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LESSON 3 THERMODINAMICS OF THE ATMOSPHERE

• Equation of state for an ideal gas. Gasses mixture

• Work and heat. The first law.

• Changes of phase

• Air parcel. Adiabatic processes.

• Water steam: Moist air. Saturation

• Moist air processes. Diagrams

• Vertical stability

Equipo docente:Alfonso Calera BelmonteAntonio J. Barbero

Departamento de Física AplicadaUCLM

Physics

Environmental

Hurricane Wilma (10/19/2005) Photo from http://www.nasa.gov/mission_pages/station/multimedia/hurricane_wilma.html

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STATE EQUATION FOR AN IDEAL GAS

TMR

Vm

VRT

Mm

RTVn

p 11 KkgKJ

MR

r

Vm

mV

v

11314.8 KkmolkJRnRTpV

rTpv

0q 0q

0w

0w

wqdu

FIRST LAW

System

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/firlaw.html

The first law states the conservation of energy

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SYSTEM PROPERTIES

Specific enthalpySpecific internal energy u pvuh

Specific heat

pp T

hc

vv T

uc

dvpw

Trabajo

Relationship for specific heats for an ideal gas

rTrdTd

vpdTd )( rcpvu

dTd

dTdh

v

Mayer relationship rcc vp

Any extensive property has an associated intensive property given by itself divided by the mass of the system

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dvpdTcq v

THE FIRST LAW APPLIED TO AN IDEAL GAS

dpvdTcdpvdTrcdpvvpddTcq pvv )()(

dvpdpvvpd )(

dpvdTcq p

dpvdvpdudh dpvdhq

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wduq

dpvdTcq p Remark:

5

V

RTnp i

i

V

nRTp

......21

i

ii

ii

nnn

ny

n

n

p

pMolar fraction

The partial pressure of a component in a mixture is proportional to its molar fraction.

IDEAL GASSES MIXTURE. DALTON’S MODEL

• An ideal gas consists on a set of non interacting particles whose volume is very little if compared with the total volume occupied by the gas. Non interacting particles minds negligible forces from one particle to another.

• Every component in the mixture behaves as if it were the only component occupying the whole volume available at the same temperature the mixture has.

• As a consequence: every component exerts a partial pressure, being the sum of all partial pressures the total pressure of the mixture.

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PHASE: Aggregation state physically homogeneous having the same properties

PHASE CHANGES:

CHANGES OF STATE AT CONSTANT PRESSURE: Entalphy

Water:L S 540 kcal/kg

S L 80 kcal/kg

Transitions between solid, liquid, and gaseous phases typically involve large amounts of energy compared to the specific heat

The latent heat is the energy released or absorbed during a change of state

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T (ºC)

heat

0

ice

ice + water

CHANGES OF STATE IN WATER

Let us consider ice at 1 atm

100

water steam

water +

steam

80 kcal/kg

540 kcal/kg

1 kcal/kg·ºC

The change líquid steam involves a great amount of energy!

0.5 kcal/kg·ºC

If heat were added at a constant rate to a mass of ice to take it through its phase changes to liquid water and then to steam, the energies required to accomplish the phase changes would be as follows:

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Moist air: dry air + water steam

Dry air Moist air Saturated air

Líquid

Moist air in contact with liquid water is described according the following model: 1) Dry air and water steam behave as independent ideal gasses (then the presence of each of them do not affect the behaviour of the other) 2) The equilibrium of the liquid water and steam phases is not affected by the presence of the air

(dry air composition: see following slide)

MOIST AIR

Steam

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Pressure of a vapour given off by (evaporated from) a liquid or solid, caused by atoms or molecules continuously escaping from its surface. In an enclosed space, a maximum value is reached when the number of particles leaving the surface is in equilibrium with those returning to it; this is known as the saturated vapour pressure or equilibrium vapour pressure

Vapour pressure is increasing up to... Saturated vapour pressure: function of T

WHY IS MOIST AIR LESS DENSE THAN DRY AIR AT SAME TEMPERATURE? http://www.theweatherprediction.com/habyhints/260/

SATURATED AIR

What is the vapour pressure?Dry air (majority components)

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QUESTION:

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Liquid water and steam phases coexists. The saturation vapour pressure is given by the liquid-vapour curve as a function of temperature.

