Understanding atmospheric radiation is not so simple. But now we have a line by line model of absorption and emission of radiation in the atmosphere we can do some “experiments”. See Part Two and Part Five – The Code.
Many people think that models are some kind of sham and climate scientists should be out there doing real experiments. Well, models aren’t a sham and climate scientist are out there doing lots of experiments. Various articles on Science of Doom have outlined some of the very detailed experiments that have been done by atmospheric physicists, aka climate scientists.
When you want to understand why some aspect of a climate mechanism works the way it does, or what happens if something changes then usually you have to resort to a mathematical model of that part of the climate.
You can’t suddenly increase the amount of a major GHG across the planet, or slow down the planetary rotation to ½ its normal speed. Well, not without a sizable investment, a health and safety risk, possible inconvenience to a lot of people and, at some stage, awkward government investigations.
You can’t stop the atmosphere emitting radiation or test a stratosphere that gets cooler with height. But you can attempt to model it.
Mathematical models all have their limitations. We have to understand what the model can tell us and what it can’t tell us. We have to understand what presuppositions are built into the model and what can change in real life that is not being modeled in the maths. It’s all about context.
(Well-designed) models are not correct and are not incorrect. They are informative if we understand their limitations and capabilities.
In contrast to mathematical models built around the physics of climate mechanisms, many people commenting in the blog world (or even writing blogs) have a vague mental model of how climate works. This of course is way way ahead of a climate model built on physics. It has the advantage of not being written down in equations so that no one can challenge it and seemingly plausible hand-waving argument 1 can be traded against hand-waving argument 2. Unfortunately, on this blog we don’t have the luxury of those resources and – where experiments are not available or not possible – we will have to evaluate the results of mathematical models built on physics and observations.
All the above is not an endorsement of what GCMs tell us. And not an indictment. Hopefully no one reading the above paragraphs came to either conclusion.
When I first built the line by line model it had more limitations than today. One early problem was the stratosphere. In real life the temperature of the stratosphere increases with height. In the model the temperature decreased with height.
This was expected. O2 and O3 absorb solar radiation (primarily ultraviolet) and warm mainly the middle layers of the stratosphere. But the model didn’t have this physics. The model, at this stage, primarily modeled the absorption and emission of terrestrial (aka ‘longwave’) radiation by the atmosphere.
So, after a few versions a very crude model of solar absorption was added. Unfortunately, this solar absorption model still did not create a stratosphere that increased with temperature. This was quite disappointing.
Then commenter Uli pointed out that the model had too much stratospheric water vapor and I added a new parameter to the model which allowed stratospheric water vapor to be set differently from the free troposphere. (So far I’ve been using a realistic level of 6ppmv).
The result was happily that the stratosphere, left to its own (model) devices, started increasing with temperature. The starting point is simply a temperature profile dictated to the model, and the finish point is how the physics ends up calculating the final temperature profile:
Figure 1 – A warmer stratosphere and a happier climate model
At the same time, I’ve been updating the model so that it can run to some kind of equilbrium and then various GHGs can be changed.
This was to calculate “radiative forcing” under various scenarios, and specifically I wanted to show how energy moved around in the climate system after a “bump” in something like CO2. This is something that many many people can’t get right in their heads. One of the objectives of the model is to show bit by bit how the increased CO2 causes a reduction in net outgoing radiation, and how that in turn pushes up the atmospheric and surface temperature.
On this journey, once the model stratosphere was behaving a little like its real-life big brother it occurred to me that maybe we could answer the question of why the stratosphere was expected to cool with increased CO2.
See Stratospheric Cooling for some background.
Previously I have worked under the assumption that there are lots of competing “terms” in the energy balance equation for how the stratosphere responds to more CO2 and so simple conceptual models are not going to help.
Now the Science of Doom Climate Model (SoDCM) comes to the rescue.
In fact, while I was waiting for lots of simulations to finish on the PC I was reading again the fascinating Radiative Forcing and Climate Response, by Hansen, Sato & Ruedy, JGR (1997) – free paper – and in a groundhog day experience realized I didn’t understand their flux graphs resulting from various GCM simulations. So the SoDCM allowed me to solve my own conceptual problems.
Let’s take a look at stratospheric cooling.
