Concepts: The Greenhouse Effect,
Atmospheric Composition and Structure
•Earth’s Energy Balance w/an absorbing atmosphere
•What makes a good greenhouse gas?
• A Closer Look at Earth’s Atmosphere
Continue reading chapter 3 (41 – 49) of your text
Keep up by working on assignment 2

Today—Atmosphere’s Greenhouse
Effect
•Magnitude of Greenhouse Effect
•Definition of Greenhouse Effect
•Energy Balance Do-over (“One-Layer Model”)
•Terrestrial Emission and Absorption Spectra

Solar energy flux absorbed by Earth
F in
= F out
Energy flux radiated from
“bare” Earth
I in
(1-A) / 4 = s
T
E
4
•Earth absorbs F
IN
= 240 W/m 2 of energy
(averaged over whole earth surface, day and night)
•If the earth system radiates like a blackbody then T
E
= 255 K = -18 C
•The actual average surface temperature of Earth is about 288 K = 15 C!

I in
/4 = 343 Wm -2
(I in
/4)A = 96 Wm -2
F
IN
~ 250 Wm -2
F out
= s
T
E
4 = 250 Wm -2 planet
“Bare rock” Model (i.e. no atmosphere)
Predict T
E
~ 255 K when atmosphere is neglected

T true
- T brm
288 K – 255 K = 33 K
The atmosphere increases the average surface temperature by about 13%
Let’s create an improved physical model that can predict this effect.

The trapping of outgoing (“longwave”) radiation by atmospheric components which leads to a warmer surface (we’ll come back with a more formal definition).

Let’s model the Earth system as a planetary surface with an absorbing atmosphere above the surface.
Simplifying assumptions
1. The atmosphere does not absorb any incoming solar radiation.
2. The atmosphere absorbs outgoing terrestrial radiation with a single absorption efficiency:  .
3. The atmosphere has a uniform temperature.
4. The surface, atmosphere, and Earth system all achieve radiative equilibrium (F in
= F out
).

I in
/4 = 343 Wm -2
(I in
/4)A = 96 Wm -2
(1-

) s T sf
4
s T atm
4
Atmosphere T atm
F
IN
~ 250 Wm -2 s
T sf
4
s T atm
4
Surface T sf
Assume atmosphere absorbs fraction “ surface.
 ” of outgoing radiation from
 ranges from 0 to 1 (i.e. it is a fraction)
ATM then emits radiation in all directions (up/down) like a blackbody that has an efficiency of “  ” and T atm
.

Consider the flow in and flow out for surface, atmosphere and “Earth system” (surface + atmosphere) separately.
SURFACE BUDGET (1-layer model)
Energy flow in = solar radiation not reflected
+ radiation down from atmosphere
= I in
(1-A)/4 + s T atm
4
Energy Flow out = s T sf
4
ATMOSPHERE BUDGET (1-layer model)
Energy flow in = outgoing terrestrial radiation absorbed
= s T sf
4
Energy Flow out = (up + down) =2 s T atm
4

SURFACE BUDGET (1-layer model)
Energy flow in = Energy flow out
I in
(1-A)/4 + s T atm
4 = s T sf
4
Compared to bare rock model, energy in is higher, so
T sf must be higher for energy out to balance!
ATMOSPHERE BUDGET (1-layer model)
Energy flow in = Energy Flow out
s T sf
4 = 2 s T atm
4 T sf
4 /2 = T atm
4
Plug this into surface budget and solve for T
E

(from 1-layer model)
Energy flow in = Energy flow out
Absorbed Solar Radiation + Downward Atmospheric Radiation = Outgoing Surface Radiation
I in
(1-A)/4 + s T atm
4 = s T sf
4
I in
(1-A)/4 = (1 /2) s T sf
4
T sf
 


 s
250
1 

2




1
4
You don’t need to memorize this equation, just understand the consequences
If the avg. absorptivity of atmosphere is  =
0.75, then T sf
= 289 K!

1. An atmosphere that absorbs outgoing radiation from the surface slows the net energy flow out from the surface. This causes the surface temperature to increase.
2. We assumed the atmosphere has a uniform absorptivity/emissivity at all wavelengths. This is not a good assumption. There were other assumptions as well.
3. The radiation that actually leaves the “Earth system”
(surface + atmosphere) to space is a combination from the warm surface and colder atmosphere. It must be equivalent to 250 W/m 2 at equilibrium.

