- #1
stevecarson
- 4
- 0
Re: the absorption & re-emission of long-wave radiation in the Earth's atmosphere.
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.
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.