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].
Figure 1
And here we’ve zoomed in by expanding the x-axis:
Figure 2
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%):
Figure 3
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):
Figure 4
Zooming in a little:
Figure 5
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.
Conclusion
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.
Related Articles
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.
References
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)
Very nice. Cold you set water vapor to zero?
See Visualizing Atmospheric Radiation – Part Four.
So only the central line of the CO2 absorption band remains opaque up to ~ 15 km, but the important side bands within the CO2 13-17 micron band radiate to space from low down in the atmosphere and then peak at around 4 km . This agrees almost exactly to what I calculated – see graph here.
So I think Pekka Pirilä is missleading when he implies that most radiation in the 15 band originates from the stratosphere. Most radiation is actually from the lower troposphere peaking around 4 km above the surface, and surprisingly about 5% comes from the surface.
Clive,
I have said it clearly that my comment was about the wavelengths of strongest absorption. Extending the analysis down to 13 µm is highly misleading as that’s already in the region of the atmospheric IR window as you can see from SoD’s Figure 2 in Part Two. The absorptivity of CO2 is down by a factor of more than 10000 from the peak at 13 µm.
According to SoD’s calculation the stratosphere appears to be fully opaque over the range 645-695 1/cm or 14.4-15.5 µm and perhaps a little beyond that. You should not choose the range to include the really weak tails.
The range I give above is based on the uppermost layer of Sod, but the second layer from top is also fully within the stratosphere. Based on that the range of full opacity extends to 640-700 1/cm or 14.3-15.6 µm and almost full opacity to 625-715 µm or 14.0-16.0 µm. That’s about as far as it’s justifiable to extend the analysis of the 15 µm peak.
Pekka,
I don’t think that is completely true. Take a look at the absorptivity from the lecture notes ofCabellero here and then also take a look at a real IR spectrum from space here. I also have some doubts about the details of SoDs spectrum in fig 2, because (unless I am mistaken), it doesn’t include doplar broadening, (nor radiative transfer from lower levels ?). It is a valiant piece of work but the shape doesn’t quite reproduce experimental data.
So, Yes 13-17 microns cover the edges of the CO2 band, and below 13 microns is more or less the IR window. However the plank spectrum is ignorant of all this and more radiative flux passes through the shoulders than through the central line. As a result the radiation escaping to space between 13-17 microns originates from a wide range of heights in the atmosphere.
If CO2 increase then the effective height increases and OLR decreases assuming constant T and lapse rate. What surprised me is that if CO2 decreases then atmospheric OLR also decreases. Radiation from the surface increases exponentially and dominates below 100ppm. Another way of saying the same thing is that the IR window widens.
Clive,
Ir’s clear that the model of SoD is not complete and fully realistic. He tells that clearly in his post. Using the Lorentz line shape that cannot handle Doppler broadening is just one of the limitations. As far as I understand there’s no attempt to compensate for that by changing the line width from the collisional value. Thus the lines are too narrow at high altitudes. That increases transmission but cannot make much difference when the whole line is too weak as the absorption lines are close to 13 µm. If those wavelengths are calculated correctly we have, indeed quite a lot of radiation from the surface to space. On the other hand the band width used in the calculation causes “numerical broadening” that may lead to significant opposite errors in the results at altitudes where the lines are narrow in comparison with the band width.
The strongest absorption lines of CO2 at wavelengths around 13 µm by a factor of 10000 weaker than the main line. Only a logarithmic plot may make anyone think that such a weak tail can be considered a significant part of a broad absorption peak that’s formed from the main peak and the side peaks related to the rotational states. At 14 µm the lines have still a strength that’s almost 1% of the main peak. That’s enough to make the stratosphere as a whole rather opaque.
More accurate calculations of the transmissivity of the stratosphere require the use of Voigt line shape and very narrow bands in calculation because the lines are so narrow and the absorption minima between the lines deep. Lacking data from such calculations I cannot say much more about the outcome.
Off hand Eli has to agree with Clive. As one rises from the tropopause in the stratosphere the temperature increases, thus one would see a sharp upward going spike in the emission spectrum
http://rabett.blogspot.com/2009/12/answer-to-puzzler-couple-of-days-ago.html
Chris Colose gives a simple model of the greenhouse effect using the formula:
Ts ~ Te + Γ H,
where Ts is the surface temperature, Te is the effectuve temperature of radiation to space, Γ is the lapse rate, and H is “the flux-weighted mean altitude of the emission to space”, ie, the effective altitude of radiation to space. It is, to my knowledge, the simplest model of the greenhouse effect that includes both of the essential elements determining the surface temperature, and unlike other simple models used for teaching, does not encourage the misunderstandings that so commonly beset blog climate science.
