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New Science 6: How the Greenhouse Effect Works and “four pipes” to space

Posted By David Evans On September 28, 2015 @ 8:00 pm In Global Warming | Comments Disabled

The Earth’s atmosphere is a leaky bucket, with four big holes (and a lot of little ones).

Whole libraries have been filled with talk of a single characteristic emissions layer — a simplistic idea that there is one effective “surface” that radiates to space. It exists in an abstract sense, after sufficient averaging, but it’s a paradigm that doesn’t help us think clearly. In any case, it’s too simple for our purposes in this series. In reality there are many layers that radiate to space, different for each type of molecule that can emit longwave radiation (which means infrared). Then there are the surface and cloud-tops too.

Earth, Climate, Greenhouse gas emissions to space, School, student resource,

Energy comes in one way but leaves through at least four different paths.

To follow this series you’ll need to understand the concept of four pipes through which energy flows to space. It’s a powerful idea and big advance on the simpler notion of one-pipe-in and one-pipe-out. For those not as familiar with photons and excited molecules, you may want to read the “Background” section at the end of the post first.

For a photon there are a lot of paths to space

Some photons at Earths surface will be at the right wavelength to head straight for Jupiter and stopped by nothing much in the sky. But others will bump into a CO2 molecule which will eat them up (for a while) and get “excited”. Eventually either that excited molecule will spit the photon’s energy right back out in a random direction, or it will run smack into a molecule like Oxygen or Nitrogen (O2 and N2). If a collision happens the excitement (the energy) shifts to another molecule, and so the air generally warms. But O2 and N2 are not greenhouse gas molecules — they can’t release the photon’s energy, so the heat sticks around for a while. Sooner or later the energy from the photon will have been shared and smacked until it hits the jackpot, and ends up in a molecule that is a greenhouse gas, and also happens to be high enough, in thin enough air, to have a sufficiently direct line to space, where it might get ejected in the right direction and leave the Earth forever. This is the top of the emissions layer. It’s different for each type of molecule, and even at different wavelengths for the same molecule. The ones packed in near the surface can’t eject anything to space; there are too many other molecules in the way. The height of the emissions layer turns out to matter a lot — if we thicken the blanket, the layer at the top that can emit is raised, and is also colder. A colder body can’t emit as much.

I know the greenhouse effect is the source of much debate among skeptics; I’ll diplomatically refer people to past discussions of thermodynamics on this site. None of that has changed. We don’t want to rehash that.  I think skeptics who have worked doggedly to test the basic theory of greenhouse deserve some credit for intuitively knowing that “something is wrong” with the theory — they are right, CO2 has only a minor effect. But the details matter, and we have to get them correct. Let’s not get stuck in a semantic debate with badly defined words. This is about the net flow of energy — a river that runs inexorably from the Sun to Earth and on to space. Comments that imply that photon “knows” what direction it’s headed in or the temperature of its destination don’t belong here. Let’s talk about the four pipes instead. These diagrams are important.

– Jo

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6. How the Greenhouse Effect Works

Dr David Evans, 28 September 2015, David Evans’ Basic Climate Models Home, Intro, Previous, Next, Nomenclature.

Before proposing a feedback in response to increased CO2 that is omitted from the conventional basic climate model (next post), or the third error in the conventional model, we need to review some aspects of the radiation of heat to space.

All climate modelling at the basic level focuses primarily on how the outgoing longwave radiation (OLR) is affected by changes in the various climate variables. We limit this review to some background and the climate physics of OLR — this is not a complete explanation of the greenhouse effect, just enough for the modelling in this series.

This is all conventional climate science, except that we introduce the terminology of “pipes” for brevity.

The CO2 Blanket

Carbon dioxide absorbs and emits photons with wavelengths around 15 μm (microns). There are many absorption lines (distinct wavelengths, or energies, at which it absorbs) of CO2 around 15 μm, and each line is blurred by factors such as the Doppler effect so that the CO2 can effectively absorb and emit in a narrow but continuous range of wavelengths around each line. The end result is that, in the current atmosphere, CO2 absorb photons from ~13 μm to ~18 μm, with various probabilities. Absorption is less likely at wavelengths further from an absorption line — a photon on such a wavelength can on average travel further through a cloud of CO2. CO2 also has other absorption lines, but these are not so relevant to its effect on climate. These issues are well explained at greater depth on the Barrett-Bellamy website (see the last diagram!).

