session 2, unit 3 atmospheric thermodynamics. ideal gas law various forms

Session 2, Unit 3

Atmospheric Thermodynamics

Ideal Gas Law

Various forms

1

Where

TM

RP

RT

PM

V

m

RTM

mnRTPV

Hydrostatic Equation

Air density change with atmospheric pressure

dPdzg

gdz

dP

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

dPdTcdPdudq

dPdw

v

Heat Capacity

At constant volume

At constant pressuredT

ducgasidealFor

dT

du

dT

dqc

v

constconstv

constpp dT

dqc

Heat Capacity

Relationships

v

p

vp

pp

vv

C

C

RCC

CMc

CMc

Concept of an Air Parcel

An 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 Process

Reversible adiabatic process of air

T

dT

R

C

P

dP

lawgasidealwithCombine

dPdTc

dqprocessAdiabatic

dPdTcdq

dPdTRcdqlawgasidealUse

dPPddTcdqdPsubtractandAdd

dPdTcdq

p

p

p

v

v

v

0

0

)(:

)(:

Lapse Rate

Combine hydrostatic equation and ideal gas law

For adiabatic process

dzRT

gM

P

dPRT

PMgg

dz

dP

T

dT

R

C

P

dP p

Lapse Rate

Therefore

dT/dz is Dry Adiabatic Lapse Rate (DALR)

dzC

gMdT

p

Dry Adiabatic Lapse Rate Dry adiabatic lapse rate (DALR)

Or on a unit mass basis

Or the expression in the textbook:

km

C

ft

F

km

C

m

K

kg

smPa

g

kg

KmolPam

molgsm

C

gM

dz

dT

ooo

p

101000

37.578.900978.0

1000/314.85.3

/29/81.9 2

3

2

kmKKkgJ

sm

c

g

dz

dT

p

/8.9/1004

/81.9 2

DALRkm

C

R

gg

dz

dT oc

95.91)/(

Lapse Rate

Effect 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 Rate

Superadiabatic 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 Temperature

Current 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

P

PTT o

o

DALRdz

dT

z actual

Session 2, Unit 4

Turbulence and Mixing

Air Pollution Climatology

Atmospheric Turbulence

Turbulent 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 Stability

NeutralStableUnstable

Richardson Number and Stability

Stability parameter

Richardson number Stable Neutral Unstable

zT

gs

2_

dz

dT

zg

Ri

u

Stability Classification Schemes

Pasquill-Gifford Stability Classification Determined based on

Surface wind Insolation

Six classes: A through F

Turner’s Stability Classification Determined based on

Wind speed Net radiation index

Seven classes Feasible to computerize

Inversions

DefinitionTypes Radiation inversion Evaporation inversion Advection inversion Frontal inversion Subsidence inversion

Fumigation

Planetary Boundary Layer

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

Planetary Boundary Layer

Neutral conditions Mixing height

Increased wind speed and surface roughness cause higher h.

f

uh *

Planetary Boundary Layer

Unstable conditions Mixing height

21

0

2

dz

dTDALRC

dtHh

p

t

t

Planetary Boundary Layer

Stable conditions Mixing height

Lf

uh *4.0

Surface Layer

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

Surface Layer

Monin-Obukhov length

Monin-Obukhov length and stability classes

kgH

TuCL p

3*

Surface Layer Wind Structure

Neutral air

0

* lnz

z

k

uu

a

Surface Layer Wind Structure

Unstable and stable air

L

z

airstableFor

L

zx

xarcxx

airunstableFor

L

z

z

z

k

uu

m

m

ma

5

161

2)tan(2

2

1ln

2

1ln2

ln

41

2

0

*

Friction Velocity

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

L

z

z

z

uku

m

a

0

*

ln

L

z

z

z

uku

m

a

0

*

ln

Power Law for Wind Profile

Wind profile power law

Value of p

p

mm z

z

u

u

Estimation of Monin-Obukhov Length

For unstable air

For stable air

Bulk Richardson Number

L

zRi

Ri

Ri

L

z

51

2

2

2

p

RbRi

u

DALRdz

dT

T

gzRb

Air Pollution Climatology

Meteorology vs. climatologyMeteorological measurements and surveysPollution potential-low level inversion frequency in US

Air Pollution Climatology

Mean maximum mixing heightdetermined by Morning temperature sounding Maximum daytime temperature DALR

Stability wind rose