this week solar and terrestrial radiation earth’s energy balance (simple climate models!) the...
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This Week
• Solar and Terrestrial Radiation
• Earth’s Energy Balance (Simple Climate Models!)
• The Greenhouse Effect
• Climate Forcings
•Aerosols, Clouds and the Planetary Albedo
READING: Chapter 7-8 of text
Announcements Problem Set 2 due Tuesday Oct 16.
NO CLASS Tu OR WED.Atmospheric Composition and Climate
Recent and Past Climate Change
Sun and Earth as Black Bodies
max ~ 0.5 microns
max ~ 10 microns
Solar Radiation Spectrum: Blackbody 5800 K
4
0
d T
Solar Radiation vs. Altitude
Kirchoff’s Law
For any object: …very useful!
Emissivity (,T) = Absorptivity
Radiative Equilibrium For the Earth
DS-E
rs
Solar flux at Earth’s location = = 1370 W m-2
2
4 Ss S
S E
rF T
D
Solar flux intercepted and absorbed by Earth, distributed over its surface area = Fs(1-A)/4
Radiative Balance: Terrestrial Flux Out = Solar Flux AbsorbedTE
4 = Fs(1-A)/4 TE = 255 K
Greenhouse Effect
f
absorption of outgoing terrestrial radiation by the atmosphere
Greenhouse Model
Atmospheric Layer Tatm
Absorptivity = f
Earth’s Surface Tsurf
Fs(1 – A)/4
Tsurf4
(1-f)Tsurf4
fTatm4
fTatm4
fTsurf4 = 2fTatm
4
Tsurf = (2)1/4Tatm
Radiative Balance for Atmospheric Layer:
Fs(1 – A)/4 = (1-f)Tsurf4 + fTatm
4
Radiative Balance for Earth + Atmosphere:
Terrestrial Radiation Spectrum From Space
Scene overNiger valley,N Africa
surface
top of stratosphere
troposphere
composite of several blackbody radiation spectra corresponding to different temperatures
Effect of Greenhouse Gas Addition
1.1. Initial state
2. 2. Add to atmosphere a GG absorbing at 11 m; emission at 11 m decreases (we don’t see the surface anymore at that but the atmosphere)
3. At new steady state, total emission integrated over all ’s must be conserved Emission at other ’s must increase The Earth must heat!
3.
Example of a GG absorbing at 11 m
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 =
particles in 0.1-1 msize range are efficient scatterers of solar radiation
Typical U.S. Aerosol Size Distributions
Freshurban
Agedurban
rural
remoteWarneck [1999]
modis.gsfc.nasa.gov
Smoke particles from biomass burning in Southeast Asia appear as white haze
F = - FsA/4
F ~ 0.9 W/m2 from direct effect of aerosol
Aerosols Tend to Increase Earth’s Albedo
Global Climate Forcings Since 1750
IPCC [2001]
To F
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 time to, relative to CO2:
2
1 kg X
1 kg CO
GWP
o
o
o
o
t t
t
t t
t
F dt
F dt
Gas Lifetime
(years)
GWP for time horizon
20 years 100 years 500 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
IPCC 2001
Earth’s Energy Balance
A + B C + D
Con
cent
rati
on m
olec
cm
-3
time
Rate of reaction at any time, t, is the slope of the tangent to curve describing change in concentration with 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)
t1t2
Chemical Kinetics (Reaction Rates)
Unimolecular: A B
Bimolecular: A + B C
Termolecular: A + B + M C + M
[ ] [ ]Id A d Bk A
dt dt
Lifetime = 1/k; k has units of s-1
[ ] [ ] [ ]IId A d B d Ck A B
dt dt dt
Special cases:1. B=A, rate law becomes 2nd Order in [A]2. [B]>>[A] rate law becomes pseudo-first order in [A]
M is total air number densityAKA: Pressure dependent bimolecular reactions
Examples - decomposition: N2O5 NO3 + NO2
photolysis: O3 + hv O2 + O
kII, bimolecular rate constant, has units of cm3 molec-1 s-1
Example- OH + CH4 H2O + CH3
First order process
Rate Expressions for Gas-phase 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?
AB*
PotentialEnergy
ReactionProgress
T1
C+D
Reaction rate constants are often functions of Temperature due to energy requirements
Ea1
Ea2
T2
A+B
Energy barriers are common: higher T gives higher energy collisions, increasing the probability of a reaction
Energy Requirements Affect Rates
1. A + B AB* k1
2. AB* A + B k2
3. AB* + M C + M* k3
4. M* M + heat k4
Assume lifetime of AB* very short, reacts as soon as its formed(quasi steady state approximation):
1 2 3
*0 * *
d ABk A B k AB k AB M
dt
1
2 3
*t
k A BAB
k k M
3 *d C
k AB Mdt
3 1
2 3
d C k k A BM
dt k k M
A bimolecular reaction which requires activated complex to be stabilized by collisions with surrounding gas molecules “M”
[M] is TOTAL AIR NUMBER DENSITY
Termolecular (Pressure Dependent) Reactions
0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
2.5
x 10-11
Pressure (Torr)
Ra
te C
on
sta
nt
(cm
3 mo
lec-1 s
-1
ClO + ClO --> Cl2O2
OH + NO2 --> HNO3O + O2 --> O3
T=250 K
kClO+ClO and kO+O2 have been scaled
Termolecular Rate Constants: Examples
1. What was the important assumption we made in deriving the rate constant for a termolecular reaction?
2. Does [AB*] change with time?
Questions
Con
cent
rati
on m
olec
cm
-3
time
t1
[AB*](t)
Con
cent
rati
on m
olec
cm
-3time
At equilibrium (forward rate = reverse rate)
forwardeq
reverse
kC DK
A B k
to equilibrium
A+B C + Dkforward
kreverseA+B C
Approach to EquilibriumQuasi Steady State of Intermediate
[C](t)
[A](t)
H2O + O* 2OH
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
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?