Archive for April, 2011

In his excellent book, A First Course in Atmospheric Radiation, Grant Petty introduces a number of spectral measurements of atmospheric radiation which are very illuminating.

In this article I am going to reproduce them, along with a lot of Petty’s comments and explanations – hard to improve on what he has to say. (See the book recommendation).

For people confused about how the atmosphere absorbs and emits radiation these might be helpful. For people spreading confusion about how the atmosphere absorbs and emits these will be hard to explain.

Grant Petty (2006)

From Grant Petty (2006)

Figure 1 – The atmosphere above Nauru and Alaska under cloud-free conditions

A few basics first of all – if the atmosphere didn’t emit radiation then the upward looking spectrometer would measure a flat line at zero, as the (extremely low) emission from space at 3K would not even register on the spectrometer. (Note 1).

So where we see very low radiance measurements this is because the atmosphere is transparent at these wavelengths/wavenumbers. (Note 2).

Nauru is in the tropical western Pacific where atmospheric temperatures are warm and humidity is high. Barrow is in the Arctic, and so temperatures in winter are very cold and the atmosphere contains only small amounts of water vapor.

1. The two dashed curves are the Planck function (note 3) at the warmest atmospheric emission seen by the spectrometer at each location.

2. In the tropical example there are two spectral regions where the measured radiance is very close to the 300K reference curve: >14 μm (<730 cm-1 ) and <8 μm (>1270 cm-1). Therefore, the atmosphere must be quite opaque in these bands because the radiation is being emitted from the warmest – and, therefore, lowest – levels of the atmosphere. The >14 μm region is the region of strong absorption of CO2 and, above 15 μm, of water vapor, and the <8 μm region is the water vapor region.

3. In the arctic example we can also see these two water vapor regions, but it’s clear that these are somewhat weaker, with variable radiance. This is because the water vapor concentration is much lower in the colder arctic.

4. In the tropical example, in the region from 8 – 13 μm, the radiances are well below the 300K reference curve and in some cases even a little below the 245K reference curve – this is because the atmosphere is quite transparent in this region.

5. In the arctic example this is much clearer. The 8 – 13 μm region (with the exception of 9.6 μm) is almost at zero radiance because, with much lower water vapor concentration, the spectrometer is almost measuring the radiance of space.

6. The 9.6 μm region in both examples is due to ozone emission. It’s not as obvious in the tropical example because water vapor emission extends across this band.

7. The 15 μm band in the arctic example has an interesting feature. At the center of the band the radiance is a little lower than at the edges of the band. Why is this? The center of the band is the most opaque so it should be measuring the temperature of the lowest levels of the atmosphere, almost at the surface. And the edges of the band – a little less opaque – should be measuring the temperature a little higher up. The reason is that in the arctic in wintertime it is very common to see a temperature inversion, where the surface is colder than the atmosphere a few hundred meters above.

Now let’s review a very interesting pair of measurements. One from 20km looking down – with the simultaneous surface measurement looking up:

From Grant Petty (2006)

From Grant Petty (2006)

Figure 2 – Upwards and downwards measurements at the polar ice sheet

Petty now asks a few questions – in the manner of all good textbook writers. I attempt to answer these questions and if I embarrass myself by getting them wrong, please speak up. I know someone will..

a) what is the approximate temperature of the surface of the ice sheet and how do you know?

b) what is the approximate temperature of the near-surface air, and how do you know?

c) what is the approximate temperature of the air at the aircraft’s flight altitude of 20km, and how do you know?

d) identify the feature seen between 9 – 10 μm in both spectra

e) in fig 1 (fig 8.1) we saw evidence of a strong inversion in the near-surface atmospheric temperature profile. Can similar evidence be seen here?

If you want to check your understanding – try and answer the above questions before reading on. Anyway, you can’t rely on my answers..

My answers, for review:

a) the surface temperature is approx. 268K. The atmosphere is most transparent at 900 cm-1 & 1150 cm-1, so, looking downward at these wavelengths we should see the surface emission. And ice, like water, emits at very close to a blackbody at these wavenumbers.

b) the near surface temperature is approx. 268K. Looking upwards where the atmosphere is most opaque (15 μm) we should see the temperature of the atmosphere closest to the surface. At 15 μm we see a temperature of 268K.

c) the approx. temperature of the air at 20km is 225K. Looking downward from the aircraft where the atmosphere is most opaque (15 μm) we should see the temperature of the atmosphere closest to the measurement device. At 15 μm we see a temperature of 225K (corrected Jan 28th, 2014 thanks to Mike B). Note that we don’t want to rely on the brightness temperature seen at the strongest water vapor absorption (<8 μm) because the water vapor concentration is low when the atmosphere is very cold.

d) the feature seen between 9 – 10 μm in both spectra is the ozone absorption. In the downward looking spectrum from the aircraft we see a colder brightness temperature than the rest of the 8 – 13 μm band – because the rest of the band is viewing the surface, while the ozone absorption centered at 9.6 μm sees the atmosphere much closer to the aircraft. Looking upwards from the surface, the rest of that band sees (very cold) space, while the ozone band reflects the temperature of the lower stratosphere, around 235K.

e) No.

