Here we get into the nitty-gritty (as much as we can) of the energy coming off the planet. Looking at the spectrum of outgoing infrared we can learn a lot from the Nimbus data. In the graph below we can see a lot more energy comes from certain wavelengths, and given that the curve would follow the “grey” shape if it was a single body emitting, we can also see how some “pipes” are blocked.
The CO2 band shows a large obvious indentation, but don’t be fooled, most of that curve looks the same at much lower concentrations of CO2. As CO2 levels rise in our atmosphere there is little effect on the radiance of the coldest parts of the CO2 band, what changes is in the “wings”.
The hotter a thing is, the more energy it radiates, so in this graph the higher amounts of OLR (outgoing longwave radiation) are coming off the warmer surface or air closer to it. Turn things upside down in your mind, the high readings come from low-altitude places which are warm (like the surface), and as the readings get lower in radiance, they must be coming from colder spots at higher altitudes. The lowest part of the CO2 absorption band in the graph is in the stratosphere, where it’s very cold. The highest parts of the CO2 band in the graph are from CO2 low in the atmosphere. The “wings” represent emissions from CO2 all the way up and down the vertical air column.
In terms of “pipes” David has managed to estimate the comparative sizes of different pipes, with a table I haven’t seen elsewhere — which I’ve graphed here. (Though we expect the IPCC crew would have done this ).
This graphic below is roughly the size and height of the emissions escaping to space. (The CO2 height is the height of its “average” emitting temperature, which is not that useful, as most of the emissions are coming from lower down and further up rather than at the “average”. We don’t use that height in the analysis that follows.) See below how David calculated this and all his references. I’m surprised at how big the CO2 pipe is. A similar amount of energy is coming off CO2 molecules as is radiating from cloud tops or from the surface?
Don’t miss David’s figure 1 below, which is an important graph we will need to refer too. Those emission layers matter!
14. Emission Layer Parameters
We are going to add a model of outgoing longwave radiation (OLR) to the sum-of-warmings model we completed in the last post. However before we can construct the OLR model we need some basic information about OLR — such as how much OLR comes from each emission layer. In this post we collect that information from various sources.
We described how the greenhouse effect works in post 6, where we discussed emission layers and pipes. Most OLR is emitted by the four main emission layers — the CO2 emissions layer, the water vapor emission layer (WVEL), the cloud tops, and the surface. Nearly all OLR is emitted by the main four emission layers plus the ozone and methane emission layers, so in this post we are going to collect parameters on those six emission layers.
We are only concerned here with the average OLR, heights, and temperatures for each emission layer — averaged over area, time of day, time of year, and applicable wavelengths. What follows in this blog series is not terribly sensitive to these emission layer parameters, so we are a bit approximate. Several parameter values were estimated from ratios of areas on Nimbus spectra diagrams (such as Fig. 2 below). Overlaps in emission wavelengths were ignored when partitioning the Nimbus spectra between emission layers (at a given wavelength, the highest emission layer should apply). We assume that all the OLR comes from the main six emission layers.
We speak of “the emission layer” of a gas as its average, but bear in mind that the notion of the height of an emissions layer can be further refined to depend on wavelength. Viewed as wavelength-dependent, the CO2 emission layer descends from the lower stratosphere to the surface in the wide wings around 15 μm, because at wavelengths further away from an absorption line it takes a greater amount of CO2 to achieve a certain probability of absorption — see the Nimbus spectra, such as in Fig. 2 below, and note the sloping walls of the well centered on 15 μm as the temperature climbs (“the wings”). While some OLR comes from far below the emission layer (some emitted photons get lucky and escape to space despite long odds), and some from far above the emission layer (where the odds of a photon emitted upwards escaping to space are high), on average the emissions occur at about the height of the emissions layer, whose temperature and thus height we can estimate. Interestingly most of the significant changes in the emission spectrum due to increased CO2 occur in the wings of the 15 μm well, in emissions from the troposphere — see the last diagram on this page of the Barrett-Bellamy website.