Understanding Flux Curves
In this simulation:
- CO2 at 280 ppm
- no ozone, CH4 or NO2 for longwave absorption
- boundary layer humidity at 80%
- free tropospheric humidity at 40%
- stratospheric water vapor at 6 ppmv
- tropopause at 200 hPa
- top of atmosphere (TOA) at 1 hPa
- solar radiation at 242 W/m² with some absorbed in the stratosphere and troposphere as shown in figure 1 of Part Nine – Reaching Equilibrium
The surface temperature reached equilibrium at 281K and the tropopause was at 11 km:
The equilibrium was reached by running the model for 500 (model) days, with timesteps of 2 hours. The ocean depth was only 5 meters simply to allow the model to get to equilibrium quicker (note 1).
Then at 500 days the CO2 concentration was doubled to 560 ppm and we capture a number of different values from the timestep before the increase and the timestep after the increase.
Let’s take a look at the up and down fluxes through the atmosphere. See also figure 6 of Part Two. In this case we can see pre- and post-2xCO2, but let’s first just try and understand what these flux vs height graphs actually mean:
Figure 3 – Understanding the Basics
If flux just stays constant (vertical line) through a section of the atmosphere what does it mean?
It means there is no net absorption. It could mean that the atmosphere is transparent to that radiation. It could mean that the atmosphere emits exactly the same amount that it absorbs. Or some of both. Either way, no change = no net radiation absorbed.
Take a look in figure 3 at the (pre-CO2 doubling) upward flux above 10km (in the stratosphere). About 237 W/m² enters the bottom of the stratosphere and about 242 W/m² leaves the top of atmosphere. So the stratosphere is 5 W/m² worse off and from the first law of thermodynamics this either cools the stratosphere or something else is supplying this energy.
Now take a look at the (pre-CO2) downward flux in the stratosphere. At the top of atmosphere there is no downward longwave radiation because there is no source of this radiation outside of the atmosphere. So downward flux = 0 at TOA.
At the bottom of the stratosphere, about 27 W/m² is leaving. So zero is entering and 27 W/m² is leaving – this means that the stratosphere is worse off by 27 W/m².
If we add up the upward and downward longwave fluxes through the stratosphere we find that there is a net loss of about 32 W/m². This means that if the stratosphere is in equilibrium some other source must be supplying 32 W/m².
In this case it is the solar absorption of radiation.
If we were considering the troposphere it would most likely be convection from the surface or lower atmosphere that would be balancing any net radiation loss from higher up in the troposphere.
So, to recap:
- think about the direction radiation is travelling in:
- if it is reducing in the direction it is travelling then energy is absorbed into that section of the atmosphere
- if it is increasing in the direction it is travelling then energy is being lost from that section of the atmosphere
- if plots of flux against height are vertical that means there is no change in energy in that region
- if flux vs height is constant (vertical) then it either means
- the atmosphere is transparent to that radiation, OR
- the atmosphere is isothermal in that region (emission is balanced by absorption)
Take another look at figure 3 below 10km:
- The upward radiation is reducing with height – energy is absorbed by each level of the atmosphere. This is a net heating.
- The downward radiation is increasing – energy is lost from each level of the atmosphere. This is a net cooling.
- The slope of the curves is not equal. This is because energy is transferred via convection in the troposphere.
Understanding these concepts is essential to understanding radiation in the atmosphere.
Upward Flux from Changes in CO2
Let’s take a closer look at the upward and downward changes due to doubling CO2. So the “pre” curve is the atmosphere in a nice equilibrium condition. And the “post” curve is immediately after CO2 has been doubled, long before any equilibrium has been reached.
Let’s zoom in on the upward fluxes in the stratosphere pre- and immediately post-CO2 doubling:
Even though the curves are roughly parallel from 10km through to 30km you should be able to see that there is a larger gradient on the post-2xCO2 curve. So pre-CO2 increase, the stratosphere loses a net upward of about 5 W/m², and after CO2 increase the stratosphere loses a net upward of about 6 W/m².
This means more CO2 increases the cooling of the stratosphere when we consider the upward flux. So now the question is, WHY?
