Global Warming; Understanding the Forecast

David Archer

Global Warming Book

Chapters I, 2, 3 and 4

Reading assignment, Module 5

Chapter 2, Blackbody RadiationHow light can carry

heat energy through empty space

A thermometer is like an atomic speedometer

◦ Heat is the kinetic energy of atoms◦ Atoms move faster if it is hot and slower when it

is cold◦ Too much heat energy can cause the chemical

bonds to break (cooking food denatures the protein)

◦ Touching a hot object is an example of heat conduction

Heat

A vacuum is an excellent insulator, because it contains no molecules to absorb heat energy (Thermos bottle).

Between Earth and the Sun is 150 million km of vacuum, how can heat travel through this space?

Electromagnetic waves carry energy through a vacuum.

Light

Electric and magnetic fields in a vacuum fit together to form a closed, self replicating cycle, travelling at light speed

The electromagnetic radiation comes in a full range of frequencies, denoted by the Greek letter ν, and in units of Hz = cycles / second

The waves have wavelength, λ

The constant speed of light makes it possible to relate the frequency and the wavelength

c= λ ν

Electromagnetic waves:

Scientists who discuss infrared (IR) light use a third way of describing different colors called wave number

Wave number is the number of cycles per cm of length

Wave number is designated with “n” Wavelength in cm / cycle is inverted, to get

the wave number in cycles / cm

Wave number

A substance that can interact with light (absorb) at all possible frequencies is called a blackbody

The light emitted is called blackbody radiation A plot of intensity vs. wavelength of light is

called a spectrum The IR light emission spectrum of a blackbody

depends only on the temperature of the object intensity given by the Stefan-Boltzmann

equation

Blackbody Radiation

is the intensity and represents the total rate of energy emission from the object at all frequencies in units of Watts/m2

is a number from 0 to 1, for a perfect blackbody =1

is a constant is the Kelvin temperature raised to the

fourth power

Stefan-Boltzmann Equation

The value of the Stefan–Boltzmann constant is given in SI units by

σ = 5.670373(21)×10−8 W m−2 K−4

Value of σ 

A room temperature object “glows” in the infrared region, we can’t see it

As objects get hotter, their energy glows in the visible range

The Sun glows in the visible range The Earth glows in the IR range “Earth light” called terrestrial radiation, is IR

Blackbody spectra

Light carries energy through the vacuum of space

If an object can absorb light, it can also emit light

An object that can emit all frequencies of light is called a blackbody, and emits light energy at a rate equal to εσT4

Take Home Points Chapter 2

Chapter threeThe Layer Model

Our first Climate Model

A toy, demonstrating an idea Demonstrates how the greenhouse effect

works First step - construct a Bare Rock Model

without an atmosphere Step two – demonstrate the greenhouse

effect by adding an atmospheric layer

Layer Model

First assumption: energy fluxFlux out = Flux in

1350 W/m2 incoming, some is reflected back, called albedo, designated with α

◦ Mars, 15% reflected, α = 0.15 (no clouds)◦ Venus, 70% reflected, α = 0.7 (acid clouds)◦ Earth, 30%reflected, α = 0.3

So 70% is absorbed, or (1- α)

Algebraic Model (math )

In the Real World

When sunlight hits the Earth it comes from the same direction. The Earth makes a circular shadow. Therefore the Earth receives an influx of energy = the intensity of the sunlight, multiplied by the area of the circle.

I absorbed = 1350 W/m2 (1- α) ≈ 1000 W/m2

To get incoming flux for the planet instead of a square meter of the planet, we need to multiply by the planet area. The amount of head on sunlight can be calculated by the area of the Earth’s shadow. earth

Putting it together… Fin = earth (1- α) I sunlight

In words, flux in = Earth’s area x amount absorbed x intensity of sunlight

Intensity of the sunlight actually absorbed by the Earth is

Fin = earth (1- α) I sunlight (one direction)

The rate at which Earth loses energy by radiation to space is given by the Stefan-Boltzmann equation (ignoring temperature fluctuations for simplicity)

Fout = A εσT4 (all directions, next slide)

Flux in, Flux out

IR leaving Earth

The surface of the earth is four times larger than its shadow. When IR leaves the Earth, the rate of heat loss is the intensity of the Earthlight times the area of the surface of a sphere (the Earth)

Incoming solar radiation, outgoing IR (heat)

◦Fin = earth (1- α) I sunlight

◦Fout = εσT4

εσT4 = earth (1- α) I sunlight

Put them together

εσT4 = earth (1- α) I sunlight

Cancel Divide by 4 Equation is in units of W/m2

εσT4 ground = (1- α) I in

4As though full strength sunlight only shines

on one-fourth of the Earth

Simplify the terms

Rearrange to solve for T

]

Solving for the temperature of the Earth gives a value of 255 K, or about -15°C

The average temperature of the Earth is closer to +15°C

Repeating the calculations for Venus and Mars, Bare Rock Model results in temperatures that are too cold for all three of the terrestrial planets

