# The Azimuth Project Blog - a quantum of warmth (Rev #28, changes)

Showing changes from revision #27 to #28: Added | Removed | Changed

This page is a blog article in progress, written by Tim van Beek.

## Or: what is the "greenhouse effect" physically?

#### The Case of the Missing 33 Kelvin Continued

Last time, when we talked about putting the Earth in a box , we saw that a simple back-of-the-envelope calculation about of the energy balance and the resulting black body temperature of the earth is comes surprisingly close to the real right world. answer. But there is a gap: The the black body temperature calculated with a zero dimensionalenergy balance model is about 33 kelvin lower than the estimated average surface temperature on earth.

In such other a words, situation, our as model theoretical predicts physicsists, an we Earth congratulate that’s ourselves 33 on °C a colder successful than first it approximation, really is!, and look out for the next most important effect that we need to include in our model.

This In effect such needs a to situation, as theoretical physicists, we start by patting ourselves on the back and congratulating ourselves on a successful first approximation. and then look out for the next most important effect that we need to include in our model.

This effect needs to:

1) have a steady and continuous influence over thousands of years,

2) have a global impact,

3) be rather strong, because heating the planet Earth by 33 kelvin on the average needs a lot of energy. power.

The simplest explanation would of course be that there is something fundamentally wrong with our back-on-the-envelope back-of-the-envelope calculation calculation.

One possibility, as Itai Bar-Natan mentioned, is geothermal energy. It certainly matches point 1, maybe matches point 2, but it is hard to guess if it matches point 3. As John pointed out, we can look it up on theItai Bar-Natan mentioned last time, is geothermal energy. It certainly matches point 1, maybe matches point 2, but it is hard to guess if it matches point 3. As John pointed out, we can check the Earth’s energy budget on Wikipedia, Wikipedia. which This says suggests that it the does geothermal not. heating is very small. Should we trust Wikipedia? I don’t know. We should check it out!

But I will not do that today. Instead I would like to talk about the most prominent explanation:

Most of you will of course have heard about the effect that climate scientists talk about, which is often - but confusingly - called “greenhouse the effect”, ‘greenhouse effect’, or “back ‘back radiation”. radiation’. The However, the term that is most accurate isdownward longwave radiationdownward longwave radiation (DLR), however, so I would like to usethat instead.

In order to assess if this is a viable explanation of the missing 33 kelvin, we will first have to understand the effect better. So this is what I will talk about today.

In order to get a better understanding, we will have to peek into our simple model’s box and figure out what is going on in there in more detail.

#### Peeking into the Box and Splitting up: Surface and Atmosphere

To get a better approximation, instead of treating the whole earth as a black body, we will have to split up the system into the Earth itself, and its atmosphere. For the surface of the Earth it is still a good approximation to say that it is a black body.

The atmosphere is more complicated. In a next approximation step, I would like to pretend that the atmosphere is a body of its own, hovering above the surface of the earth, as a separate system. So we will ignore that there are several different layers in the atmosphere doing different things, including interactions with the surface. Okay, Well, we are not going to ignore the interaction with the surface completely, as you will see.

Since one can quickly get lost in details when discussing the atmosphere, I’m going to cheat and look up the overall average effects in an introductory meteorology textbook:

• C.Donald Ahrens: Meteorology Today, 9th edition, Books/Cole 2009.

• C. Donald Ahrens: Meteorology Today, 9th edition, Brooks/Cole, Florence, Kentucky, 2009.

Here is what atmosphere and Earth’s surface do to the incoming radiation from the sun Sun (from page 48):

Of 100 units of inbound solar energy flux flux, 30 are reflected or scattered back to space without a contribution to the energy balance of the Earth. This corresponds to an overall average albedo of 0.3 of for the Earth.

The next graphic shows the most important processes of heat and mass transport caused by the remaining 70 units of energy flux, with their overall average effect (from page 49):

#### Conduction and Convection?

Introductory classes for partial differential equations sometimes start with the one dimensional heat equation: equation. This equation describes the temperature distribution of a rod of metal that is heated on one end and kept cool on the other. The kind of heat transfer occurring here is calledconduction . The atoms or molecules stay where they are and transfer energy by interacting with their neighbours. neighbors.

Heat However, heat transfer by conduction isnegligible for gases like the atmosphere; atmosphere. why Why is it there in the graphic? The answer may be that conduction is still important for boundary layers. Or maybe the author wanted to include it to avoid the question “why is conductionnot in the graphic”? graphic?” I don’t know. But I’ll trust that the number associated with the “convection and conduction” part is correct, for now.

