Greenhouse Law formula is expressed below, where C is ______ and F is

______:

?F = a Ln(C/C

0

)

a.

a.

carbon dioxide (CO

2

) concentration, the radiative forcing

b.

carbon monoxide (CO) concentration, the frictional forcing

c.

the centrifugal forcing, the solar forcing

d.

carbon dioxide (CO

2

), the magnetic forcing

e.

a.

both b and c

5 points

·

·

Question 2

(short

–

answer question

)

·

·

At the beginning of the industrial revolution in 1850, the CO

2

concentration

was 280 ppm. Today, it is 416 ppm. 1) If

CO

2

concentration reaches 500

ppm, how much extra radiativ

e forcing is the Earth’s surface receiving,

relative to 1850? 2) What is the equivalent temperature change?

·

?F (Wm

–

2

) = a ln(C/C

0

),

?T(K) = ?*?F

·

a = 5.35, ? = 0.8 per (Wm

–

2

)

Question 3

Typically, the time of day when relative humidity is highest is ________.

a.

at dawn

b.

in the evening

c.

in the late afternoon

d.

at midnight

e.

at sunset

5 points

Greenhouse Law formula is expressed below, where C is ______ and F is

______:

?F = a Ln(C/C0)

a.

a.

carbon dioxide (CO2) concentration, the radiative forcing

b. carbon monoxide (CO) concentration, the frictional forcing

c.

the centrifugal forcing, the solar forcing

d. carbon dioxide (CO2), the magnetic forcing

e.

a. both b and c

5 points

?

? Question 2 (short-answer question)

?

? At the beginning of the industrial revolution in 1850, the CO2 concentration

was 280 ppm. Today, it is 416 ppm. 1) If CO2 concentration reaches 500

ppm, how much extra radiative forcing is the Earth’s surface receiving,

relative to 1850? 2) What is the equivalent temperature change?

? ?F (Wm

-2

) = a ln(C/C0), ?T(K) = ?*?F

? a = 5.35, ? = 0.8 per (Wm

-2

)

Question 3

Typically, the time of day when relative humidity is highest is ________.

a. at dawn

b.

in the evening

c. in the late afternoon

d. at midnight

e.

at sunset

5 points

?if the quantity of carbonic acid increases in
geometric progression, the augmentation of the
temperature will increase nearly in arithmetic
progression? (1896)

?F (Wm-2) = a ln(C/C0)
a = 5.35

?T(K) = ?*?F

Svante Arrhenius
Climate Sensitivity: change in global
mean temperature in response to a
doubling of CO2 volume mixing ratio.

Let’s talk about climate sensitivity with a little more specificity in terms of CO2
emissions. Once again, as shared in previous lecture slides, this slide shows
the “greenhouse law” formulated by Svante Arrhenius.

CO2 carbon dioxide CH4 methane

N2O nitrous oxide

It is important to note that, although we are focusing on CO2 to examine
climate sensitivity here, we all know that there are other molecules that can
absorb long wave back radiation: water molecule (H2O), methane (CH4),
nitrous oxide (N2O), etc.

What is a logarithm?
• logbX “the log to base b of X” is the power that b

must be raised to get X

• So, what is log10100? (= 2)

• Logs with the base e (LogeX) are written in Ln X
(natural logarithm)

• e=2.71828…. (mathematical constant)

• Definition:

Arrhenius’s greenhouse law tells us that the relationship between climate

sensitivity and carbon dioxide (CO2) concentration is a natural logarithm.

?F (Wm-2) = a ln(C/C0)

This means that… (see next slide)

Radiative ‘forcing’ of CO2 is
logarithmic!

Increasing CO2 concentration à

In
cr

ea
si

ng
ra

di
at

iv
e

fo
rc

in
g

in
W

m
2

Radiative forcing, defined as the difference between radiant energy
received by the Earth and energy re-radiated to space logarithmically
increases with increasing CO2 concentration. More importantly, the increase
in radiative forcing slows down as CO2 concentration increases.

?if the quantity of carbonic acid increases in
geometric progression, the augmentation of the
temperature will increase nearly in arithmetic
progression? (1896)

?F (Wm-2) = a ln(C/C0)
a = 5.35

?T(K) = ?*?F

Svante Arrhenius
Climate Sensitivity: change in global
mean temperature in response to a
doubling of CO2 volume mixing ratio.

At the beginning of the industrial
revolution, CO2 concentration was
280 ppmv (parts per million by volume)

As of May 2013, CO2 concentration was
398 ppmv.

How much extra radiative forcing is the
Earth’s surface getting in 2013, relative to
1850?