0.000

0.020

0.040

0.060

0.080

0.100

0 10 20 30 40 50

P (

ba

r)

T (ºC)

Presion de vapor del agua (liq) en funcion de la temperatura

Liquid-steam equilibrium (water)

Triple point coordinates: 0.01 ºC, 0.00611 bar

0.024http://www.lsbu.ac.uk/water/phase.html

The phase diagram of water

Properties of Water and Steam in SI-Units(Ernst Schmidt)Springer-Verlag (1982)

SATURATION:

Vapour pressure

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0.000

0.020

0.040

0.060

0.080

0.100

0 10 20 30 40 50

P (

ba

r)

T (ºC)

Presion de vapor del agua (liq) en funcion de la temperatura

Linear interpolation

12

12

11 PP

TT

TTPP i

i

barCP 06632.0)º38(

1 2 i

12

Relationship between partial pressure of vapor, total pressure and specific humidity:

The partial pressure from a component of a gasses mixture is proportional to its molar fraction (Dalton)

pw

w

MmMm

M

mm

p

Mm

Mm

Mm

p

ssv

vv

s

v

s

s

v

v

v

v

v

1

s

v

mm

w kg vapor/kg dry air Mass of water vapor

Mass of dry air =

Specific humidity

Mixture rate or

s

s

v

v

v

v

v

Mm

Mm

Mm

y

pw

wpv

622.0s

v

MM

MOISTURE CONTENT OF THE AIR

Specific humidity (or moisture content of air) is the ratio of the mass of water to the mass of dry air in a given volume of moist air

Remark: v indicates vapors indicates dry air

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Determine the vapor pressure in air with specific humidity 6 g kg-1, when the total pressure is 1018 mb.

mbpw

wv

p 7.91018622.0006.0

006.0

Determine the specific humidity of an air mass at a total pressure of 1023 mb if the partialpressure of vapor is 15 mb.

00926.0151023

15622.0

v

v

pp

pw

. . . .

. . . .

. ..

.

.. ..

.

.

.

..

EXEMPLES

kg vapor/kg dry air

http://www.natmus.dk/cons/tp/atmcalc/atmocalc.htm

Calculator for atmospheric moisture

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Relative humidity: quotient between the molar fraction of water vapor in a given sample of damp air and the molar fraction of water vapor in saturated air at the same temperature and pressure.

pTsatv

v

y

y

,,

pyp vv

pyp satvsatv ,, pTsatv

v

p

p

,,

As the molar fraction and vapor partial pressure are proportional, the relative humidity can be also expressed as

Another form

In the troposphere p >> pv,sat

p

p

pp

pw satv

satv

satvsat

,

,

,

pp

ppp

w v

v

v

satww

RELATIVE HUMIDITY

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EXEMPLEConsider an air mass at 1010 mb and 20 ºC in which the partial vapor pressure is 10 mb. Calculate its relative humidity, actual specific humidity and saturation specific humidity.

P

T

pv

pv,sat

w

wsat

%)43(428.039.23

10

,,

pTsatv

v

pp

00622.0101010

10622.0

v

v

ppp

w kgkg-1

0147.039.231010

39.23622.0

,

,

satv

satvsat pp

pw kgkg-1

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Dew point: the temperature at which air must be cooled at constant pressure in order for it to become saturated with respect to a plane surface of water.

0.000

0.020

0.040

0.060

0.080

0.100

0 10 20 30 40 50

P (

ba

r)

T (ºC)

Presion de vapor del agua (liq) en funcion de la temperatura

Dew point 17.5 ºC

0.012

Exemple. Damp air mass cooling down from 40 ºC up to 10 ºC (pv = 20 mb, total pressure 1010 mb)

v

vC pp

pw º40

10126.0020.0010.1

020.0622.0

kgkg

v

vC pp

pw º10

10748.0012.0010.1

012.0622.0

kgkg

The air keeps its specific humidity but increases its relative humidity

Atmospheric Science: An Introductory Survey by Wallace & Hobbs

Pressure vapor of water as a function of temperature

What is the initial relative humidity? And the final one?