The unknown is T

Far IR – the water in the atmosphere absorbs so strongly in this range that it renders the atmosphere, in effect, opaque

Mid IR – blackbody radiators can radiate strongly in the range (human skin radiates strongly at the lower end). This IR is absorbed by molecular vibration

Near IR – infrared photography (next to visible)

Frequency ranges of IR, divided into three parts

Range Wavelength cm Wave number

Far IR 1mm - 10μm 0.10 cm – 0.001cm

10 cycles/cm – 1000 cycles/cm

Mid IR 10 – 2.5 μm 0.001-0.00025 cm

1000 – 4000 cycles/cm

Near IR 2500 - 750 nm 0.00025 – 0.000075 cm

4000-13,333 cycles/cm

Converting λ to n

The Layer Model with a Greenhouse Effect

Figure 3.4 An Energy diagram for a planet with a single pane of glass for an atmosphere. The glass is transparent to incoming visible light but a blackbody to infrared light.

Very simple – a pane of glass suspended by magic above the ground

Incoming sunlight goes through the glass because it is transparent to visible light, and goes to the ground like before

Planet radiates IR as before, εσT4

In The IR range, the glass pane is a blackbody, absorbing and emitting all frequencies of IR

Greenhouse effect adds heat to the model

Temperature of the ground, and Temperature of the glass The rate of energy going out of the layer

equals the rate of energy going in (the layers are in a state of energy balance)

There is only one temperature for each of the layers at which both energy budgets will be in balance

Solve for one and substitute to back to solve for the other

Two unknowns

Intensity in = intensity outI up, glass + I down, glass = I up, ground

This is IR intensity, so use the S-B equation

2εσT4 (glass)

= εσT4(ground) (eq. 3-7)

Both the ground and the glass have to be in a state of balance

Energy budget for the pane of glass

Different that the Bare Rock Model because now there is heat flowing down from the pane of glass

I up, ground + I in, solar= I down, glass

These intensities expand to 3-8 Combine 3-7, and 3-8, eliminate one of the

temperatures, solve for the other, and substitute back to the original equation to get the second temperature.

Energy budget for the ground

• Solving for the temperature of the glass gives the same answer as solving for the temperature of the ground in the Bare Rock Model.

• The skin temperature of the model is always the same

• The place in the Earth system where the temperature is the most directly controlled by incoming sunlight is at the top layer, where infrared radiates to space.

• We will call this temperature the skin temperature of the Earth

• Plug in the skin temperature for the outermost glass temperature, and we see that the ground temperature is warmer than the skin temperature by a factor of the fourth root of 2 (comes out to about 19%)

• The glass layer warms the ground by trapping outgoing heat

Kitchen sink analogy Used throughout the book Read page 26 and understand the analogy Water flows into the sink at some rate Water flows down the drain at some rate As the sink fills the water is heavier and

goes down the drain faster Eventually the sink reaches an equilibrium

between inflow and outflow of water

Greenhouse effect Water is analogous to energy flowing into

and out of the Earth system Outgoing IR flows faster as the temperature

of the earth increases by εσT4

Greenhouse effect is like a piece of carrot in the drain

Watery (energy) outflow is slower until the level in the sink rises and pushes the water out faster, coming into balance again.

The outflow of IR energy from a planet must balance heating from the sun.

The planet accomplishes this act of energetic housekeeping by adjusting its temperature

Absorption of outgoing IR light by the atmosphere warms the surface of the planet as the planet strives to balance its energy budget

Take home points, Chapter 3

Chapter fourGreenhouse Gases

Why some gases are greenhouse gases, but most aren’t, and some are stronger than others

In Chapter 3 the Layer Model was an idealization

Chapter 4 and beyond, we will add things to the model one at a time

Before adding atmospheric components, we need to study the gases

Models

Concentration is the amount of “stuff” in a given volume

Concentration changes as gases expand or contract

Better to use proportions, such as % The CO2 concentration in the atmosphere is

about 0.039% This corresponds to 390 ppm ppm is a mixing ratio of CO2 in the

atmosphere

About Gases:

The total pressure of a mixture of gases is the sum of the partial pressures exerted by each gas

Written as pCO2 = partial pressure of CO2 ppm ≈ μatm So the concentration of CO2 is

approximately equal to the partial pressure of CO2

390 ppm CO2 ≈ 390 μatm CO2

Pressure:

Kinetic Energy is ~ equal for all gases

Heavier gases will move slower, depending on their mass

KE = ½mv2

As the mass gets larger, the velocity of the gas is slower, keeping the KE constant

Kinetic Energy:

Atoms – the mass is in the nucleus, the electrons are in shells (orbitals)

Outer orbitals participate in sharing electrons, forming covalent bonds

There is an optimal nuclear distance that is low energy

If the nuclei get too close or too far apart, they readjust to the optimal distance