There is sufficient CO2 in our atmosphere to make it quite opaque at the wavelengths at which CO2 absorbs and emits. A photon near 15 μm can only travel, on average, a few meters through the troposphere before being absorbed by a CO2 molecule. CO2 is a slightly heavier molecule than N2 or O2, so it tends to settles to the bottom of the atmosphere. Nonetheless, CO2 concentrations are moderately uniform throughout the troposphere, gradually decreasing with height, and the CO2 blanket persists well into the lower stratosphere.

OLR consists of the infrared photons that escape to space. The crucial observation here is that, at the wavelengths at which CO2 absorbs and emits, the photons that contribute to OLR nearly all come from the very top layer of CO2.

The CO2 emission layer is the optical upper boundary of the CO2 surrounding the Earth. It is at the effective or average height of emission to space on the wavelengths at which CO2 absorbs and emits: photons on those wavelengths emitted well below the layer are usually absorbed before they reach space, photons on those wavelengths that are emitted upwards from above the layer mainly make it to space, and an observer in space at those wavelengths can only “see” into the atmosphere about as deep as the CO2 emission layer (about one optical depth).

The “greenhouse effect” works by displacing the layer from which OLR is emitted.

Figure 1: The “greenhouse effect” works by displacing the layer from which OLR is emitted, from the warm surface to some colder place high in the atmosphere

 

Sometimes we extend the concept to be wavelength-specific: the CO2 emission layer can be at different heights at different wavelengths. At wavelengths where CO2 absorbs with lower probability, the emission layer is at a lower altitude, because photons can go through more of the CO2 cloud yet still escape to space. At the edges of the band of wavelengths at which CO2 absorbs, the emission layer can be down on the surface because it takes a whole atmosphere of CO2 to raise the total probability of absorption to that of one optical depth.

Blankets of Other Greenhouse Gases

Likewise, there is a water vapor emissions layer (WVEL) for water vapor, the effective upper optical boundary of the water vapor in the atmosphere. Water vapor is the main greenhouse gas; CO2 is the second most influential. Because water vapor is not well mixed in the atmosphere, the WVEL can change height frequently in a given location. In the modeling here we use the WVEL concept only as a global average.

There is a separate emission layer for each greenhouse gas — so they exist for methane, ozone, etc.

The Four Main Emission Layers

Earth’s OLR is mostly emitted by four disparate emissions layers:

The Earth mainly emits to space from four emission layers

Figure 2.

 

The (infrared) atmospheric window is the collection of wavelengths at which photons can pass through the atmosphere without being absorbed by any greenhouse gas. Photons in the atmospheric window emitted by the land or sea surface are free to escape to space if the sky is clear of clouds — but clouds are opaque to those photons and absorb them. Clouds emit infrared at a wide range of wavelengths, similar to the surface, so the OLR in the atmospheric window comes from the surface and from cloud tops.

Above each point on the Earth’s surface, OLR at different wavelengths physically originates from several widely-different altitudes. The Earth’s emission spectrum, such as observed by the Nimbus satellites (later in this series), is clear evidence of the disparate nature of the physical emission layers.

Pipes

We introduce the term “pipe” as shorthand for the outgoing longwave radiation (OLR) over a group of electromagnetic wavelengths and from a particular emissions layer — it’s so much easier to say “CO2 pipe” than “OLR emitted by the CO2 emission layer on the wavelengths absorbed and emitted by CO2”.

The Earth loses heat to space via four main “pipes”

Figure 3.

 

There are also minor pipes for the minor GHGs: ozone, methane, nitrous oxide, etc.

How Much OLR is Emitted by an Emission Layer?

The amount of OLR emitted by a physical emission layer (i.e. escaping through its pipe) is determined almost solely by, and increases with, its temperature — by Planck’s law (which underlies the Stefan-Boltzmann law).

At a given wavelength, the temperature of a physical emission layer of greenhouse gas is the average temperature of the gas molecules that emit to space on that wavelength — which are close together in height because they are near the top of the cloud of such molecules in the atmosphere, and thus have about the same temperature.

The total OLR can be determined from the temperatures of the various physical emission layers: determine the OLR from each emission layer from its average temperature, then sum the OLRs from each of the emission layers.

The Greenhouse Effect

The greenhouse effect is basically a displacement of OLR, from being emitted at the warm surface to being emitted from a colder place high in the atmosphere, which emits less because it is colder. So the presence of a GHG “traps” some heat. See Fig. 1.