http://weathersavvy.com/Q-dew_point1.html

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TEMPERATURE AND HUMIDITY DAILY CYCLE

40

60

80

100

20

25

30

35

0 3 6 9 12 15 18 21 24

Hora

Tem

pera

ture

ºC

Rel

ativ

e hu

mid

ity

%

If the vapor of water in the air remains constant... Constant vapor pressure

24 mb

MINIMUM OF TEMPERATURE

MAXIMUM OF

MOISTURE

MINIMUM OF

MOISTURE

MAXIMUM OF TEMPERATURE

TEMPERATURE DAILY CYCLE

MOISTURE DAILY CYCLE

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ENTHALPY

The heat content, usually called the enthalpy, of air rises with increasing water content.

Specific enthalpySpecific internal energy u pvuh

This hidden heat, called latent heat by meteorologists and air conditioning engineers, has to be supplied or removed in order to change the relative humidity of air, even at a constant temperature. This is relevant to conservators. The transfer of heat from an air stream to a wet surface, which releases water vapour to the air stream at the same time as it cools it, is the basis for psychrometry and many other microclimatic phenomena. Control of heat transfer can be used to control the drying and wetting of materials during conservation treatment.

The enthalpy of dry air is not known. Air at zero degrees celsius is defined to have zero enthalpy. The enthalpy, in kJ/kg, at any temperature, t, between 0 and 60C is approximately:

h = 1.007t - 0.026 below zero: h = 1.005t

http://www.natmus.dk/cons/tp/atmcalc/ATMOCLC1.HTM#enthalpy

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vs

vs

s

v

s

s

s

hmm

hmH

mH

mH

vs hwhh

Specific(kJ/kg dry air)

vs HHH vvss hmhm Enthalpy of air-water vapor mixture

Sensible heat:

Sensible heat is defined as the heat energy stored in a substance as a result of an increase in its temperature

Units: kJ/kg dry air o en kcal/kg dry air (specific magnitude). Specific heat of dry air is 0.24 kcal/kg

Latent heat:

The heat released or absorbed per unit mass by a system in a reversible isobaric-isothermal change of phase. In meteorology, both the latent heats of evaporation (or condensation), fusion (melting), and sublimation of water are important

http://www.shinyei.com/allabout-e.htm#a19

Remark: v indicates vapors indicates dry air

Really the sensible heat is the same as enthalpy; the heat absorbed or transmitted by a substance during a change of temperature which is not accompanied by a change of state

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ADIABATIC SATURATION PROCESS

Air flows across a pipe or duct adiabatically insulated where there is an open water reservoir. As air moves around, its specific humidity increases. It is assumed that air and water are in contact time enough until saturation is reached.

T1

1

T2

2

About adiabatic saturation and humidity http://www.taftan.com/xl/adiabat.htmhttp://www.shinyei.com/allabout-e.htm

Adiabatic saturation temperatureT2 = Tsa

Adiabatic isolation

The enthalpy of the wet air remains constant because the adiabatic isolation. As a consequence, the air temperature decreases when the saturated air leaves the pipe.

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PSYCHROMETER

)()(

)()(')()(

saliqv

saliqsavssas

ThTh

ThThwThThw

Determination of w specific humidity of the air from three properties: pressure p, temperature T and adiabatic saturation temperature Tsa

dry

T

Wet bulb temperature Adiabatic saturation temperature

Psichrometric chartsaT

wet

)()(

'sag

sav

TppTp

w

M J Moran, H N Shapiro. Fundamentos de Termodinámica Técnica. Reverté (1994)

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It consists of two thermometers, one of which (the dry bulb) is an ordinary glass thermometer, while the other (wet bulb) has its bulb covered

with a jacket of clean muslin which is saturated with

distilled water prior to an observation. When the bulbs are suitably

ventilated, they indicate the

thermodynamic wet- and dry-bulb

temperatures of the atmosphere.