If we want to understand the answer, the most useful ingredient is to look at the spectral characteristics of pre- and post. Here we take the radiation leaving at TOA and subtract the radiation entering at the tropopause. So we are considering the net energy lost (why lost? because this calculation is energy out – energy in), and as a function of wavenumber.
Here is the spectral graph of energy lost by the stratosphere due to upwards radiation, before the CO2 increase:
The post-CO2 doubling looks very similar so here is a comparison graph, with a slight smoothing (moving average window) just to allow us to see a little more clearly the main differences:
So we see that in the case of post-2xCO2, the energy lost is a little higher, and it is in the wavenumber region where CO2 emits strongly. CO2’s peak absorption/emission is at 667 cm-1 (15 μm).
Just to confirm, here is the difference – post-2xCO2 minus pre-2xCO2 and not smoothed:
We can see that the main regions of CO2 absorption and emission are the reason. And we note that the temperature of the stratosphere is increasing with height.
So the reason is clear – due to principles outlined earlier in Part Two. Because the stratospheric temperature increases with height, the net emission (i.e., emission less absorption) of radiation, as we go up through the stratosphere will be a progressively higher value. And once we increase the amount of CO2, this net emission will increase even further.
This is what we see in the spectral intensity – the net change in stratospheric emission [(out-in)2xCO2 - (out-in)1xCO2] increases due to the emission in the main CO2 bands.
Downward Flux from Changes in CO2
Here is what we see when we zoom in on the downward flux in the stratosphere:
Of course, as already mentioned, the downward longwave flux at TOA must be zero.
This time it is conceptually easier to understand the change from more CO2. There’s one little fly in the understanding ointment, but let’s come to that later.
So when we think about the cooling of the stratosphere from downward flux it’s quite easy. Coming in at the top is zero. Coming out of the bottom (pre-CO2 increase) is about 27 W/m². Coming out of the bottom (post-2xCO2) is about 30 W/m². So increasing CO2 causes a cooling of about 3 W/m² due to changes in downward flux.
Here is the spectral flux (unsmoothed) downward out of the bottom of the tropopause, pre- and post-2xCO2:
And as with figure 7, below is the difference in downward intensity as a result of 2xCO2. This is post less pre, so the positive value overall means a cooling – as we saw in the total flux change in figure 8.
The cause is still due to the CO2 band but the specifics are a little different from the upward change. Here the center of the CO2 band has zero effect. But the “wings” of the CO2 band – around 600 cm-1 and 700 cm-1 are the places causing the effect:
The temperature is reducing as we go downwards so the emission from the center of the CO2 band cannot be increasing as we go downward. If we look back at figure 7 for the upward direction, the temperature is increasing upward so the emission from the center of the CO2 band must be increasing.
And the conceptual fly in the ointment alluded to earlier – this one can be confusing (or simple..) – if the starting flux at TOA is zero and the temperature decreases downward surely the downward flux only gets less? Less than zero? Instead, think of the whole stratosphere as a body. It must emit radiation due to its temperature and emissivity. It can’t absorb any radiation from above (because there is none), so it must emit some downward radiation. As its emissivity increases with more GHGs it must emit more radiation into the troposphere. It’s simple really.
Let’s now finalize this story by considering the net change in flux with height due to CO2 increases. Here if “net” is increasing with height it means absorption or heating. And if “net” is reducing with height it means emission or cooling. See note 2 where the details are explained.
So the blue line (upward flux) decreasing from the tropopause up to TOA means that the change in flux is cooling the stratosphere. And likewise for the green line (downward flux). This is just the results already shown as spectral changes now shown as flux changes:
If we combine figure 11 for the total net effect of doubling CO2:
From the tropopause at 11km through to TOA we can see that the combined change in flux due to CO2 doubling causes a cooling of the stratosphere. (And from the surface up to the tropopause we see a heating of the troposphere).
By comparison, here is an extract from Hansen et al (1997):
The highlighted instantaneous graph is the one for comparison with figure 12.
This is the case before the stratosphere has relaxed into equilibrium. Note that the “adjusted” graph – stratospheric equilibrium – has a vertical line for ΔF vs height, which simply means that the stratosphere is, in that case, in radiative equilibrium.
