5/20/19,
rev 3/9/22,9/15/22,6/25/23,8/15/23,4/15/24,4/26/24,5/24/24,9/2/24,10/7/24
Climate Change
Drivers*
Dan Pangburn, P.E.** (ret),
MSME, ASME life member
pangburndan@gmail.com
CONTENTS
1. Introduction
2. CO2
does not control climate
3. Environmental Protection
Agency mistakes
4. Thermalization
reduces CO2 influence on climate. How GHE works.
5.
Radiance calculated by MODTRAN6
6. Water vapor
7. Effect of water
vapor increase
8. Water vapor change
with time
9. World Sources of Increased
Water Vapor
10. Effect of TPW increase on clouds
11. Approximate
effect on the planet of the net of ocean surface temperature (SST)
12. Comparison of
approximation with ‘named’ ocean cycles
13. Atmospheric
carbon dioxide
14. Climate
sensitivity determined using MODTRAN6
15. Sunspot numbers
16. AGT measurement
data set
17. The AGT Model
18. Comments
regarding the method used in developing and using Equation (1)
19. Results from the AGT model, Tambora
20. Attribution
quantified by sunspot number anomaly proxy.
21. Hind Cast
Estimate
22. Step changes in
AGT are not possible
23. Caveats on
Predictions
24. Conclusions
25. References
· * This document is periodically updated to improve clarity and
incorporate revisions, improvements, and new data.
** P.E.
stands for Professional Engineer. A Professional Engineer is a person who has
been tested by and certified by a state government as one who, subject to
liability, may decide the design and functional adequacy of things that, if
inadequate, could endanger the public.
Summary
Thermalization and the steep decline with altitude of the
population density of water vapor (WV) molecules up to the tropopause, about
8-16 km, explain why water has a dominate effect on climate. Additional atmospheric carbon
dioxide (CO2) and other trace greenhouse gases have little if any net
effect on climate. Much of upward photon emission from WV molecules goes
directly to space, especially from around 4 km and wavenumber 500 and
substantially at lower wavenumbers up to the tropopause, which is at about 10
km on average, 16 km at low latitudes. Above the tropopause the atmosphere is
cooled mostly by outward directed radiation from CO2.
Reported average global temperature (AGT) since before 1900
is accurately explained (95+% match with measured trend 1895-2023). Although
the warming influence of WV increase is closely proportional to the increase
due to the sun (part of which is quantified by a proxy; the time-integral of
sunspot number anomalies), the temperature change 1909-2023 is probably best explained
by derived attribution of ocean cycles to the average global temperature trajectory,
sunspot number anomaly proxy and measured increasing atmospheric water vapor. Since
about 2005 the increasing water vapor has been countering the AGT decline which
might otherwise be occurring.
A note about insignificant
factors:
In just about all properties and processes there are
inconsequential exceptions and/or uncertainties. These are often allowed-for by
claiming them to be ‘insignificant’. An insignificant factor is one that is
small compared to known uncertainties. In all that follows, insignificant
factors are excluded whether explicitly stated or not.
Meaning of terms
The words ‘water
vapor’ can be misinterpreted. WV is a transparent gas. If something is visible,
like steam or a cloud, it is not WV but is condensed liquid water droplets or
tiny bits of ice.
The term ‘vapor
pressure’ has different meanings in different disciplines. In meteorology it
means the partial pressure of WV in the atmosphere. In most other disciplines
and general use, it means the pressure developed by the liquid as a result of
its impetus to change phase and become a gas. This impetus depends only on the
temperature of the liquid water. It is unambiguously called saturation vapor pressure. The pressure of WV in the atmosphere is identified as its
partial pressure.
Another
difference in term usage is the meaning of the word ‘feedback’. In engineering
it usually refers to feedback factor, a dimensionless number which is the ratio minus 1 of response with feedback to the response if there were no feedback. In most
science disciplines it refers to the magnitude of the response to a forcing
which contributes to the cause of the forcing. In Climate Science it is
measured in W/m2.
1. Introduction
The only way that energy can significantly leave
earth is by thermal radiation. Only solid or liquid bodies and greenhouse gases
(ghg, AKA RAG for Radiatively Active Gas) can significantly absorb/emit in the wavelength range of significant terrestrial
radiation. Ghg significantly absorb/emit only at specific wavelengths which are
characteristic for each molecule specie. They both absorb and emit at the same
frequency signature. Both magnitude and frequency can be calculated using Quantum Mechanics [52] (some prefer to call it Quantum
Physics). In the range of terrestrial temperatures, non-ghg must
transfer energy by thermal conduction in the gas to ghg (or to liquid or solid
bodies) for this energy to be radiated. Note: The expression ‘greenhouse gas’
is somewhat misleading (greenhouses actually work primarily by suppressing
convection). A more correct understanding is that so-called ghg can
significantly absorb/emit radiation in the wavelength range of significant
infrared radiation associated with earth temperatures.
The word ‘trend’ is used here for temperatures in two
different contexts. To differentiate, α-trend (period about 69.6 yr) is an
approximation of the net of measured ocean surface temperature oscillations
after averaging-out the year-to-year fluctuations in reported average global
temperatures. The term β-trend (period = centuries) applies to the slower
average energy change of the planet which is associated with change to the
average temperature of the bulk volume of the material (mostly ocean water)
involved.
Some ocean cycles have been named according to the particular area
of the oceans where they occur. Names such as PDO (Pacific Decadal
Oscillation), ENSO (el Nino Southern Oscillation), and AMO (Atlantic Multi-decadal
Oscillation) might be familiar. They report the temperature of the water at or
near the surface. The average temperature of the bulk water that is
participating in these oscillations cannot significantly change so quickly
because of high effective thermal capacitance [1]. The effective thermal
capacitance of the planet is approximately equivalent to the top 110 meters of
the oceans.
This high thermal capacitance absolutely prohibits the rapid (year-to-year)
AGT fluctuations which have been reported, from being a result of any credible net
forcing. According to one assessment [1], the time constant (time to reach
63.2% (=1-1/e) of the final change following a step change in forcing) is about
5 years. A likely explanation for much of the reported year-to-year
fluctuations is that they substantially involve the roiling (at the observed
tiny fluctuation magnitude) ocean surface [44]. Volcanic activity is
occasionally also a temporary contributor. A simple
calculation shows the standard deviation of the reported annual average surface
measurements to be about ±0.09 K with respect to a smoothed trend.
The ꞵ-trend (centuries) is a better indicator of the change in global energy;
which is the difference between energy received and energy radiated by the
planet.
Knowledge of the kinetic theory of gases, thermalization,
Maxwell-Boltzmann distribution of speed among atmospheric gas molecules, some
thermodynamics, the absorb/emit wavelengths of water vapor and other ghg, heat
transfer analysis, and the rudiments of Quantum Mechanics, the equipartition of energy, and spectroscopy provide understanding
and a rational explanation of what
happens with terrestrial thermal radiation.
All gas molecules which are significantly IR-active at earth
temperatures are called ghg molecules. This includes water vapor molecules.
2. CO2
does not control climate
What
is meant by the statement that carbon dioxide (CO2) is a greenhouse
gas (ghg)? If by that is meant CO2 absorbs electromagnetic radiation with
a wave length of 15 microns (including +/- a micron or so due mostly to
pressure broadening, especially near sea level), well, that was demonstrated in
the lab a long time ago and remains true. But if by that is meant CO2 substantially
contributes to global warming, there is multiple compelling evidence (most
identified earlier [2] ) that CO2 has little, if any, controlling effect
on climate:
2.1. In the late Ordovician Period (about 450 mya), the planet plunged into and
warmed up from the Andean/Saharan ice age, all at about 10 times the current CO2
level [3].
2.2. Over the
Phanerozoic eon (last 542 million years) there is no correlation between CO2 level and AGT [3].
2.3. Antarctic
ice core data show that during the last and previous glaciations AGT trend
changed direction before CO2 trend [2].
2.4. Since about 2001, average
temperature uptrend calculated by Global Climate Models (GCMs, AKA General
Circulation Models) which assume CO2 causes Anthropogenic Global Warming (AGW) is about twice what is measured. [13]. The one Russian model output essentially matches measurements
but carries the usual ‘free world’ suspicions as to its authenticity. This is
shown, with recent data added, on Figure 0.1.
Figure 0.1: Comparison of GCM output with
measured.
2.5. Analysis of CO2
and temperature data 2002-2008 shows a close correlation between dCO2/dt and
lower tropospheric temperature. This demonstrates that CO2 level follows
temperature and not the reverse. [30]
2.6. Average global water vapor has been increasing faster
than possible, calculated on the basis of increased vapor pressure of water
resulting from global average temperature increase of the liquid surface water.
(Section 8 here) This demonstrates that WV increase has been driven by factors
in addition to increased evaporation.
2.7. The data from all reporting agencies agree that at least as far back as 2002 average
global temperature tracks WV not CO2 (Figure 0.2).
Figure 0.2 Average global
temperature tracks water vapor not CO2.
2.8. Hitran [52] using Quantum
Mechanics calculates, besides many other things, the relative absorb/emit
intensity of water vapor molecules vs CO2 molecules. Comparison at
zero altitude is shown in Figure 0.25.
The increases of WV and CO2 over the last 36
years are calculated as follows:
CO2 increase in 3.6 decades [21], Jan 1988 thru
2023: 423 - 349 = 74 ppmv
Average global water vapor increase trend from Figure 3,
which is a graph of NASA/RSS TPW data, is 0.04161/29 * 100 * 10 = 1.43 % per
decade.
The ground level population of WV molecules averaged about
8000 [63, 64]. Figure 2, at 30 degrees latitude (area to pole = area to
equator) also averages global WV ≈ 8,000 ppmv. WV increase in 3.6 decades =
0.0143 * 8,000 * 3.6 = 411.8 ppmv.
