The earth’s surface is not a black-body. A blackbody has an emissivity and absorptivity = 1.0, which means that it absorbs all incident radiation and emits according to the Planck law.
The oceans, covering over 70% of the earth’s surface, have an emissivity of about 0.96. Other areas have varying emissivity, going down to about 0.7 for deserts. (See note 1).
A lot of climate analyses assume the surface has an emissivity of 1.0.
Let’s try and qualify the effect of this assumption.
The most important point to understand is that if the emissivity of the surface, ε, is less than 1.0 it means that the surface also reflects some atmospheric radiation.
Let’s first do a simple calculation with nice round numbers.
Say the surface is at a temperature, Ts=289.8 K. And the atmosphere emits downward flux = 350 (W/m²).
- If ε = 1.0 the surface emits 400. And it reflects 0. So a total upward radiation of 400.
- If ε = 0.8 the surface emits 320. And it reflects 70 (350 x 0.2). So a total upward radiation of 390.
So even though we are comparing a case where the surface reduces its emission by 20%, the upward radiation from the surface is only reduced by 2.5%.
Now the world of atmospheric radiation is very non-linear as we have seen in previous articles in this series. The atmosphere absorbs very strongly in some wavelength regions and is almost transparent in other regions. So I was intrigued to find out what the real change would be for different atmospheres as surface emissivity is changed.
To do this I used the Matlab model already created and explained – in brief in Part Two and with the code in Part Five – The Code (note 2). The change in surface emissivity is assumed to be wavelength independent (so if ε = 0.8, it is the case across all wavelengths).
For the tropical atmosphere:
- ε = 1.0, TOA OLR = 280.9 (top of atmosphere outgoing longwave radiation)
- ε = 0.8, TOA OLR = 278.6
- Difference = 0.8%
Here is the tropical atmosphere spectrum:
We can see that the difference occurs in the 800-1200 cm-1 region (8-12 μm), the so-called “atmospheric window” – see Kiehl & Trenberth and the Atmospheric Window. We will come back to the reasons why in a moment.
For reference, an expanded view of the area with the difference:
Now the mid-latitude summer atmosphere:
- ε = 1.0, TOA OLR = 276.9
- ε = 0.8, TOA OLR = 272.4
- Difference = 1.6%
And the mid-latitude winter atmosphere:
- ε = 1.0, TOA OLR = 227.9
- ε = 0.8, TOA OLR = 217.4
- Difference = 4.6%
Here is the spectrum:
We can see that the same region is responsible and the difference is much greater.
The sub-arctic summer:
- ε = 1.0, TOA OLR = 259.8
- ε = 0.8, TOA OLR = 252.7
- Difference = 2.7%
The sub-arctic winter:
- ε = 1.0, TOA OLR = 196.8
- ε = 0.8, TOA OLR = 186.9
- Difference = 5.0%
We can see that the surface emissivity of the tropics has a negligible difference on OLR. The higher latitude winters have a 5% change for the same surface emissivity change, and the higher latitude summers have around 2-3%.
The reasoning is simple.
For the tropics, the hot humid atmosphere radiates quite close to a blackbody, even in the “window region” due to the water vapor continuum. We can see this explained in detail in Part Ten – “Back Radiation”.
So any “missing” radiation from a non-blackbody surface is made up by reflection of atmospheric radiation (where the radiating atmosphere is almost at the same temperature as the surface).
When we move to higher latitudes the “window region” becomes more transparent, and so the “missing” radiation cannot be made up by reflection of atmospheric radiation in this wavelength region. This is because the atmosphere is not emitting in this “window” region.
And the effect is more pronounced in the winters in high latitudes because the atmosphere is colder and so there is even less water vapor.
Now let’s see what happens when we do a “radiative forcing” calculation – we will do a comparison of TOA OLR at 360 ppm CO2 – 720 ppm at two different emissivities for the tropical atmosphere. That is, we will calculate 4 cases:
- 360 ppm at ε=1.0
- 720 ppm at ε=1.0
- 360 ppm at ε=0.8
- 720 ppm at ε=0.8
And, at both ε=1.0 & ε=0.8 we subtract the OLR at 360ppm from OLR at 720ppm and plot both differenced emissivity results on the same graph:
We see that both comparisons look almost identical – we can’t distinguish between them on this graph. So let’s subtract one from the other. That is, we plot (360ppm-720ppm)@ε=1.0 – (360ppm – 720ppm)@ε=0.8:
Figure 6 – same units as figure 5
So it’s clear that in this specific case of calculating the difference in CO2 from 360ppm to 720ppm it doesn’t matter whether we use surface emissivity = 1.0 or 0.8.
The earth’s surface is not a blackbody. No one in climate science thinks it is. But for a lot of basic calculations assuming it is a blackbody doesn’t have a big impact on the TOA radiation – for the reasons outlined above. And it has even less impact on the calculations of changes in CO2.
The tropics, from 30°S to 30°N, are about half the surface area of the earth. And with a typical tropical atmosphere, a drop in surface emissivity from 1.0 to 0.8 causes a TOA OLR change of less than 1%.
Of course, it could get more complicated than the calculations we have seen in this article. Over deserts in the tropics, where the surface emissivity actually gets below 0.8, water vapor is also low and therefore the resulting TOA flux change will be higher (as a result of using actual surface emissivity vs black body emissivity).
I haven’t delved into the minutiae of GCMs to find out what they assume about surface emissivity and, if they do use 1.0, what calculations have been done to quantify the impact.
The average surface emissivity of the earth is much higher than 0.8. I just picked that value as a reference.
The results shown in this article should help to clarify that the effect of surface emissivity less than 1.0 is not as large as might be expected.
Note 1: Emissivity and absorptivity are wavelength dependent phenomena. So these values are relevant for the terrestrial wavelengths of 4-50μm.
Note 2: There was a minor change to the published code to allow for atmospheric radiation being reflected by the non-black surface. This hasn’t been updated to the relevant article because it’s quite minor. Anyone interested in the details, just ask.
In this model, the top of atmosphere is at 10 hPa.
Some outstanding issues remain in my version of the model, like whether the diffusivity improvement is correct or needs improvement, and the Voigt profile (important in the mid-upper stratosphere) is still not used. These issues will have little or no effect on the question addressed in this article.
Note 3: For speed, I only considered water vapor and CO2 as “greenhouse” gases. No ozone was used. To check, I reran the tropical atmosphere with ozone at the values prescribed in that AFGL atmosphere. The difference between ε = 1.0 and ε = 0.8 was 0.7% – less than with no ozone (0.8%). This is because ozone reduces the transparency of the “atmospheric window” region.