADIABATIC LAPSE RATE.

ADIABATICHEATING

MOIST ADIABATIC LAPSE RATE2 TO 3 F/1000FT.

MOIST ADIABATIC LAPSE RATE5.5 F/1000FT.

Figure 2-6.—Adiabatic cooling and heating process.

Atmospheric resistance to vertical motion(stability), depends upon the vertical distribution of theair’s weight at a particular time. The weight varies withair temperature and moisture content. As shown infigure 2-7, in comparing two parcels of air, hotter air islighter than colder air; and moist air is lighter than dryair. If air is relatively warmer or more moist than itssurroundings, it is forced to rise and is unstable. If theair is colder or dryer than its surroundings, it sinks untilit reaches its equilibrium level and is stable. Theatmosphere can only be at equilibrium when light air isabove heavier air—just as oil poured into water rises tothe top to obtain equilibrium. The stability of airdepends a great deal on temperature distribution and toa lesser extent on moisture distribution.

Since the temperature of air is an indication of itsdensity, a comparison of temperatures from one level toanother can indicate how stable or unstable a layer ofair might be—that is, how much it tends to resistvertical motion.

Lapse Rates

In chapter 1, it was shown that temperature usuallydecreases with altitude and that the rate at which itdecreases is called the lapse rate. The lapse rate,commonly expressed in degrees Fahrenheit per 1,000feet, gives a direct measurement of the atmospheres sresistance to vertical motion. The degree of stability ofthe atmosphere may vary from layer to layer as

2-14

STANDARDAIR

MOIST AIR ISLIGHTER THANSTANDARD AIR.

HOT AIR ISLIGHTER THANSTANDARD AIR.

- ON LOOSING ITSMOISTURE IT THENBECOMES...

DRY AIR ISHEAVIER THANSTANDARD AIR.

COLD AIR ISHEAVIER THANSTANDARD AIR.

- IF COOLED, ITTHEN BECOMES...

STANDARDAIR RELATIVE

OR TAIR WILL RISE.(UNSTABLE)

HOT MOIS

RELATIVEOR

AIR WILL SINK.(STABLE)

COLD DRY

B

A

AG5f0207

Figure 2-7.—Moisture content and temperature determines weight of air.

indicated by changes of lapse rate with height. (Seetable 2-1 and fig. 2-8.)

DRY ADIABATIC LAPSE RATE.—If a parcelof air is lifted, its pressure is DECREASED, sincepressure decreases with height, and its temperature fallsdue to the expansion. If the air is dry and the process isadiabatic, the rate of temperature fall is 1°C per100 meters of lift (10°C per Kin), or 5 l/2°F per 1,000feet of lift. If that parcel descends again to higherpressure, its temperature then INCREASES at the rateof 1°C per 100 meters or 5 1/2°F per 1,000 feet. This isknown as the dry adiabatic lapse rate.

MOIST (SATURATION) ADIABATIC LAPSERATE.—When a mass of air is lifted, it cools at the dryadiabatic lapse rate of 5 1/2°F per 1,000 feet as long asit remains unsaturated (relative humidity below 100percent). If the original moisture is being carried alongwith the mass as it ascends and it cools to its saturationtemperature, the relative humidity reaches 100 percent.Condensation takes place with further cooling. Foreach gram of water condensed, about 597 calories ofheat are liberated. This latent heat of condensation isabsorbed by the air, and the adiabatic cooling rate isdecreased to 20 to 3°F per 1,000 feet instead of 5 1/2°Fper 1,000 feet. The process during the saturatedexpansion of the air is called the saturation adiabatic,the moist adiabatic, or the pseudoadiabatic process.The pseudoadiabatic process assumes that moisturefalls out of the air as soon as it condenses.

Assume that a saturated parcel of air having atemperature of 44°F is at 5,000 feet and is forced over a

12,000-foot mountain. Condensation occurs from5,000 to 12,000 feet so that the parcel cools at the moistadiabatic rate (3°F per 1,000 ft) and reaches atemperature of approximately 23°F at the top of themountain. Assuming that the condensation in the formof precipitation has fallen out of the air during theascent, the parcel heats at the dry adiabatic rate as itdescends to the other side of the mountain. When itreaches the 5,000-foot level, the parcel has descended7,000 feet at a rate of 5 1/2°F per 1,000 feet. This resultsin an increase of 38.5°F. Adding the 38.5°F increase tothe original 12,000 feet temperature of 23°F, the parcelhas a new temperature of 61.5°F.

