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
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