#### What is Latent Heat?

There is a label “latent heat” on the left part of the atmosphere: Latent latent heat is energy input that does not result in a temperature increase, or energy output that does not result in a temperature decrease . This can happen, for example, when there is a phase change of a component of the system: system. When For fluid example, when liquid water at 0°C freezes, it turns into ice at 0°C while losing energy to its environment. But the temperature of the whole system stays at 0°C.

The human body uses this effect, too too, , when it cools itself by sweating. This cooling effect works as long as the fluid water turns into water vapor and withdraws energy from the skin in the process.

The picture above shows a forest with water vapor (invisible), fluid (dispersed in the air) and snow. As the sun Sun sets, parts of the water vapor will eventually condense, and fluid water will turn into ice, releasing energy to the environment. During the phase changes there will be energy loss without a temperature decrease of the water.

#### Downward Longwave Radiation: The Atmosphere is not a Black Body

When there is a lot of light there are also dark shadows. — main character in Johann Wolfgang von Goethe: Goethe's "Götz von Berlichingen"Götz von Berlichingen

Last time we pretended that the Earth as a whole behaves like a black body.

Now that we split up the Earth into surface and atmosphere, you may notice that that:

a) a lot of sunlight passes through the atmosphere and reaches the surface surface, and

b) there is a lot of energy flowing downwards from the atmosphere to the surface in form of infrared radiation. This is called downward longwave radiation.downward longwave radiation.

Observation a) shows that the atmosphere does not act like a black body at all. Instead, it has a nonzero transmittancetransmittance, which means that not all incoming radiation is absorbed.

Observation b) shows that assuming that the black body temperature of the Earth is equal to the average surface temperature could go wrong, because because—from - from the viewpoint of the surface surface—there - there is an additional inbound energy flux from the atmosphere.

The reason for both observations is that the atmosphere consists of a various couple of different gases, like O$0_2, N_2$2 , and N$CO_2$2 . , These H molecules can absorb and emit radiation at certain frequencies only. This fact lead to the development of quantum mechanics, which can be used to calculate the characteristic2O (water vapor) and CO2. Any gas molecule can absorb and emit radiation only at certain frequencies, which are called its emission spectrum . for This every fact led to the development of quantum mechanics, which can be used to calculate the emission spectrum of any molecule.

#### Molecules and Degrees of Freedom

When a photon hits a molecule, the molecule can absorb the photon either and by gain energy in three main ways:

• an electron climbing the orbital stairs to a higher energy level,

• stronger vibration or

• stronger rotation.

• One of its electron can climb to a higher energy level.

• The molecule can vibrate more strongly.

• The molecule can rotate more rapidly.

To get a first impression of the energy levels involved in these three processes, let’s have a look at this graphic:

This is taken from the book

• Sune Svanberg: “Atomic and Molecular Spectroscopy: Basic Aspects and Practical Applications”, Advanced Texts in Physics, 4th edition, Springer 2004

• Sune Svanberg, Atomic and Molecular Spectroscopy: Basic Aspects and Practical Applications, 4th edition, Advanced Texts in Physics, Springer, Berlin, 2004.

The Y-axis y-axis shows the energy difference in ‘eV’, or ‘electron volts’. Anelectron volt . is the amount of energy an electron gains or loses as its potential changes by one volt.

Accoding to quantum mechanics, a molecule can emit and absorb only photons whose energy matches the difference of one of the discrete energy levels in the graphic, for either any one of the three processes.

It is possible to use the characteristic absorption and emission properties of molecules of different chemical species to analyze the chemical composition of an unknown probe of gases (and other materials, too). These methods are usually called names involving the word spectroscopy‘spectroscopy’ , . like, For for example, infrared spectroscopy for involves methods that examine what happens to infrared radiation when you send it to your probe.

By the way, Wikipedia has a funny animated picture with of the different vibrational modes of a molecule on the page aboutinfrared spectroscopy.

The But reason why does so much of the radiation of from the sun Sun passes pass through, through but the atmosphere, while a lot of infrared radiation does emitted not by but the flows Earth instead bounces back to the surface, surface? The answer to this puzzle involves the a specific property of certain components of the atmosphere.

#### Can you see an electron hopping?

Here is a nice overview of the spectrum of electromagnetic radiation:

The energy $E$ and the wavelength $\lambda$ of a photon have a very simple relationship:

$E = \frac{c \; h}{\lambda}$

where $h$ is the Planck constant and $c$ is the speed of light . They In short, photons with longer wavelengths have the less values energy.