Therefore, WV molecules have increased 411.8/74 = 5.56
times faster than CO2 molecules 1988-2024. (Much of the world human population
has been falsely indoctrinated)
Figure
1.5 shows that below the tropopause, absorbed radiation energy is emitted primarily
from water vapor. Well above the tropopause, radiation emitted from
molecules there to space is primarily from CO2 molecules. If you
ignore the increase in water vapor near the surface, WV averages
about 8,000 ppmv. The increase in absorbers at ground level since 1900 is then
about 8,412/8,295 - 1≈ 0.01 = 1%. WV above the tropopause (~10 km) is limited
because of the low temperature (~ -50 °C, saturation vapor pressure of ice 3.94
Pa [58], total pressure 26,500 Pa) to about 3.94/26,500 = 0.000149 = 149 ppmv while
the CO2 fraction remains essentially constant with altitude at (in
2019) about 410 ppmv; up from about 295 ppmv in 1900. The increase in emitters
to space at high altitude (~> 20 km, 0.055 atm), and accounting for the
lower atmospheric pressure, is (410 + 149)/(295 + 149) * 0.055 ≈ 0.069 = 6.9%.
This (increased CO2 adds more % high altitude (low temperature) emitters than absorbers) explains
why CO2 increase does not cause significant warming (except at the
poles). The result being that Climate Sensitivity is not significantly
different from zero.
The exception at the poles is because
it’s cold there at ground level so WV molecule count is already low.
Figure 0.25: At zero altitude, CO2 absorb/emit is barely discernable
compared to WV.
2.9. (Slightly different calc than at 2.8) Global average water vapor at
zero altitude is about 8,000 ppmv. Based on TPW percent increase (Figure 3), WV
increase since Jan 1988 has been about 0.0416/29 * 8,000 = 11.48 ppmv per year.
CO2 (349 ppmv in 1988) increase has been about (423– 349)/36 = 2.056
ppmv per year. Therefore, about 11.48/2.056 ≈ 5.6 WV molecules were added for
each CO2 molecule.
2.10. CO2 increased 2002 to 2018 by 40% of the increase 1800 to 2002
1800 avg. Lawdome, Neftel, Friedli = 281.6 ppmv
2002 avg. Mauna Loa/Keeling = 373.3 ppmv
Nov, 2018 Keeling = 410.0 ppmv
(410-373.3)/(373.3-281.6) = 0.40 à 40%
2.11. Stochastic
assessment of data over the phanerozoic eon (541 million years ago to present)
by D. Koutsoyiannis concludes that CO2 change follows temperature change. [66]
The recent
temperature data which track water vapor, and two previous 30+ year downtrends
in temperature with relentlessly rising CO2, demonstrate that CO2
has little if any effect on average global temperature. A possible explanation
for the insensitivity of AGT to CO2 is that the small percent
increase in the number of absorbers near the surface (water vapor and CO2)
is compensated for by the large percent increase in emitters (mostly CO2)
above the tropopause. [51]
3. Environmental Protection
Agency mistakes
The US EPA asserts [10] Global Warming Potential (GWP) is a
measure of “effects on the Earth's warming” with “Two key ways in which these
[ghg] gases differ from each other are their ability to absorb energy (their
"radiative efficiency"), and how long they stay in the atmosphere
(also known as their "lifetime").”
The EPA calculation overlooks the very real phenomenon of
thermalization. Trace ghg (all ghg except water vapor) have little if any effect on
climate because absorbed energy is immediately thermalized which allows energy flow to be redirected to water vapor [51]. Thermalization is a key factor in
understanding the radiant energy flow by which CO2 and other ghg
except water vapor (WV) have little if any net effect on climate.
The EPA calculation of the GWP of a
ghg also erroneously overlooks the fact that any added outgoing radiation cooling from the
increased temperature the ghg might have produced is also integrated over the
“lifetime” of the gas in the atmosphere so the duration in the atmosphere
‘cancels out’. Therefore GWP, as calculated by the EPA, egregiously
overestimates the influence on average global temperature of noncondensing
greenhouse gases. The influence (forcing) of a ghg cannot be more than
determined by its immediate concentration.
The EPA assessment completely
ignores the effect of increasing water vapor which, by far, is the most important ghg and
appears to be the only ghg that has a significant effect on climate.
4. Thermalization reduces
CO2 influence on climate.
At a scale of
the size of atoms, the atmosphere consists of gas molecules with empty space
between them. Activity of the gas molecules determines the properties which can be measured as
temperature and pressure. Imagery of the activity of the molecules making up
the atmosphere is helpful. Wikipedia, in the article on kinetic theory of
gases, has a pretty good 2-D animation of the 3-D activity. It shows simulated
molecules bouncing elastically off each other and the walls of the container.
At any point in time, the speed (and energy) of the molecules ranges from zero
to high values with the highest probability being towards the low end. (This
fairly simple perception works well for consideration of macroscopic properties
such as pressure, temperature and viscosity. A deeper understanding involves
probability, molecule configuration, electric fields and the sometimes
contentious Quantum Mechanics.)
The average amount of time that passes between absorption
and emission of a photon by a molecule of CO2 in the atmosphere is up to about 1.1 second [5, 6]. (Common sense mandates that if this elapsed time was zero
there would be no way to determine absorption)
The elapsed time between collisions between gaseous
molecules at sea level average temperature and pressure averages about 0.0002 µsec [7]. Each collision results in
transferring at least part of the momentum and energy, which a ghg molecule
acquired from the photon, to neighboring molecules. After multiple collisions,
essentially all of the added photonic energy becomes distributed among other
molecules. The energy in all absorbed photons is thermalized.
Energy transfer at the gas molecule level is a mechanism which
contributes to the misleadingly named greenhouse effect (GHE). Radiation energy
travels from molecule to molecule at 99.97 % of the speed of light in a vacuum
but effectively dwells in the ghg molecules for up to about 1.1 second. Emission can
be from any ghg molecule as indicated by the Maxwell-Boltzmann energy
distribution. More ghg molecules means longer cumulative dwell time. This slows
passage of the energy through the atmosphere so a steeper temperature gradient
(higher surface temperature) is required to maintain the energy flux.
The process of sharing the energy with other molecules is
thermal conduction in the gas. The process of absorbing photons and sharing the
absorbed energy with other molecules is thermalization. Thermalized energy carries no identity of the molecule
that absorbed it. Ghg
molecules can absorb/emit only photons with certain quanta of energy. Energy
itself is quantized at the extremely fine level of 6.626E-34 J s (Planck
constant). For all practical purposes, the wavelength spectrum is continuous
and there are no forbidden wavelengths of photons. But only terrestrial
wavelength photons at about 15 microns can be absorbed/emitted by CO2 molecules.
Emission of
electromagnetic radiation from both solid and liquid surfaces of the earth
complies with the Planck spectrum (with emissivity ≈0.99) and Stephan-Boltzmann
(T4) law. Most particles of clouds, smoke and aerosols emit
similarly because they typically contain millions of molecules. Emission of
radiation from gas molecules is different (the only gas molecules which can
absorb/emit significantly at earth temperatures are ghg molecules i.e. they are IR-active). Emission
from ghg is restricted to specific wavelengths which are characteristic for
each ghg species. Potential for emission depends on the energy levels of
individual molecules. Molecule energy levels are determined probabilistically
according to the Maxwell-Boltzmann distribution. The average molecule energy
level of the Maxwell-Boltzmann distribution exhibits as the temperature of the
gas.
A ghg molecule which
is above absolute zero will emit photons (of allowed wavelength for that
molecule). This radiant thermal emission from a gas which contains both ghg and
non-ghg involves, for lack of a better term, reverse-thermalization, where ghg
which have been cooled by photon emission are rewarmed by thermal conduction
from surrounding molecules. Reverse-thermalization might alternatively be
explained by collisions at adequate energy level between like-species of ghg
molecules. The end result at the macro level would look about the same (emission
from the planet, except at the poles, is dominated by water vapor molecules).
Significant terrestrial thermal radiation is nearly all in
the wavelength range 6.5-200 microns (wavenumber 1538-50/cm). (Note: Divide 104
by either one to get the other; e.g. 104/wavenumber 667 = 15
microns, 104/15 microns = wavenumber 667). An early report, which was
useful for development of guided missiles, is helpful in understanding Quantum Mechanics as applied to water vapor and carbon dioxide in the atmosphere [45].
Radiation from
the surface is very close to the Planck spectrum from a black body at the
specified surface temperature. Below wavenumber 550 about 95% of thermal
radiation that gets absorbed from the surface is absorbed by WV within the
first meter; 99% within two meters. Above about 550/cm the absorption by WV
declines rapidly and absorption by CO2 increases. Above about 2 km
and below the tropopause some of the energy absorbed by the CO2 is
redirected to WV via thermalization. More CO2 simply means that the
energy redirection occurs at lower altitudes.
Thermalized energy carries no identity of the molecule that
absorbed it. The thermalized radiation warms the air, reducing its density,
causing updrafts which are exploited by soaring birds, sailplanes, and
occasionally hail. Updrafts are matched by downdrafts elsewhere, usually spread
out but sometimes recognized by pilots and passengers as ‘air pockets’ and micro
bursts.
5. Radiance
calculated by MODTRAN6
MODTRAN6 [48] is
a computer program developed for the Airforce Research Laboratory which
(besides other things) can calculate the radiation flux at selected elevations
in the atmosphere for specified constituents and conditions. It contains
default values for several environments including the tropics and the 1976
Standard Atmosphere. Values for the rate-of-change of water vapor and
atmospheric temperature vary with altitude for different latitudes and seasonal
conditions as shown in MODTRAN documentation [28].
Figures 0.5 and
0.6 are typical graphs calculated by MODTRAN6. They show radiation flux
absorbed by ghg other than water vapor (WV) being 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, for CO2, the redirection at 20 km
is greatest and at 50 km and higher some of the flux returns to the CO2
molecules. Somewhere in the vicinity of 20 km some of the energy is redirected
back to the CO2.
The ‘notches’
are evidence of energy redirection from CO2 to WV. Redirection is
possible because of continuous thermalization and reverse-thermalization at all
altitudes in the gaseous atmosphere.
Figure
0.5: TOA flux for 1976 Standard Atmosphere at MODTRAN6 default values.