Taking a broader view, by the conservation of energy the OLR is equal to the ASR in steady state. Just consider the four main pipes shown in Fig. 3. The total OLR through the four pipes is equal to the ASR, yet the amount of OLR in each pipe is determined by the temperature of its emission layer. Therefore the temperatures of the four emissions layers must be such that they collectively emit OLR equal to the ASR. If the ASR changes, then there is a corresponding adjustment to the OLR — which may involve warming the surface, changing the height of the WVEL or cloud tops (thus changing their temperature), or adjusting the lapse rate (which changes the relative temperatures of the various emission layers).

Increasing the CO2 concentration reduces the amount of OLR through/in the CO2 pipe. If the CO2 pipe is slightly “squeezed” (to use an analogy), so less OLR goes through it, what is going to happen? Obviously more OLR must flow through the other three pipes, collectively. That will involve the surface pipe carrying more OLR, which would require the surface to warm — and the $64 trillion question is, how much warmer?

(Btw, note that energy can effectively change wavelengths via collisions between molecules. For example, a photon at one wavelength might be absorbed by a GHG molecule, which then transfers some of that energy to a molecule of another species of GHG via a collision, which then emits a photon at a different wavelength.)

The Characteristic Emission Layer is Unrealistically Simple

OLR is sometimes modeled as coming from a single layer, called the “characteristic emission layer”. However this layer is only a modeling construct, an average of the physical emission layers. There is no single surface — a layer of molecules at much the same average temperature — from which OLR physically originates. The temperature of the characteristic emissions layer is not directly relevant to OLR, because it is not where outgoing emissions physically originate.

The characteristic emission layer is too simple for our purposes in this blog post series, a simplification too far. As Albert Einstein famously opined, “Everything should be as simple as possible, but no more so.”

Background

- Photons

Energy (or heat) only enters or leaves the Earth’s climate in significant quantities as radiation, which is best viewed for these purposes as consisting of bazillions of photons. Photons can be thought of as tiny massless particles of energy, traveling close to the speed of light. The higher the frequency of a radiation, the smaller its wavelength and the higher the energy in each of its photons (its energy is proportional to its frequency, which is inversely proportional to its wavelength).

In decreasing order of energy: x-ray photons, ultraviolet photons, visible photons, infrared photons, radio-frequency photons.

- Molecules and Atoms Absorb and Emit Photons

A molecule is group of two or more atoms, tightly bound together by chemical bonds so that it acts as a single object for most purposes. Molecules and atoms vibrate internally in various ways, and these vibrations store energy. Crucially, due to the geometry and internal states of the atom or molecule, it can only store certain exact amounts of energy — it cannot store just any amount or a continuum of values, only certain discrete values (hence the name for the study of atomic and sub-atomic particles, “quantum physics”).

When a photon collides with an atom or molecule, it will be absorbed by the atom or molecule if the energy of the photon exactly matches the difference between the amount of energy currently stored by the molecule or atom and an amount that it could store. If the photon is absorbed, the photon ceases to exist and its energy is transferred to the molecule or atom, which is now in a higher energy state (i.e. it vibrates more).

Conversely, a molecule or atom can emit a photon, creating it from scratch and firing it off in a random direction with energy equal to the difference between the stored energy of the atom or molecule in its initial state and its lower energy level after the emission.

Notice that the energy and thus the wavelength of an emitted photon are exactly the same as that of an absorbed photon that changed the energy level of the atom or molecule previously — it’s a reversible process, as the energy stored in the atom or molecule moves up or down with the absorption or emission of a photon. Thus a molecule or atom absorbs and emits photons on exactly the same wavelengths.

Nearly all the “objects” in the atmosphere are molecules, principally N2 (nitrogen) and O2 (oxygen); there are very few lone atoms.

A greenhouse gas (GHG) is characterized by being able to absorb and emit photons of relatively low energy, the infrared photons. A GHG molecule consists of three or more atoms — the torsional vibration modes that are made possible by having two or more inter-atom bonds can store relatively low amounts of energy. Most (all?) atmospheric molecules with three or more atoms are GHGs: H2O, CO2, O3 (ozone), CH4 (methane), N2O (nitrous oxide), etc. The atmospheric molecules with only two atoms, principally N2 and O2, are not GHGs — their lowest absorption energy is higher than the energy typically carried by the infrared photons in the atmosphere, so they don’t absorb the photons and they are transparent to the radiation.

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