Several Temperatures in Different Ways
Here we develop
the physics, chemistry and biology to quantify the effect of
atmospheric carbon dioxide (CO2) on Earth's
There are five mechanisms and three different
Four show a
small cooling effect, one warms surface and cools upper
atmosphere with no net bulk effect. I am unaware of a rigorous
mathematical description of the greenhouse gas theory that
purports to do this and show a warming affect.
of research attempts, promoters cannot reduce greenhouse gas
theory (GHGT) to mathematics of science and engineering.
Stefan-Boltzmann Law of Radiation
non-radiating O2 is exchanged for absorbing/emitting
CO2, the emissivity, e, of a planet to space must
increase. While emissivity of CO2 is less that global
emissivity, it is greater than the O2 it replaced by
fossil fuel combustion.
Law of Radiation is,
I = σ e
increases with CO2
at constant I, T goes down. Therefore, CO2
causes global cooling.
This is true
for all bodies of matter, no matter the composition, rotation
speed or weather.
I = radiating
intensity, irradiance, power of any radiating body, w/m2,
of its spherical surface, measured by Earth satellite
spectrophotometers to be about 239. It is only a transfer rate
when surroundings do not radiate, at 0K.
Outer space at 3.7K
radiate with very low intensity.
T = temperature
of radiating body, K, estimated for Earth to be 4.60C + 273.15 =
Stefan-Boltzmann radiation law constant, 5.67
e = emissivity
of radiating body, fraction 0 < e < 1. e varies with
composition. Perfect radiator black body e = 1, radiates a given
intensity at lowest possible temperature. Colorful Earth
radiator e = 0.70827 emits given intensity at temperature higher
than black body.
5.67*0.70827(277.750/100)4 = 5.67*0.70827*59.51 =
5.67*42.152 = 239.0
If doubling CO2
from 400 to 800 ppmv increases emissivity 0.001 from 0.70827 to
0.70927, T would drop -0.098C from 4.600C to 4.502C.
5.67*0.70927(277.652/100)4 = 5.67*0.70927*59.43 =
5.67*42.152 = 239.0
of Energy of Atmosphere
Law Thermodynamics: Input Rate = Output Rate + Accumulation
At steady-state, Accumulation Rate = 0 and this ordinary
differential equation becomes an algebraic one.
solar + absorption of thermals and evaporation from surface +
absorption from surface radiation = radiation to space,
79 + 97 + 23 =
absorption spectrum overlaps solar spectrum tail a small amount
at two wavelengths, the 79 value would increase a small amount
with CO2; a cooling effect on surface neglected by
greenhouse gas theory.
Some climatologists say CO2
affects the rate of heat transfer from surface by thermals and
evaporation, 17 + 80 = 97, but I shall neglect that
controversial effect here.
However, once quantified, this model
structure can assess the effect on global temperatures.
additional 161 is transmitted through atmosphere from sun to
surface, 1 is retained by surface. 160 is transferred from
40 is transmitted through atmosphere as radiation
from surface directly to space, 97 is transferred to atmosphere
by convection and evaporation and 23 is absorbed from surface
is 79 + 161 = outgoing 199 + 40 + 1 = 240. Transfer to space =
energy flows come from the
Kiehl-Trenberth diagram, as promoted by the UN's discredited
Energy Transfer Law
The rate of
radiant energy transfer between radiating body 1 and radiating
surroundings 0 is,
I0 =σ [e1
neglecting complicated geometry effects here.) For transfer from
Earth to space, I shall assume surroundings at T0 =
3.7K, neglecting starlight, so,
= 5.67 [0.70827 (277.75/100)4 1.0 (3.7/100)4]
= 5.67 [0.70827*59.51 1.0*0.00000187] = 5.67[42.152
0.000002] = 239.00 0.000010626 = 239.00.
So there is no
problem equating Earth's radiation intensity to space with its
radiant heat transfer rate to space. Intensity only equals
radiant energy transfer rate when T0 = 0.
If this is
applied to transfer from surface 1 to atmosphere 0, rate I1
I0 is constant (I1 actually drops a
little when incoming drops due to increased atmospheric CO2
absorption), and e1 is constant, then when e0
increases with CO2, either T1 must
increase to overcome increased resistance to heat transfer by
increased e0 (as postulated by GHGT and the only
possible warming mechanism I can find), or T0 must
They both change in such a way as to reduce global T
from S-B Law.
