14 February 2020
Do Additional Greenhouse Gases Warm or Cool the Earth?
If the Earth’s atmosphere had no infrared-active gases, commonly
and confusingly called greenhouse gases, at all, the Earth would be colder on
average. The Earth’s surface would
absorb more of the sun’s insolation, since water vapor would not be present to absorb
the incoming energy from the sun and there would be no clouds. Some of the heat absorbed by the surface
would still be transferred to the nitrogen, oxygen, and argon molecules or
atoms striking the Earth’s surface. The
remaining energy would be radiated from the surface. Virtually all the energy radiated from the
Earth’s surface would travel at the speed of light through the atmosphere into
space and be almost instantaneously lost.
The day to night temperature changes would be much more dramatic than
they are now. The greenhouse gases benefit
us greatly by moderating the day to night temperature changes. At sufficiently low concentrations, each
infrared gas with a non-overlapping absorption frequency with respect to other
infrared-active gases already present, will slow down the rate of cooling at
the surface and in the troposphere. This
allows the surface and the troposphere to be warmer than they would be were the
infrared-active gas not present.
This is how the idea of a greenhouse effect comes
about. This paper Is not disputing that
infrared active gases allow the Earth’s surface to be warmer than it would be if
they were not in the atmosphere. The
question being examined is whether the further addition of an infrared-active
gas will warm or cool the Earth’s surface and its lower atmosphere, the
troposphere, when its atmospheric concentration is increased.
How does a low concentration of an infrared-active gas
significantly slow down the cooling rate of the surface and the
troposphere? Suppose this gas molecule
absorbs the longwave thermal radiation emitted from the Earth’s surface in the
lower troposphere and enters an excited vibrational state. If that absorbed energy were simply
immediately re-emitted and carried off the previously absorbed energy at the
speed of light, the absorption event would have no significant effect on the
temperature of the surface. The key fact
here is that the excited molecule has billions of collisions per second with
the 2500 times as plentiful non-infrared-active molecules of nitrogen and
oxygen and atoms of argon. That absorbed
infrared energy is converted into kinetic energy passed to the molecules that
collided with the excited molecule long before the lifetime of the excited
molecule for re-emission of the absorbed energy by radiation. What is the overwhelmingly dominant means of
energy transport through the troposphere at this point? It is the convection transport from warmer to
cooler portions of the atmosphere, which is generally upward and to the higher
latitude regions of the Earth. The speed
of that transport of energy is about 8 orders of magnitude slower than the
speed of light. So that first act of
longwave thermal radiation absorption from the Earth’s surface is of immense
importance, but after that initial conversion of infrared radiation from the
surface into kinetic energy shared by all the molecules (mostly nitrogen and
oxygen) and atoms (argon mostly) of our troposphere, the role of any further
radiation from infrared-active molecules is a faster means of cooling than is
the convection cooling mechanism.
Let us examine why this is true. If the mean free path for absorption of a
given wavelength of the longwave thermal radiation from the surface is short
enough that there is an absorption event by an infrared molecule in the lower
troposphere, subsequent absorptions of any emitted thermal radiation by
molecules at that wavelength at higher altitudes will prevent that radiation
from escaping into space. This does slow
down the cooling of the lower atmosphere in this very limited context. This is what the standard view of greenhouse
gases focusses on. The problem is that
the alternative to that infrared-active gas emitting thermal radiation to a
higher altitude is its being much, much more slowly transported to higher
altitude by convection. Adding more of
that infrared-active gas to the atmosphere results in moving energy upward
through the troposphere in steps at the speed of light instead of having more
of it moving upward in the slow convection currents. The implication here is that a very low
concentration of an infrared gas in the atmosphere will produce a warmer Earth
surface and troposphere, but subsequent additions simply speed up the transport
of energy to higher altitudes. Then the
added infrared emitting gas molecules in the upper troposphere and the
stratosphere radiate thermal energy at a faster rate directly into space. For an infrared-active molecule, the initial
effect of adding it to the atmosphere is likely to be warming effect, but its
warming effect rapidly passes through a maximum and then further additions
start bringing down the temperature at the surface and in the troposphere.
Let us pause and get a better understanding of how carbon
dioxide absorbs longwave radiation from the surface of the Earth. An infrared-active molecule has an absorption
spectrum over a range of wavelengths with absorption probabilities varying with
wavelength over orders of magnitude. The
absorption probability at a wavelength is usually given in terms of an
effective cross section, as though the size of the molecule were different for
the absorption event at each wavelength.
