This Week
READING: Chapter 7-8 of text
Announcements
Problem Set 2 due Tuesday Oct 16.
NO CLASS Tu OR WED.
Atmospheric Composition and Climate
• Solar and Terrestrial Radiation
• Earth’s Energy Balance (Simple Climate Models!)
• The Greenhouse Effect
• Climate Forcings
•Aerosols, Clouds and the Planetary Albedo
Recent and Past Climate Change
Sun and Earth as Black Bodies
max ~ 0.5 microns
max ~ 10 microns
Solar Radiation Spectrum: Blackbody 5800 K

  d    T
0
4
Solar Radiation vs. Altitude
Kirchoff’s Law
Emissivity (,T) = Absorptivity
For any object:
…very useful!
Radiative Equilibrium For the Earth
rs
DS-E
2
 rS 
-2
 = 1370 W m
 DS  E 
Solar flux at Earth’s location = Fs   TS4 
Solar flux intercepted and absorbed by Earth, distributed over its surface
area = Fs(1-A)/4
Radiative Balance: Terrestrial Flux Out = Solar Flux Absorbed
TE4 = Fs(1-A)/4
TE = 255 K
Greenhouse Effect
absorption of outgoing terrestrial radiation by the atmosphere
f
Greenhouse Model
Radiative Balance for
Earth + Atmosphere:
Fs(1 – A)/4 = (1-f)Tsurf4 + fTatm4
(1-f)Tsurf4
fTatm4
Atmospheric Layer Tatm
Absorptivity = f
fTatm4
Fs(1 – A)/4
Tsurf4
Radiative Balance for
Atmospheric Layer:
fTsurf4 = 2fTatm4
Tsurf = (2)1/4Tatm
Earth’s Surface Tsurf
Terrestrial Radiation Spectrum From Space
composite of several blackbody radiation spectra
corresponding to different temperatures
Scene over
Niger valley,
N Africa
troposphere
surface
top of stratosphere
Effect of Greenhouse Gas Addition
Example of a GG absorbing at 11 mm
1.
1. Initial state
2.
2. Add to atmosphere a GG
absorbing at 11 mm;
emission at 11 mm
decreases (we don’t see
the surface anymore at
that , but the atmosphere)
3.
3. At new steady state, total
emission integrated over all ’s
must be conserved
e Emission at other ’s must
increase
e The Earth must heat!
Question
1. Does increasing CO2 cause a warming or cooling of the
stratosphere? Why?
2. Early in Earth’s history, the sun was likely ~30% less
intense than now. Supposing the greenhouse effect was
the same, what would the average temperature have
been?
3. There is evidence for at least two global glaciation
events in Earth’s history (“Snowball Earth”). Provide a
mechanism using your climate model and C-cycle
knowledge to explain how Earth might have emerged
from this snowball climate state?
Scattering of Radiation by Aerosol
By scattering solar radiation, aerosols
increase the Earth’s albedo
Scattering efficiency is maximum when
particle diameter = 
eparticles in 0.1-1 mm
size range are efficient scatterers of solar
radiation
Typical U.S. Aerosol Size Distributions
Fresh
urban
Aged
urban
rural
remote
Warneck [1999]
Aerosols Tend to Increase Earth’s Albedo
F = - FsA/4
F ~ 0.9 W/m2
from direct effect
of aerosol
Smoke particles from biomass
burning in Southeast Asia appear
as white haze
modis.gsfc.nasa.gov
Global Climate Forcings Since 1750
To  F
IPCC [2001]
Questions
1. What is the SIGN of the radiative forcing caused by an
increase in the solar constant?
2. CFC-12 absorbs in the atmospheric window (8-13 microns)
and has an atmospheric lifetime of ~ 100yrs. Which would
be more effective in terms of reducing anthropogenic
contributions to global warming over the next hundred
years, reducing CFC 12 emissions by 10 kg, or CO2 emissions
by 10,000 kg?
Global Warming Potential (GWP)
• The GWP measures the integrated radiative forcing over a
time horizon t from the injection of 1 kg of a species X at
t t
time to, relative to CO2:
o
GWP 