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Vmm vs Density of the moist air (kg/m3)

vs mmV

v

1

Specific volume (m3/kg)

w, pv

T (dry)

h

T (wet bulb)

v

Psychrometric chart

VALID FOR A GIVEN PRESSURE

http://www.taftan.com/thermodynamics/SPHUMID.HTM

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30 ºC

30%

18 ºC

13.5 ºC

19 ºC

0.0080

0.0095

= 0.0095-0.0080 =

= 0.0015 kg·kg-1

EXEMPLEAn air mass at 30 ºC having a 30% relative humidity undergoes an adiabatic saturation process. Then it is cooled down to 13.5 ºC, and after it is warmed up to 19 ºC. What is its final relative humidity? How much has been changed its specific humidity ?

70%

25

If liquid freezes into solid water (ice), the internal energy is reduced further owing to the much tighter packing of water molecules in the solid phase.

An air parcel is a glob of atmospheric air containing the usual mixture of non-condensing gases plus a certain amount of water vapor.

Water in the gaseous form exists in any parcel of air with relative humidity greater than 0%. If the amount of water vapor (and other environmental conditions) is such that the relative humidity of the air parcel reaches 100%, it is said that the parcel is saturated.

Under conditions of saturation, water in the vapor form can change its phase from vapor to liquid. Then that water vapor condenses into liquid water dropletsWhen phase changes occur, there is a readjustment of the forms of energy associated with the water molecules. In the vapor phase, water has a relatively large amount of internal energy represented by its looser internal molecular structure. When vapor condenses to liquid, the internal energy of the water molecule in the liquid phase is smaller, owing to its tighter molecular structure.

AIR PARCEL

Its composition remains roughly constant whereas this glob moves across the atmosphere from one site to another.

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AIR PARCEL: MODEL

We’ll consider that air parcels obey the following model:

constantPV

Any air parcel is adiabatically isolated and its temperature changes adiabatially when it rises or descends.

1

The movement of air parcels is slow enough to make possible to assume that their kinetic energy is a very little fraction of their total energy.

2

It is assumed that any air parcel is in hidrostatic equilibrium with its environment: it has the same pressure that its environment has.

3

What does hidrostatic equilibrium mean?

Are we able to calculate temperatures from that or some related formula?

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HIDROSTATIC EQUATION

dz

gSdz z p

S

Air mass contained in dz: dzS

Weight of air contained in dz: dzSg

Net pressure force:

Ascending: pS

Descending: )( dppS

dpSdppSpS )(

The net pressure force goes upwards, because dp is a negative quantity

Pressure forces: p+dp

-Sdp

Air column, density

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We assume that every air layer is near equilibrium

Weight equilibrates the pressure forces

dzSgdpS gdz

dp

v

1

As a function of specific volume:

dpvdzg

dz

gSdz z p

S

p+dp -Sdp

HIDROSTATIC EQUATION (Continued)

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Moist air == dru air +

+ water vapor

vsvs

Vmm Density of

moist air:

s: density that the same dry air mass ms would have if the dry air were the only component in the volume V

v: density that the same water vapor mass mv would have if the water vapor were the only component

“Partial” densities

V ms mv

VIRTUAL TEMPERATURE

Ideal gas

Dalton’s law vs ppp

Trp sss

Trp vvv Tr

pTrpp

v

v

s

v

Virtual temperature is an adjustment applied to the real air temperature to account for a reduction in air density due to the presence of water vapor

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Tr

p

Tr

pp

v

v

s

v

Virtual temperature definition Tvirtual

The ideal gas equation can be written as:

Virtual temperature is the temperature that dry air should have so that its density be the same than that of the moist air at the same pressure.

Moist air is less dense than dry air virtual temperature is larger than absolute temperature

Density of moist airConstant of

dry air

Moist air pressure

622.0s

v

v

s

M

M

r

r

virtuals Trp

1111ew

wT

pp

TT

vvirtual

1111

p

p

Tr

p

r

r

p

p

Tr

p v

sv

sv

s

11pp

TT

vvirtual

Virtual temperature calculator: http://www.csgnetwork.com/virtualtempcalc.html

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Potential temperature is the temperature that a parcel of dry air would have if it were brought dry adiabatically from its original position to a standard pressure p0 (generally the value 1000 mb is taken as the reference p0).