Here, from a figure in Prof. Howard “Cork” Hayden’s The Energy
Advocate, February 2020 (Vol.24, No.7) is the absorption spectrum near
the main 15 µm
(micrometer) absorption line for CO2:
As Prof. Hayden explains, if the concentration of carbon
dioxide in the atmosphere were only 40 ppm by volume (ppmv) or a bit less than
one-tenth the present concentration, any radiation at the wavelengths above the
red line in the figure at 1 x 10-22 m2 cross-section
would be absorbed within a travel distance of 10 meters. At that same very low concentration of CO2,
the absorption distance for radiation in the weaker absorption peaks above the
lowest red line is less than 100 meters.
The troposphere in the U.S. Standard Atmosphere is 11,000 meters in
altitude. All parts of the absorption
spectrum above the lower red line for as low a concentration of carbon dioxide
as 40 ppmv are already absorbed many times traveling through the troposphere
from the surface to the upper troposphere.
At 400 ppmv, carbon dioxide will add absorption events for the first
time in the lower cross-section parts of the spectrum, but the additional first
time absorptions are decreasing rapidly as more CO2 is added to the
atmosphere, while the rapid transport effects of carbon dioxide are moving more
and more energy to space more quickly than convection would at an increasing
rate as CO2 is added.
I am going to develop a simple model for how the
infrared-active gases warm the Earth, according to those who believe in
catastrophic or even moderate man-made global warming. This is not a model that I believe is
correct. This is intended as an exercise
in determining a very generous upper limit on the size of the greenhouse gas
warming claims based on additions of such gases to the atmosphere above those of
the present and then showing that those claims are false in the context I have
set up above.
I will start with a two layer atmosphere in which radiation
from the Earth’s surface, is absorbed entirely in the lower layer L1, which
radiates half that energy upward to atmospheric layer L2 where it is absorbed
and half back down to the surface where all of it is absorbed. All of the surface absorbed half from L1 is
re-emitted upward and is re-absorbed in L1.
Layer L2 emits half the energy it absorbed from L1 directly to space,
where it is permanently lost, and half back to L1 where all of it is absorbed. Each layer L1 and L2 always emits half of its
absorbed radiation energy upward and half downward. The surface always emits its absorbed energy
back to L1, where it is absorbed. I
believe this isotropic emission idea is incorrect, but we are going to do this
exercise because it will give us insight and because it is rather a fun task to
work out. Note also that I am entirely
ignoring convection as an energy transport mechanism for the sake of this
argument.
The results are that space receives a series of emission
energy originating with an emission of one unit of energy from the Earth’s
surface, Sp, whose sum is
So, all of the unit of energy emitted
from the surface is eventually emitted into space. In fact, the first 5 emissions to space
already total 0.7627 of the total energy of 1.
In this crazy model we have assumed all the energy emitted from the
surface is absorbed in L1, despite the fact that the atmospheric window
actually allows about 70% of all surface radiated longwave energy to pass
through the atmosphere unabsorbed and directly into space. So Sp really equals 0.3 and the first five
emissions to space really equal 0.2288. In
this simple model with no thermalization of the absorbing molecule and no significant
half-life before it re-emits energy as radiation, sending more than 3/4ths of
the surface emitted energy into space takes about the time it would take
radiation traveling at the speed of light, 3 x 108 m/s, to travel
through the troposphere about 11,000 m high five times. That time is 3.7 x 10-5 s. In comparison, it takes hours for the
alternative heat dissipation process of convection currents to raise surface
energy to the top of the troposphere where it can be directly emitted to space
as radiation.
Of course, the catastrophic man-made
global warming argument does not emphasize the speed with which energy is
emitted to space by a radiation-centric model.
They emphasize the added time radiation energy spends near the surface
because of their isotropic emission model in comparison to the time it would
take to go directly from the surface to space if there were no infrared-active
molecules. So what enhancement of
radiative energy dwell time are they getting?
With this two atmospheric absorption layer model it would be that the
sum of radiation back to the surface from L1, Su, is
This means that the energy dwell time in
the lower troposphere has been doubled by this two-layer 100% radiative energy
loss model with isotropic emission. But
keeping about 76% of this energy around for about 3.7 x 10-5 s is
not such a big deal.
What if we put three atmospheric
absorbing layers into the model? Then I
find that the series of emissions to space from the top layer L3 is
Sp = 1/8 + 1/8 + 7/64 + 3/32 + 41/512 + 35/512
+ 239/4096 + 577/16384 + ….
These first eight terms sum to 0.695129,
so with eight emissions from L3 to space 69.5% of the unit of energy emitted
from the surface has been lost to space.
