Analyzing the Earth’s Heat Radiation Using MODTRAN
Update
By Ed Caryl
The Climate Team has always claimed that a doubling of CO2 would add 3.7 Watts/m2 to the
global climate budget and thus this would fry us all. This fate is their religion’s version of Hell,
except we will all suffer this rather than just the “sinners,” thus giving them leverage to force us
to do their will. Many bloggers, and some others, notably even the Berkley Earth Surface
Temperature (BEST) study,i have pointed out that there are many locations that are cooling
rather than warming. The warmists would have us believe that these cooling stations are just due
to local phenomenon, such as albedo change, land use, site moves, or other changes, and that the
warming stations are not due to UHI.
The greenhouse effect is described as an increase in downward infrared radiation due to water
vapor, carbon dioxide, methane, ozone, and CFC’s in the atmosphere. But strangely, there are
very few measurements of this radiation to tell us if this is true, measuring the spectrum. Each of
the above gases absorbs and re-emits radiation at specific wavelengths. These emission lines
should change when the mixture of gases changes. A spectrometer designed to operate at these
wavelengths will tell us if this is true.
MODTRAN is a computer program that was initially developed by the US Air Force in the late
1980’s that does a line-by-line analysis of the IR spectrum transmitted by the atmosphere. An online version is available at the University of Chicago, here.ii
In the previous versions of this paper, the relative humidity inputs were entered in MODTRAN
directly in percent. At least two comments were received that pointed out the humidity input
should have been a scaling factor on the humidity provided by the model selected. Such is the
value of on-line peer review. A search was performed for the humidity provided by the models.
All that was found was a one-sentence statement that for all the models, surface relative humidity
was ≦80%. No further data could be found. This author has emailed the University of Chicago
for information, but no answer has been received as of this writing. In this document we have
used 80% as the humidity with a scale factor of 1, and all humidity values have been scaled to
that. The result now makes sense, and more closely agrees with observations.
In the 24 year history of MODTRAN, the US Air Force and many other organizations, including
climate scientists, have validated the software for their own purposes. The best way to prove that
it is valid for climate studies, is to show comparable spectra from other sources.
Infrared astronomers are quite familiar with the problem of atmospheric IR. IR astronomy is not
easily done on the earth’s surface because the lower atmosphere is nearly opaque to IR because
of moisture in the air. Consequently IR astronomy is done at high altitudes, at very cold, or at
very dry locations, or all three. The Atacama Desert in Chile, the top of Mauna Kea in Hawaii,
the south pole, airborne observatories, or satellites are the favored locations.
The web was searched for any image of this “back radiation” spectrum. None were found for any
temperate or tropical zone. The only spectra found are from the Arctic at -10°C, and the south
pole at -30°C. From the spectral shape, it appears that the Arctic data was taken at Summit Camp
on the Greenland ice sheet. Those are the next figures with the MODTRAN version for
comparison.
Figure 1a and b
The 1a is from Petty (2006), found at skepticalscience here.iii 1b is from MODTRAN. The
scaling is slightly different, the resolution is not as high, the shape is very nearly the same.
Figure 2a and b
Figure 2a from South Pole station here.iv The bottom trace is 1 standard deviation. figure 2b is
from MODTRAN.
At sea level, with a clear sky, temperature at 15°C, 50% humidity, and 400 ppm CO2, in other
words, conditions that apply over much of the earth, the spectrum of downward IR, the back
radiation from the sky, looks like this.
Figure 3
The atmospheric back radiation reported by MODTRAN (sensor looking up). This spectrum (the
red trace) is simply the black-body radiation from all gases, water vapor and CO2, in the
atmosphere.
Figure 4
The same MODTRAN settings as in figure 3 with zero CO2. The CO2 peak disappears.
Over most of the earth, figure 3 is the spectrum seen by a spectrometer looking at the sky. Only
at very cold, very dry, and/or very high locations will the spectra be much different from a black
body. The available literature use either figure 1a or 2a over and over, with their deep notch due
to lack of water vapor, as if those spectra represent the whole globe. They do not.
From the top of the atmosphere we have a similar situation. The available spectra are taken over
deserts. The following figure is from the University of Chicago web site here,v and is a
comparison of the IRIS Satellite spectra with MODTRAN set for desert conditions. If
MODTRAN had been set for the exactly the same temperature and humidity as the satellite had
observed, the match would have been nearly exact.
Figure 5
This is a screen grab from the University of Chicago web site, here.
Why CO2 Does Less Than Water Vapor
When I first began exploring MODTRAN, the numbers it produced for downward radiation at
the surface, the back radiation, seemed to make no sense. It nearly always produced the same
number, and I thought that perhaps that part of the program was broken. On reflection, it became
clear that the numbers were correct and that I had fallen into the warmist trap of believing that
CO2 really does something to the Greenhouse effect. When the numbers in the very low
humidities were charted, all became clear.
Here is what Modtran says about downward or back radiation at the earth’s surface for values of
humidity from 0 to 80% and CO2 from 0 to 1000 ppm.
Figure 6
There is very little change in the downward radiation for any humidity from 40% and above and
for any CO2 concentration from 50 to 1000 ppm, or indeed for any concentration of CO2 up to
10,000 ppm.
Here are the Excel numbers copied from MODTRAN used to draw the above chart.
Figure 7
As you can see, only in the driest desert on earth will increasing CO2 increase the back radiation
very much. Water vapor is by far the strongest greenhouse gas, but it is nearly saturated above
10% humidity. At 10% humidity and above, no amount of CO2 does very much. Most of the
humidity on earth is in that area on the right of figure 6, where doubling CO2 will do little to
increase the long-wave radiation from the sky. Yet another CAGW fail.
