This first part considers some elementary points. In the next part we will consider more advanced aspects of this subject.
Since 1978 we have had satellites continuously measuring:
- incoming solar radiation
- reflected solar radiation
- outgoing terrestrial radiation
To see how we can differentiate the solar and terrestrial radiation, take a look at The Sun and Max Planck Agree – Part Two.
Top of Atmosphere Satellite Measurements
The top of atmosphere (TOA) radiation from the climate system is usually known as outgoing longwave radiation, or OLR. “Longwave” is a climate convention for wavelength >4μm.
Here’s what the OLR looks like to the satellites. I thought it might be interesting for some people to see how the values change each month:
All of this data comes from CERES – Clouds and the Earth’s Radiant Energy System. You can review this data for yourself here. How accurate is the data?
The uncertainty of an individual top-of-atmosphere OLR measurement is 5 W/m², while the uncertainty of average OLR over a 1°-latitude x 1°-longitude box, which contains many viewing angles, is ≈1.5 W/m²
from Dessler et al (2007) writing about the CERES data.
If we summarize this data into monthly global averages:
The average for 2009 is 239 W/m². This average includes days, nights and weekends. The average can be converted to the total energy emitted from the climate system over a year like this:
Total energy radiated by the climate system into space in one year = 239 x number of seconds in a year x area of the earth in meters squared
= 239 x 60 x 60 x 24 x 365 x 4 x 3.14 x (6.37 x 106 )²
= 239 x 3.15 x 107 x 5.10 x 1014
ETOA= 3.8 x 1024 J
The reason for calculating the total energy in 2009 is because many people have realized that there is a problem with average temperatures and imagine that this problem is carried over to average radiation. Not true. We can take average radiation and convert it into total energy with no problem.
What about the radiation from the surface?
What do the satellite measurements say about surface radiation?
Well strictly speaking – they say a lot, but only once certain theories of radiative transfer are embraced.
To be more accurate, what satellite measurements OF surface radiation do we have?
That’s because the atmosphere interacts with the radiation emitted from the surface. So any top-of-atmosphere measurements by satellite are not “unsullied surface measurements”.
There are temperature stations all around the world – not enough for some people, and not as well-located as they could be – but what about stations for measuring radiation upwards from the earth (and ocean) surface?
Thin on the ground, extremely thin.
Luckily, there is a very simple formula for radiation emitted from the surface of the earth:
E = εσT4
where σ is a constant = 5.67 x 10-8, ε = emissivity, a property of surface material, and T = temperature in K (absolute temperature)
This equation is called the Stefan-Boltzmann equation. More about it in Planck, Stefan-Boltzmann, Kirchhoff and LTE. It is a well-proven equation with 150 years of evidence behind it – and from all areas of engineering and physics. It is used in calculations for heat-exchangers and boilers, for example.
Still, many people when they find out that the radiation from the surface of the earth is calculated not measured are very suspicious. It’s good to be skeptical. Ask questions. But don’t assume it’s made up just because it’s calculated. Why trust thermometers? They actually rely on material properties as well..
Anyway, back to the emission of radiation from the surface. What about this parameter emissivity, ε?
Emissivity is a function of wavelength. This means it varies as the wavelength of radiation varies. Some examples, not all of them materials from the surface of the earth:
Note that reflectivity = 1 – emissivity in the graph above.
Without going into a lot of detail, all it means is that the measurement of emissivity needs to be for the appropriate temperature. See note 1.
If we measure emissivity of water one day, we find it is the same the next day and also in 589 days time. It is a material property which means that once measured, the only questions we have are:
a) what is the temperature of the surface
b) what is the material of the surface (so we can look up the measured emissivity for this temperature)
Generally the emissivity of the earth’s surface is very close to 1 (for “longwave” measurements).
Oceans, which cover 71% of the earth’s surface, have an emissivity of about 0.98 – 0.99.
The average temperature of the earth’s surface (including days, nights and all locations) is around 15°C (288K). Average temperature is a problematic value because radiation is not linearly dependent on temperature – it is dependent on the 4th power of temperature. See The Dull Case of Emissivity and Average Temperatures for an example of the problems in using “average temperature”.
Here is an example of measurement of upward surface radiation:
The line with the x’s is the measured surface upward radiation.
Here is the actual temperature:
And calculated emitted radiation:
Note how it matches the measured value. You can see this in more detail in The Amazing Case of “Back Radiation” – Part Three.