POTENTIAL TEMPERATURE

rTvp

0p

dpTdT

r

cp

p

p

Tp

pdp

TdT

r

c

00

lnlnppT

r

cp

0ppT r

cp

286.01004

287

11

11

kgKJ

kgKJcr

pDry air

0 dpp

rTdTcp

pcr

pp

T

0

286.0pconstanteT

0 dpvdTcq p

ADIABATIC PROCESS

32

1000

600

100

200

300

400

800

0

10

100 200 300 400

P (m

b)

T (K)

=100K =200K =300K =400K =500K

PSEUDOADIABATIC CHART

286.0pconstanteT

Exemple. An air parcel at 230 K lies in the 400 mb level and goes down adiabatically up to the 600 mb level. Calculate its final temperature.

230 KAdiabatic dropping

constant

All points in this line have the same potential temperature

259 KPhysics

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Continuous lines in K: Dry adiabaticsAlong these lines the potential temperature is constant ( cte)

Dashed lines in K: Pseudoadiabatics(for moist air, wet bulb cte)

Continuous lines in g/kg: Saturation mixing ratio lines(specific humidity for saturation ws)

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ExempleAn air mass at 1000 mb and 18 ºC has a mixed ratio of 6 gkg-1. Find out its relative humidity and its dew point temperature.

USE OF PSEUDOADIABATIC CHART

* Plot the T, p coordinates on the thermodynamics diagram (red point)

* Read the saturation mixing rate. See that ws = 13 gkg-1

* Relative humidity %)46(46.0136

satww

* Dew point temperature: draw a horizontal line across the 1000 mb ordinate up to reaching the saturation mixing ratio line corresponding to the actual mixing ratio (6 gkg-1). Its temperature is 6 ºC, that is to say, when reaching this temperature a water vapor content of 6 gkg-1 become saturating, then liquid water condenses.

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ws = 13 gkg-1

6 ºC18 ºC

1000 mb

%)46(46.0136

sww

Dew point

ExempleAn air parcel at 1000 mb and 18 ºC has a mixing ratio of 6 gkg-

1. Find out its humidity and dew point

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LIFTING CONDENSATION LEVEL

The level where a wet air parcel ascending adiabatically becomes saturated

During the lifting process the mixing ratio w and the potential temperature remain constant, however the saturation mixing ratio ws drops because the temperature is decreasing. Saturation is reached when the the saturation mixing ratio equals the actual mixing ratio w.

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• The ascending condensation level of an air parcel can be found in the pseudoadiabatic chart in the intersection point of the following lines:

• the potential temperature line (dry adiabatic line) in the point

determined by the temperature and pressure of the air parcel; • the equivalent potential temperature line (pseudoadiabatic line)

passing through the point indicating the wet bulb temperature and the pressure of the air parcel;

• the saturation mixing ratio line (constant humidity line) passing through the point indicating the dew point and the pressure of the air parcel;

NORMAND’S RULE

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Air parcel at pressure p, temperature T, dew point TR and wet bilb

temperature Tbh.

constant

sat constant

wsat constant

1000 mb

p

T

T TR

Condensation level

Tbh

bh

p

dry adiabatic line

pseudoadiabatic line

Sat. mixing ratio line

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EXEMPLE 1. Lifting condensation level

A) An air parcel at 15 ºC has a dew point temperature of 2 ºC. It lifts adiabatically from the 1000 mb level. Find out its lifting condensation level and the temperature in this level.

B) If this air parcel goes on ascending over the condensation level and reaches a level 200 mb above, find out its final temperature and the amount of water condensed during the ascending process.

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15 ºC

1000 mb

830 mb

630 mb

-15 ºC

TR=2 ºC

4.5 g/kg

2.0 g/kg

Condensado:4.5-2.0=2.5 g/kg

-1 ºC

A) An air parcel at 15 ºC has a dew point temperature of 2 ºC. It lifts adiabatically from the 1000 mb level. Find out its lifting condensation level and the temperature in this level.