In the unusual
situation where surroundings do not obey Kirchhoff's Law,
absorptivity = emissivity, a0 = e0,
because surroundings has energy transfer by means other than
radiation, like thermals plus evaporation = 97 from surface to
atmosphere, one cannot replace e0 with a0.
appropriate values (T1 = 14.85C, T0 =
-18.15C, e1 = 0.1615 and e0 = 0.167)
= 5.67 [0.1615 (288/100)4 0.167 (255/100)4]
= 5.67 [0.161*68.797 0.167*42.283] = 5.67[11.111 7.061] =
62.998 40.037 = 22.961 = 23.
emissivity = 0.1615, radiates I = 63, 40 directly to space and
23 absorbed by atmosphere.
pure water has e = 0.96, ocean phytoplankton absorb solar
power, reducing its emissivity. Emissivity of atmosphere seen
from surface = 0.167.
Emissivity of atmosphere to space is 0.830
because it receives 97 by convection and evaporation and does
not obey Kirchhoff's Law: emissivity = absorptivity.
radiates directly to space with effective emissivity = 0.1025.
Now we can find
weighted average global emissivity from atmosphere and surface
e = (0.831*199
+ 0.1025*40)/239 = 0.708
the initial assumption precisely.
I realize these
average emissivity values may not be acceptable to some, but
they do fit the observed data and are hard to determine from
first glance, assuming I1
I0 and T0
are constant, increasing CO2
increases heat transfer resistance,e0,
so surface radiating T1must
increase to accommodate.
This could be the basic claim of GHGT
global radiating T.
The amounts depend on the effect of CO2
on emissivity of the atmosphere.
consistent with the slope of T vs. altitude in troposphere, lapse
rate = -g/Cp (universal gravity constant / heat capacity)
because kinetic energy of gas decreases as its gravitational
potential energy increases with altitude, by energy conservation
increases atmosphere Cp because CO2Cp> O2Cp,
making the slope less negative.
It rotates counterclockwise
about its radiating centroid T near 5 km and -18C (which
decreases a bit by transfer rate to space).
This causes lower
atmosphere T to increase and upper atmosphere T to decrease.
of Energy of Earth
Law Thermodynamics: Input rate = output rate.
alb) S/4 + IO = I Is
S = solar
radiation intensity, 1365 to 1370 w/m2 incident disk
or 1365/4 to 1370/4 w/m2 of incident sphere
reflectivity, fraction, mostly by clouds, estimate 0.7. Some say
CO2 affects albedo through cloud formation; this
could be a significant cooling effect.
intensity of surrounding space = 0.000010626 @ 3.7K = negligible
P = energy
absorbed by plant photosynthesis
IO = sum inputs
(core, volcanoes, fires) minus other outputs, negligible
substituting gives the overall relationship:
I = (1
alb) S/4 P = σ e (T/100)4
Dividing by σ e
gives the overall relationship for T:
= (1 alb) S/4σe P/σe
increases, T increases. If alb, e or P increase, T decreases.
All we need to do is find the effect of CO2
on alb, e and P to quantify its effect on T. Easy to show
causes increases in e and P, decreasing T.
If Earth were a
perfect black body emitter and P = 0,
1366/4*5.67*1.000 = 42.1605 = 2.5484 or T = 254.8K =
Earth's surface is a colorful 0.612 emitter using surface T =
1366/4*5.67*0.612 = 68.8897 = 2.8814 or T = 288.1K =
14.95 (-18.33) = +33.3C is the difference between colorful
Earth's radiating surface temperature and its theoretical black
body equivalent when radiating at same intensity, 239.
Al Gore and the US Environmental Protection Agency (EPA), among
others, mistakenly declared this 33C to be the greenhouse
corrected emissivity value for radiating 239 at T = 4.6C, e =
0.708, corresponding black body would radiate at T = 273.15
18.35 = 254.80
5.67*1.0(254.803/100)4 = 5.67*1*42.152 = 5.67*42.152
This means the
so called greenhouse effect is 4.60 (-18.35) = +22.95C, not
molecules are made by living flora by
photosynthesis chemical reaction of xCO2 + 0.5yH2O
+ sunlight = CxHy + (x+0.25y)O2, catalyzed by
chlorophyll, according to biology.