?if the quantity of carbonic acid increases in
geometric progression, the augmentation of the
temperature will increase nearly in arithmetic
progression? (1896)

Radiative forcing since 1850 AD

5.35Wm-2 •ln
398ppm
280ppm
”

#
$

%

&
‘

=1.9Wm-2

We must multiply this times a
“sensitivity factor” ? to calculate
temperature change

? is usually assumed to be about 0.8
per (Wm-2). So, 0.8 * 1.9 = ~1.5K
(kelvin).

Account for the Greenhouse Effect
(one layer atmosphere model)

sTs
4 =

S
4
1- Albedo( )+sTe

4

sTs
4 = 2sTe

4

sTe
4 =

S
4
1- Albedo( )

Ts = 2
1
4Te240 Wm-2 coming into surface

240 Wm-2 leaving into space

340 Wm-2 available before accounting for albedo

*Remember S is the solar constant 1365Wm2

Ts is earth surface temp.
Te is temp at the top of the
atmosphere where energy is
radiated back to space

1)

2)

3)

4)

Here is our one layer atmosphere model that we reviewed previous week. Although this
is a great model to help us learn how a climate model works, it is a little too simple to
represent our true atmosphere.

Can you think about what is unrealistic about this layer model?
Although there are a number of answers, what stands out most in terms of the
greenhouse effect is that 1) not all atmospheric gases are greenhouse gases; and 2) the
temperature of the atmosphere is not vertically homogenous.

1) Not all atmospheric gases are greenhouse gases.
This layer model is based upon a simple concept of “what goes in, must come out”.
With this, in the second equation, the Earth’s back radiation is completely absorbed by
the atmosphere (greenhouse gases) and radiated equally back to the surface of Earth
and to space (equation 2, in slide). However, in reality, we all know that greenhouse
gases are definitely not a major component of the atmosphere! This week, let’s talk
about what make greenhouse gases – greenhouse gases! After this week, you should
be able to explain “what are greenhouse gases” from a slightly different perspective –
in a quantum mechanical way.

2) temperature of the atmosphere is not vertically homogenous.
Of course, when you are away from a heat source (in this case, the surface of the Earth),
temperature decreases. However, such diffusion cannot be expressed by a simple layer
model. Therefore, climate scientists combine multiple layer models vertically and
horizontally to make a climate model close to reality.

Composition of the Atmosphere including
variable components (by volume)

As we learned in previous lectures, major composition of the atmosphere is nitrogen,
oxygen, and argon. Very interestingly, greenhouse gases consist of only a fraction of
the atmosphere, and are called trace gases.

Radiative forcings, IPCC 2013

That said, although small, these gases are important in altering the Earth’s energy
budget. Based on the IPCC’s (Intergovernmental Panel on Climate Change)
assessment report (IPCC 2007), greenhouse gases, such as CO2, CH4, N2O, and
Halocarbons, show positive radiative forcing. This means that these gases
contribute to warming of the atmosphere.

CO2 carbon dioxide CH4 methane

N2O nitrous oxide

Important to note that, although we are focusing on CO2 to examine climate
sensitivity here, we all know that there are other molecules that can absorb long
wave back radiation: water molecules (H2O), methane (CH4), nitrous oxide (N2O),
etc.

Elements
Atoms

Nucleus
Protons (+)
Neutrons (o)

Electrons (-)

• All matter, including minerals, rocks, and gas
molecules, are made of atoms

The chemical composition
First, let’s review basic chemistry.

Atoms

• Smallest particle into which an element can be divided
while still retaining the chemical characteristics of that
element

Here is an example of an oxygen atom. This conceptualized view is only an
approximation or model showing the nucleus of the atom surrounded by
orbiting electrons (middle figure). A more realistic view consists of electron
shells surrounding the nucleus. Electrons are in the probability clouds (far right
figure). This expression is based on quantum mechanics.

Carbon atom

Electron cloud

Nucleus

Composed of a nucleus surrounded by electrons
Nucleus is composed of protons (+) and neutrons (0)

Carbon atom

Electron cloud

Nucleus

Carbon has 6
electrons…

Electron (–)

Proton (+)
Neutron

Number of neutron adds
mass to the atom.

Number of electrons (-)
orbiting nucleus
determined by the
number of positively
charged protons.

Negatively charged
electrons balance the
positive charges of the
protons.

Carbon atom

Electron cloud

Nucleus

Carbon has 6
electrons…

…and a nucleus
of 6 protons …

…and 6 neutrons.