The theory about emitted radiation
E = εσT4
– is a solid theory, backed up over the last 150 years.
If we calculate the average radiation from the surface, globally annually averaged, we get a value around 390 W/m².
If we calculate the total surface radiation over one year, we get Esurf = 6.2 x 1024 J.
The Inappropriately-Named “Greenhouse” Effect
The surface radiates around 390 W/m². The climate system radiates around 239 W/m² to space:
How does this happen?
As I found with previous articles, many people’s instinctive response is “you’ve made a mistake”.
Usually those that just aren’t happy with this diagram solve the “dissonance” by concluding that there is something wrong with the averaging, or Stefan-Boltzmann’s law, or the measurement of emissivity around the planet.
Here’s the total energy for one year radiated from top of atmosphere and from the surface:
Remember that the top of atmosphere number is measured. Remember that the surface radiation is calculated, and relies on measurements of temperature, the material property called emissivity and an equation backed up by 150 years of experimental work across many fields.
This effect which we see has come, inappropriately, to be called the “greenhouse” effect. We could convert the effect to a temperature but there are more important things to move onto.
Before examining how this amazing effect takes place and what happens to all this energy – “Does it just pile up and eventually explode, no – so obviously you made a mistake”, and so on – I’ll leave one thought for interested students..
We have looked at the average radiation from surface and top of atmosphere (and also totaled that up).
Instead, we could take a look at some individual ocean locations where the temperature is well known. We have the CERES monthly averages on a 1° x 1° grid above.
Take a few ocean locations and find the average temperatures for each month.
Then calculate the surface radiation using the known emissivity of 0.99. Compare that to the top of atmosphere radiation from the CERES charts at the start of the article. Also calculate what value of ocean emissivity would actually be needed for surface radiation to equal the top of atmosphere radiation (so as to make the “greenhouse” effect disappear). Please report back in the comments.
The reason I chose the ocean for this exercise is because the emissivity is well known and measured so many times, because ocean surfaces don’t change temperature very much from day to night (because of the high heat capacity of water) and because oceans cover 71% of the earth’s surface. If ocean data verifies the “greenhouse” effect to you, then it’s pretty hard to find emissivity values of other surface types that would make the “greenhouse” effect disappear.
Interaction of Matter with a Radiation Field
Huh? Let’s choose a different heading..
What Happens to Radiation as it Travels Through the Atmosphere
If longwave radiation (remember this is the radiation emitted by the earth and climate system) was transparent to the various gases in the atmosphere the surface radiation would not change on its journey to the top of atmosphere. See The Hoover Incident for more on this and the consequences.
Instead at each height in the atmosphere there is absorption of some radiation. The detail gets pretty complicated because each gas absorbs at very selective wavelengths (see note 2).
The very fact that radiation can be absorbed by gases shows that you shouldn’t expect the radiation going into a layer of atmosphere to be the same value when it emerges the other side. Here’s a simple diagram (which also can be found in Theory and Experiment – Atmospheric Radiation):
If a proportion of the upward radiation is absorbed by the atmosphere so that less radiation emerged than entered (the red text and arrows) then isn’t this a first law of thermodynamics problem?
Well, being specific:
Energy In – Energy Out = Energy Retained in Heating the Layer
So if the temperature of that layer was not increasing or decreasing then:
Energy in = Energy out.
So surely, absorption of radiation with no continuous heating is a problem for the first law of thermodynamics?
Of course, energy transfer can also take place via convection. So it is theoretically possible that energy could be absorbed as radiation and leave via convection. But that isn’t really possible all through the climate as convection would need to transfer energy from high up in the atmosphere to the surface, whereas in general, convection transfers energy in the other direction – from the surface to higher up in the atmosphere.
So what happens and how does the first law of thermodynamics stay intact?
Very simple – every layer of atmosphere also radiates energy. This is shown as blue text and arrows in the diagram.
Each layer in the atmosphere does obey the first law of thermodynamics. But by the time we reach the top of atmosphere the upwards radiation has been significantly reduced – on average from 390 W/m² to 239 W/m².
Each layer in the atmosphere absorbs radiation from below (and above). The gases that absorb the energy share this energy via collisions with other gases (thermalization), so that all of the different gases are at the same temperature.
And the radiately-active gases (like water vapor and CO2) then radiate energy in all directions.
This last point is the key point. If the radiation was (somehow magically) only upwards then the “greenhouse” effect would not occur.
Digression – Up & Down or All Around?
