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