If you’ve just stumbled across this article without reading the earlier posts, please take a few minutes to review:
- Visualizing Atmospheric Radiation – Part One with a few basic concepts
- Part Two with some calculated spectra of upward radiation from the surface through to the top of atmosphere
Most people find the actual results of radiative transfer in the atmosphere non-intuitive. Intuition is not a good guide for this topic. So a lot of misconceptions arise because the results of atmospheric physics disagree with the mental models in people’s heads. Obviously the physics must be wrong or probably climate scientists haven’t understood the basics.. Shaking of heads.
For people interested in reality, read on.
We are still looking at how radiation travels and interacts with the atmosphere before anything changes.
There is a lot of fascination in the subject of the “average height of emission” of terrestrial radiation to space. If we take a very simple view, as the atmosphere gets more opaque to radiation (with more “greenhouse” gases) the emission to space must take place from a higher altitude. And higher altitudes are colder, so the magnitude of radiation emitted will be a lesser value. And so the earth emits less radiation and so warms up.
This “average height of emission” is often supplied as a mental model and it’s a good initial starting point.
Here is the result of the atmospheric model created with a surface temperature of 288K (15°C), 80% humidity in the boundary layer and 40% humidity above that (the “free troposphere). This is a cloud-free sample – clouds are very common, but really make life complicated and we are trying to provide a small level of enlightenment. Simple stuff first.
The model is the same as in Part Two – but with 20 layers instead of 10. More layers just means better resolution plus a little bit more accuracy. Each layer contains roughly the same number of molecules (same pressure differential between each layer), so each higher layer is progressively thicker.
The graph shows how much radiation (“flux”) makes it from the surface and from each atmospheric layer in the model to the top of the atmosphere (TOA) – [update Jan 9th, see revised graph in comments].
And here we’ve zoomed in by expanding the x-axis:
The TOA flux = 239.5 W/m², so what is the level where half of this value comes from below and half from above?
If we include the surface and the first 5 layers we don’t have quite half (48%), and if we go to 6 layers we get just over half (51%). Layer 5 is centered at 1.9km with the top of this layer at 2.1km. Layer 6 is centered at 2.4km.
So let’s say the “average” height of emission to space is just over 2 km (in this example).
There’s probably a better mathematical way of expressing it (this is more like the “median height”) but in fact this “average emission height” is really a curiosity value number anyway. In the words of guru commenter Pekka Pirilä (on another topic):
Any number that is not observable and that’s not used as an input or intermediate value in any calculation that aims to produce observable results is of curiosity value only by definition.
So it’s interesting but you don’t find it a key subject of any climate science papers. Still, being as so many people find it fascinating we will see how it changes as “greenhouse” gases vary in concentration and temperature profiles change.
While we are looking at this, let’s see what wavenumbers from what levels make the largest contribution to the TOA flux. That is, let’s look at the spectral distribution vs height.
First the TOA spectra for these conditions (Ts=288K, Boundary layer humidity=80%, Free tropospheric humidity=40%):
Now to see where this all originated from we divide up the wavenumbers into bands of 100 cm-1, and we see the contribution to the TOA flux by band and height in the atmosphere (note that height in km is now ‘lying on the side’ to the left and wavenumber to the right, lost the axes labels somewhere along the way):
Zooming in a little:
We see that in the “atmospheric window” between 800 cm-1 to 1200 cm-1 the surface transmits almost “straight through” (62% of surface flux makes it straight through to the top of atmosphere in this wavenumber range). A small component comes from around the center of the CO2 band (667 cm-1) from the top layer. The rest mostly comes from the “wings” of the CO2 band and where the water vapor absorption is not so strong, around 400 cm-1.
Hopefully seeing the actual data in these different ways helps to see that “average height of emission” is not a real concept or a particularly useful concept. Perhaps it’s a bit like averaging the kg of food consumed per day per person in the entire world. You get a value but the components that made it up are so wide ranging the average has lost anything useful. It’s not like average height of male 20-year olds in Latvia.
Transmission and emission of atmospheric radiation is extremely wavelength dependent.
Part One – some background and basics
Part Two – some early results from a model with absorption and emission from basic physics and the HITRAN database
Part Four – Water Vapor – results of surface (downward) radiation and upward radiation at TOA as water vapor is changed
Part Five – The Code – code can be downloaded, includes some notes on each release
Part Six – Technical on Line Shapes – absorption lines get thineer as we move up through the atmosphere..
Part Seven – CO2 increases – changes to TOA in flux and spectrum as CO2 concentration is increased
Part Eight – CO2 Under Pressure – how the line width reduces (as we go up through the atmosphere) and what impact that has on CO2 increases
Part Nine – Reaching Equilibrium – when we start from some arbitrary point, how the climate model brings us back to equilibrium (for that case), and how the energy moves through the system
Part Ten – “Back Radiation” – calculations and expectations for surface radiation as CO2 is increased
Part Eleven – Stratospheric Cooling – why the stratosphere is expected to cool as CO2 increases
Part Twelve – Heating Rates – heating rate (‘C/day) for various levels in the atmosphere – especially useful for comparisons with other models.
The data used to create these graphs comes from the HITRAN database.
The HITRAN 2008 molecular spectroscopic database, by L.S. Rothman et al, Journal of Quantitative Spectroscopy & Radiative Transfer (2009)
The HITRAN 2004 molecular spectroscopic database, by L.S. Rothman et al., Journal of Quantitative Spectroscopy & Radiative Transfer (2005)