Figure 0.6: TOA flux for tropics atmosphere at MODTRAN6 default values.
Figures 0.5 and 0.6 are somewhat misleading;
especially below about 10 km, because they are accounting for the entire energy
flux including that involving latent heat and solar energy absorbed directly by
atmosphere and clouds. Approximately 161 W/m2 of solar energy
reaches the solid and liquid surfaces of the planet [29]. Added to this is
about 16 W/m2 of broad spectrum radiation from clouds which reaches
the surface through the atmospheric window. The
energy leaving the surface includes about 78 W/m2 from heat of
vaporization of water (annual rainfall averages about a meter and what comes
down had to have gone up). Another 17 W/m2 has been added by
convective heat transfer, leaving 161 + 16 – 78 – 17 = 82 W/m2 in
thermal radiation. This compares favorably to up radiation minus down radiation
of 345 – 271 = 74 W/m2 at zero altitude as calculated by MODTRAN6 [48] but is only about
73% of 382 – 269 = 113 W/m2 as calculated by MODTRAN [47].
The non-radiant flux is replaced with
radiant flux and the solar energy that was absorbed by the atmosphere and
clouds are incorporated with increasing altitude. Most of this takes place by
about 10 km (32,808 ft) so the graphs above the tropopause should be reasonably valid for
radiance.
Most of the photons emitted by the water vapor molecules are
at wavelengths different from the comparatively narrow band that CO2
molecules can absorb. The greatly reduced population of water vapor molecules
above the tropopause means fewer molecules capable of absorbing radiation from
water vapor molecules. Outward directed photons from WV at elevations shown on
Figure 1.5 go directly to space. Effectively, much of the terrestrial thermal
radiation energy absorbed by CO2 (and other non-condensing ghg) is
thermalized, redirected to, and radiated to space from water vapor molecules.
At very high altitudes, temperature, molecule spacing and
time between collisions increases to where reverse-thermalization to CO
2
(and O
3) molecules becomes significant as does radiation from them
to space.
This causes the spikes at the nominal wavenumbers of CO
2
and O
3.
Results from both MODTRAN and
MODTRAN6 contribute to a credible approximation of the transition of the sum of
convective, latent and radiative energy flux at the surface to purely radiative
energy flux at top-of-atmosphere (TOA). This approximation, using the default data in the codes for
standard atmosphere, is shown in Figure 0.7.
Figure
0.7: Approximate transition of surface energy flux to purely radiant flux at
TOA.
Figures 1 and 1.5 are typical graphs showing TOA thermal radiation from the planet. The TOA radiation from different
locations on the planet can be decidedly different, e.g. as shown in Figure 9
of Reference [8]. Figure 1, here, might be over a temperate ocean and thus
typical for much of earth’s surface. The area under
the black trace is about 300 W/m2 which is somewhat more than the
planet average of about 240 W/m2. Figure 1.5 is similar with area
under red curve ≈269 W/m2.
Figure 1: Thermal radiation from below assessed from top-of-atmosphere. Lower
wavenumber photons are lower energy. (original graph is from NASA [46])
Typical TOA
emission spectra are shown in Figures 1 and 1.5. A black-body emission curve
(emissivity 1) for an average global temperature of 288 K is a bit higher than
a curve for the actual surface at 288 K which has an emissivity about 0.99. The
TOA flux is the black trace in Fig 1 and the red trace in Fig 1.5. The TOA and
surface curves show radiation flux being slowed (absorbed/emitted by all ghg). between the two locations. The actual surface curve minus the TOA
curve averaged over the planet results in what is called the Greenhouse Effect (GHE).
Prominently shown
is the ‘notch’ associated with the CO2 absorb/emit band. Notch development indicating the
slowing of the flux with increasing altitude was shown in Figures 0.5 and 0.6. Existence
of this notch demonstrates that terrestrial radiation flux in this wavelength
range is especially slowed by the IR-active gas CO2.which does not
condense in the atmosphere.
Less obvious and
perhaps not even considered is the energy flux (other than WV) being redirected
with respect to wavenumber to WV. Redirection is possible because of continuous
thermalization and reverse-thermalization at all altitudes in the gaseous
atmosphere.
Water vapor is greatly reduced at higher altitudes
(>~10 km), which allows some reverse-thermalization of the radiant flux back
to CO2 at the wavenumber range 600-740. The TOA notch is about 12%
less deep above 50 km than it was at 20 km. The approximate 18 W/m2
(in Fig 1) which is not reverse-thermalized back to the notch explains the
reduced flux at the notch.
The energy entering the atmosphere from the
surface matches very closely the Planck spectrum for the temperature of the
surface and emissivity about 0.99. In Figure 1, the flux through the atmospheric
window indicates a surface temperature of about 293 K. For wavenumbers 600-740 /cm
the power (energy rate) at TOA if no CO2 is (MODTRAN at same total
flux) about 0.33 W / m^2 / cm^-1 * 140 cm^-1 ≈ 46 W/m^2. The power radiating at
the notch from the tropopause and above is about 0.2 W /m^2 / cm^-1 * 140 cm^-1
= 28 W/m^2. The 46 – 28 = 18 W/m^2 (18/300 = 0.06, 6%) that is not emitted at
the wavenumber range 600-740 has to be emitted at other wavenumbers. The re-redirected
plus un-redirected power which is emitted in the wavenumber range 600-740 (28
W/m^2) could be from both CO2 and water vapor.
Figure 1.5: Typical TOA radiant
emission (U Chicago version of MODTRAN).
An ‘experiment’
demonstrating the effect of reduced water vapor in the atmosphere already
exists. Near the poles, the extremely low temperatures result in very low water
vapor content while the CO2 level is about the same as everywhere else. With few water
vapor molecules available to emit radiation, more of the TOA emission is from CO2 molecules near 15 microns as shown in
Figure 9 of Ref [8]. Because the GHE at the poles is dominated by CO2
, an increase in CO2 causes the slight warming at the poles which has been
observed.
Approximately 98% of dry atmospheric molecules are non-ghg;
nearly all nitrogen and oxygen with about 1% argon. Near the surface, they are
substantially warmed by thermalization of the photonic energy absorbed by the
ghg molecules and, at higher altitudes, cooled by reverse-thermalization back
to the ghg molecules which radiate the energy to space.
6. Water vapor
Average measured
global atmospheric water vapor (total from surface to TOA) over the years is provided here at Figure 3.
Measured CO2 level is at Figure 7.
WV
increase is a cause of warming (average global temperature increasing) because
it is a ghg. Part of WV increase is a result of surface water warming because
its saturation vapor pressure increases with temperature. The saturation vapor
pressure increase causes an increase in the rate of WV molecules being forced
into the atmosphere (when the atmosphere at ground level is less than saturated
with WV which is usually the case). An additional source of WV increase is
human activity, especially irrigation. This increased average WV results from a
tiny increase in the average residence time of water molecules in the
atmosphere. It is discussed further in Section 9.
In the
atmosphere, condensed water can exist as water, ice or super-cooled water [56]
(super-cooled water is liquid water below 0.0 °C). Accurate numerical values
for saturation vapor pressure of liquid water [57] and ice [58] are graphed in
Figure 1.7. Saturation vapor pressure for super-cooled water can be calculated
using the Bolton equation [55]. The Bolton equation for saturation vapor
pressure in kPa vs temperature in C is
p = 0.6112 * e^(17.67 * T /
(T+243.5)) (z1)
As shown in
Figure 1.7, saturation vapor pressure increases progressively with temperature.
Of interest is the % increase in saturation vapor pressure per degree increase
in temperature. This is readily calculated from the numerical data for both
liquid water and ice from:
1/1 increase/Tave = (pj
– p(j-1)/(Tj – T(j-1))/Tave (z2)
Where,
1/1 = %/100
j and (j – 1)
are adjacent values in the table
Tave = average
temperature of the adjacent values.
The same thing
for super-cooled water is obtained using the first derivative of the Bolton
equation which is
dp/dT = p * 17.67 *
243.5/(T+243.5)^2 (z3).
This, divided by
p to get the 1/1 value curve, is shown in the bottom graph at Fig. 1.7.
Slightly more
accurate formulae for calculating saturation vapor pressure were derived by
Jianhua Huang [62].
Saturation vapor
pressure depends ONLY on the temperature of the ice or liquid water. The 1/1
change in saturation vapor pressure per Celsius degree for water, ice and
super-cooled water are shown in the lower graph of Figure 1.7.
Figure 1.7: Saturation vapor pressure of ice &water
and fractional rate of change per C degree change vs temperature.
The atmospheric
temperature decreases with altitude so the accommodation for WV increases with
altitude to about 12%/C° at the tropopause (°C is a temperature, C°
is a temperature difference and is used interchangeably with K for Kelvin
degree). Although the
accommodation per degree increases with altitude, the magnitude of a
temperature change usually decreases with altitude faster with the result that
as absolute humidity increases, relative humidity usually slightly also increases.
Based on ocean
temperatures from [59], the area-weighted change in saturation vapor pressure
per C degree at sea level is about 0.0633 / C°. The amount of compounding is
unknown but cannot be greater than 0.0633+0.0633^2+0.0633^3+… = 0.0676/C°. It
is conservatively estimated to be about 0.067/C° = 6.7%/C°
If there is no
additional source of WV, the percent change of atmospheric water vapor is
assumed to vary directly with the percent change in liquid water saturation vapor
pressure.
Figure 2: Water vapor
declines with latitude and rapidly with altitude. [9] (original from NASA)
All absorbed radiation is thermalized i.e. the absorbed
energy is shared with surrounding molecules. Only WV molecules can absorb/emit
radiation in the wavenumber range 25 to 550/cm.
At the tropopause it is very cold, about 50 degrees Celsius
below zero (-58 °F). At this low temperature nearly all WV molecules have
condensed (or cooled by radiation to space and descended) leaving only about 149 ppmv WV
above this altitude compared to a global average of about 8,000 ppmv at ground
level. Accounting also for reduced pressure to about 0.26 atm results in a WV
population per unit volume above the tropopause of 149/8000 * 0.26 ≈ 1/206 of
what it is at ground level. This huge gradation in WV molecules favors outward
radiation; with increasing amounts escaping directly to space with increasing
altitude.