My point is that using Pekka Pirilä’s definition that, it turns out that H is used as an intermediate value to produce observable results (Ts), and hence is not just of curiosity value.
Granted, it is only used for teaching, and to derive first order approximations of Ts – but that is still sufficient reason for the value to be of genuine interest.
Tom,
There was a post here on the same subject by Leonard Weinstein that got a lot of attention.
http://scienceofdoom.com/2012/07/23/how-the-greenhouse-effect-works-a-guest-post-and-discussion/
This post was derived from post at The Air Vent by the same author.
http://noconsensus.wordpress.com/2012/07/20/why-back-radiation-is-not-a-source-of-surface-heating/
Please, let’s not reopen that discussion in this thread. I believe comments are still active on Leonard’s post here.
SOD: Could you explain why the lowest level in the atmosphere emits 20 W/m2 to space while the next layer above emits only 1 W/m2? There shouldn’t be a big temperature or composition difference between these two layers (unless water vapor decreases surprising fast with altitude) and the lower layer must travel slightly further to reach space.
Frank,
Well spotted.
The code is not well-written here. The value of transmitted flux is correct but the reason is bad. This one layer is quite thin.
The program divides the atmosphere up into equal Δp – to get similar numbers of molecules per layer. But I realized that if I had a “boundary layer humidity” and a separate “free tropospheric humidity” then changing the number of layers would alter this bottom layer and skew the results.
So I implemented a parameter called boundary layer pressure, which so far has been set to 920hPa (it can be altered when calling the routine).
The program should have been altered to produce equal pressure changes for n-1 layers above the boundary layer. But this is not the case. In the 20-layer example above, the pressures of the 21 boundaries are, in 103hPa:
1.0000 0.9197 0.9075 0.8624 0.8160 0.7708 0.7248 0.6794 0.6330 0.5876 0.5420 0.4960 0.4501 0.4042 0.3586 0.3130 0.2673 0.2215 0.1755 0.1298 0.0841
Which also highlights the fact that I changed the surface pressure from 1013 hPa to 1000 hPa as a temporary measure to make it easier to confirm that the way the program was creating pressure layers boundaries was correct. And haven’t yet changed it back.
Just finishing off another article with water vapor changes then I will be cleaning up the comments in the code and publishing so people can spot any gaffes.
Frank,
I fixed up the code so that the layers are equal pressure difference.
Here is the revised 20 layer model:
And here is the zoomed in section:
And the revised pressures and heights of the 21 boundaries are, in hPa and meters:
Pb zb
1013 0
919 810
873 1240
828 1670
782 2130
736 2610
690 3120
645 3650
598 4220
553 4820
507 5470
461 6160
415 6910
370 7730
324 8640
278 9660
232 10820
187 12190
141 13930
95 16360
49 20430
SOD: I haven’t been able to master the large number of posts you have put out since the beginning of the year. I returned here today trying to understand one of your more recent posts.
If I understand correctly, you are telling me that the lowest 5% of the atmosphere emits 22 W/m2 of radiation that makes it through the TOA while the second lowest 5% of the atmosphere emits only 6 W/m2 through the TOA. This is partly because the lowest 5% of the atmosphere is considered to be the boundary layer with 80% relative humidity and most of the layers above are considered to be free troposphere with 40% relative humidity. (I think I read elsewhere, that the rest is stratosphere with a fixed 6 ppmv.)
If water vapor were the only significant GHG in the lowest layers and given twice as much water vapor in the boundary layer, I expect twice as much emission from water vapor, not four times as much, attenuated to some extent by the absorption of the water vapor above as seen in layers 3, 4, 5, 6 etc., which are gradually increasing their effective emission with altitude through the TOA despite being colder. So I would have predicted something like 10 W/m2. (Given that CO2 contributes some emission and it’s mixing ratio doesn’t change across the boundary layer, 10 W/m2 is an upper limit. If half of the emission escaping from the lowest layer through the TOA actually came from CO2 (unlikely), then I’d have predicted 7.5 W/m2.)
Looking at the column labeled zb (altitude?), however, the bottom layer is twice as thick as the next layer – which contradicts my understanding that each layer contains the same weight of atmosphere.
