Re: the absorption & re-emission of long-wave radiation in the earth's atmosphere.(adsbygoogle = window.adsbygoogle || []).push({});

I thought it all made sense until I was trying to work out how to explain it better to others!

So the Beer-Lambert equation describes the absorption at a given wavelength as exp(-k.z) where k is a constant (capture cross-section x number of molecules), z is vertical height through the atmosphere.

Simple stuff. But each layer absorbs energy, warms up and re-radiates. The radiation is equal to the absorption under a simple model so that the layer doesn't warm up. All seems fine. Of course in practice convection takes over but we haven't got to that yet.

Then I started to think about saturation, or high absorption. Take CO2 at 15um. Actually I'm not sure what k is for CO2 at 15um (anyone know?), haven't tried to look it up yet.

Case A

======

Let's suppose for sake of argument it's 0.01 m^{-1}close to the earth's surface.

From Beer-Lambert, only considering absorption..

At 10m the amount of 15um radiation is down to 90%

And at 100m the amount is down to 37%

Case B

======

Then suppose a 10x increase in CO2, just for sake of argument, and now k is 0.1m^{-1}.

At 10m the amount of 15um radiation is down to 37%

And at 100m it's zero (0.005%)

Big difference.. or is it?

What difference does this really make? Because in case A, the atmosphere heats up due to the energy it absorbs and re-emits slightly cooler (if no convection) radiation. And in case B, the same thing happens. In case A there is less absorption, but less re-radiation. In case B more absorption but also more re-radiation.

So actually you haven't reduced the 15um radiation down at all. Or have you?

How different are case A and case B?

What does saturation really mean if, as a layer absorbs some CO2, it just heats up and re-emits?

Doesn't that mean that you can't really saturate a wavelength?

I hope someone can understand my new-found confusion and help me see what is really going on. Suddenly nothing makes much sense.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Better explanation of Radiative Transfer in Atmosphere especially with Saturation

**Physics Forums | Science Articles, Homework Help, Discussion**