LECTURE 3
Basics of atmospheric composition and physics
AOSC 434
AIR POLLUTION
Russell R. Dickerson
Ib. ATMOSPHERIC PHYSICS
Seinfeld & Pandis: Chapter 1
Finlayson-Pitts: Chapter 2
1.Pressure: exponential decay
2.Composition
3.Temperature
The motion of the atmosphere is caused by differential
heating, that is some parts of the atmosphere receive more
radiation than others and become unstable.
VERTICAL PROFILES OF PRESSURE AND TEMPERATURE
Mean values for 30oN, March
Stratopause
Tropopause
Composition of the Earth’s Troposphere
H2
O2
CH4
N2
N2O
PM
CO
O3
←SO2, NO2,
CFC’s, etc
Ar
CO2
Inert gases
Banded iron formation.
Smithsonian in DC
About 3E9 years ago, cyanobacteria began producing O2 in photosynthesis;
initially consumed by iron and organic matter in oceans. O2 is toxic to
anaerobic organisms – the first great extinction. (Range of PO2 estimates)
Units of pressure:
1.00 atm. = 14.7 psi = 1,013 mb = 760 mm Hg (torr) = 33.9 ft H₂O
= 29.9” Hg = 101325 Pa
A Pascal is a Nm⁻² (kg m s-2 m-2 ) thus hPa = mb.
Units of Volume: liter, cc, ml, m³
Units of temp: K, °C
Units of R: 0.08206 L atm mole-1 K-1
8.31 J mole-1 K-1
R’ = R/Mwt = 0.287 J g-1K-1
For a mole of dry air which has the mass 29 g.
Problem for the student: calc Mwt. Wet (2% H₂O vapor by volume) air.
1A. Derive Hypsometric Equation
Start with The Ideal Gas Law
PV = nRT or P = ρR’T or P = R’T/α
Where R’ = R/Mwt
Mwt = MOLE WT. AIR
ρ = DENSITY AIR (g/l)
α = SPECIFIC VOL AIR = 1/ρ
We assume that the pressure at any given altitude is due to the weight of
the atmosphere above that altitude. The weight is mass times acceleration.
P = W = mg
But
m = Vρ
For a unit area V = Z
P = Zρg
For a second, higher layer the difference in pressure can be related to the
difference in height.
dP = − g ρ dZ
But
ρ = P/R’T
dP = − Pg/R’T * dZ
For an isothermal atmosphere g/R’T is a constant. By integrating both sides
of the equation from the ground (Z = 0.0) to altitude Z we obtain:
PZ
ò dP =
ò-
P0
0
PZ
ò
P0
1
dp =
p
Z
Z
ò0
Pg
dz
R'T
g
dZ
R'T
ln(P/P0 ) = -Z/H 0
H 0 = TR'/ g
Where H₀ = R’T/g we can rewrite this as:
PZ  P0 exp( Z / H 0 )
*HYPSOMETRIC EQUATION*
Note: Scale Height: H₀ ~ 8 km for T = 273K
For each 8 km of altitude the pressure is down by e⁻¹ or one “e-fold.”
Problems for the student: Derive an expression for pressure as a
function of altitude using base two and base ten instead of base e. Calculate
the scale height for the atmospheres of Venus and Mars.
Ans. base 2 = H₀*ln(2) = 5.5 km
base 10 = H₀*ln(10) = 18 km
1B. TEMPERATURE LAPSE RATE
Going to the mountains in Shenandoah National Park the summer is a nice
way to escape Washington’s heat. Why? Consider a parcel of air. If it
rises it will expand and cool. If we assume it exchanges no heat with the
surroundings (a pretty good assumption, because air is a very poor
conductor of heat) it will cool “adiabatically.”
Calculating the dry adiabatic lapse rate.
First Law Thermodynamics*:
dU = đQ – đW
Or
đQ = dU + đW = dU + PdV
*watch out for work done by the system or on the system.
WHERE
U = Energy of system (also written E)
Q = Heat across boundaries
W = Work done by the system on the surroundings
H = Internal heat or Enthalpy
ASSUME:
a)
Adiabatic (dQ = dH = 0.0)
b)
All work PdV work
(remember α = 1/ρ)
dH = Cp dT – α dP
CpdT = α dP
dT = (α/Cp) dP
Remember the Hydrostatic Equation
OR
Ideal Gas Law
dP  ( g )dZ
dP  (gP/R'T)dZ
  R' T / P
 R ' T ( gP )
dT 
dZ
PC p R ' T
Result:
dT / dZ   g / C p
This quantity, -g/Cp, is a constant in a dry atmosphere. It is called the dry
adiabatic lapse rate and is given the symbol γ₀, defined as −dT/dZ.
 0  9.8K / km
For a parcel of air moving adiabatically in the atmosphere:
T2  T1   0 ( Z2  Z1 )
Where Z₂ is higher than Z₁, but this presupposes that no heat is added to or
lost from the parcel, and condensation, evaporation, and radiative heating can
all produce a non-adiabatic system.
The dry adiabatic lapse rate, 0, is a general, thermodynamic property of the
atmosphere and expresses the way a parcel of air will cool on rising or warm
on falling, provided there is no exchange of heat with the surroundings and no
water condensing or evaporating. The environmental lapse rate, G, is seldom
equal to exactly the dry adiabatic lapse rate because radiative processes and
phase changes constantly redistribute heat. The mean lapse rate is about 6.5
K/km.