Your assumption that there is a sudden discontinuity between the relative humidity in the boundary layer (80%) and the free troposphere (40%) may be approximately correct in the descending regions of the subtropics, but is unlikely to be realistic for the global as a whole. If you ever want to make changes to the model, using measured absolute humidities might be preferable.
I’m not sure how your program handles the water vapor continuum. Most of the continuum appears to be water vapor dimers. If water vapor monomer concentration drops by a factor of two (as you move higher in the atmosphere), then dimer concentration drops by a factor of four.
Frank,
If I made the bottom layer (the boundary layer) of variable height then changing the number of layers would be guaranteed to change all the radiative transfer calculations due to the different humidity in boundary layer and free troposphere. So it’s kind of a compromise.
So in this version of the model the boundary layer is 80 hPa thick, while the next layer is 46 hPa thick.
So we have twice the number of molecules in layer 1 vs layers 2,3,4,etc.
The continuum is a function of the square of the concentration of water vapor molecules.
So – if the temperature was constant with height – the boundary layer with 80% relative humidity would have 4x the continuum effect of the next layer up with 40% relative humidity. And the bottom layer is twice as thick so it would have 8x the effect of the next layer up.
In reality the boundary layer is at a higher temperature which increases s.v.p so the concentration of water molecules is increased by more than than a factor of 2.
So the effect of the continuum will be a factor of say 10x lower in the 2nd layer vs the boundary layer.
As you point out, the continuum is only one part of the whole story.
We could check – I should rerun some models and separate out the effects from the different GHGs and the continuum.
This is spot on. The only reason for doing it this way is to allow a simplification – but not too simple.
Later on in Part Twelve – Heating Rates I have some standard AFGL atmospheres using the specified water vapor, ozone, CO2, etc.
I will almost no time over the next week, but next opportunity I will rerun those std atmospheres and post the graphs of TOA contribution from each level.
I had the chance to squeeze this in..
Here is the AFGL Tropical atmosphere. As suggested by Ebel, I changed the code to plot cumulative contribution from each layer:
There are more layers in this model – it just uses the values provided (temperature, humidity, etc) for every 1km in the atmosphere. So each layer has the same vertical depth.
This means (when using the standard AFGL atmospheres) that the pressure difference for each layer is not constant.
And here in contrast is the AFGL Subarctic winter:
The total TOA flux is 192 W/m2.
We can see that the surface contribution to TOA is higher – because the atmosphere transmits more.
For reference, here is the AFGL Subarctic winter profile:
The AFGL Tropical profile:
SoD and Frank,
I have played quite a lot with the model as well and all simplifications and assumptions have clear justifications. Working with the model myself I have also fair understanding of what the graphics is about. Thinking a little more about the graphs I notice that many of them have been misleading. The the observations of Frank and the improvements in the new graphs tell on the nature of these problems.
In some cases a cumulative distribution would avoid the problem and present the facts well enough, in some other cases dividing the values by the mass of the layer would be an improvement, when the masses are not equal as they cannot be, when stratosphere is studied in more detail.
One more set of graphs that I find badly misleading are those of the part nine, which tell about reaching the equilibrium. The whole dynamics shown in that part is just an artifact of the computational method rather than dynamics of any atmosphere (plus ocean), real or idealized. This is due to the way the model iterates the development of the temperature profile. The results depend on the number of iterations for each time step. Using a very large number for each time step gives the same results as my modified code that avoids the iteration totally. With the small number of iterations the little dynamics present in the atmosphere and ocean is overwhelmed by the very strong one brought in by the method.
There are certainly many other examples where working with the model and knowing, how the graphs should be interpreted, makes it difficult to notice, how misleading they are to others.
The radiation at the TOA is not the result of the transmission, but the average value of the temperatures of the pressure geometrical heights or heights from which the radiation reaches the space. Radiation that was emitted from deeper layers is largely absorbed again and does not reach, therefore, the space.
The radiated power from heights where no more radiation from deeper layers is absorbed, is determined from the Planck function corresponding to the temperature.
As illustration should be more useful a cumulative frequency curve, where in the X-axis is the sum of the radiation power and the y-axis the corresponding heights up to which this sum is reached. It’s clearer than the individual contributions of each layer and it can increasing the number of layers without substantially the clarity is lost.
Scienceofdoom,
“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”.