Figure 1: The four main emission layers and their OLR. Most of the Earth’s OLR is emitted to space through the four pipes shown, where “pipe” is shorthand for the electromagnetic wavelengths at which a type of molecule absorbs and emits, and the associated emissions layer. (The CO2 emissions layer around the center of its blockage at 15 μm is in the lower stratosphere. But averaging by wavelength across the whole CO2 blockage gives an average temperature of about 244 K, corresponding to a height around 7 km. This is in the wings of the blockage, which also happens to be where the main changes due to increasing CO2 are occurring. Hence this depiction.)
|Emission Layer||Symbol subscript||Average Temperature||Average Height||Clear Sky OLR||Overcast Sky OLR||All Sky OLR|
|Units||K||km||W m−2||W m−2||W m−2|
|CO2||C||244 1||7||48 7||48 8||48|
|Surface 9||S||288||0||119 7||0 8||45 9|
|Cloud tops||U||267||3.3 2||0||77 8||48 9|
|Water vapor||W||236 3||8||79 7||79 8||79|
|Ozone||Z||> 15||14 7||14 8||14|
|Methane||M||268 10||3||5 7||5 8||5|
|Average or total||255 4||4.8||265 6||223||239 6|
Table 1: Parameters of the OLR emission layers. Superscripts refer to the notes below. Blue cells are calculated from average temperature or height using a lapse rate of 6.5 °C per km and a surface temperature of 288 K. Orange cells were calculated from clear and overcast skies using a cloud fraction of 62% (note 5).
- The temperature at the base of the CO2 indentation/well/blockage in the Nimbus clear sky emission spectrum (Fig. 2) from 14.4 to 15.8 μm is ~215 K, consistent with emissions from the lower stratosphere. However the emissions from the “wings” of the indentation come from lower in the atmosphere, reaching close to the surface at 13 μm and 18 μm. The average temperature, formed by weighting the temperature at each frequency by the radiance of emission in the tropical Pacific Ocean Nimbus spectrum (surface temperature ~295 K) (Glickstein 2011 ), is approximately 244 K — this temperature and the corresponding height is not used in the calculations here; it is included only for completeness.
- The cloud-top height is from the study by Davies and Molloy in 2012 . Roger Davies (personal communications, 2014) explained that the value depends on measurement technique and definition, such as whether very thin clouds are included.
- The WVEL temperature is estimated from 18 to 25 μm of the tropical Pacific Ocean Nimbus clear sky emission spectrum. The jaggedness of this part of the spectrum may arise from a combination of surface and narrow water-vapor emission bands. The temperature is presumably a mean of surface and WVEL temperatures, but the contribution from each layer is uncertain because of insufficient instrumental resolution in wavelength. The spectrum cools as wavelength increases beyond 25 μm: for instance a MODTRAN simulated emission spectra (Barrett) decreases to 220 K at a wavelength of 67 μm. Accordingly the WVEL temperature is more than 220 K but less than 260 K. The average WVEL temperature is taken here as 236 K, the minimum temperature (at ~24 μm) in the Nimbus spectra in wavelengths over 18 μm.
- The mean temperature of the emission layers is the Earth’s radiating temperature, namely 255 K.
- Kiehl and Trenberth 1997 , hereafter KT97, give the cloud fraction as 62% on p.200. Their model consists of randomly overlapped low clouds (1 – 2 km) covering 49%, midlevel clouds (5 – 6 km) covering 6%, and high clouds (10 – 11 km) covering 20% of the surface.
- KT97 (Table 2) gives the clear-sky OLR as 265 W m−2 and the all-sky OLR as 235 W m−2. Trenberth, Fasullo, and Kiehl (2009)  updated the all-sky OLR to 239 W m−2.
- Using the average of the areas under the Nimbus spectrum for the tropical Pacific Ocean (Fig. 7) (clear, daytime, surface temperature ~295 K) and the Niger Valley (clear, daytime, surface temperature adjusted down from 320 K to an assumed nighttime temperature of 300 K) below 25 μm, and the MODTRAN curve (note 3) above 25 μm, the ratios of OLR from CO2 emissions (taken to be 13–18 μm) to OLR from the surface (10–13 μm and 8.0–9.3 μm) to OLR from water vapor emissions (18–67 μm and 6.6–7.5 μm but not more than 236 K (see note 3)) to OLR from ozone (9.3–10 μm) to OLR from methane (7.5–8.0 μm) were estimated, then used to partition the total clear sky OLR in those ratios. Both surface temperatures in the Nimbus spectra were a little higher than the global mean of 288 K, so the surface OLR will be a little high by this method. See also note 9.