B) If this air parcel goes on ascending over the condensation level and reaches a level 200 mb above, find out its final temperature and the amount of water condensed during the ascending process.

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EXEMPLE 2An air parcel at 900 mb and 15 ºC has a dew point temperature of 4.5 ºC. Find out the lifting condensation level, the mixing ratio, relative humidity, its wet bulb temperature, the potential temperature and the wet bulb potential temperature.

6 g·kg-1

770 mb

12 g·kg-1

5.012

6 (50%)

8.5 ºC

13 ºC 23.5 ºC

T=15 ºCTR=4.5 ºC

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dvpdTcq v

THE FIRST LAW APPLIED TO AN IDEAL GAS

dpvdTcdpvdTrcdpvvpddTcq pvv )()(

dvpdpvvpd )(

dpvdTcq p

dpvdvpdudh dpvdhq

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wduq

dpvdTcq p Remark:

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LAPSE RATE

Rate at which temperature decreases with heightdz

dT K/km ºC/km

A positive value indicates decrease of T with height

Troposphere: general decrease in T with height

Environmental lapse rate (ELR): it is the actual temperature of air we can measure (observed air temperature at any height)

Dry adiabatic lapse rate (DALR): rate which a non-saturated air parcel cools at it rises

Saturated (wet) adiabatic lapse rate (SALR): rate which a saturated air parcel cools at it rises P

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DRY ADIABATIC LAPSE RATE (DALR)

Adiabatic process

0 dzgdTcq p

First law

Hydrostatic equation

dpvdTcq p

dpvdzg

sposecaire c

gdzdT

g = 9.81 ms-2

cp = 1004 Jkg -1K-1

s = 0.0098 Km-1 = 9.8 Kkm-1

Consider a raising air parcel

Pressure and density decrease with height, then

as an air parcel rises it expands and cools

A physical change of the state of the air parcel that does not involve exchange of energy with

the air surrounding the air parcel.

Rate which a non-saturated air parcel cools at it rises

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SATURATED ADIABATIC LAPSE RATE (SALR)

When the air is saturated, condensation occurs

Latent heat of vaporization is released

That keeps the air parcel warmer than it would otherwise

Decrease in temperature with height is not as great as it would be for dry air

SALR is dependent on the amount of moisture on the atmophere

tasairesat dz

dT

More moisture in the atmosphere…

… the greater will be the release of condensation heat

… warmer the air will remain

Range for sat

4 K km-1 9 K km-1

MORE MOISTURE LESS MOISTURE

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STABLE ATMOSPHERE

STATIC STABILITY FOR NON-SATURATED AIR

Density of raising air (A is colder) is bigger than density of environmental air B

A restoring force inhibiting the vertical movement appears

Positive static stability

When the ELR is SMALLER than dry adiabatic lapse rate s

Temperature

Height

TBTA

B

Case <ss - >0

s

A

Initial conditions

Environmental lapse rate (ELR)

When raising, the air parcel pressure evens up to that of its environment

The air parcel tends to return to its original level instead of remaining on A

What will happen if we consider an ascending movement of the non-saturated air parcel ?

Could you figure out the same problem for descending non-saturated air?

dz

dT

0dz

dT0

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STABLE ATMOSPHERE

STATIC STABILITY FOR NON-SATURATED AIR (2)

Density of raising air (A is colder) is bigger than density of environmental air B

A restoring force inhibiting the vertical movement appears

Negative static stability

Temperature

Height

TA

Case <s s - >0

s

A

Environmental lapse rate (ELR)

When raising, the air parcel pressure evens up to that of its environment

The air parcel tends to return to its original level instead of remaining on A

What will happen if we consider an ascending movement of the non-saturated air parcel ?

Could you figure out the same problem for descending non-saturated air?