AVERAGE ADIABATIC LAPSE RATE.—Theaverage lapse rate lies between the dry adiabatic and themoist adiabatic at about 3.3°F per 1,000 feet.

SUPERADIABATIC LAPSE RATE.—Thesuperadiabatic lapse rate is a decrease in temperature ofmore than 5 1/2°F per 1,000 feet and less than 15°F per1,000 feet.

AUTOCONVECTIVE LAPSE RATE.—Theautoconvective lapse rate is the decrease of more than15°F per 1,000 feet. This lapse rate is rare and is usuallyconfined to shallow layers.

2-15

AG5t0201

Lapse rate Per 1,000feet

Per 100meters

Dry adiabaticSaturation (moist)

adiabaticAverageSuperadiabaticAutoconvective

5 1/2 F

2-3 F3.3 F

5 1/2-15 FMore than

15 F

1 C

.55 C

.65 C1-3.42 CMore than

3.42 C

Table 2-1.—Lapse Rates of Temperature

MOISTADIABATIC

AVERAGELAPSERATE

"DRY"ADIABATIC

SUPERADIABATIC

AUTOCONVECTIVE

AG5f0208

Figure 2-8.—Adiabatic lapse rates.

Types of Stability

In figure 2-9 a bowl is set on a flat surface with aball placed inside it. The ball rests in the bottom of thebowl; but, if you push the ball in any direction, it seeksout the bottom of the bowl again. This is referred to asABSOLUTE STABILITY (A in fig. 2-9). Turn thebowl upside down, position the ball anywhere on thebowl’s bottom surface (B in fig. 2-9) and the ball startsmoving on its own without any other force beingapplied. This is a condition of ABSOLUTEINSTABILITY. If you now remove the bowl and placethe ball on the flat surface (C in fig. 2-9), you haveNEUTRAL STABILITY—that is, if a force is appliedto the ball, it moves; but if the force is removed, the ballstops.

Air in the atmosphere reacts in a similar mannerwhen moved up or down. If it is moved up and becomesdenser than the surrounding air, it returns to its originalposition and is considered STABLE. If it becomes lessdense than the surrounding air, it continues to rise and is

considered UNSTABLE. When density remains thesame as the surrounding air after being lifted, it isconsidered NEUTRALLY STABLE, with no tendencyto rise or sink.

Equilibrium of Dry Air

The method used for determining the equilibriumof air is the parcel method, wherein a parcel of air islifted and then compared with the surrounding air todetermine its equilibrium. The dry adiabatic lapse rateis always used as a reference to determine the stabilityor instability of dry air (the parcel).

ABSOLUTE INSTABILITY.—Consider acolumn of air in which the actual lapse rate is greaterthan the dry adiabatic lapse rate. The actual lapse rate isto the left of the dry adiabatic lapse rate on the Skew-Tdiagram (fig. 2-10). If the parcel of air at point A isdisplaced upward to point B, it cools at the dryadiabatic lapse rate. Upon arriving at point B, it iswarmer than the surrounding air. The parcel therefore

2-16

AG5f0209

BALL IN BOWL FORCE MOVES BALL DISPLACED BALL OSCILLATES

(A) ABSOLUTE STABILITY

(C) NEUTRAL STABILITY

(B) ABSOLUTE INSTABILITY

BALL BALANCED ON BOWL RELEASE OF FORCEPERMITS BALL TO MOVE

BALL CONTINUESTO MOVE

BALL WILL CONTINUETO MOVE

BALL RESTING ON TABLE FORCE MOVES BALL FORCE REMOVED,BALL STOPS

BALL REMAINS INNEW POSITION

BALL EVENTUALLYRETURNS TO ORIGINAL

POSITION

Figure 2-9.—Analogy depiction of stability.

has a tendency to continue to rise, seeking air of its owndensity. Consequently the column becomes unstable.From this, the rule is established that if the lapse rate ofa column of air is greater than the dry adiabatic lapserate, the column is in a state of ABSOLUTEINSTABILITY. The term absolute is used because thisapplies whether the air is dry or saturated, as isevidenced by displacing upward a saturated parcel of

air from point A along a saturation adiabat to point B.The parce1 is more unstable than if displaced along adry adiabat.

