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?