CxHy are hydrocarbon
molecules: sugars, starches & cellulose, and which decay slowly
to oil, gas, peat, tar and coal along with decaying fauna
residue. CxHy can be natural gas, CH4, methane.
not obey Kirchhoff's law either,a0 = e0,
because of this non-radiation chemical energy transfer
mechanism.CO2 is green plant food driving the cycle
of flora fauna life.
Flora make O2 for us fauna.
Fauna make CO2 for flora.
consumption of CO2 and incident solar energy, P is,
p = pressure at
sunlight impinging on green surfaces, w/m2<160. = a(1
alb)S/4, a = absorptivity
= atmospheric composition, vol
= atmospheric composition, vol
temperature of surface leaf, K
k = kinetic
will increase P and reduce T, cooling. Increasing S or T1
will have the same effect.
sensitivity of T to CO2 depends on which temperature
you are talking about: T, T1, T0. And what
the net effect of all relevant mechanisms is. It is easy to see
why there is so much confusion and controversy.
increase in CO2, solar absorption by atmosphere
increases a bit to 79+ and surface absorption decreases a like
amount to 161-.
Therefore, surface radiation drops a like amount
to 63-. And its T1 drops to 14.85-.
With increased e0
the transfer rate from surface to atmosphere by absorption
decreases to 23-. And since the atmosphere T0
decreases to -18.15-, the net radiation rate from atmosphere to
space must drop to 199- = 79+ + 23- + 97, because CO2
is a better absorber of surface spectrum than solar spectrum.
Direct transmittance from surface to space would increase to 40+
such that the total to space remains 199- + 40+ = 239.0,
satisfying overall energy balance.
Therefore increasing CO2
causes decreases in surface T1
= 14.85-, atmosphere T0
= -18.15-, and global T = 4.60-.
There is no CO2
global warming mechanism. There are at least four global cooling
mechanisms. This refutes UN IPCC claim doubling CO2
from 400 to 800 causes Earth's T to increase 1.2C to 2.5C.
theory to support the notion of global warming, postulates heat
transfer from cold atmosphere down to warm surface, heating
Kiehl-Trenberth diagram says back-radiation transfer rate is
333, which is 2.1x that impinging surface from the sun, 161.
This extraordinary value defies common experience.
shown the existence of any back-radiation would violate the
Second Law of Thermodynamics; heat only transfers from hot to
cold or from high intensity radiators to lower intensity
If back-radiation existed, it would lead to creation
of energy, a violation of the First Law of Thermo, constituting
a perpetual motion machine of the first and second kinds, which
is impossible, but just what AGW proponents need to support
their perpetual global warming idea.
climatologist, Dr. Roy Spencer says satellites measure Earth's
global temperature, their spectrometers actually measure
radiation intensity, I = 239, a pole to pole, day/night,
Roy must assume a corresponding
emissivity, e, to infer or deduce an estimate of T.
Since e is
hard to determine from first principles physical properties of
dissimilar surface + atmosphere and is likely to change,
particularly with CO2, using satellite inferred T is
fraught with error.
He must get distance between radiator and
spectrometer accurately, which is not easy for a 50 km thick
atmosphere and rocky mountains.
T is a point
property of matter indicating its kinetic energy. We have no way
in physics to average T over different phases and compositions
of matter. You can't even calculate the average T of your moving
car: engine, cylinders, a/c, radiator, exhaust, body, interior,
Wouldn't mean much if you could.
By the way, how
are global temperature maps constructed? If they are from
closely spaced thermometers, averaged daily, that would be
But if from spectrometers,
how are emissivities of
ocean, desert, jungles, cities, mountains, ice and clouds
assigned to each point of radiating intensity, for a
corresponding S-B radiating T?
And averaged over sphere?
of Spencer's writings indicates he equates/confuses radiation
intensity with radiant heat transfer rate, which have the same
units, w/m2. The former is given by S-B Law for
intensity, irradiance, radiance, power, exitance, emission.
latter is driven by a difference in intensities between two
radiators or a radiator and its surroundings. Both are vectors
with direction, not scalars.