Consequently, 69.5% of the energy is lost in about 8 (11,000 m) / 3 x 108
m/s or 2.9 x 10-4 s.
Su = ½ + 3/8 + 5/16 + 17/64 + 29/128 +
99/512 + 169/1024 + 577/4096 + 1731/16384 + …..
The first eight terms of Su sum to 2.01898. So when Sp is a bit over 2/3 after eight
terms and must sum to one, Su is a bit over 2 and seems most likely to sum to
about 3.
So, let us make a leap here and assume
that with an atmospheric absorption model of n layers with isotropic emission,
Su will sum to about n. [If someone has
the time to work this series out to more terms or can find a way to solve it
exactly, I would enjoy seeing the result.]
Alright now, let us assume that we have
100 absorption layers in our atmosphere, corresponding to an absorption distance
of about 110 m. Most of the radiation
energy emitted from the surface will find its way to space in less time than
100 (11,000) / 3 x 108 = 3.7 x 10-3 s. If you have 10,000 atmospheric absorption
layers (an absorption distance of about 1.1 m), the time is then 0.37 s. But the alternative means of removing that
energy to space is convection and that takes hours to do the job.
In fact, radiation between the layers only occurs long after
an absorption event during which time many, many collisions with other
molecules would occur and the absorbing molecule would give up virtually all
the energy it had absorbed from radiation from another layer to the 2500 times
as plentiful non-greenhouse gas molecules in the air. It is a comparatively very long time before
the infrared-active molecule emits radiation again. In the meantime, it is only 1/2500 of the
molecules moving energy as part of a convection current. Yet insofar as these infrared-active
molecules do emit radiation, they are acting to speed up the emission of
surface energy to space. They are
therefore acting to cool the atmosphere from top to bottom of the troposphere
compared to the convection energy transport mechanism.
The lesson here is that the very first absorption event of
thermal radiation from the surface in the atmosphere is very important because
it puts the transfer of that energy into the hands of a much slower convection
cooling process than is that of radiation.
However, whatever further thermal radiation events occur in the
atmosphere simply speed up the loss rate of energy to space compared to the
rate due to convection. The addition of
further infrared-active gases to the atmosphere causes there to be more
absorption layers in the model. If the
atmospheric load of infrared absorption gases was so high that the mean free
path length for absorption of their emissions was as short as 1 meter, then the
time to dissipate most of the energy to space would still be less than a second,
while the time it takes for the alternative energy transport by convection is
still hours.
Do additional greenhouse gases warm or cool the Earth? The addition of a gas in just enough
concentration that there is absorption by that gas in the lower troposphere
once which would not otherwise have occurred at a given wavelength slows the
rate of radiative heat loss and may be regarded as effectively warming the
Earth. It does this by converting the
cooling mechanism from rapid radiative cooling to that of slow convection
cooling. However, once that threshold
concentration is exceeded for a given wavelength, additions of that gas simply
cool the atmosphere more quickly than would the alternative of convection
currents. At such an above threshold
concentration, that gas can be regarded as cooling the Earth faster compared to
the rate it would cool without its addition.
The lapse rate is the temperature gradient with altitude in
the troposphere. At normal levels of
humidity, the adiabatic lapse rate is less than the dry lapse rate is. This tells us that at normal water vapor
concentrations, the water vapor concentration is already high enough to produce
a cooling effect on the surface and lower troposphere temperatures. Water vapor does this with the cooling effect
at the surface as liquid water becomes water vapor and then the water vapor rises
with convection until it reaches an altitude at which it condenses and releases
energy. At the warm surface it cools
with evaporation and at the cooler altitudes it warms by condensing. The evaporation process increases the water
molecule’s kinetic energy, including its vibrational modes, and the molecule
carries that energy upward by convection and then releases the kinetic energy
of evaporation as it condenses to liquid or solid form. Each
water molecule carries more energy per molecule at a given temperature than can
a nitrogen or oxygen molecule. Thus, as
they rise with convection, they are transporting more energy upward per
molecule than are the dry air molecules in the same convection current. In addition, the water molecule is radiating
energy to the layer of air above it, which is usually cooler and able to absorb
that radiated energy if it also has water vapor molecules in it or sometimes if
it has carbon dioxide in it.