STABILITY.—Consider a column of dry air inwhich the actual lapse rate is less than the dry adiabaticlapse rate. The actual lapse rate is to the right of the dryadiabatic lapse rate on the Skew-T diagram (fig. 2-11).

2-17

AG5f0210

A

SATURATIONADIABATIC

LAPSERATE

DRYADIABATIC

LAPSERATE

ACTUALLAPSERATE

-10 0 10

B B1

POINTS B (DRY ADIABATIC) AND B (MOIST ADIABATIC)WARMER THAN SURROUNDING AIR

1

Figure 2-10.—Absolute instability (any degree of saturation).

AG5f0211-10 0 10

DRY ADIABATICLAPSE RATE

ACTUALLAPSE RATE

B

POINT B COLDER THANTHE SURROUNDING AIR

A

Figure 2-11.—Stability (dry air).

If the parcel at point A were displaced upward to pointB, it would cool at the dry adiabatic lapse rate; and uponarriving at point B, it would be colder than thesurrounding air. It would, therefore, have a tendency toreturn to its original level. Consequently, the column ofair becomes stable. From this, the rule is establishedthat if the actual lapse rate of a column of DRY AIR isless than the dry adiabatic lapse rate, the column isstable.

NEUTRAL STABILITY.—Consider a column ofDRY AIR in which the actual lapse rate is equal to thedry adiabatic lapse rate. The parcel cools at the dryadiabatic lapse rate if displaced upward. It would at alltime be at the same temperature and density as thesurrounding air. It also has a tendency neither to returnto nor to move farther away from its original position.Therefore, the column of dry air is in a state ofNEUTRAL STABILITY.

Equilibrium of Saturated Air

When saturated air is lifted, it cools at a ratedifferent from that of dry air. This is due to release ofthe latent heat of condensation, which is absorbed bythe air. The rate of cooling of moist air is known as thesaturation adiabatic lapse rate. This rate is used as a

reference for determining the equilibrium of saturatedair.

ABSOLUTE STABILITY.—Consider a columnof air in which the actual lapse rate is less than thesaturation adiabatic lapse rate. The actual lapse rate isto the right of the saturation adiabatic lapse rate on theSkew T diagram (fig. 2-12). If the parcel of saturated airat point A is displaced upward to point B, it cools at thesaturation adiabatic lapse rate. The air upon arriving atpoint B becomes colder than the surrounding air. Thelayer, therefore, would be in a state of ABSOLUTESTABILITY. From this, the following rule isestablished: If the actual lapse rate for a column of air isless than the saturation adiabatic lapse rate, the columnis absolutely stable and the parcel would return to itsoriginal position. Dry air cools dry adiabatically and isalso colder than the surrounding air. Therefore, this ruleapplies to all air, as is evidenced when an unsaturatedparcel of air is displaced upward dry adiabatically topoint B. Here, the parcel is more stable than the parceldisplaced along a saturation adiabat.

INSTABILITY.—Consider now a column of air inwhich the actual lapse rate is greater than the saturationadiabatic lapse rate (fig. 2-13). If a parcel of moist air atpoint A is displaced upward to point B, it cools at the

2-18

AG5f0212 -10 0 10

B B

SATURATIONADIABATIC

LAPSERATE

DRYADIABATIC

LAPSERATE

ACTUALLAPSERATE

1

POINTS B (DRY ADIABATIC) AND B (MOIST ADIABATIC)WARMER THAN SURROUNDING AIR

1

A

Figure 2-12.—Absolute stability (any degree of saturation).

saturation adiabatic lapse rate. Upon arriving at point Bthe parcel is then warmer than the surrounding air. Forthis reason, it has a tendency to continue moving fartherfrom its original position. The parcel, therefore, is in astate of INSTABILITY. The following rule isapplicable. If the actual lapse rate for a column ofSATURATED (MOIST) AIR is greater than thesaturation adiabatic lapse rate, the column is unstable.

