# The Azimuth Project Blog - the color of night (Rev #3)

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

When we talked about putting the Earth in a box, we saw that there is a gap of about 33 kelvin between the temperature of a black body in Earth’s orbit with an albedo of 0.3, and the estimated average surface temperature on Earth. An effect that explains this gap would need 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.

Last time, 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 the atmosphere.

With the help of quantum mechanics we saw that:

• Earth emits mainly infrared radiation, while the radiation from the sun is mostly in the visible and ultraviolett range,

• only very special components of the atmosphere react to infrared radiation. Not the main components $O_2$ and $N_2$, but minor components with different atomic species, like $H_2 O$ and $CO_2$.

• This downward longwave radiation leads to an increased incoming energy flux from the viewpoint of the surface (without violating any laws of thermodynamics).

This is an effect that certainly matches points 1 and 2: It is both continuous and global. But how strong is it? And is it even measurable? How could we know?

#### Survival in a combat zone

There has been a lively - sometimes hostile - debate about the “greenhouse effect” which is the popular name for the increase of incoming energy flux caused by infrared active atmospheric components, so maybe you think that the heading above refers to that.

But I have different point in mind: Maybe you heard about guiding systems for missiles that chase “heat”? Do not worry if you have not, the important part is that knowlegeable people working for the armed forces of the USA know about this, and know that an important aspect of the design of aircrafts is to reduce the infrared emission. Let’s see what they wrote about this back in 1982:

The engine hot metal and airframe surface emissions exhibit spectral IR continuum characteristics which are dependent on the temperature and emissivity-area of the radiating surface. These IR sources radiate in a relatively broad wavelength interval with a spectral shape in accordance with Planck’s Law (i.e., with a blackbody spectral shape). The surface- reflected IR radiation will also appear as a continuum based on the equivalent blackbody temperature of the incident radiation (e.g., the sun has a spectral shape characteristic of a 5527°C blackbody). Both the direct (specular) as well as the diffuse (Lambertian) reflected IR radiation components, which are a function of the surface texture and the relative orientation of the surface to the source, must be included. The remaining IR source, engine plume emission, is a composite primarily of C02 and H20 molecular emission spectra. The spectral strength and linewidth of these emissions are dependent on the temperature and concentration of the hot gaseous species in the plume which are a function of the aircraft altitude, flight speed, and power setting.

This is an excerpt from page 15 of

• Military Handbook SURVIVABILITY ENHANCEMENT, AIRCRAFT CONVENTIONAL WEAPON THREATS, DESIGN AND EVALUATION GUIDELINES, MIL-HDBK-268(AS), 5 August 1982

You may notice that the designers point out the difference of a continuous black body radiation and the molecular emission spectra of $CO_2$ and $H_2 O$. The reason for this, as mentioned last time in a quantum of warmth, is that according to quantum mechanics molecules can emit and absorb radiation at specific energies, i.e. wavelengths, only.

This may be a way for us to find out how much infrared radiation we get from the atmosphere! We would 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 is the characteristic molecular spectrum of $CO_2$!

#### Measuring DLR

What is the place with the least water wapor, the clearest night sky, on Earth?

Tim van Beek: Compare black body radiation to the emission spectrum of CO2 and H2O.

#### How to know where does it comes from?

When you measure some infrared radiation coming from the sky, there are two indications why this radiation has to come from “greenhouse gases” in the atmosphere:

• It is infrared. Sunlight doesn’t have much radiation in the infrared regime.

• It is not black body radiation, but is concentrated at the characteristic wavelengths of well known gas components of the atmosphere. Infrared radiation from the surface is to a good approximation black body radiation.

Devices to measure the infrared radiation of the planetary surface are called pyrgeometer, for pyr = fire and geo = earth.

Tim van Beek: The following is just a random collection of material right now!

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

Also have a look here.

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

category: blog