For pure curiousity value:
Employing a very different method I estimate the effective emission altitude at 1.9km, the effective emission temperature at 276K and a GHE magnitude at 12 degrees C. The result is based on surface emissivity of 0.93 and atmospheic emissivity proportional to the square of temperature.
How can I post the sum curve? As email, but with what address?
You could create a JPG or PNG of your graph using Paint, upload to a photo hosting service and post a link. That’s what most of us do.
http://www.bilder-hochladen.net/files/big/h9qc-r-02e7.jpg
Ebel,
That’s a very sensible approach. I’ll update the code and plot cumulative values for future graphs.
[...] a look at Part Three – Average Height of Emission and Part Four – Water Vapor for more [...]
[...] Part Three – Average Height of Emission - the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions [...]
[...] Part Three – Average Height of Emission - the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions [...]
[...] Visualizing Atmospheric Radiation – Part Three – Average Height of Emission Visualizing Atmospheric Radiation – Part Five – The Code [...]
[...] Part Three – Average Height of Emission - the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions [...]
[...] Part Three – Average Height of Emission - the complex subject of where the TOA radiation originated from, what is the “Average Height of Emission” and other questions [...]
I have been working on a different approach to calculating the effective emission height for CO2 in the atmosphere. Instead of calculating radiative transfer from the surface up through the atmosphere to space, I decided to do exactly the opposite. IR photons originating from space are instead tracked downwards to Earth in order to derive for each wavelength the height at which more than half of them get absorbed within a 100 meter path length. This identifies the height where the atmosphere becomes opaque at a given wavelength. This also coincides with the “effective emission height” for photons to escape from the atmosphere to space. I wrote a program to do this using a standard atmospheric model and a line by line calculation for CO2 absorption using data from the HITRAN spectroscopy database. The effective emission height looks like this.
I have also written this up here and used the result to estimate the radiative forcing caused by a doubling of CO2. I get 3.5 watts/m2
Clivebest,
Have you taken the Voigt profile into account. It’s likely to have a significant influence near 667 1/cm and some influence over the range from 645 to 690.
As you notice, your results are closely related to those of SoD. Your graph is a nice way of presenting this particular point, while the same physics is taken fully into account in SoD’s model.
I must admit that I don’t fully understand the Voigt profile! The Fortran program uses Lorentz function and integrates over multiple line overlap to calculate absorption cross-sections. For sure it can be improved.
I think SoD’s model is great. It inspired me to try another approach.
The basic idea of the Voigt profile is simple. In very rare atmosphere collisions are so infrequent that the related Lorentz profile is very narrow. Under such conditions the Doppler effect starts to be of similar importance. The Doppler effect alone would result in a Gaussian line profile from the Maxwell-Boltzmann distribution of the molecular velocities. The widths of the to profiles taken alone are comparable in the upper stratosphere. At lower altitudes the Doppler effect is insignificant and above the stratopause it starts to dominate. The most difficult range to calculate is that where the both effects are comparable. There the far tails are given by the Lorentz profile but the central peak is significantly broader and lower.
I found a paper that published Matlab-code for calculating the Voigt lineshape fast enough to make it practical. It’s certainly slower than calculating the Lorentz profile, but fast enough when applied with care only when it may matter.
Using the Voigt profile for the stratosphere makes little difference on any results that concern troposphere or surface. Thus it’s of interest only when we want to study what happens at altitudes of more than 30 or 40 km. Even significant changes at those altitudes have little influence on the radiative balance of the troposphere. If those changes do influence troposphere, that must happen trough other mechanisms related to the dynamic behavior of the stratosphere.
Reply to SOD February 24, 2013 at 2:12 am:
I’m confused when looking at the graph you posted of the cumulative TOA flux from various layers of the tropical atmosphere. The surface layer seems to be emitting about 30 W/m2 through the atmosphere – reasonably consistent with the 40 W/m2 in the KT energy balance diagram. The tropics are a little warmer than the global average used by KT and the atmospheric window is probably narrowed by the enhanced water vapor continuum in the humid tropics.