to
to t

F1 kg X dt
F1 kg CO2 dt
to
Gas
Lifetime
(years)
GWP for time horizon
100 years 500 years
20 years
CO2
~100
1
1
1
CH4
12
63
23
7
N2O
114
279
300
158
CFC-12 (CF2Cl2)
100
10340
10720
5230
HFC-134a (CH2FCF3)
14
3580
1400
4
SF6
3200
15290
22450
32780
Earth’s Energy Balance
IPCC 2001
Chemical Kinetics (Reaction Rates)
Rate of reaction at any time, t, is the slope of the tangent to
curve describing change in concentration with time
Concentration molec cm-3
A+BC+D
t1
t2
time
Rates can change w/time because reactant concentrations can change
w/time. Note this is just the concept of mass balance
d[A]/dt = d[B]/dt = -d[C]/dt = -d[D]/dt (by mass conservation)
Rate Expressions for Gas-phase Reactions
d [ A]
d [ B]
I
Unimolecular: A
B

 k  A 
First order process
dt
dt
Lifetime = 1/k; k has units of s-1
Examples - decomposition: N2O5  NO3 + NO2
photolysis: O3 + hv  O2 + O
Bimolecular: A + B
C

d [ A]
d [ B] d [C ]
 k II  A B   

dt
dt
dt
kII, bimolecular rate constant, has units of cm3 molec-1 s-1
Example- OH + CH4  H2O + CH3
Special cases:
1. B=A, rate law becomes 2nd Order in [A]
2. [B]>>[A] rate law becomes pseudo-first order in [A]
Termolecular: A + B + M
C + M
M is total air number density
AKA: Pressure dependent bimolecular reactions
Questions
1. Which of the following are examples of first order
reactions?
a. Photolysis of stratospheric gases
b. Dry deposition of gases to Earth’s surface
c. Uptake of CO2 by plants
2. Atmospheric hydrogen peroxide is produced by the
self reaction of HO2: HO2 + HO2  H2O2 + O2
a. Write an expression for the loss rate of HO2
and for the production rate of H2O2.
b. Is this a first-order loss process?
Question
• If the rate constant for HO2 + HO2
 H2O2 + O2 is 1x10-12 cm3 molec-1 s-1,
what is the HO2 lifetime?
Energy Requirements Affect Rates
Reaction rate constants are often functions
of Temperature due to energy requirements
T2
Potential
Energy
A+B
AB*
Ea2
Ea1
T1
C+D
Reaction
Progress
Energy barriers are common: higher T gives higher energy
collisions, increasing the probability of a reaction
Termolecular (Pressure Dependent) Reactions
A bimolecular reaction which requires activated complex to be
stabilized by collisions with surrounding gas molecules “M”
1. A + B AB*
2. AB* A + B
3. AB* + M  C + M*
4. M*  M + heat
k1
d C 
k2
 k3  AB * M 
dt
k3
k4 [M] is TOTAL AIR NUMBER DENSITY
Assume lifetime of AB* very short, reacts as soon as its formed
(quasi steady state approximation):
d  AB *
dt
 0  k1  A B   k2  AB *  k3  AB * M 
k1  A B 
 AB *t 
k 2  k3  M 
d C 
dt

k3 k1  A B 
k 2  k3  M 
M 
Termolecular Rate Constants: Examples
-11
x 10
T=250 K
Rate Constant (cm3 molec-1 s-1
2.5
2
1.5
1
0.5
ClO + ClO --> Cl2O2
OH + NO2 --> HNO3
O + O2 --> O3
0
0
100
200
300
400
Pressure (Torr)
500
kClO+ClO and kO+O2 have been scaled
600
700
Questions
1. What was the important assumption we made in
deriving the rate constant for a termolecular reaction?
2. Does [AB*] change with time?
Quasi Steady State of Intermediate
A+B
C
t1
[C](t)
[AB*](t)
time
kforward
C+D
kreverse
[A](t)
Concentration molec cm-3
Concentration molec cm-3
A+B
Approach to Equilibrium
to equilibrium
time
At equilibrium (forward rate = reverse rate)
C  D  K   k forward 


eq
A
B
k
  
 reverse 
OH is produced in the atmosphere by the reaction of
an energetically “hot” oxygen atom (we’ll talk about why
its “hot” later) with H2O
H2O + O*  2OH
1. What is the rate expression for the loss of O* by
this reactive process?
2. What is the rate expression for the production
of OH by this reactive process?
3. Typically [O*] is << 1x106 molecules/cm3, while
[H2O] in the troposphere can be ~ 1x1015
molecules/cm3. If the bimolecular rate constant
for the above reaction is 1x10-11 cm3 molec-1 s-1,
what is a typical lifetime for [O*] w.r.t this
reaction in the troposphere?