Notice as well that the magnitude of my graph is a lot higher. There may be a lot of reasons for that, including that fact that mine is one specific case rather than some climatic mean, and also that the absorption of solar radiation in my model has been treated very crudely. (Lots of other factors include missing GHGs like CH4, N2O, etc).
So we have seen that the net emission of radiation by CO2 bands is what causes the cooling from upward radiation and the cooling from downward radiation when CO2 is increased.
For further insight, I amended the model so that on the timestep before and just after equilibrium the stratosphere was:
A) snapped back to an isothermal case, with the temperature set at the tropopause temperature just calculated
B) forced into a cooling at 4 K/km (c.f. the troposphere with a lapse rate of 6.5 K/km)
Case A, temperature profile just before and after equilibrium:
And the comparison to figure 11:
We can see that the downward flux change is similar to figure 11, but the upward flux is different. It is fairly constant through the stratosphere. This is not surprising. The flux from below is either transmitted straight through, or is absorbed and re-emitted at the same temperature. So no change to upward flux.
But the downward flux only results from the emission from the stratosphere (nothing transmitted through from above). As CO2 is increased the emissivity of the atmosphere increases and so emission of radiation from the stratosphere increases. The fact that the stratospheric temperature is isothermal has a small effect as can be seen by comparing the green curve on figures 15 & 11. But it isn’t very significant.
Now let’s consider case B. First the temperature profile:
Now the net flux graph:
Here we see that the effect of increased CO2 on the upward flux is now a heating in the stratosphere. And the net change in downward flux still has a cooling effect.
Here we see that for a stratosphere where temperature reduces with altitude, doubling CO2 would not have a noticeable effect on the stratospheric temperature. Depending on the temperature profile (and other factors) there might be a slight cooling or a slight heating.
This is a subject where it’s easy to confuse readers – along with the article writer. Possibly no one that was unclear before made it the whole way and said “ok, got it”.
Hopefully, if you only made it only part of the way through, you now have a better grasp of some of the principles.
The reasons behind stratospheric cooling due to increased GHGs have been difficult to explain even for very knowledgeable atmospheric physicists (e.g., one of many).
I think I can explain stratospheric cooling under increasing CO2. I think I can see that other factors like the exact temperature profile of the stratosphere on any given day/month and the water vapor profile (not shown in this article) will also affect the change in stratospheric temperature from increasing CO2.
If the bewildering complexity of up/down, in-out, net of in-out, net of in-out for 2xCO2-original CO2 has left you baffled please feel free to ask questions. This is not an easy topic. I was baffled. I have 4 pages of notes with little graphs and have rewritten the equations in note 2 at least 5 times to try and get the meaning clear – and am still expecting someone to point out a sign error.
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 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 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 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)
Radiative Forcing and Climate Response, by Hansen, Sato & Ruedy, JGR (1997) – free paper
Note 1: The relative heat capacity of the ocean vs the atmosphere has a huge impact on the climate dynamics. But in this simulation we were interested in reaching an equilibrium for a given CO2 concentration & solar absorption – and then seeing what happened to radiative balance immediately after a bump in CO2 concentration.
For this requirement it isn’t so important to have the right ocean depth needed for decent dynamic modeling.
Note 2: The treatment of upward and downward flux can get bewildering. The easiest approach is to just consider the change in flux in the direction in which it is travelling. But because upward and downward are in opposite directions, F↑ is in the direction of z, and F↓ is in the opposite direction to z, so heating and cooling are in opposite directions.
Due to changing GHGs:
If F↑(z)2xCO2 – F↑(z) < 0 => Heating below height z (less flux escaping);
F↑(z)2xCO2 – F↑(z) > 0 => Cooling below height z
If F↓(z)2xCO2 – F↓(z) < 0 => Cooling below height z (less flux entering);
F↓(z)2xCO2 – F↓(z) > 0 => Heating below height z
So for example for figure 11 – the net upward = F↑(z) – F↑(z)2xCO2 & net downward = F↓(z)2xCO2 – F↓(z)
dF↑(z)/dz < 0 => Heating of that part of the atmosphere (upward flux is reducing due to being absorbed)
dF↓(z)/dz < 0 => Cooling of that part of the atmosphere (downward flux is increasing as we go down due to more being emitted, or rewritten is very strange English to match the equation: downward flux is decreasing in the upward direction)