The ‘hash’ in graphs of TOA radiation flux vs wavenumbers,
e.g. Figure 1 or 1.5, is evidence of radiation originating from a range of
altitudes (temperatures).
Although WV is reduced to 149 ppmv above the tropopause, CO2
remains at its ground level ppmv value. Therefore, above the tropopause most of
the remaining thermalized energy is reverse-thermalized to CO2
molecules which emit it to space. An analysis which includes the processes
above the tropopause is at [65].
At very high altitudes, increased molecule spacing and
greatly diminished water vapor molecules result in the sharp peaks at nominal
absorb/emit wavelengths of non-condensing ghg (See Figure 1 & 1.5).
A common observation which demonstrates that water vapor increase contributes to global warming is cloudless nights cool faster and farther when absolute
water vapor content of the atmosphere is lower. This simple observation also
demonstrates the existence of the misleadingly named greenhouse effect (GHE)
and that water vapor is a ghg.
7. Effect of water vapor
increase
Energy goes from
ghg molecule to ghg molecule by electromagnetic radiation (EMR) at the speed of
light in the atmosphere. The photon energy absorbed by a molecule is immediately shared with surrounding molecules. More ghg molecules means more time
spent absorbed and less time at the speed of light. That is why more water
vapor (and at the poles more CO2) slows the rate of energy flow from
the surface to space so the surface temperature must increase to maintain the
energy flux.
The average global water vapor increase 1895-2023 is about
10.6% (Fig 3). The average global temperature increase 1895 to 2023
attributable to WV increase according to Equation (1) and temperature data thru
2023 is about 0.885 K (Table 1).
The procedure to determine the effect of water vapor
increase using MODTRAN [47] is to determine a total radiant flux for a
particular base condition (scale factor = 1), apply the scale on water vapor
and then by trial-and-error change to temperature offset, determine the surface
temperature which produces the same total radiant flux for the condition of
study as for the base condition. The difference in surface temperature between
the base condition and the condition under study is the effect on surface temperature
of the change to WV. The default levels for all noncondensing ghg (e.g. 400
ppmv for CO2) were used for all cases to prevent any calculated
effect from a change to them.
Water vapor change is
investigated at three scales. All available conditions were evaluated with
vapor pressure (VP) held constant and also with relative humidity (RH) held
constant. In all conditions except 10% increase for tropical atmosphere, the
temperature change was greater with RH held constant. The base condition always
gave exactly the same results for RH as VP except Flux for tropical atmosphere.
Table 0.5 Temperature change as determined by
MODTRAN [47] for several conditions. All are clear sky except one with light
rain and one using the std cirrus model as noted.
Condition
|
Flux,
W/m2
|
Held
constant
|
WV scale
|
Surface
temp, K
|
∆T, K
|
Tropical
atmosphere
(up to
20 deg latitude, 34.2% of area)
|
298.52
|
VP
|
1
|
299.7
|
base
|
1.1
|
300.59
|
0.89
|
1.2
|
301.07
|
1.37
|
296.824
|
RH
|
1
|
299.7
|
base
|
1.1
|
300.53
|
0.83
|
1.2
|
301.38
|
1.68
|
Mid-latitude
summer
(20 to
60 deg latitude, 52.4% of area)
|
288.064
|
VP
|
1
|
294.2
|
base
|
1.1
|
294.595
|
0.395
|
1.2
|
294.97
|
0.77
|
RH
|
1.1
|
294.78
|
0.58
|
1.2
|
295.35
|
1.15
|
Mid-latitude
winter
|
234.118
|
VP
|
1
|
272.2
|
base
|
1.1
|
272.43
|
0.23
|
1.2
|
272.645
|
0.445
|
RH
|
1.1
|
272.49
|
0.29
|
1.2
|
272.765
|
0.565
|
Subarctic
summer
(above
60 deg latitude, 13.4% of area)
|
269.538
|
VP
|
1
|
287.2
|
base
|
1.1
|
287.55
|
0.35
|
1.2
|
287.88
|
0.68
|
RH
|
1.1
|
287.69
|
0.49
|
1.2
|
288.165
|
0.965
|
Subarctic
winter
|
201.305
|
VP
|
1
|
257.2
|
Base
|
1.1
|
257.37
|
0.17
|
1.2
|
257.52
|
0.32
|
RH
|
1.1
|
257.4
|
0.2
|
1.2
|
257.59
|
0.39
|
1976 Std
atmosphere
|
266.272
|
VP
|
1
|
288.2
|
base
|
1.1
|
288.55
|
0.35
|
1.2
|
288.88
|
0.68
|
RH
|
1.1
|
288.7
|
0.5
|
1.2
|
289.19
|
0.99
|
Mid-latitude
summer, light rain & nimbo-stratus
|
283.542
|
VP
|
1
|
294.2
|
base
|
1.1
|
294.55
|
0.35
|
1.2
|
294.88
|
0.68
|
RH
|
1.1
|
294.69
|
0.49
|
1.2
|
295.17
|
0.97
|
Mid-latitude
summer, Std cirrus model
|
270.448
|
VP
|
1
|
294.2
|
base
|
1.1
|
294.56
|
0.36
|
1.2
|
294.9
|
0.7
|
RH
|
1.1
|
294.71
|
0.51
|
1.2
|
295.2
|
1.0
|
MODTRAN6 [48] provides
similar capability but imposes predefined WV vs altitude profiles for each
condition in place of selecting to hold either VP or RH constant. The WV
profiles incorporate the constraint that humidity cannot exceed 100%. The
already high WV in tropical areas is apparently not compatible with increasing
it by 10%. Similar plots to those made by MODTRAN are obtained by setting
MODTRAN6 to radiance, sensor altitude to 99 km, spectral range wavenumbers 250
to 1500, and resolution to 1.2/cm.
Table 0.6: Summary of results using MODTRAN6.
Condition
|
Flux,
W/m2
|
WC mult
|
Water
column, atm-cm
|
Temperature,
K
|
∆T, K
|
Mid-latitude
summer
(52.4 %)
|
269.594
|
1
|
3635.9
|
294.2
|
base
|
1.1
|
3999.49
|
295.636
|
1.436
|
Mid-latitude
winter
|
249.969
|
1
|
1059.7
|
272.2
|
Base
|
1.1
|
1165.67
|
272.34
|
0.14
|
Tropics
(34.2 %)
|
268.546
|
1
|
5119.4
|
299.7
|
base
|
1.1
|
5631.34
|
304.325
|
4.625
|
Subarctic
summer
(13.4 %)
|
265.441
|
1
|
2589.4
|
287.2
|
base
|
1.1
|
2848.34
|
287.81
|
0.61
|
Subarctic
winter
|
231.737
|
1
|
517.73
|
257.2
|
base
|
1.1
|
569.503
|
257.196
|
-0.004
|
US
standard, 1976
|
269.339
|
1
|
1762.3
|
288.15
|
base
|
1.1
|
1938.53
|
288.69
|
0.54
|
Area weighted,
winter/summer average results in ∆T of 0.5 K for MODTRAN and 0.75 K (excluding
tropics) for MODTRAN6 for 10% water vapor increase. These compare to 0.885 K for 10.6% WV increase as determined by Equation (1) (Table 1).
8. Water vapor change
with time
Water vapor is the ghg which makes earth warm enough for
life as we know it. Increased atmospheric water vapor contributes to planet warming.
Water vapor molecules are more effective at absorbing terrestrial thermal
radiation than CO2 molecules. Humanity’s contribution to atmospheric
water vapor increase is primarily (≈ 90%) as a result of increased irrigation
(Figure 3.5), with comparatively small contribution from cooling towers at
electricity generating facilities. Fossil fuels make an insignificant
contribution to water vapor. Switching to ‘renewables’ will have little, if
any, effect on climate.
TPW is increased by increasing evaporation and
also by decreased condensation/absorption of WV where the water is cold.
Increased AGT causes both and also increases the capacity of the atmosphere to
hold water which allows an increase in TPW with no increase in relative
humidity.
Because water vapor is a ghg, increased water vapor causes
the planet to warm, which further increases saturation vapor pressure of liquid
water and therefore further increases water vapor so there is a cumulative
effect. In control system analysis and electric circuit analysis as done by
engineers, this is called positive feedback and is quantified by a
dimensionless number which is the ratio minus one of the change with feedback
to the change if there was no feedback. This cumulative effect also increases
the rate of cooldown. (The term ‘feedback’ has a different meaning to Climate
Scientists and is quantified in units of W/m2).
Planet warming increases the saturation vapor pressure of
water (Figure 1.7) contributing to the water vapor increase. At present water
vapor is increasing faster than possible based on AGT increase alone. Global
temperature increase Dec 1978 – Dec 2023 from the UAH [4] trend is about 0.142
K per decade (this automatically includes any feedback effect). The assessment
in Sect 6 resulted in the calculation of average saturation vapor pressure
increase with temperature of 6.7% per degree C including compounding. The
percent increase in water vapor is assumed to be about the same as the percent
increase in saturation vapor pressure. Percent increase in water vapor due to temperature
increase = 0.142 * 6.7% = 0.95% per decade.
Measured % increase of Total Precipitable Water (TPW) from
Figure 3 is 0.04161/29 = 1.43% per decade. Thus, measured increase in WV is
about 1.43/0.95 ≈ 1.5 times the amount for liquid water temperature increase
alone.
The comparison of the measured WV change with the WV change
calculated from temperature change over the full time period since Jan 1988 can
be calculated incrementally and shown graphically. The file for calculated
change is generated in EXCEL where each row contains:
WVn = WV(n-1)
+ (Tn – T(n-1))* R * (WV(n-1) +F) (z4)
Where:
WVn = calculated WV in month n, kg/m^2
Tn = temperature anomaly in month n, K
R = effective
rate of WV increase resulting from feedback of temperature increase, 0.067/K (=
6.7 %/K)
F = added to avoid circular reference of (WV(n-1)+WVn)/2. F is calculated as an increase to each month equal to half a
month at the final slope. This requires iteration.