This is a stretching vibration

Gases, Vibrations and Light

If a molecule has more than two atoms, there is flexibility in the bond angles

This is a bending vibration To interact with IR light, the molecule must

be electrically lopsided A charge separation results in a dipole

moment One side is partially positive while the other

is partially negative Written δ+ and δ-

Molecular vibration

Symmetrical molecules with only two of the same atom are never greenhouse gases

O2 and N2 are the two major components of the atmosphere

These gases do not absorb or emit IR light

Molecular gases

The gases NO and CO have their bonding electrons drown toward the more electronegative atom

Electronegativity increases across a period Electronegativity decreases down a group

Both of these molecules are electrically lopsided, but in low concentrations and not very reactive

Simple example:

3 or more atoms with two or more bonds (think springs for the bonds and weights for the atoms)

Particularly carbon dioxide, it is symmetrical, but the stretching and bending sets up a dipole moment

Or water that has a permanent dipole

Better example:

Vibrational modes of a CO2molecule that interact with IR in the atmosphere.

Vibration modes of a water molecule that interact with IR light in the atmosphere

Water vapor is very electrically lopsided and can absorb and emit lots of frequencies of infrared light.

The solid line is a model generated spectrum of the infrared light escaping to space from the top of the atmosphere

Broken lines are blackbody spectra at different temperatures

Atmospheric window is between about 900-1000 cm-1 where no gases absorb or emit IR light

CO2, H2O, O3 and CH4 absorb IR emitted from the ground and emit lower intensity IR from high altitudes where air temps are colder

Figure 4-3

How a Greenhouse Gas Interacts with Earthlight

The area under the curve is the amount of emitted IR light

• Figure 4-3 is constructed so the area under the curve of a spectrum is proportional to the total energy flux

• You can eyeball the energy change as the area change

• This trick works with the jagged spectrum as well, representing the total energy loss of the planet to space

• The atmospheric absorption band takes a bite out of the energy lost to space, decrease the area, decrease the outgoing energy

• Carbon dioxide absorbs in the middle of the Earthlight

• Methane absorbs on the fringes of the Earthlight region• Water absorbs over a wide range of

frequencies

The atmosphere is call optically thick in the 700 cm-1 in the CO2 bend frequency range

The atmosphere is called optically thin in the atmospheric window

Thick and Thin:

As the CO2 concentration is increased to 100 ppm, the center of the peak runs into the

blackbody curve from just a bit colder than 220K, and it doesn’t get any deeper as the CO2 concentration is raised to 1000 ppm.

This is the band saturation effect, the band is the range of frequencies, and the saturation means “used up”, all absorbed by the CO2

The Band Saturation Effect

Figure 4-5 A demonstration of band saturation by CO2

The center of an absorption band gets saturated as the gas gets more concentrated,

but the band gets fatter

More CO2 will always make it warmer The middle is saturated but the edges are

not Edges get fuzzy with Doppler shifting Bands are smeared out by pressure

broadening

Band Saturation Effect:

The more abundant the greenhouse gas, the less powerful each molecule is in warming the climate

The most dilute gases have awesome climate changing power

Methane has an off-peak location, but the band is not saturated

This makes a molecule of methane about 40x more powerful than a molecule of CO2 as a greenhouse gas

GHG:

Climate sensitivity, abbreviated ΔT2x Sensitivities of climate models are often

compared as the average equilibrium temperature change from doubling carbon dioxide

Earths temperature rises in proportion to the number of CO2 doublings

This is the first benchmark that climate scientists compare between models

Doubling CO2

The Greenhouse Effect of Gases• Begin with the top panel, no

carbon dioxide, assume the energy budget of the Earth was in balance at 270K

• In the middle, add 1000 ppm, decreasing the outgoing flux. The ground and the atmosphere respond by warming up 8.5 K

• In the bottom panel, the total outgoing energy flux is restored to its original value.

• CO2 takes a bite out of the top, to generate the middle, but the bottom bulks up everywhere to

compensate

http://understandingtheforecast.org/Projects/infrared_spectrum.html

Look at the exercises, we will run some models in class on Monday 10/22

Power points and module 5 homework will be on e-College by tonight

Mod 5 quiz on Wednesday 10/24

Exercises, page 40-41

Gases absorb or emit IR light if they vibrate at the frequency of the light and if its vibration has a dipole moment that affects the electric field

Oxygen and Nitrogen are not greenhouse gases. All molecules of three of more atoms, including CO2, water vapor, ozone, and methane, are greenhouse gases.

Take home points, Chapter 4

A greenhouse gas has a stronger impact on the relative balance of the Earth if it interacts with light in the middle of the Earthlight spectrum.

Band saturation: A greenhouse gas at relatively high concentrations like CO2 will be less effective molecule per molecule, than a dilute gas like methane.

Cont.