Electron (–)

Proton (+)
Neutron

Number of protons
defines the chemical
element and atomic
number (e.g. atomic
number of hydrogen
(H) is 1, He is 2, Li is
3, …)

ION = Charged Particle

CATION = Positive Charge
(lose electrons, i.e., Fe+2)

ANION = Negative Charge
(gain electrons, i.e., O-2)

BONDING
Each atom may or may not be connected to other atoms

with different types of bonding. Here, we learn three
major bondings: ionic bond, covalent bond, and

hydrogen bond.

Sodium atom Chlorine atom

Ionic Bond
Here is an example of NaCl, also know as salt.

Sodium loses one electron… …and chlorine acquires it.

Electrical
attraction

Sodium atom Chlorine atom Cation (+) Anion (–)

Ionic Bond
Sodium and chlorine are attracted to each other and create ionic bonding.

Carbon atoms
are arranged in
regular tetrahedra…

…that share electrons
with neighboring atoms.

Carbon
atoms Electrons

Nucleus

Covalent Bond

Covalent bond is one of the strongest bonds. In this type of bonding, the atoms
share an electron with adjacent atoms, so they are not easily separable.
Examples of covalent bonds are ozone (O3), hydrogen (H2), water (H2O), methane
(CH4), ammonia (NH3), and CO2 (carbon dioxide).

The Hydrogen Bond
• Chemistry of water

– Atoms and molecules
– Two hydrogen and one oxygen molecule (H2O)
– Covalent bonds
– Electrical polarity

of water molecule
– Hydrogen bonds

The hydrogen bond is a unique and weak bond. It is the electrostatic attraction

between two polarized groups of atoms/molecules. One most famous example
is a water molecule. Although, as we saw in the previous slide that a water

molecule is a covalent bond, the bonds connecting water molecules are

hydrogen bonds. This occurs because the molecular structure of water is

unique and naturally polarized (electronically imbalanced) – I call this

molecular structure a Mickey Mouse structure! Because water molecules are
polarized, each molecule is attracted electrostatically. Therefore, water has a

wonderful surface tension. In our childhood, we all tried to put as many water

drops as possible on a surface of the coin… We are able to do this because of

the hydrogen bond.

Okay – let’s continue to learn about greenhouse gases in the following lecture

slides.

http://www.ces.fau.edu/nasa/mod
ule-2/how-greenhouse-effect-
works.php

This figure shows the blackbody spectra of Earth and sun. The incoming radiation from
the sun is much more intense (Y-axis) than that of outgoing radiation from the Earth
because the energy emitted from a blackbody is proportionate to its temperature to the
fourth (sT4) – i.e. the sun emits a far greater amount of energy than the Earth. Incoming
solar radiation is shortwave (X-axis, wavelength in microns) and in the wavelength range
of ultraviolet and visible radiation (shown as the rainbow spectrum of colors). Outgoing
Earth’s radiation is long wave and and is in the range of infrared radiation (shown in red).

Below the blackbody spectra, molecules in the atmosphere, known as greenhouse gases,
interfere with incoming and outgoing radiation. For instance, ozone (O3) in the
stratosphere absorbs some of incoming radiation and is known as the ozone layer. That
said, greenhouse gases (N2O, O3, CO2, and H2O) mainly interfere with outgoing radiation.

Let’s talk about the molecular motion of these greenhouse gases to understand the
greenhouse effect.

Molecular Motions and the Greenhouse Gases H2O and CO2

2349cm-1 667cm-1

Here are the physical causes (molecular motion) of the greenhouse effect. But first… it
may be a bit chunky, so sit back, take a deep breath!

Gas molecules can absorb or emit radiation in the infrared range in two different
ways. One way is by changing the rate at which the molecules rotate. The theory of
quantum mechanics describes the behavior of matter on a microscopic scale – that is,
the size of molecules and smaller. According to this theory, molecules can rotate only
at certain discrete frequencies as if vibrations of a piano string in that they tend to be
at specific “ringing” frequencies. (The rotation frequency is the number of revolutions
that a molecule completes per second.) The molecule can absorb incident wave
(energy), if this incident wave has just the right frequency.

This frequency of the radiation that can be absorbed or emitted depends on the
molecule’s structure. The H2O molecule is constructed in such a manner that it
absorbs infrared radiation of wavelengths of about 12 micrometers and longer. This
interaction gives rise to a very strong absorption feature in Earth’s atmosphere called
the H2O rotation band. As shown in the previous slide, virtually 100 % of infrared
radiation longer than 12 micrometers is absorbed with a combination of CO2 and H2O.

(By the way, the H2O rotation band extends all the way into the microwave region of
the electromagnetic spectrum, i.e. above a wavelength of 1000 micrometer, which is
why a microwave oven is able to heat up anything that contains water.)