For GISS [23] thru Dec 2021, F = 0.0241234/24 = 0.001005 kg/m^2/month.
Slope at F = 0 is 0.0241226. Effect over 34 yr = (0.0241234 - 0.0241226)*34 = 0.000027
kg/m^2
The starting calculated WV is adjusted to make the starting
trends the same.
The results of this algorithm are
shown along with the actual WV anomaly measured and reported by NASA/RSS [11]
(plus 28.73). The calculated WV increase since Jan 1988 for
GISS reported temperatures [23] is shown in Figure 2.8 and for UAH reported
temperatures in Figure 2.9. Figure 2.8 also shows the linear trends assuming
three different values for average relative humidity remaining constant with
increasing air temperature (as calculated in GCMs).
Figure 2.8: Measured WV vs calculated WV based on GISS reported average global temperatures [23] thru 2021. (R = 0.067/K) and trends assuming constant relative humidity.
Figure 2.9: Measured WV vs calculated WV based on UAH reported average global temperatures [4] thru 2023. (R = 0.067/K
The average ratio of measured-WV/WV-calculated-from-temperature-increase
is obtained by the ratio of the slopes of the regression lines. The ratio for GISS
thru 2021 with WV increase, R = 0.067 %/C° is 0.041882/0.0241234= 1.736. The
ratio for UAH thru 2023 is 0.04161/0.018203 = 2.28. The observation that measured
WV increased faster than the determination using temperature demonstrates that there
has to be an additional source of WV above that resulting from just temperature
increase. The most likely cause of increased average WV is a tiny increase in
the average residence time of a water molecule in the atmosphere. This is
quantified at Sect 12 in [61].
The increased water vapor might also eventually cause
increased cloud cover and/or lower average cloud altitude which counters
temperature increase and would eventually limit it. Sustained increase of only
about 1.7% of cloud area would result in an eventual temperature decline of 0.5
°C [22].
More water vapor in the atmosphere means more warming. Water
vapor exhibits a logarithmic decline in absorption effect for equal added
increments of water vapor (Fig. 3 of Ref. [12]).
Sect 9 of [61] includes a graph which shows the
average global temperature increase vs average global WV increase.
Essentially all of the ghg effect on earth comes from water
vapor. Clear sky water vapor measurements over the non-ice-covered oceans in
the form of total precipitable water (TPW) have been made since 1988 by Remote
Sensing Systems (NASA/RSS) [11]. A graph of this measured ‘global’ average anomaly
data, with a reference value of 28.73 added, is shown in the left graph of
Figure 3. This data is extrapolated earlier using CO2 level as a
proxy, with the expression kg/m^2 TPW = 4.5247 * ppmvCO2^0.31286. This produced a match with the magnitude and
slope of the trend at the intersection of the extrapolation with the measured
values. The result is the right-hand graph of Figure 3 which shows approximately 10.6%
increase 1900-2023.
Figure 3: Average clear air Total Precipitable Water over all non-ice-covered
oceans as measured by NASA/RSS using satellite
based instrumentation and with extrapolation by me. (Left graph is by month, right graph is
by year average.). Estimated future assumes continuation of the slope of the monthly trend.
Clouds (average emissivity about 0.5) consist of solid
and/or liquid water particles that radiate approximately according to Planck spectrum and Stephan-Boltzmann (S-B) law (each
particle contains millions of molecules).
A corroboration of the long-term temperature trend is as follows: Assume that at the beginning of the warm up the temperature increase was caused by something else. Then the WV increase can be calculated from that temperature increase using the saturation vapor pressure vs temperature for water and the assumption that % increase in WV = % increase in saturation vapor pressure. But the WV has increased more than that so there has to be an additional source of WV. The additional source of WV (nearly all from irrigation) is the something else that produced the initial warming.
9. World Sources of Increased
Water Vapor
Irrigation, industrialization, and, increasing population
are causing the rise in atmospheric water vapor (WV) above that from feedback
(engineering definition of feedback) due to liquid water temperature increase.
A survey of available on-line literature provides direct and indirect
quantification of significant global sources of the extra increase.
Transportation fuel, linearly interpolated to 2017,
amounts to 113E15 BTU/y [31]. Energy content of a typical liquid fuel is
115,000 BTU/gal [32]. Liquid fuels weigh about 6.073 lb/gal = 2.75 kg/gal.
Therefore transportation fuels amount to
113E15 * 2.75/115000
= 2.7E12 kg fuel/y (a)
About 1.42 kg of WV is produced for each kg of liquid fuel
[32] so the amount of WV produced by transportation is
2.7E12 * 1.42 = 3.8E12
kg WV/y (b)
World electricity generation is now about 25,000
TWH/y [33]. At an average efficiency of 50% this requires a thermal input of
50,000 TWH/yr. Fuel source fractions of energy [34] in 2017 are approximately 0.38
coal, 0.36 natural gas and 0.26 non fossil fuel.
Coal combustion produces about 0.4 kg WV/kg coal [35].
Energy content of bituminous coal is about 8200Wh/kg [36]. The amount of WV
resulting from burning coal to generate electricity is then
50E15 * 0.38 *
0.4/8200 = 0.93E12 kg WV/y (c)
The amount of WV produced by natural gas (nearly all
methane, CH4) is readily calculated from the dominant chemical
reaction
CH4 + 2O2
=> CO2 + 2H2O (d)
Where a mole of methane weighs about 16 g and the two moles
of WV weigh about 18 g each.
Natural gas energy content is about 15,400 Wh/kg [36]. The
amount of WV resulting from burning natural gas to generate electricity is then
50E15 * 0.36 *36/16/15400
= 2.6E12 kg WV/y (e)
The total WV from all fossil fuel used to generate
electricity is then
0.9E12 + 2.6E12 = 3.5E12
kg WV/y (f)
Waste energy during electricity generation can be
approximately accounted for by evaporation of water in cooling towers, etc. At
50% efficiency the waste energy is the same as the energy in the electricity
produced, 25,000 TWH/yr = 25E12 kWh/y.
Latent heat of water = 2257 kJ/kg = 0.627 kWh/kg = 1.594
kg/kWh.
The amount of WV from waste heat (cooling tower, etc.)
during electricity generation is then
25E12 * 1.594 =
39.8E12 kg WV/y (g)
Irrigation is by far the largest source of WV. The increase
in irrigation is indicated by the increase in withdrawal for agriculture as
shown in Figure 3.5 [37].
Figure 3.5: Global water withdrawal includes both ground
water and surface water [37]
The total agricultural area equipped for irrigation in 2009
was 311E10 m2 of which 84% were actually being irrigated [38].
Estimating an increase of 2% to 2017, the total area being irrigated is now
about
311E10 * 0.84 * 1.02
= 266E10 m2 (h)
This is more than 4 times the area of France.
Total annual fresh water withdrawal (both ground and
surface) is now (2015) 3,986 km3 = 3.986E15 kg/y [39]. Of this, about
70% is for agricultural use [40]. This works out to
3.986E15 * 0.7/266E10
= 1052 kg/m2/y ≈ 1 m/y (i)
which appears reasonable because average rainfall for the
planet is about 1 m/y.
Evapotranspiration, WV from plants and landscape, is
discussed in the ‘thematic discussion’ of Aquastat [37]. From there, the amount
of precipitation on land is 110,000 km3 of which the fraction
evapotranspirated is 0.56 + 0.05 = 0.61. Given the planet surface area of
510.1E6 km2, and land fraction of 0.29 this results in the equivalent liquid depth of the total amount of water leaving the surface as WV as
110,000 *
0.61/0.29/510.1E6 = 0.00045 km = 0.45 m (j)
Water weighs 1000 kg/m3 so evapotranspiration
amounts to 450 kg/m2
Worldwide about 86% of irrigated area is flood irrigated
[54]. To simplify calculation, assume all irrigation is flood irrigation
approximated as furrow type [41]. Optimum frequency is to flood the furrows
about every 10 days [42]. Thus about half the area is covered by water 10% of
the time where evaporation from the water is about one meter per year [43] and
the rest of the time, the additional evaporation is assumed to be according to
the calculated evapotranspiration. Evapotranspiration prior to irrigation must
have been low or irrigation would not be done. Evapotranspiration with
irrigation, to be cost effective, is most likely to be much more than calculated.
These two uncertainties are assumed to approximately cancel each other. A further assumption is that, on average, irrigation is
applied for about 1/3 year. The total amount of WV resulting from irrigation is
then
[(0.1 * (1 + 0.45)/2
+ 0.9 * 0.45) * 266E10]/3 = 42.3E10 m3 = 42.3E13 kg/y (k)
These calculations are summarized in Table 1
Water vapor source
|
E13 kg/y
|
%
|
Irrigation
|
42.3
|
90.0 %
|
Transportation fuel
|
0.4
|
0.8 %
|
Fossil fuel for electricity generation
|
0.3
|
0.7 %
|
Cooling towers, etc. for electricity generation
|
4.0
|
8.5%
|
Total
|
47.0
|
100 %
|
Table 0: Summary of
contributions to atmospheric water vapor.
From Table 0, approximately 42.3/47 = 0.90 or 90% of atmospheric WV
increase above that due to feedback (engineering definition of feedback) from
liquid water temperature increase results from irrigation. WV added by
irrigation might be particularly influential because it is added at locations
where natural WV is low aiding evaporation, and water is shallow so it would
warm quickly.
The assessment here that irrigation accounts for 90% of WV corroborates what Shiklomanov
1997 determined as mentioned by Doll in 2002 [60].
Given the earth area of 510E12 m^2 and average annual
precipitation of about a meter or 1000 kg/m^2 the increased water use, mostly
for irrigation, results in 47E13/5.1E17 = 0.0009 = 0.09 % equivalent increase
in global precipitation.