$h \approx 4 \times 10^{-15} eV \times s$

Planck’s constant is

where “eV” is short for “electron volt”, and

$h \approx 6 \times 10^{-15} eV \times s$

while the speed of light is

$c \approx 3 \times 10^{8} m/s$

Plugging that these into the formula we get that a photon with an energy of one electron volt has a wavelength of about$1.2$ micro micrometers, meter, which is just outside the visible range range, a bit towards the infrared direction. The visible range corresponds to 1.6 to 3.4 electron volt. volts. If you like want, to, you can scroll up to the graphic with the energy levels and calculate which process processese will result in which kind of radiation.

Electrons that take a step down the orbital ladder in an atom emit a photon. Depending on the atom and the kind of transition, some of those photons will be in the visible range, and some will be in the ultraviolett. ultraviolet.

#### There is no Infrared from the Sun (?)

From the Planck distribution, we can determine that sun the Sun and earth, Earth, as which are approximately black bodies, emit radiation mostly at very different wavelenghts: wavelengths:

This graphic is sometimes called “twin ‘twin peak graph”. graph’.

Oversimplifying, we could say: The Earth emits infrared radiation; the sun Sun emits almost no infrared. So, if you find infrared radiation on earth, you can be sure that it did not come from the sun. Sun.

The problem with this statement is that, strictly speaking, the sun Sun does emit radiation at wavelengths that are in the infrared range. This is the reason why people have come up with the termdoes emit radiation at wavelengths that are in the infrared range. This is the reason why people have come up with the term near-infra-red radiation , which we define to be the range of 0.85 and 5.0 micro micrometer meter wavelength. Radiation with longer wavelengths is calledfar infrared . With these definitions we can say that the sun Sun radiates in the near-infra-red range, and earth does not.

Only certain components of the atmosphere emit and absorb radiation in the infrared part. These are called—somewhat misleadingly—greenhouse gasesgreenhouse gases. I would like to call them ‘infrared-active gases’ instead, but unfortunately the ‘greenhouse gas’ misnomer is very popular. Two prominent ones are H2O and CO2:

The atmospheric window at 8 to 12μm is quite transparent, which means that this radiation passes from the surface through the atmosphere into space without much ado. Therefore, this window is used by satellites to estimate the surface temperature.

It is not a coincidence that molecules made of different kinds of atoms like CO2 react to infrared radiation, while those with one kind like O2 do not. The deeper reason is that molecules with different kinds may have a so-called‘dipole moment’.

Since most radiation coming from the Earth is infrared, and only some constituents of the atmosphere react to it—excluding the major ones—a small amount of, say, CO2 could have a lot of influence on the energy balance. Like being the only one in a group of hundreds with a boom box. But we should check that more thoroughly.

#### Can a Cold Body Warm a Warmer Body?

Downward longwave radiation warms the surface, but the atmosphere is colder than the surface, so how can radiation from the colder atmosphere result in a higher surface temperature? Doesn’t that violate the second law of thermodynamicssecond law of thermodynamics?

The answer is: no, it does not. It turns out that others have already taken pains to explain this on the blogosphere, so I’d like to point you there instead of trying to do a better job here:

• Roy Spencer, Yes, Virginia, cooler objects can make warmer objects even warmer still , BLOG, 23 DATE??? July 2010.

• The Science of Doom, The amazing case of “back-radiation” . , 27 July 2010.

#### It's the Numbers, Stupid!

Shut up and calculate! — Leitmotiv of several prominent physicists after becoming exhausted by philosophical discussions about the interpretation of quantum mechanics.

Maybe we have succeeded by now to convince the imaginary advisory board of the zero dimensional energy balance model project that there really is an effect like “downward ‘downward longwave radiation”. radiation’. It certainly should be there if quantum mechanics is right. But I have not explained yet howbig it is. According to “Meteorology Today”, it is big. But maybe the people book who contributed to the graphic got fooled somehow; and there really is a different explanation for the case of the missing 33 kelvin.Meteorology Today, it is big. But maybe the people who contributed to the graphic got fooled somehow; and there really is a different explanation for the case of the missing 33 kelvin.

What do you think?

When we dip our toes into a new topic, it is important to keep simple yet fundamental questions like this in mind, and keep asking them.

In this case we are lucky: it is possible to measure the amount of downward longwave radiation. There are a lot of field studies, and the results have been incorporated in global climate models. But we will have to defer this story to another day.

category: blog, climate