1. Give one way the 1-layer model could be improved to better match reality.
2. A greenhouse gas absorbs radiation at wavelengths characteristic of a planet’s surface emission spectrum. Use the 1-layer model equation to explain exactly how increasing the amount of a greenhouse gas affects Earth’s surface temperature.
3. Choose the most accurate statement:
1. Without humans, there would be no greenhouse effect
2. The greenhouse effect stabilizes Earth’s temperature
3. By increasing the amount of gases that absorb outgoing radiation, humans have increased the greenhouse effect
4. The atmosphere’s greenhouse effect is analogous to: a. A real greenhouse b. Orange peels or egg shells in your sink’s drain c. A heat lamp

Concepts: The Greenhouse Effect,
Atmospheric Composition and Structure
•Earth’s Energy Balance w/an absorbing atmosphere
•What makes a good greenhouse gas?
• A Closer Look at Earth’s Atmosphere
Continue reading chapter 3 (41 – 49) of your text
Keep up by working on assignment 2

Today—Greenhouse Gases
•Overview of Important Greenhouse Gases
•Why are some gases greenhouse gases and some aren’t?
•Why are some greenhouse gases better than others?

Energy flow in = Energy flow out
Absorbed Solar Radiation + Downward Atmospheric Radiation = Outgoing Surface Radiation
T sf
 


 s
250
1 

2




1
4
If the atmosphere absorbs a greater amount of outgoing radiation emitted by the surface, that is  increases, surface temperature must go up.
It is hard to see how this is like plugging your drain from this equation, but the kitchen sink is a good analogy.

Water in (l/s) Water in (l/s) water level water level
Water out (l/s)
(depends on water level)
Initially, the water level is constant, so water flow rate in must equal water flow rate out
Plugging drain causes water flow rate out to be less than flow rate in. Water level rises.

Water in (l/s) Water in (l/s) water level water level
Water out (l/s)
(depends on water level)
Initially, the water level is constant, so water flow rate in must equal water flow rate out
Eventually water level gets high enough that the flow rate out balances the flow rate in, and a new equilibrium is achieved with a higher water level

1
T sf
 


 I in
 1
4 s

1


A

2





4
In class, I often round numbers to nice values, e.g. 250 W/m 2
I shouldn’t do this because the resulting temperature is very sensitive to the inputs.
For example, suppose I use I in
0.75, I get T sf
= 288.8 K
= 1370 W/m 2 , A = 0.28, e =
If I round A up to 0.30, T sf
= 286.8 K!
Recall global warming so far has been ~ 0.5 – 1 K increase in temperature over the past 50 – 100 years!

How was it that we could assume blackbody radiation?

Terrestrial Radiation Spectrum From Space
This figure shows the wavelengths of light that actually reach space and how much energy they are carrying
Scene over
Niger valley,
N Africa Lots of information in this figure!

Fig 3-13 in your text
This figure shows what fraction of radiation the atmosphere absorbs at different wavelengths.
•This spectrum is what we used to determine “  ” in our 1-layer model.
The atmosphere absorbs “bands” of wavelengths sometimes with 100% efficiency and sometimes with less than 20% efficiency .

Important Greenhouse Gases on Earth
Greenhouse gases on Earth absorb radiation in the infrared (IR) region of the spectrum.
H
2
O vapor contributes the most to the atmosphere’s absorbance in the IR.
CO
2 is the next in importance for IR absorption
CH
4
, O
3
, CFCs, and N
2
O all contribute smaller, but still important, amounts of absorption in the IR.

Why are some gases greenhouse gases and some aren’t?
The answer lies in our analogy to charges on springs interacting with EM radiation.
IR radiation carries enough energy to make molecules vibrate and rotate.

Why are some gases greenhouse gases and some aren’t?
Recall Kirchoff’s law: to absorb radiation, the molecules must be able to emit that radiation.
This means they must be able to generate an oscillation in the electric and magnetic fields when they vibrate and rotate

O
 + H  + H
 -
O
 +  -
C O
H
+
H
+
O
-
 -
O
 +  -
C O
H
+

O
-
H
+
H
+ 
 -
O
H
 +

Why are some gases greenhouse gases and some aren’t?
Recall Kirchoff’s law: to absorb radiation, a body must be able to emit that radiation.
N-N and O-O have special symmetry which means the electric field is constant when they vibrate or rotate.
N
2 and O
2 don’t generate oscillations in the electric and magnetic fields when they vibrate or rotate, thus they can’t absorb IR radiation.