- Because the OLR from the CO2 emission layer depends only on the layer’s temperature, the clear-sky and overcast emissions are the same. Similarly for the water vapor, ozone, and methane emission layers. We follow KT97 in assuming the OLR from the surface is zero in overcast skies. Thus the difference in total OLR between clear and overcast skies is the same as the difference between OLR from the surface and the cloud tops.
- KT97 (p.206) give the OLR in the atmospheric window as 99 W m−2 under clear skies (so that OLR must originate near the surface), and 80 W m−2 under all-sky (so 38 W m−2 from near the surface under clear sky, and the remaining 42 W m−2 from cloud tops). Costa & Shine (2012)  show that the KT97’s clear sky OLR of 99 W m−2 consists of 66 W m−2 from the surface itself and the rest from the water-vapor continuum near the surface. However, “surface” may conveniently be taken to include the near surface because the two layers undergo the same temperature changes and because the water-vapor continuum emission altitude is determined chiefly by pressure and is invariant. Finally, KT97 take the atmospheric window as 8–12 μm, but in the Nimbus diagrams it appears to be 8–13 μm. The OLR figures from the surface and clouds tops here are a little higher, presumably due to including the OLR in 12–13 μm.
- The methane temperature is from the tropical Pacific Ocean Nimbus clear sky emission spectra 7.5–8.0 μm (Fig. 2).
The energy budget diagram in KT97 (their Fig. 7) labels 40 W m−2 of OLR as “Atmospheric Window”, and shows another 30 W m−2 of OLR coming from clouds (in contrast to 165 W m−2 of the OLR from clear air). Their 40 W m−2 is all-sky OLR from 8 to 12 μm from the surface; here it is 45 W m−2 because it is for 8 to 13 μm. Their 30 W m−2 is total clear-sky OLR minus all-sky (KT97 p. 201); here it is 34 W m−2 because we updated the total all-sky OLR from 235 to 239 W m−2 in line with Trenberth, Fasullo, and Kiehl 2009 .
Figure 2: The Nimbus emission spectrum over the tropical Pacific Ocean, partitioned approximately into emissions from various layers, ignoring overlaps. Dashed curves represent blackbody radiances at the indicated temperatures in Kelvin. From Petty 2006  Fig. 6.6, via Kaempfer 2011  and Glickstein 2011 .
[1^] Glickstein, I. (2011, March 10). Visualizing the “Greenhouse Effect” – Emission Spectra. Retrieved Aug 28, 2014, from Watts Up With That?: http://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/
[2^] Davies, R., & Molloy, M. (2012). Global cloud height fluctuations measured by MISR on Terra from 2000 to 2010. Geophysical Research Letters, L03701.
[3^] Kiehl, J. T., & Trenberth, K. E. (1997). Earth’s Annual Global Mean Energy Budget. Bulletin of the American Meteorological Society, 198 – 208.
[4^] Trenberth, K. E., Fasullo, J. T., & Kiehl, J. (2009). Earth’s Global Energy Budget. Bulletin of the American Meteorological Society, March, p. 311.
[5^] Costa, S. M., & Shine, K. P. (2012). Outgoing Longwave Radiation due to Directly Transmitted Surface Emission. American Meteorological Society.
[6^] Petty, G. W. (2006). A First Course in Atmospheric Radiation, 2nd Edition. Sundog Publishing.
[7^] Kaempfer, N. (2011, May 24). Atmospheric Physics Remote Sensing. Retrieved October 15, 2014, from IAP Microwave Physics, University of Bern: http://www.iapmw.unibe.ch/teaching/vorlesungen/atmosphaerenphysik/FS_2011/AT_FS11_Remote_sensing_1_handout.pdf