...and < 0

dz

dT

TB

B

Initial conditions

The ELR is negative (of course, it is SMALLER than that of the dry air)

0dz

dT0

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About thermal inversionshttp://www.aviacionulm.com/meteotemperatura.htmlhttp://www.sagan-gea.org/hojared/hoja20.htmhttp://www.rolac.unep.mx/redes_ambientales_cd/capacitacion/Capitulo1/1_1_2.htmhttp://en.wikipedia.org/wiki/Thermal_inversion

http://www.sma.df.gob.mx/sma/gaa/meteorologia/inver_termica.htm

THERMAL INVERSION

Cold air

Warm air layer

Very cold air

Thermal inversions play a significant role on the contaminants gathering

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UNSTABLE ATMOSPHERE

Static unstability

ELR is BIGGER than the dry air lapse rate

Temperature

Height

TB TA

B

Case >s s - < 0

s

A

Initial conditions

Environmental lapse rate (ELR)

STATIC UNSTABILITY FOR NON-SATURATED AIR

Density of raising air (A is warmer) is smaller than density of environmental air B

A force in favor of further vertical movement appears

When raising, the air parcel pressure evens up to that of its environment

The air parcel tends to move away from its original level

dz

dT

0dz

dT0

Physics

Environmental

51

Stable

<sPositive static stability

<0 <sNegative static stability

(inversion)

Unstable >sConvective mixing

Neutral stability: =s

STATIC STABILITY NON-SATURATED AIR (SUMMARY)

s

s

Physics

Environmental

52

Ground

EXEMPLE ON STABIBLITY AND UNSTABILITY

Environmental lapse rate (ELR)

Dry Adiabatic Lapse Rate (DALR)

As the air parcel is unsaturated, it lifts

along the dry adiabatics

temperature

The air parcel temperature here is lower than

sourrounding air temperature Any air parcel which overtakes this level sinks to equilibrium

levelInversion level

ELR > DALR s

What will happen to an unsaturated air parcel initially lying on the ground?

53

http://www.adi.uam.es/docencia/elementos/spv21/sinmarcos/graficos/entalpiadevaporizacion/evapor.html

Enthalpy of change of state data

http://www.adi.uam.es/docencia/elementos/spv21/sinmarcos/graficos/entalpiadefusion/efusion.html

http://www.usatoday.com/weather/wwater0.htm

Other related sites

http://www.usatoday.com/weather/whumdef.htm

BIBLIOGRAPHY

http://www.usatoday.com/weather/wstabil1.htm (usa unidades inglesas)

Stability and unstability discussions

http://www.qc.ec.gc.ca/meteo/Documentation/Stabilite_e.html

http://www.cesga.es/telecursos/MedAmb/medamb/mca2/frame_MCA02_3.html

http://www.geocities.com/silvia_larocca/Temas/emagrama2.htm

http://www.usatoday.com/weather/whumdef.htmOn humidity and its measure

M J Moran, H N Shapiro. Fundamentos de Termodinámica Técnica. Reverté (1994)

Basic books:

John M Wallace, Peter W Hobbs, Atmospheric Science. An introductory survey. Academic Press (1997)

On specific heathttp://www.engineeringtoolbox.com/36_339qframed.html

http://seaborg.nmu.edu/Clouds/types.html

Clouds

http://www.gordonengland.co.uk/conversion/specific_energy.htm

Physics

Environmental

http://www.indiana.edu/~geog109/topics/08_stability/LapseStability_CB_L.pdf

54

-10 -5 0 5 10 15 20 25 30 35 40

1050

1000

950

900

850

800

750

700

temperature ºC

pressure mb

Continuous red lines labelled in K: dry adiabatics

Continuous black lines labelled in g·kg-1: saturation mixing ratio

Discontinuous grey unlabelled lines: pseudoadiabatics

2.0 3.0 4.0 6.0 8.0 10.0 12.0 15.0 20.0 25.0 30.0

280

290

300

310

320

PSEUDOADIABATIC CHART

Physics

Environmental

55

-10 -5 0 5 10 15 20 25 30 35 40

1050

1000

950

900

850

800

750

700

temperature ºC

pressure mb

Continuous red lines labelled in K: dry adiabatics

Continuous black lines labelled in g·kg-1: saturation mixing ratio

Discontinuous grey unlabelled lines: pseudoadiabatics

2.0 3.0 4.0 6.0 8.0 10.0 12.0 15.0 20.0 25.0 30.0

280

290

300

310

320

PSEUDOADIABATIC CHART

Physics

Environmental