You will often see explanations with “the layer then radiates both up and down” – and I think I have used this expression myself. Some people then respond:
Doesn’t it radiate in all directions? Looks like another climate science over-simplication..
This is a good point. Radiation from the atmosphere does go in all directions not just up and down.
In the radiative transfer equations this is taken into account. The simplified explanation just makes for an easier to understand point for beginners. See Vanishing Nets under Diffusivity Approximation for more about the calculation.
End of digression.
Radiation Through the Atmosphere
Solar radiation is mostly absorbed by the earth’s surface (because the atmosphere is mostly transparent to solar radiation). This heats the surface, which radiates upward. The typical radiation from the earth’s surface at 15°C measured just above it looks something like this:
The atmosphere absorbs this longwave radiation and consequently radiates in all directions. This is why, when we view the spectrum of the upward radiation at the top of atmosphere we see something like this:
Note the reversal of the x-axis direction.
The “missing bits” in the curve are the wavelengths where the radiatively active gases have absorbed and re-radiated. Some of the radiation is downward, which explains where the “missing radiation” goes.
At the surface we can measure this downward radiation from the atmosphere. See The Amazing Case of “Back Radiation” -Part One and the following two parts for more discussion of this.
But – as already stated – at each height in the atmosphere, energy fluxes are balanced:
Energy in = Energy out
Or – the difference between energy in and energy out results in increasing or decreasing temperature.
If you like, think of the atmosphere as a partial mirror reflecting a proportion of the radiation at a number of layers up through the atmosphere. It’s a mental picture that might help even though what actually happens is somewhat different.
No explanation of radiation would be complete without people saying that this argument is falsified by the fact that convection hasn’t been discussed. Just to forestall that: Convection moves heat from the surface up into the atmosphere very effectively and cools the surface compared with the case if convection didn’t occur.
But – emission and absorption of radiation still takes place. Convection doesn’t change the absorption of radiation (unless it changes the concentration of various gases). But convection, by changing the temperature profile, does change emission.
As we will see in Part Two, absorption is a function of concentration of each gas; while emission is a function of concentration of each gas plus the temperature of that portion of the atmosphere.
The atmosphere interacts with the radiation from the surface and that’s why the surface radiation has been reduced by the time it leaves the climate system.
The satellites measure the value at the top of atmosphere very comprehensively.
For those convinced that there is no “greenhouse” effect, I recommend focusing on the emissivity measurements used in the calculation of emission from the surface.
The ocean has been measured at 0.98-0.99 and covers 71% of the surface of the earth but perhaps the average surface emissivity at terrestrial temperatures is only 0.61.. A measurement snafu..
In the next part we will consider in more detail how the different effects cause changes in the OLR.
Part Two – introducing a simple model, with molecules pH2O and pCO2 to demonstrate some basic effects in the atmosphere. This part – absorption only
Part Three – the simple model extended to emission and absorption, showing what a difference an emitting atmosphere makes. Also very easy to see that the “IPCC logarithmic graph” is not at odds with the Beer-Lambert law.
Part Four – the effect of changing lapse rates (atmospheric temperature profile) and of overlapping the pH2O and pCO2 bands. Why surface radiation is not a mirror image of top of atmosphere radiation.
Part Five – a bit of a wrap up so far as well as an explanation of how the stratospheric temperature profile can affect “saturation”
Part Six – The Equations – the equations of radiative transfer including the plane parallel assumption and it’s nothing to do with blackbodies
Part Seven – changing the shape of the pCO2 band to see how it affects “saturation” – the wings of the band pick up the slack, in a manner of speaking
And Also –
Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory.
An analysis of the dependence of clear-sky top-of-atmosphere outgoing longwave radiation on atmospheric temperature and water vapor, Dessler et al, Journal of Geophysical Research (2008).
Note 1: Radiation from a surface at 15°C (288K) will have a peak radiation at 10μm with radiation following the Planck curve. The average emissivity for 288K needs to be the wavelength-dependent emissivity weighted appropriately for the corresponding Planck curve. This will be very similar for the emissivity for the same surface type at 300K or 270K but is likely be totally different for the emissivity for the surface at 3000K – not a situation we find on earth.
Note 2: The most common gases in the atmosphere, Nitrogen and Oxygen, don’t interact with longwave radiation. They don’t absorb or emit – at least, any interaction is many orders of magnitude lower than the various trace gases like water vapor, CO2, methane, NO2, etc. This is after taking into account their much higher concentration. See CO2 – An Insignificant Trace Gas? Part Two