# The Azimuth Project Blog - the color of night

## Or: how big is the "greenhouse effect" really?

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

In a quantum of warmth, we refined our zero dimensional energy balance model that treats the Earth as an ideal black body, and separated the system into a black body surface and a box containing the atmosphere. In good vibrations I tried to explain that it is possible to understand the aborption and emission spectra of the molecules of the atmosphere with quantum mechanics.

With the help of quantum mechanics we saw that only very special components of the atmosphere react to infrared radiation. Not the main components $O_2$ and $N_2$, but minor components with more than two atoms in a molecule, like $H_2 O$, $O_3$ and $CO_2$. With the help of this knowledge, it is possible to calculate the effect these gases have on incoming radiation, if certain parameters are known:

• the pressure,

• temperature and

• the concentration of each gas.

Therefore, we will need to calculate thermodynamic properties of the atmosphere, at least approximately, to determine the molecular emission spectra.

#### The Vertical Structure of Earth's Atmosphere

If you get into a balloon an start climbing, what would you expect to experience? Does it constantly get cooler? Just under 200 years ago, Edgar Allan Poe tried to scare his readers by a story of a man who reached the moon this way, in the Unparalleled Adventure of one Hans Pfaall (Wikipedia). Meanwhile, we know that things look a little bit different than Poe imagined:

As you can see, it is possible to discern certain areas according to their temperature profile:

Tim van Beek: Short explanation of each layer.

If you are into natural sciences and someone shows a schematic picture to you, as I have done, you are probably curious as how this looks like in actual measurements, so here we go:

In case you are interested in the sources and more details, both pictures are taken from this book:

• Vardavas, Taylor: “Radiation and Climate”, Oxford University Press, International Series of Monographs on Physics, 2007

According to the authors, the last graphic shows

Selected vertical temperature proﬁles measured by individual radiosonde balloon ascents over Scandinavia, in the months indicated, representing the four seasons.

Tim van Beek: Adiabatic lapse rate and why this does not explain the 33 kelvin gap?

What about the dependency of emission and absorption on the concentration of infrared active gases?

Tim van Beek: Explanation of the log dependency.

Tim van Beek: Equations of radiation transfer of the atmosphere (at least a simple approximate version of it). Why it is too complicated to solve by hand.

#### Calculating the DLR

Calculating the DLR on a sheet of paper, even with the use of a pocket calculator, would quickly turn out to be quite a task.

We could start by making some assumptions about the different layers of the atmosphere. We would also need to look up molecular spectra. Thankfully, for this task there is some help: The HITRAN database. HITRAN was founded by the US air force. Why? I don’t know, but I guess that they needed the data for air craft design, for example. Look out for the interview with Dr. Laurence Rothman for some background information about HITRAN; there is a link to it on the home page.

But anyway: We see that this task is complicated enough to justify the effort to write computer code to handle it. But we are lucky: Not only have others done this already for us. In fact you can find a survey of some of the existing software programs on Wikipedia:

A kind soul has provided a web interface to one of the most prominent software programs, MODTRAN, for us to play around with:

Now that we have some confidence in the theory behind DLR, we are ready to look into measurements.

#### Measuring DLR

To measure DLR and check that it is really the energy flux coming from infrared active components of the atmosphere and not some strange artifact, we have to

• point some measurement device to the sky, to measure what goes down, not what goes up and

• check that the spectrum we measure consists of the characteristic molecular spectra of $CO_2$, $H_20$ etc.

The kind of measurement device we could use for this is called pyrgeometer, for pyr = fire and geo = earth.

For starters we should look for conditions where there is minimum radiation from other sources, no clouds and only a small amount of water vapor. What would be a good place and time on Earth to go to? A dedicated team of scientists decided to weather the grim conditions of the antarctic during polar night for this purpose:

• Michael S. Town, P. Walden, Stephen G. Warren: Spectral and Broadband Longwave Downwelling Radiative Fluxes, Cloud Radiative Forcing, and Fractional Cloud Cover over the South Pole online here.

Also:

• Dan Lubin, David Cutchin, William Conant, Hartmut Grassl, Ulrich Schmid, Werner Biselli: Spectral Longwave Emission in the Tropics: FTIR Measurement at the Sea Surface and Comparison with Fast Radiation Codes, online here.

Also:

• “Measurements of the radiative surface forcing of climate”, online here.

Tim van Beek: I would like to add radiation measurements, maybe some can be found here:

Als

• Baseline Surface Radiation Network (BSRN) here.

Just to have a number, the flux of DLR (downwards longwave radiation) is about 300 $W m^{-2}$.