The former intensity, I, is not
called radiant heat transfer rate because it isn't.
When two facing
plates are radiating at each other with equal intensities in
opposite directions, there is no radiant heat transfer between
them and their temperatures remain constant.
(Note if emissivities differ when I1 = I0, so will
radiator Ts. Chrome and wood on a beach have different steady
temperatures, chrome is hotter because its emissivity is low and
reflectivity is high, radiating with same I as high emissivity,
The walls of my office radiate, but no heat
transfers between them.
engineers design and operate radiant/conductive/convective
furnaces with chemical reactions for a living. You can't control
something unless you can measure it or reliably infer it from
measurements and known constants of nature.
[CO2] and T may be correlated over significant
periods does not mean one causes the other; a third input may
drive them both.
Solar irradiance is not constant and dominates
all other influencers of T.
CO2 in water, beer, soda, Champagne and oceans
decreases with temperature. Cooling drives CO2 from
the atmosphere into the ocean; warming drives it back out.
simple energy balance on oceans confirms the measured 800 year
lag of [CO2] following T, following S; a well-known
inconvenient truth for
Al Gore's embarrassing Academy Award
There is no
known mechanism in the literature quantifying any effect of [CO2]
change on climate change.
The notion of
building a thermostat to adjust fossil fuel combustion rate to
control the temperature of the Earth was shown to be
unmeasurable, unobservable and uncontrollable by control systems
mathematical analysis in 1997, before Kyoto Protocol. In other
words, it can never work.
acceptable engineering practice to infer fundamental
constants/properties like an emissivity or reaction rate
constant by measuring related variables and using one of these
laws of physics to deduce it.
Resulting law has predictive power
so long at the property does not change.
This know-how is
particularly useful for rigorous differential equations
accounting for dynamics of mass and energy accumulation rates.
Stability analysis shows no tipping points.
But to fit
arbitrary algebraic polynomial, exponential, sine, log or hockey
stick equations to measured transient data is unacceptable since
it is well known in chemical control systems engineering that
they will have no predictive power.
The UN IPCC use
of such models confirms they have no greenhouse gas law built on
accepted physics and engineering and should be summarily
Calling for more research funding after repeated
failures is compelling evidence the science and engineering of
global warming and climate change is far from settled. In fact,
this brief essay should settle the matter, save money and
delight those practicing the scientific method.
I used only
three laws of nature here: S-B Law, 1st Law of Thermo
and Chemical Reaction Rate Law. And 10th grade
World has been spending $1 billion per day for a decade
on global warming/climate change research to quantify the effect
of fossil fuel combustion production of CO2 on
A large government is shutting down its
coal industry in 2014 on the mistaken belief CO2
causes great harm, when it is benign and net beneficial.
paper proves it is all unnecessary, worthless.
Since Earth is
warming half the time and cooling the other half, reputable
climatologists report a consensus of imminent, significant,
prolonged global cooling, and the effect of increasing CO2
on temperature is vanishingly small, be prepared.
energy production from oil, gas, coal and nuclear. For goodness'
Look before you leap. Do no harm. Think before you speak and
write. Play it on the safe side. Better safe than sorry. Know
what you are saying and doing. Do not frighten people
Supply relevant, valid evidence for every claim;
lest they be dismissed as frivolous. Perform an accurate
scientific, engineering and economic analysis before devising a
plan and implementing it.
Provide performance measures and
fulfill them. Be prudent & frugal. Be a fiduciary with other
people's money. Foresee unintended consequences. Analysis comes
before synthesis, always. Avoid attempting the impossible.
building perpetual motion machines, in violation of the 2nd
Law of Thermo.
Learn from your mistakes, admit them, apologize,
accept consequences and reconcile with Nature and Nature's God (TJ,
Honesty is the best policy.
Skepticism is a
wise starting position.
can't find a mathematical description of a consensus greenhouse
gas theory, I call it a greenhouse gas hunch.
After all, CO2
is green plant food. No self-respecting environmentalist would
consider depriving Earth's flora of its sustenance. Even for
personal political or financial gain.