10. Effect of TPW increase on clouds (added 9/17/18)
As TPW is
increased, condensation (cloud formation) could occur at lower average cloud
altitude and thus higher temperature except that increased atmospheric
temperature increases the accommodation for WV more than that same surface
temperature increase increases WV which reduces the formation of clouds. If lower
altitude, higher temperature clouds occur, they would radiate more energy to
the cosmic background and might partially counter the warming from the
increased GHE from increased water vapor.
11. Approximate effect on
the planet of the net of ocean surface temperature (SST)
The average global ocean surface temperature oscillation is
only about ±1/7 C°. It is defined to not
significantly add or remove planet energy. The net influence of SST
oscillation on reported AGT is defined as α-trend. In the decades immediately
prior to 1941 the amplitude range of the trends was not significantly
influenced by change to any candidate internal forcing effect; so the observed
amplitude of the effect on AGT of the net ocean surface temperature trend
anomaly then, must be approximately the same as the amplitude of the part of
the AGT trend anomaly due to ocean oscillations since then. This part is A ≈ 0.3
C° total highest-to-lowest extent with a period of approximately 69.6 years
(verified by high R2 in Table 1).
The measured AGT trajectory (Figure 9) suggests that the
least-biased simple wave form of the net effect of average surface temperature
oscillation of all of the oceans on average global temperature is approximated
by the sine wave:
Toceans = A/2
* sin((y – 1925) * 2 * π/69.6) (z5)
Where:
Toceans
is the effective temperature anomaly of the planet surface as a result of the
average ocean surface temperature oscillation, C°.
A = Effective
peak to peak amplitude of the ocean oscillation average, C°.
y = year
This puts the most recent maximum in 2012. R2
in equation (1) was obtained with A=0.2716. Equation (z5) is graphed in Figure 4
for A=0.298.
Figure 4: Effect on
planet surface temperature of ocean surface temperature oscillations (α-trend).
They do not on the long term significantly affect the bulk energy of the
planet.
In previous releases of this analysis, the effect of ocean
oscillations on planet surface temperature was approximated with a saw-tooth
wave form of period 64 years. The improvement by using the sine wave function is tiny.
12. Comparison of
approximation with ‘named’ ocean cycles
Named ocean cycles include, in the Pacific north of 20N,
Pacific Decadal Oscillation (PDO); in the equatorial Pacific, El Nino Southern
Oscillation (ENSO); and in the north Atlantic, Atlantic Multidecadal
Oscillation (AMO).
Ocean cycles are perceived to contribute to AGT in two ways:
The first is the direct measurement of sea surface temperature (SST). The
second is warmer SST contributes to increased atmospheric water vapor which acts as a forcing
and therefore has a time-integral effect on temperature. The approximation, Equation
(z5), accounts for both ways.
Measured SST data are available for three named cycles:
PDO index [17], ENSO 3.4 index [18] and AMO index. The poor correlation between
the sine approximation (z5) and measured PDO is shown in Figure 5.
Figure 5: Comparison
of idealized approximation of ocean cycle effect and the calculated effect from
PDO and ENSO.
The AMO index [19] is formed from area-weighted
and de-trended SST data. It is shown with two different amounts of smoothing in
Figure 6 along with the good match with the sine approximation, (z5) with A =
0.298.
Figure 6: Comparison
of idealized approximation of ocean cycle effect and the AMO index through 2020.
The high Coefficient of Determination in Table 1 and the
comparison in Figure 6 corroborate the assumption that the sine profile defined
by Equation (z5) provides adequate approximation of the net effect of all named
and unnamed ocean cycles in the calculated AGT anomalies. The AMO index, which
dominates the effect of ocean cycles, might or might not have started the
decline indicated by the approximation. The agency (NOAA) stopped reporting AMO
in Jan 2023.
13. Atmospheric carbon
dioxide
The level of atmospheric carbon dioxide (CO
2) has
been widely measured over the years. Values from ancient times were determined
by measurements on gas bubbles which had been trapped in ice cores extracted
from Antarctic glaciers [20]. Spatial variations between sources have been
found to be inconsequential [2]. The best current source for atmospheric carbon
dioxide level [21] is Mauna Loa, Hawaii. The left graph in Figure 7 provides
insight as to the fraction of atmospheric CO
2 for various times and
conditions. The planet came perilously close to extinction of all land plants and
animals due to the low level of CO
2 at the end of the last
glaciation. For plant growth, even at the current level the atmosphere is
impoverished for CO
2.
Figure 7: Atmospheric
carbon dioxide levels.
The trajectory shape, including
data back to 1700 from Law Dome (275 ppmv), was used as a proxy to extrapolate
TPW back to 1700.
14. Climate sensitivity
determined using MODTRAN6
MODTRAN6 calculates the radiation flux given inputs of water
vapor, CO2, and surface temperature. The procedure to determine
Climate Sensitivity (CS) to CO2 is simply to find the flux change separately
from CO2 change and temperature change holding water vapor constant
and then apply:
ꝺT/ꝺCO2 = ꝺT/ꝺFlux *ꝺFlux/ꝺCO2 * CO2/T
This gets the temperature change as a ratio to CO2
change. Multiply by the CO2 ppmv change to get the temperature
change in K.
For the 1976 standard atmosphere;
Water column, atm, cm
|
CO2
|
Temperature, K
|
Flux
|
Partial derivative
|
1762.3
|
400
|
288.15
|
269.339
|
|
400
|
288.35
|
269.611
|
ꝺT/ꝺF = 0.2/0.272 = 0.735
|
407
|
288.15
|
269.320
|
ꝺF/ꝺCO2 = -0.019/7 = -0.00271
|
ꝺT/ꝺCO2 = 0.735 * -0.00271 * 400/288.15
= -0.00276 K/ppmv CO2
Because the temperature is reduced by added CO2
the temperature must be increased by the same amount to obtain the required
flux. Climate Sensitivity, increasing pre-industrial CO2 = 275 ppmv
by 275 ppmv, for this calculation is then CS = 275 * 0.00276 = +0.76 K.
The same procedure was applied to the other conditions which
have default values available in MODTRAN6. Like zones were averaged winter and
summer and zones weighted 34.2% tropics (to ±20 deg latitude), 52.4% mid
latitude (±20 to ±60 deg latitude), and 13.4% subarctic (±>60 deg latitude).
This calculation, which does not account for the increase in WV, resulted in CS = 1.07 K for doubling CO2 to 550 ppmv
from 275 ppmv.
These calculations of CS use the default values in MODTRAN6.
Assessments in Section 2 have determined that CS is not significantly different
from zero.
15. Sunspot numbers
Sunspots have been regularly recorded since 1610. In 2015
historical (V1) SSN were reevaluated in light of current perceptions and more
sensitive instruments and are designated as V2. The V2 SSN data set is used
throughout this assessment. V2 SSN [15] are shown in Figure 8.
Sunspot numbers (SSN) are seen to be in cycles each lasting
approximately 11 years. Cycle 24 which peaked in 2014, was comparatively low.
It became near zero in late 2018. Cycle 25 is substantially higher than 24 but
monthly data indicate it has peaked.
The Maunder Minimum (1645-1700), an era of extremely low SSN,
was associated with the Little Ice Age. The Dalton Minimum (1790-1820) was a
period of low SSN and low temperatures. An unnamed period of low SSN (1880-1930)
was also accompanied by comparatively low temperatures.
An assessment of this is that sunspots are somehow related
to the net energy retained by the planet, as indicated by coincident changes to
the average global temperature trend. Fewer sunspots are associated with
cooling, and more sunspots are associated with warming. Thus the hypothesis is
made that SSN are proxies for the rate at which the planet accumulates (or
loses) radiant energy over time. Therefore the time-integral of the SSN anomalies
is a proxy for some of the amount of energy retained by the planet above or
below breakeven.
Also, a lower solar cycle over a longer period might result
in the same increase in energy retained by the planet as a higher solar cycle
over a shorter period. Both amplitude and duration are inherently accounted for
in Equation (1).
SSN change correlates with change to Total Solar Irradiance
(TSI) so SSN anomaly could also be acting as proxy for TSI anomaly. Because AGT
change has been found to correlate with SSN change, the SSN change might also
act as a catalyst on some other factor (perhaps clouds [22]) which have a substantial
effect on AGT. Considered forcings are a power thing so each yearly average
power quantity is divided by the effective thermal capacitance to obtain the
temperature increment (an energy thing). Ocean cycles are considered to contribute
temperature directly; any accompanying forcing averages to zero over time.
Figure 8: V2 SSN [15] thru 2020
16. AGT measurement data
set
In the last few years, reported temperature data, especially
land temperature data, have been changed by the reporting agencies. This
detracts from their applicability in any correlation.
Rapid year-to-year changes in reported temperature anomalies
are not physically possible for true energy change of the planet. The sharp
peak in 2015-2016, which coincides with an extreme El Nino, is especially
distorting.
A further bit of
confusion is introduced by satellite determinations. Anomalies they report as
AGT anomalies are actually for the lower troposphere (LT), have a different
reference temperature (reported anomalies determined using satellite data are
about 0.2 K lower), and appear to be somewhat more volatile (about 0.15 K
further extremes than surface measurements) to changes in forcing. They are, however, essentially free from
uncertainty in UHI effect on measurements.
The data set used for this assessment is the current (4/14/24)
HadCRUT5 data set [23] which reports through 2023. This set is graphed in
Figure 9.
Figure 9: HadCRUT5 data set as used here.
Temperature measurements of the equatorial Pacific which are
used for determining ENSO (Ninos) have a temperature trend of zero as shown inf
Figure 9.2.
Figure 9.2 Temperature measurements in the equatorial
Pacific for determining Nino.
17. The AGT Model
Most modeling of global climate has been with Global Climate
Models (GCMs) where physical laws are applied to a three-dimensional grid
consisting of hundreds of thousands of discrete blocks (elements). Interactions
between the discrete blocks are analyzed using super computers with an end
result being calculation of the AGT trajectory. This might be described as a
‘bottom up’ approach. Although theoretically promising, multiple issues
currently exist with this approach. Reference [13]
discloses
that essentially all of the more than 100 current GCMs are obviously faulty. The growing separation between calculated and measured AGT
as shown at Figure 9 in Ref. [14] also suggests some factor is missing.