NEUTRAL STABILITY.—Consider a column ofsaturated air in which the actual lapse rate is equal to thesaturation adiabatic lapse rate. A parcel of air displacedupward cools at the saturation adiabatic lapse rate andis at all times equal in temperature to the surroundingair. On that account it tends neither to move fartheraway from nor to return to its original level. Therefore,it is in a state of NEUTRAL STABILITY. The rule forthis situation is that if the actual lapse rate for a columnof saturated air is equal to the saturation adiabatic lapserate, the column is neutrally stable.

Conditional Instability

In the treatment of stability and instability so far,only air that was either dry or saturated was considered.Under normal atmospheric conditions natural air isunsaturated to begin with, but becomes saturated iflifted high enough. This presents no problem if theactual lapse rate for the column of air is greater than the

dry adiabatic lapse rate (absolutely unstable) or if theactual lapse rate is less than the saturation adiabaticlapse rate (absolutely stable). However, if the lapse ratefor a column of natural air lies between the dryadiabatic lapse rate and the saturation adiabatic lapserate, the air may be stable or unstable, depending uponthe distribution of moisture. When the actual lapse rateof a column of air lies between the saturation adiabaticlapse rate and the dry adiabatic lapse rate, theequilibrium is termed CONDITIONALINSTABILITY, because the stability is conditioned bythe moisture distribution. The equilibrium of thiscolumn of air is determined by the use of positive andnegative energy areas as analyzed on a Skew-T, Log Pdiagram. The determination of an area as positive ornegative depends upon whether the parcel is beinglifted mechanically (by a front or orographic barriers)or by convective means and whether the environment iscolder or warmer than the ascending parcel. Positiveareas are conducive to instability. Negative areas areconducive to stability.

Conditional instability may be one of three types.The REAL LATENT type is a condition in which thepositive area is larger than the negative area (potentiallyunstable). The PSEUDOLATENT type is a condition inwhich the positive area is smaller than the negative area(potentially STABLE). The STABLE type is acondition in which there is no positive area. Figure

2-19

AG5f0213

-10 0 10

B

SATURATIONADIABATIC

LAPSE RATE

ACTUALLAPSERATE

POINT B WARMER THANTHE SURROUNDING AIR

A

Figure 2-13.—Instability (saturated air).

2-14 shows an example of analyzed positive and thenegative energy areas as they would appear on aSkew-T, Log P diagram.

Autoconvection

AUTOCONVECTION is a condition startedspontaneously by a layer of air when the lapse rate oftemperature is such that density increases withelevation. For density to increase with altitude, thelapse rate must be equal to or exceed 3.42°C per 100meters. (This is the AUTOCONVECTIVE LAPSE

RATE.) An example of this condition is found to existnear the surface of the earth in a road mirage or a dustdevil. These conditions occur over surfaces that areeasily heated, such as the desert, open fields, etc.; theyare usually found during periods of intense surfaceheating.

Convection Stability and Instability

In the discussion so far of convection stability andinstability, PARCELS of air have been considered. Letus now examine LAYERS of air. A layer of air that is

2-20

500

600

700

850

1000

-20

30

20

-10

0

10

ISOBARS mb

SAT

UR

AT

ION

AD

IAB

AT

++

++++++++++++

UPPERNEGATIVE

AREA(BLUE SHADING)

EL

POSITIVEAREA

(RED SHADING)

NEGATIVEAREA(BLUE

SHADING)

SA

TU

RA

TIO

NM

IXIN

G-R

AT

IOLIN

E

ISO

TH

ER

MS

C

DR

YA

DIA

BAT

LFC

LCL

POINT A

T T

TT

d

d

AG5f0214

Figure 2-14.—Example of positive and negative energy areas (mechanical lifting).

originally stable may become unstable due to moisturedistribution if the entire layer is lifted.

Convective stability is the condition that occurswhen the equilibrium of a layer of air, because of thetemperature and humidity distribution, is such thatwhen the entire layer is lifted, its stability is increased(becomes more stable).

Convective instability is the condition ofequilibrium of a layer of air occurring when thetemperature and humidity distribution is such that whenthe entire layer of air is lifted, its instability is increased(becomes more unstable).

CONVECTIVE STABILITY.—Consider a layerof air whose humidity distribution is dry at the bottomand moist at the top. If the layer of air is lifted, the topand the bottom cool at the same rate until the topreaches saturation. Thereafter, the top cools at a slowerrate of speed than the bottom. The top cools saturationadiabatically (.55°C/100 meters), while the bottomcontinues to cool dry adiabatically (1°C/100 meters).The lapse rate of the layer then decreases; hence, thestability increases. The layer must be initially unstableand may become stable when lifting takes place.

