Session 2, Unit 3Atmospheric Thermodynamics

Ideal Gas LawVarious forms

1

Where

TMRP

RTPM

Vm

RTMmnRTPV

Hydrostatic EquationAir density change with atmospheric pressure

dPdzg

gdzdP

dzgdP

First Law of Thermodynamics

For a body of unit mass

dq=Differential increment of heat added to the body

dw=Differential element of work done by the body

du=Differential increase in internal energy of the body

dudwdq

dPdTcdPdudqdPdw

v

Heat CapacityAt constant volume

At constant pressuredTducgasidealFor

dTdu

dTdqc

v

constconstv

constpp dT

dqc

Heat CapacityRelationships

v

p

vp

pp

vv

CC

RCC

CMcCMc

Concept of an Air ParcelAn air parcel of infinitesimal dimensions that is assumed to be Thermally insulated – adiabatic Same pressure as the environmental

air at the same level – in hydrostatic equilibrium

Moving slowly – kinetic energy is a negligible fraction of its total energy

Adiabatic ProcessReversible adiabatic process of air

TdT

RC

PdP

lawgasidealwithCombine

dPdTcdqprocessAdiabatic

dPdTcdqdPdTRcdqlawgasidealUse

dPPddTcdqdPsubtractandAdddPdTcdq

p

p

p

v

v

v

00

)(:)(:

Lapse RateCombine hydrostatic equation and ideal gas law

For adiabatic processdz

RTgM

PdP

RTPMgg

dzdP

TdT

RC

PdP p

Lapse RateTherefore

dT/dz is Dry Adiabatic Lapse Rate (DALR)

dzCgMdT

p

Dry Adiabatic Lapse Rate Dry adiabatic lapse rate (DALR)

Or on a unit mass basis

Or the expression in the textbook:

kmC

ftF

kmC

mK

kgsmPa

gkg

KmolPammolgsm

CgM

dzdT

ooo

p

101000

37.578.900978.0

1000/314.85.3/29/81.9 2

3

2

kmKKkgJ

smcg

dzdT

p

/8.9/1004/81.9 2

DALRkm

CRgg

dzdT o

c

95.91)/(

Lapse RateEffect of moisture

Because

Wet adiabatic lapse rate < DALR(temperature decreases slower as air parcel rises)

Condensation

VaporWaterAir Ppp CCC )1(

VaporWaterpAirpp wCCwC ,,' )1(

pp

AirpVaporWaterp

CC

CC

'

,,

Lapse RateSuperadiabatic lapse rate (e.g., 12oC/km)Subadiabatic lapse rate (e.g., 8oC/km)Atmospheric lapse rate Factors that change atmospheric

temperature profile Standard atmosphere

(lapse rate ~ 6.49 oC/km or 3.56 oF/1000 ft)

Potential TemperatureCurrent state: T, PAdiabatically change to: To, Po

Set Po = 1000 mb, To is potential temperature If an air parcel is subject to only adiabatic transformation, remains constantPotential temperature gradient

1

PP

TT oo

DALRdzdT

z actual

Session 2, Unit 4Turbulence and MixingAir Pollution Climatology

Atmospheric TurbulenceTurbulent flows – irregular, random, and cannot be accurately predicted Eddies (or swirls) – Macroscopic random fluctuations from the “average” flow Thermal eddies

Convection Mechanical eddies

Shear forces produced when air moves across a rough surface

Lapse Rate and StabilityNeutralStableUnstable

Richardson Number and Stability

Stability parameter

Richardson number Stable Neutral Unstable

zT

gs

2_

dzd

T

zg

Ri

u

Stability Classification Schemes

Pasquill-Gifford Stability Classification Determined based on

Surface wind Insolation

Six classes: A through FTurner’s Stability Classification Determined based on

Wind speed Net radiation index

Seven classes Feasible to computerize

InversionsDefinitionTypes Radiation inversion Evaporation inversion Advection inversion Frontal inversion Subsidence inversionFumigation

Planetary Boundary LayerTurbulent layer created by a drag on atmosphere by the earth’s surfaceAlso referred to as mixing heightInversion may determine mixing height

Planetary Boundary LayerNeutral conditions Mixing height

Increased wind speed and surface roughness cause higher h.

fu

h *

Planetary Boundary LayerUnstable conditions Mixing height

21

02

dzdTDALRC

dtHh

p

t

t

Planetary Boundary LayerStable conditions Mixing height

Lfu

h *4.0

Surface LayerFluxes of momentum, heat, and moisture remain constantAbout lower 10% of mixing layer

Surface LayerMonin-Obukhov length

Monin-Obukhov length and stability classes

kgHTuC

L p3*

Surface Layer Wind Structure

Neutral air

0

* lnzz

ku

ua

Surface Layer Wind Structure

Unstable and stable air

Lz

airstableForLzx

xarcxx

airunstableFor

Lz

zz

ku

u

m

m

ma

5

161

2)tan(2

21ln

21ln2

ln

41

2

0

*

Friction Velocity

Measurements of wind speed at multiple levels can be used to determine both u* and z0

Lz

zz

uku

m

a

0

*

ln

Lz

zz

uku

m

a

0

*

ln

Power Law for Wind ProfileWind profile power law

Value of p

p

mm zz

uu

Estimation of Monin-Obukhov Length

For unstable air

For stable air

Bulk Richardson Number

LzRi

RiRi

Lz

51

2

2

2

pRbRi

u

DALRdzdT

TgzRb

Air Pollution ClimatologyMeteorology vs. climatologyMeteorological measurements and surveysPollution potential-low level inversion frequency in US

Air Pollution ClimatologyMean maximum mixing heightdetermined by Morning temperature sounding Maximum daytime temperature DALRStability wind rose