The approach in the analysis presented here is ‘top down’.
This type of approach has been called ‘emergent structures analysis’. As
described by Dr. Roy Spencer in his book The great global warming Blunder, “Rather
than model the system from the bottom up with many building blocks, one looks
at how the system as a whole behaves.” That approach is used here with strict
compliance with physical laws.
The basis for the algorithm for assessment of AGT is the first law of
thermodynamics, conservation of energy, applied to the entire planet as a
single entity. Much of the available data are forcings or proxies for forcings
which must be integrated (mathematically as in calculus, i.e. accumulated over
time) to compute energy change. Energy change divided by effective thermal
capacitance is temperature change. Temperature change is expressed as anomalies
which are the differences between annual averages of measured temperatures and
some baseline reference temperature; usually the average over a previous
multiple-year time period. (Monthly anomalies, which are not used here, are
referenced to previous average for the same month to account for seasonal norms.)
With CO2
rejected as a significant contributor to warming, the remaining factors to be
explicitly considered are:
Ocean cycles
SSN
WV
the tiny net feedback from the degree
or so increase in AGT which has occurred since the depths of the Little Ice
Age.
These factors
are combined in an EXCEL file, with coefficients (A,B,C,D,F) assigned to each
factor. The file is set up for numerical integration in yearly steps, where any
EXCEL row is as follows:
Tanom = Tanom(n-1) + A/2 * sin((yn
– 1925) * 2 * π/69.6)– A/2 * sin((y(n-1) – 1925) * 2 * π/69.6)+
thcap-1 * {B*[Sy-Sref] + C*(lnTPWn - lnTPW(n-1)]
– F * [(Ty/T1700)4 – 1]} (1)
Where:
Tanom =
Calculated average global temperature anomaly at the end of year y with respect
to the baseline of the anomaly for the measured temperature data set, K
A =
highest-to-lowest extent in the sine approximation of the net effect on
planet AGT of all ocean cycles, K
y = year for
which the net gain or loss in temperature (energy) is being calculated
n = any year
thcap = effective thermal capacitance [1] of the planet = 17±7
W yr m-2 K-1
1895 =
Selected beginning year of acceptably accurate worldwide temperature anomaly
measurements to be compared to calculated anomalies.
B = combined
proxy factor and influence coefficient for energy change due to sunspot number
‘anomaly’ change, W yr m-2
Sy
= average daily v2 sunspot numbers [15,16] in year y
Sref =
baseline for referencing SSN anomalies. Average v2 SSN 1640-2018.
C = combined
proxy factor & influence coefficient for energy change due to TPW change, W
yr m-2
TPWn
= total precipitable water in year y, kg m-2 (from measurements and
extrapolation for Fig 3)
F = 1 to
account for change to S-B radiation from earth due to AGT change, W yr m-2
Ty
= AGT calculated by adding the HadCRUT4 reference temperature to the reported
anomaly, K
T1700
= AGT in 1700 = 288.05 K
D = starting
value for Tanom (Tanom in 1699) which shifts the calculated trajectory
vertically on the graph, without changing its shape, to best match the measured
data, K.
The attribution of each factor is determined by maximizing
the Coefficient of Determination, R2. Wikipedia has a good example
for how to set up the file to determine R2.
18. Comments
regarding the method used in developing and using Equation (1)
Selection of causal factors must be rational; projections
before and after the matched period must be reasonable; and R2 must
be high for results to be useful.
Equation (1) is calibrated against measured AGT to determine
the partial attribution of each preselected main causal factor of climate
change. The attribution of each factor is revealed by the derived coefficients
which are adjusted by trial-and-error to obtain the highest R2. Best
estimate for the coefficients is the set which produces the best match of
calculated to measured AGT 1895-2023.
Several runs with different assumed values for Sref showed
low sensitivity to this parameter and also indicated lower sensitivity to SSN
than previously determined. The average SSN value, including 60 years of zero
SSN preceding the start of the warmup in 1700, is 66. Setting Sref = 66
resulted in estimated AGT at the depths of the Little Ice Age (LIA) to be about
1.1 K below current measured AGT. This determination of LIA AGT is consistent
with estimates of AGT at the depths of the LIA by others.
19. Results from the AGT model
By definition, energy change (the average power or forcing)
for each year divided by effective thermal capacitance is temperature change
for that year.
In all cases in this document coefficients (A, B, C, & D)
are reported which achieved maximum R2. F=1 for all cases which
accounts for increased temperature driving absorb/emit as well as the radiation
which goes through the ‘atmospheric window’. Incremental convergence to maximum
R2 is accomplished by sequentially and
repeatedly adjusting the coefficients.
Measured temperature anomalies in Figure 10 are data as
shown in Figure 9. The excellent match of the up and down trends since before 1900 of
calculated and measured temperature anomalies, shown here in Figure 10, demonstrate
the usefulness and validity of the calculations. All reported values since
before 1900 are within the range ±2.5 sigma (±0.225 K) from the calculated
trend. Note: The variation is not in the method, or the measuring instruments
themselves, but results from the effectively roiling (at this tiny magnitude of
temperature change) of the object of the measurements. [44]
Sunspot numbers for
the years 2017-2023 are from Australian Bureau of Meteorology [16]. After 2023 the assumptions for the calculations are listed on the graph.
Some noteworthy volcanoes and the year they occurred are also
shown on Figure 10. Prior to 1988 only an approximation of the WV trend is
available so no consistent AGT response is observed. The slight reduction of
measured temperature compared to calculated temperature in 1991 might have been
contributed to by mount Pinatubo, Volcano Explosivity Index (VEI) = 6.
Much larger volcanoes, VEI 7 or more (each VEI
number is ten times the intensity of the next lower number), can cause significant
temporary global cooling from the added reflectivity of aerosols and airborne
particulates. The Tambora eruption, VEI 7, which started on April 10, 1815 and
continued to erupt for at least 6 months, was approximately ten times the
magnitude of the next largest in recorded history and led to 1816 which has
been referred to as ‘the year without a summer’. The cooling effect of that
volcano exacerbated the already cool temperatures associated with the Dalton
Minimum.
Figure 10: Measured average global temperature anomalies with calculated past and future trends using Sref = 66 and with V2 SSN. R2 = 0.930.
Notice also in
Figure 10 the small difference in prediction with and without sunspots. This
is because AGT is dominated by WV and, if the WV continues to increase at
the trend rate since 1988, it might prevent the temperature decline many are
predicting as a result of the quiet sun.
Coefficients in Equation (1) which were determined by
maximizing R2 identify contributions for each of the factors
explicitly considered. Factors not explicitly considered (such as unaccounted for residual (apparently random)
variation in reported annual measured temperature anomalies, aerosols, CO2,
other non-condensing ghg, volcanoes, ice change, etc.) must find room in
the unexplained residual, and/or by occupying a fraction of the effect
otherwise accounted for by each of the factors explicitly considered.
Values of the derived coefficients and other results are
summarized in Table 1. Note that a coefficient of determination, R2
= 0.93 means a correlation coefficient of 0.96. Each % cause includes the added amount
from its effect on AGT.
Some of the variation of measured temperatures
is removed by smoothing using a 5-year running average. The coefficients are
unchanged but results in a higher R2. The resulting graph is shown
in Figure 10.6 and the associated data as file # Zs5sm in Table 1.
Figure 10.6: Measured
average global temperature anomalies with calculated past and future trends using
Sref = 66, V2 SSN and measured temperatures 5-year smoothed prior to maximizing
R2. R2 = 0.958.
The effect of different values for thcap have also been
investigated [53].
Table 1: A, B, C, D refer to coefficients in Equation 1. The column headed # is a code identifying the particular EXCEL file used.
#
|
Fig
|
Period end
|
OCEAN
A
|
SUN
B
|
TPW
C
|
Starting anomaly
D
|
R2
|
1895-end ΔTTPW K
|
% cause of 1909-end AGT change
|
sun
|
sea
|
TPW
|
ZsH5t
|
10
|
2020
|
.2716
|
.0015
|
129.6
|
-.477
|
.930
|
.885
|
16.1
|
16.6
|
67.3
|
Zs5sm
|
10.6
|
2020
|
.2716
|
.0015
|
129.6
|
-.477
|
.958
|
.885
|
16.1
|
16.6
|
67.3
|
As shown in Figure 11, the AGT increase trend referred to as
Global Warming or Climate Change has been profoundly dominated by water vapor
increase trend. The future AGT trend depends primarily on WV. Long term WV
increase correlates with irrigation increase and is inherently self-limiting.
AGT increase is therefore also inherently self-limiting. Short term WV fluctuation
appears to vary randomly with ocean surface temperature roiling and occasional
transients associated with el Nino/la Nina. The attribution to WV assumes
continuation of prior TPW increase trend, 0.051 kg/m2/yr, which
might not occur.
Figure 11: Attribution
of each factor to temperature change as of 2023 for both cases.
The high
attribution of WV to AGT is explained by the population gradient from global
average of about 8,000 ppmv (0.8%) WV at surface (4% in the tropics) to 149
ppmv at the tropopause. Most of the outward directed photons from WV molecules can
make it all the way to space. This is demonstrated by the ‘hash’ in radiation flux
from the WV as shown in TOA graphs of radiation flux vs wavenumber, Figures 1
and 1.5.
20. Attribution
quantified by sunspot number anomaly proxy.
Although the
comparatively weak connection between AGT and SSN (which acts as a proxy for
the influence of solar change on AGT change) is demonstrated, the mechanism by
which this takes place remains somewhat speculative.
Various papers have been written
that indicate how the solar magnetic field associated with sunspots can
influence climate on earth. These papers posit that decreased sunspots are
associated with decreased solar magnetic field which decreases the deflection
of and therefore increases the flow of galactic cosmic rays on earth.