Why are some greenhouse gases more important than others?
1. Amount: more there is, more radiation can be absorbed
2. Ability: depends on the wavelength
3. Location (both in the atmosphere and in the outgoing radiation spectrum)

Why are some greenhouse gases more important than others?
1. Amount and 2. Ability
Amount of radiation absorbed by a gas depends on the concentration of the gas, its ability to absorb, and the length the light travels through the gas.
fraction absorbed =  = P(  )*Concentration*length
This equation is true only when the concentration is small.
WHY?

Why are some greenhouse gases more important than others?
BAND SATURATION (amount and ability, cont’)
1
 
As the concentration of a gas is increased, eventually 100% of the radiation in a certain wavelength range will be absorbed. Increasing the concentration past this point leads to smaller and smaller increases in the total amount of radiation absorbed.

Fig 3-13 in your text
This figure shows how efficiently the atmosphere absorbs different wavelengths.
•This spectrum is what we used to determine “  ” in our 1-layer model.
The atmosphere absorbs “bands” of wavelengths sometimes with 100% efficiency and sometimes with less than 20% efficiency .

Concepts: The Greenhouse Effect,
Atmospheric Composition and Structure
•Earth’s Energy Balance w/an absorbing atmosphere
•What makes a good greenhouse gas?
• A Closer Look at Earth’s Atmosphere
Continue reading chapter 3 (41 – 49) of your text
Keep up by working on assignment 2

Today—Atmospheric Structure and
Composition (1)
•A closer look at atmospheric pressure
•Talking about gases (PV=nRT): concentrations vs mixing ratios
•Saturation Vapor Pressure of Water (not related to “band saturation”)

Review—Greenhouse Gases (GHGs)
•Overview of Important Greenhouse Gases
•H
2
O and CO
2 are the most important (based on total amount of radiation absorbed)
•Can’t forget about CH
4
, O
3
, CFCs, N
2
O
•Why are some gases greenhouse gases and some aren’t?
•To absorb IR (which the Earth emits), gases must be able to emit it, which requires vibrations and rotations change the electric field.
•Why are some greenhouse gases better than others?
•Amount, ability, location
•On a per molecule basis, some of the best GHGs are CFCs and CH than CO
2
4
, but there’s so much less of these the total amount absorbed is still smaller.

Fig 3-13 in your text
This figure shows how efficiently the atmosphere absorbs different wavelengths.
•This spectrum is what we used to determine “  ” in our 1-layer model.
The atmosphere absorbs “bands” of wavelengths sometimes with 100% efficiency and sometimes with less than 20% efficiency .

Terrestrial Radiation Spectrum From Space
This figure shows the wavelengths of light that actually reach space and how much energy they are carrying
Measured over
Niger valley,
N Africa atmosphere
Surface seen through the transparent
“atmospheric window”

How Does Addition of a Greenhouse Gas Warm the Earth?
1.
1. Initial state
Example of a GHG absorbing at 11 m m
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!
2.
2. Add to atmosphere a
GHG absorbing at 11 m m; emission at 11 m m decreases (we don’t see the surface anymore at that
, but the atmosphere)
3.

Questions
1. Water vapor causes the atmosphere to absorb ~90% of the outgoing radiation that has a wavelength of ~ 20 microns. CO
2 causes the atmosphere to absorb ~100% of the outgoing radiation with a wavelength of 15 microns.
That is, in both wavelength bands, the radiation detected in space originated from the atmosphere. Why, then does the emission spectrum look like it is from two different blackbodies (T
1
~ 260K and T
2
~ 220 K) ?

