this week (4) concepts: the greenhouse effect, atmospheric composition and structure

This Week (4)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 textKeep 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

A Brief Review

Iin (1-A) / 4 = TE4

Fin = Fout

•Earth absorbs FIN = 240 W/m2 of energy (averaged over whole earth surface, day and night)

•If the earth system radiates like a blackbody then TE = 255 K = -18 C

•The actual average surface temperature of Earth is about 288 K = 15 C!

Solar energy flux absorbed by Earth

Energy flux radiated from “bare” Earth

Energy Balance Cartoon

planet

Iin/4 = 343 Wm-2

(Iin /4)A = 96 Wm-2

FIN ~ 250 Wm-2 Fout = TE4 = 250 Wm-2

“Bare rock” Model (i.e. no atmosphere)

Predict TE ~ 255 K when atmosphere is neglected

Magnitude of Greenhouse Effect

288 K – 255 K = 33 K

Ttrue - Tbrm

The atmosphere increases the average surface temperature by about 13%

Let’s create an improved physical model that can predict this effect.

Definition of Greenhouse 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).

“1-Layer” Radiative Equilibrium Model

Let’s model the Earth system as a planetary surface with an absorbing atmosphere above the surface.

Simplifying assumptions1. 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 (Fin = Fout).

Energy Balance Cartoon-1 Layer Model

Surface Tsf

Iin/4 = 343 Wm-2

(Iin /4)A = 96 Wm-2

FIN ~ 250 Wm-2

Tsf4

Atmosphere Tatm

(1-) Tsf4

Tatm4

Tatm4

Assume atmosphere absorbs fraction “” of outgoing radiation from surface. 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 Tatm.

Balancing the Energy CheckbookConsider 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

= Iin(1-A)/4 + Tatm4

Energy Flow out = Tsf4

ATMOSPHERE BUDGET (1-layer model)

Energy flow in = outgoing terrestrial radiation absorbed = Tsf

4

Energy Flow out = (up + down) =2Tatm4

Balancing the Energy CheckbookSURFACE BUDGET (1-layer model)

Energy flow in = Energy flow out

Iin(1-A)/4 + Tatm4 = Tsf

4

ATMOSPHERE BUDGET (1-layer model)

Energy flow in = Energy Flow out

Tsf4 = 2Tatm

4

Tsf4/2 = Tatm

4

Compared to bare rock model, energy in is higher, so Tsf

must be higher for energy out to balance!

Plug this into surface budget and solve for TE

New Surface Energy Balance(from 1-layer model)

Energy flow in = Energy flow outAbsorbed Solar Radiation + Downward Atmospheric Radiation = Outgoing Surface Radiation

Iin(1-A)/4 + Tatm4 = Tsf

4

Iin(1-A)/4 = (1- /2)Tsf4

14

250

12

sfT

You don’t need to memorize this equation, just understand the consequences

If the avg. absorptivity of atmosphere is = 0.75, then Tsf

= 289 K!

1-Layer Model Summary

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/m2 at equilibrium.

Questions1. 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 effect2. The greenhouse effect stabilizes Earth’s temperature3. 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 greenhouseb. Orange peels or egg shells in your sink’s drainc. A heat lamp

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?

Review: How An Absorbing Atmosphere Affects Surface TemperatureEnergy flow in = Energy flow out

Absorbed Solar Radiation + Downward Atmospheric Radiation = Outgoing Surface Radiation

14

250

12

sfT

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.

The Kitchen Sink Analogy (again!)Water in (l/s)

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

Water in (l/s)

water level

Plugging drain causes water flow rate out to be less than flow rate in. Water level rises.

The Kitchen Sink Analogy (again!)Water in (l/s)

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

Water in (l/s)

water level

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

Words of Caution about Calculations

14

1

4 12

insf

I AT

In class, I often round numbers to nice values, e.g. 250 W/m2

I shouldn’t do this because the resulting temperature is very sensitive to the inputs.

For example, suppose I use Iin = 1370 W/m2, A = 0.28, e = 0.75, I get Tsf = 288.8 K

If I round A up to 0.30, Tsf = 286.8 K!

Recall global warming so far has been ~ 0.5 – 1 K increase in temperature over the past 50 – 100 years!

What Causes The Atmosphere to Absorb Outgoing Radiation?

Sun and Earth Emission Spectra From Space

How was it that we could assume blackbody radiation?