Molecular Motions and the Greenhouse Gases H2O and CO2

2349cm-1 667cm-1

The second way in which molecules can absorb or emit infrared radiation is by changing
the amplitude at which they vibrate. Molecules not only rotate, they also vibrate – their
constituent atoms move toward and away from each other. As shown in the lower figures,
The molecular structure of water is electrically lopsided; a molecule is bent to its lowest
energy state. This is because oxygen has two pairs of electrons hanging off it, which push
the hydrogen toward the other side (Mickey Mouse structure!). Hydrogen atoms hold their
electrons more loosely than oxygen atoms in chemical bonds, so each hydrogen has a
slightly positive charge. The oxygen end of the molecule has a slight negative charge. Thus,
water has a dipole moment built into its resting structure. Rotating an H2O molecule would
oscillate the electric field and generate light. Due to the complex arrangement of the nuclei
in H2O, there are many modes of vibration for the water molecule, including a symmetric
stretch and a bend.

The CO2 molecule can vibrate in three ways. The bending mode of vibration (upper figure).
This vibration has a frequency that allows the molecule to absorb infrared radiation at a
wavelength of about 15 micrometers, which gives rise to a strong absorption feature in
Earth’s atmosphere called the 15-micrometer CO2 band. Also, similar to a H2O molecule,
the oxygen of a CO2 molecule tends to pull on electrons more tightly than carbon does, but
the oxygen atom on one side pulls the electrons just as tightly as the other oxygen on the
other side. Therefore, the molecule has no permanent electrical field asymmetry (dipole
moment). This imbalance makes CO2 an important one for our climate. In fact, most gases
in the atmosphere do not absorb or emit infrared light at all (e.g. N2). Why? Because
vibrations in their bonds do not create an imbalance in the electrical field.

Molecular Motions and the Greenhouse Gases H2O and CO2

2349cm-1 667cm-1

What does all of this information mean? Your take home note is…. in order for gas
molecules to interfere with electromagnetic energy (to emit or absorb infrared
light);
1) frequency of the molecular vibration must be equal to the frequency of the

light (only a specific frequency of light can cause a specific molecular
vibration!), and

2) the molecule must be electronically lopsided.

I am sharing a Youtube video that is very well made and that allows us to visually
perceive these molecular motions. Please see a following slide.

Youtube video – https://youtu.be/3ojaDMadZXU

Please view this Youtube video to further your understanding of molecular motion.
Particularly, the part from 2:40 to 4:47 is relevant to this lecture.

NASA, Robert Rohde – http://earthobservatory.nasa.gov/Features/EnergyBalance/page7.php en:NASA Earth Observatory

Atmospheric gases only absorb some wavelengths of energy but are transparent to
others. The absorption patterns of water vapor (blue peaks) and carbon dioxide (pink
peaks) overlap in some wavelengths. Water vapor is naturally electrically lopsided
and can absorb and emit lots of frequencies of infrared light. Interesting about H2O
is that not only is it a greenhouse gas, when we increase the surface temperature,
more water will evaporate, which significantly increase the amount of water vapor in
the atmosphere. Interestingly, this then makes H2O the most concerning greenhouse
gas with greater uncertainty.

Carbon dioxide is not as strong a greenhouse gas when compared to water vapor,
but it absorbs energy in wavelengths (12-15 micrometers) that water vapor does not.
This is an important wavelength range because it is close to the peak intensity of
outgoing radiation (thus effectively absorbs outgoing energy).

(Illustration NASA, Robert Rohde)

https://cimss.ssec.wisc.edu/sage/meteorology/lesson1/AtmAbsorbtion.htm

Atmospheric Absorption of incoming shortwave and
outgoing longwave radiation

Total atmospheric absorption is indicated by the bottom row. The white areas
indicate regions of the electromagnetic spectrum not affected (low absorption) by
the atmosphere where solar radiation can reach the Earth’s surface and terrestrial
radiation can escape out to space. Note the prominent role that water vapor has in
absorbing Earth’s long wave radiation.

Outgoing spectrum of the Earth
With an atmosphere

Okay – this is the last figure of today’s lecture.

In this figure, smooth curves show blackbody spectra for temperatures ranging
from 300 K, surface temperature on a hot summer day, down to 220 K, which is
about the coldest it gets in the atmosphere, up near the troposphere at about 10-
km altitude. There is also a jagged-looking curve (denoted as “Atmosphere”)
moving among the smooth ones. This is a model-generated spectrum of the
infrared light escaping to space at the top of the atmosphere. This is jagged-
looking because CO2, water vapor, ozone, and methane absorb specific
wavelengths