•Thin collection of mainly gases and some condensed phases that extends from Earth’s surface to about 100 Km.
•Primary components (% by volume)
•N
•O
•H
2
2
2
(78%)
(21%)
•Argon (0.9%)
•CO
O vapor (0.00001 – 4%)
2
(0.038%)
•Many trace and ultra-trace components that are important
•OH, CH
4
, Ozone, Nitrogen oxides,
CFCs, more

Atmospheric Pressure
Gas pressure is a force per unit area:
•P = Force/Area =Newton/m 2
“Atmospheric pressure” is the weight exerted by the air above on a unit area of surface (same thing as said above)
The reason why there is an atmosphere is because Earth’s gravity is holding it from escaping (mostly) to space (same as you).
Pressure at the surface = Mass of the atmosphere*9.8 m/s 2 surface area of the Earth
Mass of the atmosphere = 5.2x10
18 kg = 5.2x10
6 Gigatons

Vertical Profiles of Pressure
Mean values for 30 o N, March
Pressure decreases with increasing altitude.
1 hPa = 1 mbar ~ 0.001 atm log(P) is a straight line when plotted vs. altitude.
The x-scale here is a “logscale” specially formatted so that it is equivalent to taking the log and plotting the result.

Pressure Decreases Exponentially W/Alt.
Flipping the axes of the previous plot will convince you:
Gases (air) are compressible fluids unlike liquids like water.
P altitude
An exponential decay means pressure decreases more slowly as you get higher and higher.
“Compressible” bricks stacked on top of each other

Questions
1. What fraction of the atmosphere’s mass is below 15 km? Below 50 km?
2. We learned earlier that gravity keeps the atmosphere from flying into space. What keeps the atmosphere from being squeezed down into a very thin layer?
3. Does air density decrease, increase, or stay constant with altitude.

Gravity
Barometric Law
Pressure Gradient Force
P(z
2
)
P(z
1
)
A difference in pressure between two locations is a force that will move an air parcel from high pressure to low pressure.
This pressure gradient force is always trying to push the atmosphere up and out to space.
The force to due to gravity on average balances this gradient force.
Are these two forces always in balance?

Ideal Gas Law: PV=nRT
An ideal gas can be described by PV = nRT
The atmosphere is a collection of many different gases.
If each individual gas behaves like an ideal gas, then the collection of gases behaves like one ideal gas.
P atm
= P
N2
+ P
O2
+ P
Ar
+ P
H2O
+ P
CO2
+ …
P atm
= (n/V)RT = (density)RT
Here, density is an amount per volume of air: mass/volume, number/volume.
Density is directly proportional to P/T.

Ideal Gas Law: PV=nRT
The ideal gas law allows us discuss amounts of different components in the atmosphere relative to each other.
We can relate the concentration of a component to its mixing ratio defined as the relative contribution to the total pressure.
Concentration: (typically) number of X/volume of air
Mixing Ratio: P x
/P atm
= (n x
/V)/(n atm
/V)
See notes for examples

Gas-Liquid-Solid Transitions
The atmosphere contains not just gases, but also
“condensed” phases: e.g. liquid water and water ice.
As the pressure of water vapor increases in a volume of air at constant T, eventually it will condense into liquid.
The pressure of water vapor that was reached when it condensed out into liquid water is known as the saturation
vapor pressure of water. The air is “saturated” with water vapor—it can’t hold any more vapor.
wait Condensation occurs

Saturation Vapor Pressure
The pressure of water vapor that a volume of air can hold before condensation is a strong (exponential!) function of air Temperature only.
If the actual pressure of water is less than its saturation vapor pressure, no condensation will occur.
Can the actual pressure of water ever be higher than its saturation vapor pressure?

Questions
1. Suppose you measure that there is 10 mbar pressure of water in the air outside your room/apt. and the temperature is 20 C. Is there dew on your window? What if the temperature dips to less than 10 C?
2. If there is 10 mbar of H surface is ~ 1000 mbar).
2
O outside your room, what is the mixing ratio of water? (atmospheric pressure at the
3. What does this stuff have to do with climate change or the energy balance of the Earth system?
4. The mixing ratio of CO
2 is ~380 ppm throughout the atmosphere. Is the concentration (amount/volume) the same at the ground as it is in the stratosphere?

Temperature
Temperature decreases with height in the troposphere because of the work it must do to expand as it rises into areas with lower pressure.
In the stratosphere this cooling due to expansion work is overcome by heating caused by the absorption of UV light by ozone.

Lapse rates
From the ideal gas law and thermodynamics, we can calculate that as dry air rises it should cool at a rate of
9.8 K/km. This is the dry lapse rate.
Observations (like the figure) of the temperature in the troposphere show that the air actually cools by only
6.5 K/km. This is the wet lapse rate.
Latent heat released as clouds form in the rising air causes the smaller decrease (the wet lapse rate).
Lapse rate is defined as the rate at which the temperature decreases with altitude.