Problem left to the students: Derive a new expression for the change in
pressure with height for an atmosphere with a constant lapse rate,
TZ  T0  Z
2. STABILITY AND THERMODYNAMIC
DIAGRAMS
Gray lines – thermodynamic property
Black lines – measurements or soundings
Three days
Ga < γ₀ stable
Gb = γ₀ neutrally stable
Gc > γ₀ unstable
On day a a parcel will cool more quickly than surroundings – air will be
cooler and return to original altitude.
On day b a parcel will always have same temperature as surroundings –
no force of buoyancy.
On day c a parcel will cool more slowly than surroundings – air will be
warmer and rise.
a
Convective Instability
dry air
b
c
19
Example 1, early morning
Pressure, mb
Temp., °C
Dew point,
°C
1000
7
6
920
7
7
870
6
0
840
3.5
-1.5
700
-8
-16
500
-27
-36
300
-58
Tropopause
Inversion
layer
Saturated air
250
-67
200
-65
(T = TD)
Example 2, mid-day
Pressure, mb
Temp., °C
Dew point,
°C
1000
8.5
5.5
Tropopause
860
0.5
-3
710
-8
-17
550
-21.5
-31.5
490
-22.5
330
-45
285
-51
200
-51
-45
Frontal
Inversion
layer
Skew-T handout
Very important for air pollution and mixing of emissions with free
troposphere. Formation of thermal inversions.
In the stratosphere the temperature increases with altitude, thus stable or
stratified.
DFN: Potential temperature, θ : The temperature that a parcel of air would
have if it were brought to the 1000 hPa level (near the surface) in a dry
adiabatic process. You can approximate it quickly,
 z  TZ  Z 0
or a proper derivation from dq = CpdT – dp = 0 yields:
θz = T (1000 hPa/Pz) R’/Cp
= T (1000 hPa/Pz)0.286
DIURNAL CYCLE OF SURFACE
HEATING/COOLING:
z
Subsidence
inversion
MIDDAY
1 km
Mixing
depth
NIGHT
0
MORNING
T
NIGHT
MORNING AFTERNOON
If the parcel reaches saturation, the condensation of
water adds heat, and the rising air cools at a new, slower
rate, Gs. For details, see Wallace and Hobbs.
Since Gs< Gd, we must also consider conditions between
the two stability criteria for dry and saturated.
  Gs
  Gs
Gs    Gd
  Gd
  Gd
Absolutely stable
Saturated neutral
Conditiona lly unstable
Dry neutral
Absolutely unstable
G = parcel lapse (thermodynamically determined) rate.
 = environment (observed) lapse rate.
24
Plume looping, Baltimore ~2pm.
Plume Lofting, Beijing in Winter ~7am.
High levels of air pollution in Beijing contain a large quantity of PM 2.5. ©
iStockPhoto.com/beijingstory.
Marshall J PNAS 2013;110:8756-8756
©2013 by National Academy of Sciences
Chinese Y12 (Twin Otter) for the airborne
campaign over NE China April 2005
►
↑ ~ 15 μg m-3
~ 100 μg m-3 ↓
5 April 2005 Ahead of Front
4000
3500
← Shenyang, 5 April 2005
Altitude (m)
3000
2500
2000
1500
1000
500
← NE USA median
0
0
200
400
600
800
[CO] (ppb)
1000
1200
1400
Mean SO2 in NE China and NE US
4500
NE China mean (8
flights from April 2005)
4000
Altitude (m)
3500
NE US mean (381
flights from 2000-2003)
3000
2500
NE China flight ahead
of cold front 5 April
2005)
2000
1500
1000
500
0
0
5
10
15
SO2 (ppb)
20
25
DISCOVER-AQ Case Study
MODIS true color image 21 July 2011
Baltimore, MD
✪

Bay breeze:
Winds veer w/ alt
Washington, DC
UMD Cessna
Hot (Tmax > 100oF)
Humid, rel stable PBL.
Ozone over Har ord Cnty Airport, MD
21 July 2011 ~14:00 EST Descent
3000
2500
Al tude (m)
2000
1500
1000
500
0
20
40
60
80
Temp (C) and Ozone (ppb)
100
120
PM2.5 ~ 40 mg m-3 
UMD Cessna
Atmospheric Circulation and Winds
Copyright R. R. Dickerson 2011
44
ITCZ
Copyright R. R. Dickerson 2011
45
Mid latitude cyclone with fronts
Copyright R. R. Dickerson 2011
46
Warm Front
Fig. 9.13
Copyright R. R. Dickerson 2011
47
Cold front
Fig. 9.15
Copyright R. R. Dickerson 2011
48
Copyright R. R. Dickerson 2011
Fig. 49
1-17, p. 21
Copyright R. R. Dickerson 2011
Fig. 50
1-16, p. 19
Copyright R. R. Dickerson 2011
Fig. 51
1-16, p. 19
Detailed weather symbols
Copyright R. R. Dickerson 2011
52
Inversion under a high pressure system over NYC
Looking north January 2016