CONVECTIVE INSTABILITY.—Consider alayer of air in which the air at the bottom is moist andthe air at the top of the layer is dry. If this layer of air islifted, the bottom and the top cool dry adiabaticallyuntil the lower portion is saturated. The lower part thencools saturation adiabatically while the top of the layeris still cooling dry adiabatically. The lapse rate thenbegins to increase and instability increases.

To determine the convective stability or instabilityof a layer of air, you should first know why you expectthe lifting of a whole layer. The obvious answer is anorographic barrier or a frontal surface. Next, determinehow much lifting is to be expected and at what level itcommences. Lifting of a layer of air close to the surfaceof the Earth is not necessary. The amount of lifting, ofcourse, depends on the situation at hand. Figure 2-15illustrates the varying degrees of air stability that aredirectly related to the rate at which the temperaturechanges with height.

Determining Bases of Convective Type Clouds

You have seen from our foregoing discussion thatmoisture is important in determining certain stabilityconditions in the atmosphere. You know, too, that thedifference between the temperature and the dew point isan indication of the relative humidity. When the dewpoint and the temperature are the same, the air issaturated and some form of condensation cloud may beexpected. This lends itself to a means of estimating theheight of the base of clouds formed by surface heatingwhen the surface temperature and dew point are known.You know that the dew point decreases in temperatureat the rate of 1°F per 1,000 feet during a lifting process.The ascending parcel in the convective currentexperiences a decrease in temperature of about 5 1/2°Fper 1,000 feet. Thus the dew point and the temperatureapproach each other at the rate of 4 1/2°F per 1,000 feet.As an example, consider the surface temperature to be80°F and the surface dew point 62°F, a difference of18°F. This difference, divided by the approximate ratethe temperature approaches the dew point (4 1/2°F per1,000 ft) indicates the approximate height of the base ofthe clouds caused by this lifting process (18 ÷ 4 1/2) ×

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AG5f0215

STABLE

CONDITIONALLY UNSTABLE

UNSTABLE

NORMALLAPSERATE

MOISTADIABATIC

ADIABATIC ISOTHERMAL

SUPERADIABATIC

INVERSION

Figure 2-15.—Degrees of stability in relation to temperaturechanges with height.

1000 = 4,000 feet). This is graphically shown in figure2-16.

This method cannot be applied to all cloud types. Itis limited to clouds formed by convection currents, suchas summertime cumulus clouds, and only in the localitywhere the clouds form. It is not valid around maritimeor mountainous areas.

Stability in Relation to Cloud Type

The degree of stability of the atmosphere helps todetermine the type of clouds formed. For example,

figure 2-17 shows that if stable air is forced to ascend amountain slope, clouds will be layerlike with littlevertical development and little or no turbulence.Unstable air, if forced to ascend the slope, causesconsiderable vertical development and turbulence inthe clouds. The base of this type of cloud can bedetermined by mechanical lifting as analyzed on aSkew-T.

REVIEW QUESTIONS

Q2-11. What are the two basic kinds of atmosphericenergy?

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MOIST ADIABATICIN CLOUD

DEWPOINTLAPSE RATE

DRY ADIABAT

40 50 60 70 80

5,000

4,000

3,000

2,000

1,000

THE AIR

DEGREES FAHRENHEITAG5f0216

HE

IGH

TIN

FE

ET

Figure 2-16.—Determine of cloud's base when the dew point and temperature are known.

AG5f0217

UNSTABLEAIR

STABLEAIR

Figure 2-17.—Illustration showing that very stable air retains its stability even when it is forced upward, forming a flat cloud. Airwhich is potentially unstable when forced upward becomes turbulent and forms a towering cloud.

Q2-12. What is the definition of lapse rate?

Q2-13. What is the rate of rise and fall dry adiabaticlapse rate?

Q2-14. What are the three types of conditionalinstability?

SUMMARY

Understanding the basic principles of atmosphericphysics is essential in order to comprehend howweather behaves. Analyzing meteorological situationsproperly depends upon what the Aerographer's Matelearns about atmospheric physics.

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