Scene overNiger valley,N Africa

Terrestrial Radiation Spectrum From SpaceThis figure shows the wavelengths of light that

actually reach space and how much energy they are carrying

Rad

iati

on

Flu

x D

istr

ibu

tion

Lots of information in this figure!

Earth’s Atmospheric Absorption Spectrum (the longwave part)

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.

H2O vapor contributes the most to the atmosphere’s absorbance in the IR.

CO2 is the next in importance for IR absorption

CH4, O3, CFCs, and N2O 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.


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

C OO- -+

C OO- -+

OHH

+ +

-

O-

HH+ +

OHH

+ +

- OH

H++

- OH H

++

-


Recall Kirchoff’s law: to absorb radiation, a body must be able to emit that radiation.

N2 and O2 don’t generate oscillations in the electric and magnetic fields when they vibrate or rotate, thus they can’t absorb IR radiation.

N-N and O-O have special symmetry which means the electric field is constant when they vibrate or rotate.

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)


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.

1. Amount and 2. Ability

fraction absorbed = = P()*Concentration*length

This equation is true only when the concentration is small.WHY?


abili

ty t

o a

bso

rb

Fract

ion

ab

sorb

ed

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.

BAND SATURATION (amount and ability, cont’)



This figure shows how efficiently the atmosphere absorbs different wavelengths. •This spectrum is what we used to determine “” in our 1-layer model.


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

•H2O and CO2 are the most important (based on total amount of radiation absorbed)•Can’t forget about CH4, O3, CFCs, N2O

•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 CH4, but there’s so much less of these than CO2 the total amount absorbed is still smaller.



This figure shows how efficiently the atmosphere absorbs different wavelengths. •This spectrum is what we used to determine “” in our 1-layer model.


Measured overNiger valley,N Africa

Surface seen through the transparent “atmospheric window”

atmosphere

Terrestrial Radiation Spectrum From Space

This figure shows the wavelengths of light that actually reach space and how much energy they are carrying

Rad

iati

on

Flu

x D

istr

ibu

tion

How Does Addition of a Greenhouse Gas Warm the Earth?

1.1. Initial state

2.

2. Add to atmosphere a GHG 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 GHG absorbing at 11 m

Questions

1. Water vapor causes the atmosphere to absorb ~90% of the outgoing radiation that has a wavelength of ~ 20 microns. CO2 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 (T1 ~ 260K and T2 ~ 220 K) ?

Earth’s Atmosphere•Thin collection of mainly gases and some condensed phases that extends from Earth’s surface to about 100 Km.

•Primary components (% by volume)

•N2 (78%) •O2 (21%) •Argon (0.9%)•H2O vapor (0.00001 – 4%)•CO2 (0.038%)

•Many trace and ultra-trace components that are important•OH, CH4, Ozone, Nitrogen oxides, CFCs, more

Atmospheric Pressure

Gas pressure is a force per unit area: •P = Force/Area =Newton/m2

“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/s2

surface area of the Earth

Mass of the atmosphere = 5.2x1018 kg = 5.2x106 Gigatons

Vertical Profiles of PressureMean values for 30oN, 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 “log-scale” 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:

P

altitude

An exponential decay means pressure decreases more slowly as you get higher and higher.

Gases (air) are compressible fluids unlike liquids like water.

“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.

Barometric Law

P(z2)

P(z1)

Gravity

Pressure Gradient ForceA 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.

Patm = PN2 + PO2 + PAr + PH2O + PCO2 + …

Patm = (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: Px/Patm = (nx/V)/(natm/V)See notes for examples

Gas-Liquid-Solid TransitionsThe 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. Condensation occurswait

Saturation Vapor PressureThe 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 H2O outside your room, what is the mixing ratio of water? (atmospheric pressure at the surface is ~ 1000 mbar).

3. What does this stuff have to do with climate change or the energy balance of the Earth system?

4. The mixing ratio of CO2 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 stratospherethis cooling due toexpansion work isovercome by heat-ing caused by theabsorption of UVlight 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 thetemperature in the troposphere showthat the air actually cools by only6.5 K/km. This is the wet lapse rate.

Latent heat released as clouds formin the rising air causes the smallerdecrease (the wet lapse rate).

Lapse rate is defined as the rate at whichthe temperature decreases with altitude.

this week (4) concepts: the greenhouse effect, atmospheric composition and structure

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