Figure 1: Typical mid-latitude TOA emission of radiation from earth. (original graph is from NASA [1])
Logic mandates
that the elapsed time between when a molecule absorbs a photon and when it
emits one must be more than zero or there would be no indication the photon had
been absorbed. This elapsed time, called the decay time, averages about 1.1
second in the atmosphere where people are [2, 3]. The summation of decay times
in outward directed radiation flux, especially from water vapor (WV) molecules, accounts for the so called Greenhouse Effect (GHE)
Below the tropopause (below about 8 to 16 km depending mostly on
latitude; more at the equator) WV decreases from an average of
about 10,000 ppmv (1%, 4% near the equator) at ground level to, because of the
low temperature (about negative 50 °C), 203 ppmv at the tropopause (assume
about 12 km). Saturation vapor pressure of ice at -50 C/total pressure at 12 km = 3.94 Pa/19400
Pa = 0.000203 = 203 ppmv (at saturation).
The redirection mechanism is summarized as follows: Much of the radiation energy
that is absorbed by CO2 below the tropopause (18W/m^2 in the example
shown in Fig 1) is shared with all molecules (thermalization) and emitted to
space by WV molecules. This is discussed further in Sect 10 of Ref [10].
The Water Vapor Factor
Water vapor is a transparent gas
that, molecule for molecule, is more effective at absorb/emit of
earth-temperature infrared radiation (IR) than carbon dioxide. From Jan 1988
thru Dec 2022 NASA/RSS accurately measured and reported monthly the global
average water vapor as Total Precipitable Water (TPW). The anomaly data are
reported at [11]. The nominal value is about 29 kg/m^2 so the trend from Jan
1988 thru Dec 2022 is 1.36 % per decade. Given that at ground level average
global water vapor is about 0.8% or 8,000 ppmv (parts per million by volume),
the increase in water vapor molecules in 3.5 decades is about 0.0136 * 8000 *
3.5 = 381 ppmv. From Mauna Loa data at [12] the CO2 increase in that time
period is 420 - 350 = 70 ppm. Per ideal gas laws, ppm = ppmv. With that, water
vapor molecules have been increasing 381/70 = 5.4 times faster than CO2
molecules. Thus, regardless of the initial source of warming, water vapor
molecules have been increasing about 5.4 times faster than CO2 molecules. The
idea that CO2 starts the increase is ludicrous.
Further analysis shows that the
determination by molecule count that increased CO2 influence on the climate has
been only about 1/7 as much as the increased water vapor influence is still high.
Radiation from water vapor molecules can be in any direction but, because of
the steep decline with altitude of the population gradient of water vapor
molecules, the distance traveled by a photon before it encounters another water
vapor molecule is greater towards space than towards earth so the prevailing
direction of IR flux is towards space. This is shown on a Top of Atmosphere
(TOA) graph of radiation flux vs wavenumber (wavenumber is the number of
wavelengths in a centimeter) by the jagged line below about wavenumber 600. Because
of the characteristic absorb/emit signature of every gas no other gas can
significantly absorb or emit radiation in the wavenumber range occupied by
water vapor. The line is jagged because radiation that reaches TOA/space is
from water vapor molecules at different temperatures/altitudes.
Fig 1.5 is TOA graph with
overlaid constant temperature curves for black body radiation at noted
temperatures. For any specified atmosphere, these are also constant elevation
curves. The temperature and associated altitude for standard atmosphere are
shown in the upper right corner of Fig 1.5.
Figure 1.5: Typical TOA
radiant emission.
At about 2 km and higher, the outward directed radiation from water vapor can make it all the way
to space. In this altitude range energy absorbed by CO2 and other IR active
molecules is redirected with respect to wave number via gaseous conduction to
replenish the substantial energy radiated to space by water vapor molecules.
This eliminates any warming from increased CO2 (or any other IR active gas that
does not condense at earth temperatures) in the troposphere.
At the tropopause (about 8 to 16
km altitude depending mostly on latitude; higher at the equator) and above,
water vapor molecules are greatly diminished because of low temperature so
radiation to space is mostly from CO2 and other IR active molecules that do not
condense in the atmosphere. Increased CO2 in the extremely thin air there
actually counters warming.
The end result is that CO2 does
not cause significant climate change, sequestering it is an expensive mistake
and the Green New Deal will have no significant effect on climate.
Figures 2 and 3
are typical graphs showing how radiation flux absorbed by ghg other than WV is
redirected to WV with increasing altitude. The redirection is quantified by the
progressively increasing depth of the ‘notches’ at the characteristic
wavenumber ranges for each ghg (except WV). Note that, at 20 km, redirection from
CO2 is greatest and at 50 km and higher some of the flux has
returned to the CO2 molecules. Somewhere in the vicinity of 20 km the
energy that has not yet radiated to space is directed by gaseous thermal
conduction to replenish the energy radiated to space by the sparse CO2 molecules
there.
The ‘notches’ are evidence of energy redirection. Redirection is possible because of thermalization and reverse-thermalization in the gaseous atmosphere.
Energy absorbed by ozone begins to be significantly redirected to CO2 and WV above 10 km, reaches a maximum below 50 km and stays at the maximum level above 50 km where radiation from O3 itself can make it to space.
The water vapor
content of the atmosphere diminishes rapidly as the temperature decreases with
increasing altitude. Above the tropopause it has declined to a level where
emission from water vapor ceases to dominate and emission from CO2
molecules becomes significant. The result is most of the residual energy not
emitted to space by water vapor at low altitude is, at high altitude, redirected
back to the wavenumber range 600-740 cm-1 and emitted to space by CO2.
The ’redirection’ is not geometric because all wavenumbers refer to photons at
essentially the same physical location.
References:
1. NASA/GISS TOA
graph https://www.giss.nasa.gov/research/briefs/2010_schmidt_05/
2. Average
elapsed time to emit a photon https://sealevel.info/Happer_UNC_2014-09-08/Another_question.html
3. Average
elapsed time to emit a photon http://rabett.blogspot.com/2013/04/this-is-where-eli-came-in.html
4. Time between
gas molecule collisions http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/frecol.html
5. MODTRAN6
calculator http://modtran.spectral.com/modtran_home#plot
6. Climate
change drivers http://globalclimatedrivers2.blogspot.com
7. MODTRAN6
defaults http://modtran.spectral.com/modtran_faq
8. K
& T chart http://chriscolose.wordpress.com/2008/12/10/an-update-to-kiehl-and-trenberth-1997/
9. Mistakes made
by the ‘consensus’: http://consensusmistakes.blogspot.com
10. Water Vapor
vs CO2 for Planet Warming: https://watervaporandwarming.blogspot.com
11. NASA/RSS measurements thru Dec 2023 of Total Precipitable Water anomalies https://data.remss.com/vapor/monthly_1deg/tpw_v07r02_198801_202312.time_series.txt
12. Mauna Loa data for CO2:
https://www.co2.earth/monthly-co2