Unlike water vapor molecules, a carbon dioxide molecule carries
less energy at a given temperature than do the nitrogen and oxygen molecules with
which it shares a convection current. This
means an added CO2 molecule causes a convection current to become a less
effective cooling mechanism. However, it
retains the ability to warm the air layer above it throughout the troposphere as
it cools its local surroundings by radiation to the layer above it. In addition, more CO2 in the upper
troposphere and in the stratosphere means more molecules radiating energy directly
to space. There is good evidence that
the addition of more hot molecules of CO2 in the stratosphere has
resulted in a measured cooling of the
stratosphere, as would be expected because these hot molecules are effective
radiators. I believe the concentration
of carbon dioxide in the atmosphere is already high enough that additions of CO2
are cooling the troposphere as well or at least counterbalancing the mild warming
effect of additional carbon dioxide molecules to a great degree.
Whether I am right or not about this, the claim that a very
small warming effect by additional CO2 will be amplified by a
greater warming effect by increased water vapor (a positive feedback) is surely
false. The fact that the wet adiabatic
lapse rate is less than the dry adiabatic lapse rate makes it clear that the
claim of a positive feedback is wrong. The
IPCC and other alarmists depend upon this false claim of a positive feedback by
water vapor to make it appear possible that additional carbon dioxide will
cause significant harm. The reality is
that additional carbon dioxide has no net significant effect on temperatures at
the Earth’s surface or in the lower troposphere.
Meanwhile, additional carbon dioxide in the atmosphere provides
plants with the means for easier growth.
With a growing human population, this is very helpful in producing the
additional food we need to produce. This
should be a factor in reducing human anxiety for the future. Of course, I understand that some people just
have to have something to worry about. I
suggest you worry, if you must, about another ice age which additional carbon
dioxide in our atmosphere cannot prevent.
Or, you might worry about an asteroid
striking the Earth. But it is even more
foolish to worry about problems created by more CO2 in the
atmosphere.
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3 comments:
Again, another great example of closely examining CAGWH-style models. One (possibly irrelevant) point occurred to me. Is it worth noting of Professor Hayden’s paper that by Wilhelm Wien’s Peak Displacement Law, CO2 radiation at 15μm is 193K, about -80°C? I don’t imagine it matters enormously. You earlier observed, as I recall, a lesser CO2 peak activity is at 9.6μm, near Earth’s combined emission frequency of 10μm, or about 302K (29°C) where it emits a good deal more energy than at 15μm and the same discussion would apply.
The way I put it is that the polyatomic molecules such as CO2 and H2O shift the lapse rate more vertically, which has the effect of lessening the temperature differential between
differing altitudes. They increase the thermodynamic coupling between heat source (in this case, the surface) and heat sink (in this case, space).
Given that extinction depth at the surface is low, nearly all the IR radiation is thermalized, which only has the effect of increasing CAPE (Convective Available Potential Energy), which makes more efficient the convective transport of energy to the upper atmosphere.
Molecules with more specific heat capacity or latent heat capacity than that of the homonuclear diatomics would make that convective transport of energy to the upper atmosphere all the more efficient.
Once convected to the upper atmosphere, those radiative molecules radiate their energy away (something homonuclear diatomics cannot do unless perturbed via collision... but collisions happen far less frequently in the upper atmosphere).
More polyatomic molecules will emit more radiation, cooling the upper atmosphere faster than the lower atmosphere can warm it, which is why we've seen a long-term and statistically-significant temperature drop in the upper atmosphere, and why we've seen an increase of OLR of ~7 W/m^2 over ~72 years even as surface temperature showed no statistically-significant trend.
Given that mean free path length for radiation decreases exponentially with decreasing altitude (and vice versa) any downwelling radiation is quickly turned around to upwelling, and is emitted to space.
Given that the radiative flux in the IR band from solar insolation is much greater than terrestrial radiation in the same band (check the Planck curve for solar insolation vs. terrestrial radiation, if you don't believe me), a higher atmospheric concentration of polyatomic molecules will act as a 'shade' to the surface.
In fact, if you study the refrigeration cycle, you'll find that water acts as an atmospheric refrigerant (in a literal 'refrigeration cycle' sense). The same applies to CO2 to a much lesser extent since CO2 only has specific heat capacity, whereas H2O has specific heat capacity and latent heat capacity.
Thus a higher atmospheric concentration of polyatomic (radiative) molecules must cool the surface toward the temperature of the upper atmosphere (due to shifting the lapse rate more vertically, *and* due to radiatively cooling the upper atmosphere faster than the lower atmosphere can warm it), rather than the other way around (the upper atmosphere warming toward the temperature of the surface). We just have to work through the humongous thermal capacity of the planet, which warmed due to a long series of stronger-than-normal solar cycles in the now-ended Grand Solar Maximum.
We agree on nearly every aspect of you explanation.
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