Lastly, four satellite spectra (upwards radiance) from different locations:

From Grant Petty (2006)

From Grant Petty (2006)

Figure 3 – Four satellite measurements from different locations

Notice the 15 μm radiance compared with the surrounding band. Remember that the stratosphere warms from the tropopause to the stratopause:

From Grant Bigg (2005)

Figure 4 – Temperature profile of the atmosphere

The reason the brightness temperature (radiance) for the first graph – the Sahara – is at the low temperature of 215K between 14-16 μm is because the satellite is measuring the temperature of the region around the tropopause. But at the very opaque 15 μm the satellite is measuring even closer to itself – higher up in the stratosphere, which is why the brightness temperature is around 230K.

Contrast that with the Antarctic (2nd graph in Fig 3). There we see that the ice sheet is colder than the stratosphere. This is why the 15 μm radiance is higher than the radiance at all the other wavelengths.

If you compare c)  Tropical Western Pacific with d) Southern Iraq you can see the effect of water vapor. In the desert of Southern Iraq where the water vapor is low the radiance is measured from close to the surface – and therefore, is high. In the Western Pacific, where the water vapor concentration is much higher, the radiance is measured from closer to the satellite, i.e., higher up in the atmosphere, where the temperature is lower, and so is the radiance.

Comparing c) and d) for the 15 μm radiance you see that they are almost the same. Water vapor is overwhelmed by CO2 in this region and so water vapor concentration has no effect here.


Even though water vapor and CO2 are present in very low concentrations, they have a very strong radiative effect.

This is not something which is a subject of debate in spectroscopy or in atmospheric physics. The fact that many people find it difficult to understand how a gas present in 360ppm concentrations can have such a strong effect is of no scientific interest. This is because it isn’t a scientific argument.

The changing transparency/emissivity of the atmosphere at various wavelengths provides us with very valuable information about:

a) the concentration of water vapor

b) the temperatures at different heights in the atmosphere

Other articles:

Part One – a bit of a re-introduction to the subject.

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

Part Eight – interesting actual absorption values of CO2 in the atmosphere from Grant Petty’s book

Part Nine – calculations of CO2 transmittance vs wavelength in the atmosphere using the 300,000 absorption lines from the HITRAN database

Part Ten – spectral measurements of radiation from the surface looking up, and from 20km up looking down, in a variety of locations, along with explanations of the characteristics

Part Eleven – Heating Rates – the heating and cooling effect of different “greenhouse” gases at different heights in the atmosphere

Part Twelve – The Curve of Growth – how absorptance increases as path length (or mass of molecules in the path) increases, and how much effect is from the “far wings” of the individual CO2 lines compared with the weaker CO2 lines

And Also –

Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory.


Note 1: If it was daytime and the sun was directly overhead (not possible in Barrow, Alaska in March) then the sun’s radiance would add about 1 mW/m2.sr.cm-1 at 1000 cm-1, 1.7 mW/m2.sr.cm-1 at 1400 cm-1 (right hand edge of the graph), and 0.1 mW/m2.sr.cm-1 at 300 cm-1 (left edge of the graph).

Note 2: According to Kirchhoff’s law, if the atmosphere absorbs at any wavelength it also emits at that wavelength – and in equal strength. Absorptivity = Emissivity (but very very important, at the same wavelength, or range of wavelengths). See Planck, Stefan-Boltzmann, Kirchhoff and LTE.

This means that if the atmosphere is transparent at any given wavelength it doesn’t emit at that wavelength. And if it is opaque at any given wavelength it is a strong emitter.

If the absorptivity = 1 at any wavelength (or range of wavelengths) then the emissivity = 1 at that wavelength, meaning it emits like a blackbody at that wavelength.

Note 3: The Planck function is the formula for emission of thermal radiation from a blackbody – a perfect emitter and perfect absorber. There is plenty of unscientific confusion about blackbodies on the web. A blackbody is simply the maximum radiator for any given temperature. Nothing can radiate with a greater intensity at any wavelength than a blackbody and while no real surface is a perfect blackbody many surfaces come close. For example, the ocean has an emissivity of about 0.96. The atmosphere – at some wavelengths – emits very close to a blackbody, while at other wavelengths it is almost transparent and, therefore, the emissivity is close to zero.

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