My problem arises when comparing the layers immediately above the surface to the surface. The surface emissivity in the tropics is mostly ocean, perhaps 0.97-0.99. Whatever the emissivity of atmospheric layers above the surface, I assume that it must be LESS than the emissivity of the surface because there are some wavelengths where the atmosphere does have negligible emission. Unlike the surface, the atmosphere emits best at precisely the wavelengths it absorbs best. So my intuition suggest that it should be harder for the radiation emitted by these lowest layers to reach the TOA. Finally the temperature is dropping with the lapse rate, down 3 degC for the average of the first layer, down 10 degC for the second layer, etc. Those are roughly 1%, 3%, etc changes in temperature; and emitted radiation drops by the fourth power, roughly 4%, 12% etc. Despite these problems, each of the lowest layers of the atmosphere are contributing as much to the TOA flux as the surface. Above. we’ve discussed the graphs you’ve posted in your comment of January 9, 2013 at 10:12 pm. Those graphs show much less emission from the lowest layers of the atmosphere compared with the surface. It might be worth checking for a problem somewhere.
I recognize that the emissivity/absorptivity of a gas depends on the quantity of gas under consideration (and that it can never rise above 1). One set of graphs in question use layers measured in altitude; the other, pressure. When the thickness of a thin layer is doubled, the emissivity of that layer doesn’t double, because some of the radiation it emits is absorbed before it reaches the surface of that layer. Are your layers always thin enough to avoid this problem?
(FWIW, I prefer layers of constant pressure change, because they represent equal numbers of emitting molecules, except for the drying with altitude. Putting pressure on the left-hand vertical axis and altitude on the right-hand axis is the best of all world for those like me who need to stop and think about how to translate one into the other.)
Frank,
The strong dependence of the continuum absorption is probably enough to explain the importance of the two lowest layers for the emission from the tropical atmosphere.
.. absorption on the moisture is probably ..
Frank,
Interesting thoughts. I’m pretty sure the model is calculating radiative effects correctly from a number of perspectives, including the fact that the heating rates for model atmospheres are a close match with professional results.
But the whole point of this series is to test ideas and provide insight. Next weekend, when I am back in front of my (Matlab) PC I will provide some more detailed results:
a) emission from each layer
b) spectral emission from each layer
c) spectral emission from each layer that is transmitted to TOA
- and if that still leaves unanswered questions we can review what proportion of each layer’s spectrum gets absorbed in each layer above.
That’s the beauty of having a model where we can inspect the innards..
Frank,
I took the spectral emission from the surface and the lowest three layers, each 1km thick.
The emission is plotted, and the total flux is noted in the legend.
The second graph shows the TOA transmitted spectrum for each of those layers – on the same vertical axis, again with flux (transmitted TOA) noted in the legend. The graph can be expanded by clicking on it:
And the second graph on an expanded scale, again, click to expand:
You can see why it’s difficult to figure out in your head why the value should go up or down for each layer.
For a layer closer to the ground (vs a layer higher up) the emission will be higher (because temperature and water vapor concentration is higher), but the absorption through to TOA will be higher due to more GHGs above.
Which ones wins? As we see in the above graphs, the results vary for any given wavenumber.
If you want to see more layers or different layers I can easily produce those graphs. Any more specific request can probably be produced.
And here are the comparable results for the sub-arctic winter, click to expand:
And the expanded view of the transmitted TOA spectrum:
This one is probably easier to expect. The surface transmitted flux is much higher because the atmosphere has much less absorption. Therefore, the atmosphere has much less emission – and so the TOA transmitted flux from comparable atmospheric layers is much lower. However, it isn’t easy to predict whether the layer above or the layer below contributes more to the TOA transmitted flux because of the various competing effects – which vary with spectrum and temperature.
Pekka:
Each different method of presenting data can convey a slight (or sometime very) different message. The best graph or table is the one that provides the information or “picture” you are seeking.
The part of the “picture” that is missing for me is: What is happening to the photons? If I consider a thin slab of atmosphere (say 1 mb thick or 0.1% of the atmosphere) centered at a given altitude (say 1 km), what fraction of the photons emitted downward reach the surface and what fraction of those emitted upward reach space? Of those that are emitted downward (or upward) and are absorbed by the atmosphere, how far do they travel before being absorbed. There are obviously a wide range of distances traveled, so one might want to know something about that distribution: the shortest-most quickly-absorbed 5% travel an average distance of only 100? m downward, the next 15% travel an average of 250? m, the next 20% travel 400? m, the middle 20% travel an average of 700? m, and 30%? reach the surface. The best way to present this type of information would be a table.
Frank,
SoD’s model produces related information as optical depths of each layer for each wavelength in the sample. The table you are asking for could be calculated from these results and the temperatures that are also available.
Each of us looks at the same issues in different ways. Therefore the optimal set of information that we wish to have varies as well.