Why the Earth is Cooling
Here is the result of calculating the outbound long-wave radiation (OLR) at the top of the
atmosphere (TOA), or as it is labeled in MODTRAN, I out. The settings used were: CH4 - 1.8
ppm, Tropical Ozone 800 ppb, Strat. Ozone 1, Ground T offset - 0°C, hold water vapor Relative Humidity, Water Vapor Scale - at 1, 0.5, 0.1, 0.05, 0.01, 0.005, and zero; representing
80%, 40%, 8%, 4%, 0.8% and zero, Locality - 1976 U. S. Standard Atmosphere, No Clouds or
Rain, Sensor altitude 70 km, Looking Down. These values are the best at representing a global
average. The default temperature the program uses is 15°C. This produced the following table
and chart for various CO2 and water vapor values. Lesser values mean less heat escapes the earth
and the earth warms. This is the greenhouse effect.
Figure 8
TOA OLR for CO2 values from 0 to 1000 ppm and RH at 0, 0.08, 4, 8, 40, and 80%.
Figure 9
A chart of the previous table, MODTRAN output for 0, .08%, 4%, 8%, 40%, and 80% humidity,
and CO2 from 0 to 1000 ppm. The radiation (vertical) scale has been inverted so that increasing
greenhouse warming is upward. Note that both CO2 and water vapor forcing are logarithmic;
increasing amounts have decreasing effect.
With humidity set to zero, the doubling of CO2 figure actually goes to 3.297 W/m2. Any
reasonable humidity value drops that number. At the default 80% humidity, and our current CO2
value, we get 2.732 W/m2, 1 W/m2 below the IPCC favored value. Of course humidity doesn’t
stay constant, and this is all before the additional factors of clouds and rain, which will drop the
value even further into the negative territory that Willis Eschenbach noticed here.vi The dark blue
diamond in the chart and the blue value in the table are the current values with today’s CO2 and
global average humidity.
Given the data, MODTRAN can compute the outbound radiation over time due to humidity and
CO2 changes alone over time. The humidity at 600 mbars and the Mauna Loa CO2 values were
applied through MODTRAN to result in figure 10. This is a “zoom in” on the blue diamond in
figure 9, adding the time dimension. The 600 mbar level for humidity seemed a good
compromise, as only one humidity figure could be entered.
Figure 10
A chart of the outbound radiation increase since 1948. There has been a 0.8 Watt/m2 swing in
outbound radiation in that interval, but the changes bear little relationship to rising CO2. In fact,
the long term trend is cooling. Downward is cooling, upward is warming in this chart. The
change in humidity has easily overcome the increase in CO2.
Figure 11
Humidity has been decreasing in the upper atmosphere over the last 60 years by nearly 10%.
That offsets the rising CO2. We see the cooling in the 60‘s, 70’s, and 80’s, but increased solar
radiation along with ocean cycles held off the cooling over the last 20 years. That cooling has
now resumed.
Figure 12
Figure 12 shows the measured OLR over part of the interval shown in figure 10. There is a
difference in the baseline level, and the slope of the last 35 years, as well as much more
variation, due to factors not considered in the MOTRAN model, such as clouds, rain, albedo
changes, volcanic activity, etc.
None of the charts and graphs you will see in the climate literature touting global warming
caused by CO2 will include considerations that atmospheric water vapor might change as well. If
they do consider water vapor, the warmists believe that a warmer climate caused by CO2 will
increase water vapor. The problem with this is, first, it isn’t warming, second, humidity is
decreasing, and third, the sun keeps changing output.
Mother Earth has an excellent thermostat system. If somehow average humidity should increase
to 50% and CO2 increased to 800 ppm, then about 3.75 Watts/m2 heat would be added, in line
with the IPCC scenario. (The generally agreed translation of a change in radiation to a change in
temperature is a change of 1 W/m2 = a change of 0.8° to 1°C.) This much increase in humidity
and CO2 is unlikely in view of past trends, but would add about 3°C to warming. A more likely
scenario is that average global humidity will fall further, to about 40%, CO2 tops out at 600 ppm,
adding only 0.5 W/m2, perhaps resulting in a rise of about 0.5°C if nothing else changes. But
other things are changing. The sun is moving into a quiet period, perhaps subtracting 0.5 W/m2
from that, and ocean cycles are moving into cooler modes, which may more than completely
offset even this modest warming.
In light of figure 10, why have we not seen global cooling? We did in the period up to 1995.
Since then, the answers are humidity changes, clouds, and the sun (and constant temperature
record adjustments by GHCN, GISS, UEA, etc.). With falling humidity at nearly all levels in the
atmosphere, there are fewer clouds. This allows more solar radiation to reach the surface,
compensating for the radiation leaving the TOA. Fewer clouds also allows more radiation from
the surface to space. It all balances out. A link to more reading on this, here.vii
i
http://berkeleyearth.org/pdf/uhi-revised-june-26.pdf
http://forecast.uchicago.edu/Projects/modtran.html
iii http://www.skepticalscience.com/print.php?r=92
iv http://journals.ametsoc.org/doi/pdf/10.1175/JCLI3525.1
v http://forecast.uchicago.edu/Projects/modtran.doc.html
vi http://wattsupwiththat.com/2012/06/19/a-demonstration-of-negative-climate-sensitivity/
vii http://wattsupwiththat.com/2012/04/04/spencers-posited-1-2-cloud-cover-variation-found/
ii