Henrik Svensmark, a Danish physicist, found that increased
flow of galactic cosmic rays on earth caused increased low altitude (<3 km)
clouds and planet cooling. An abstract of his 2000 paper is at [24]. Marsden
and Lingenfelter also report this in the summary of their 2003 paper [25] where
they make the statement “…solar activity increases…providing more shielding…less low-level cloud cover… increase surface air
temperature.” These findings have been further corroborated by the cloud
nucleation experiments [26] at CERN.
These papers [24, 25] associated the increased low-altitude clouds with
increased albedo leading to lower temperatures. Increased low altitude clouds
would also result in lower average cloud altitude and therefore higher average
cloud temperature. Although clouds are commonly acknowledged to increase
albedo, they also radiate energy to space so increasing their temperature
increases S-B radiation to space which would cause the planet to cool. Increased
albedo reduces the energy received by the planet and increased radiation to
space reduces the energy of the planet. Thus the two effects work together to contribute
to AGT change of the planet.
A contributing or possibly alternate speculation is that
clouds might also be affected by solar wind. End result is the same: Sunspot
number anomalies are proxies for attribution of solar change to AGT change.
Simple analyses [22]
indicate that either an increase of approximately 186 meters in average cloud
altitude or a decrease of average albedo from 0.3 to the very slightly reduced
value of 0.2928 would account for all of the 20th century increase
in AGT of 0.74 K. Because the cloud effects work together, most of AGT change
is from WV change, and part of the temperature change is due to ocean
oscillation (low in 1901, 0.17 higher in 2000), substantially less cloud change
would suffice.
21. Hind Cast
Estimate
Average global temperatures were not directly measured in 1700
(accurate thermometers had not been invented yet). Recent estimates, using
proxies, are few. The temperature anomaly trend that Equation (1) calculates
for that time is consistent with other estimates.
As a possibility, the period and amplitude of oscillations
attributed to ocean cycles demonstrated to be valid after 1895 are assumed to
maintain back to 1700. Equation (1) begins integration in 1700 with D as the
beginning of the combined value.
Temperature anomalies thus calculated, estimate likely
trends since 1700 and actual trends of reported temperatures since they have been
accurately measured world wide. This
assessment is shown in Figure 12.
Figure 12: Calculated
temperature anomalies using Equation (1) with the same coefficients as for
Figure 10.6 and V2 SSN. Measured temperature anomalies from Figure 9 and anomaly
range estimates determined by Loehle are superimposed.
A survey [27] of non-tree-ring global temperature estimates
was conducted by Loehle including some for a period after 1700. Simplifications
of the 95% limits found by Loehle are also shown on Figure 12. The spread
between the upper and lower 95% limits are fixed, but, since the anomaly
reference temperatures might be different, the limits are adjusted vertically
to approximately bracket the values calculated using Equation (1). The fit
appears reasonable considering the uncertainty of all values.
Calculated temperature anomalies look reasonable back to 1700. They
qualitatively agree with Vostok, Antarctica ice core data but decidedly differ
from Sargasso Sea estimates during that time (see the graph for the last 1000
years in Reference [2]). Worldwide assessments of average global temperature,
that far back, are sparse and speculative. Ocean oscillations might also have
been different from assumed.
22. Step changes in AGT are not possible
Interpretation of a reported sudden AGT increase (or
decrease) as planet energy increase (or decrease) is physically impossible
because of the huge effective thermal capacitance which results in a 5-year
time constant [1] for thermal response of the planet to a step change in
forcing.
23. Caveats on
Predictions
1. A candidate cause must not have already been ruled out.
CO2 was ruled out in Section 2.
2. Sunspot numbers are a proxy for both the influence of TSI
and also, as found by Svensmark [24], the influence of clouds. Records for
neither TSI nor cloud cover extend back to the LIA.
3. AGT is very sensitive to total cloud cover [22] which in
turn varies with water vapor content (Fig 3), sunspots, surface temperature and
atmosphere temperature.
4. Global average ocean cycle surface temperatures (α trend) are
believed to vary in period and intensity in response to as yet uncertain cause.
The approximation here is working well since 1895. Future measurement might
indicate a different period and/or better wave form or better yet an ocean
cycle prediction based on planetary cycles or other predictable natural
phenomenon. In any event, their attribution is cyclic, i.e. no significant net
attribution on the long term.
24. Conclusions
Three factors explain essentially all of AGT change since
before 1900. They are ocean cycles, accounted for with an approximation, solar influence
quantified by a proxy which is the SSN anomaly and, the gain in atmospheric
water vapor measured since Jan, 1988 and extrapolated earlier using measured CO2
as a proxy.
Others have looked at only amplitude or only duration
factors for solar cycles and got poor correlations with average global
temperature. As sometimes done, this procedure violates the relation between
math and the physical world. The excellent (and computationally valid)
correlation comes by accounting for both amplitude and duration, which is done
in Equation (1). Prediction of future sunspot numbers more than a decade or so
into the future has not yet been confidently done.
The β-trend is the estimated true average
global temperature trend (the net average global energy trend) during the
planet warm up from the depths of the Little Ice Age.
The net effect of ocean oscillations is to cause the surface
temperature α-trend to oscillate above and below the β-trend. Equation (1)
accounts for both trends. Measured ocean cycles appear to have not yet started the
decline assumed in the approximation.
Warming attributed to increasing water vapor explains most
of past warming and the possibly still rising measured AGT trend in spite of
declining sunspot and ocean cycle forcings. Increasing WV might delay or even
prevent global cooling.
The measured water vapor increase has been markedly more
than expected from liquid surface water temperature increase alone. The extra
increase appears to be mostly (about 90%) from increased irrigation. WV
increase is ultimately self-limiting.
Long term (decades) prediction of average global
temperatures depends weakly on long term prediction of sunspot numbers. Longer
term (centuries) will depend partly on prediction of longer term variation in
solar output.
Humanity has wasted over a trillion dollars in failed
attempts using super computers to demonstrate that added atmospheric CO2
is a primary cause of global warming and in misguided activities to try to do
something about it. An unfunded engineer, using only a desk top computer,
applying a little science and some engineering, discovered a simple equation
that unveils the mystery of global warming and describes what actually drives
average global temperature. The refined version of the equation is presented herein
as Equation (1).
25. References:
1. Effective
thermal capacitance & time constant: Schwartz, Stephen E., (2007) Heat
capacity, time constant, and sensitivity of earth’s climate system, J. Geophys. Res., vol. 113, Issue D15102,
doi:10.1029/2007JD009373
2. 2008
assessment of non-condensing ghg https://www.researchgate.net/publication/350530743_Historical_Data_on_Global_Warming_provided_by_US_Government_Agencies
3.
Phanerozoic AGT & CO2: http://www.geocraft.com/WVFossils/Carboniferous_climate.html
4. UAH v 6.0
numerical data http://www.nsstc.uah.edu/data/msu/v6.0/tlt/uahncdc_lt_6.0.txt
5. Average
elapsed time to emit a photon https://sealevel.info/Happer_UNC_2014-09-08/Another_question.html
6. Average elapsed time to emit a photon http://rabett.blogspot.com/2013/04/this-is-where-eli-came-in.html.
7. Time
between molecule collisions: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/frecol.html
8. Barrett TOA radiation http://www.warwickhughes.com/papers/barrett_ee05.pdf
9. Water
vapor vs altitude http://homeclimateanalysis.blogspot.com/2010/01/earth-radiator.html
10. EPA
GWP https://www3.epa.gov/climatechange/ghgemissions/gwps.html
11. NASA/RSS TPW through Dec 2022 https://data.remss.com/vapor/monthly_1deg/tpw_v07r02_198801_202212.time_series.txt
12. Willis’
TPW graph: https://wattsupwiththat.com/2016/07/25/precipitable-water
13. Epic fail
of ‘consensus’ method http://www.drroyspencer.com/2013/06/still-epic-fail-73-climate-models-vs-measurements-running-5-year-means
14. Analysis
with V1 SSN sans water vapor: Pangburn 2014, Energy & Environment V25, No. 8 1455-1471
15. V2
sunspot numbers http://www.sidc.be/silso/datafiles
16. Australian Bureau of Meteorology: http://www.sws.bom.gov.au/Solar/1/6
17. PDO https://www.ncdc.noaa.gov/teleconnections/pdo/
18. El Nino
3.4 index http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/nino34.long.data
(Linked from http://www.cgd.ucar.edu/cas/catalog/climind/TNI_N34
)
19. AMO index http://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data
20. CO2
level at Law Dome, Antarctica: http://cdiac.ornl.gov/ftp/trends/co2/lawdome.combined.dat
21. Mauna Loa
CO2: https://www.co2.earth/monthly-co2
22.
Sensitivity of AGT to clouds http://lowaltitudeclouds.blogspot.com
23. Current HadCRUT5 data set:
https://www.metoffice.gov.uk/hadobs/hadcrut5/data/HadCRUT.5.0.2.0/download.html
24. Svensmark
paper: Phys. Rev. Lett. 85, 5004–5007
(2000) http://prl.aps.org/abstract/PRL/v85/i23/p5004_1
25. Marsden
& Lingenfelter 2003, Journal of the
Atmospheric Sciences 60: 626-636 http://www.co2science.org/articles/V6/N16/C1.php
26. CLOUD experiment at CERN http://indico.cern.ch/event/197799/session/9/contribution/42/material/slides/0.pdf
27. Loehle
non-tree-ring AGT http://www.econ.ohio-state.edu/jhm/AGW/Loehle/Loehle_McC_E&E_2008.pdf
28. MODTRAN6
defaults http://modtran.spectral.com/modtran_faq
29. K & T
chart http://chriscolose.wordpress.com/2008/12/10/an-update-to-kiehl-and-trenberth-1997/
30. MacRae assessment of dCO2/dT https://wattsupwiththat.com/2015/06/13/presentation-of-evidence-suggesting-temperature-drives-atmospheric-co2-more-than-co2-drives-temperature/
31. Transportation fuel https://www.eia.gov/outlooks/ieo/pdf/transportation.pdf
32. Fuel properties https://en.wikipedia.org/wiki/Gasoline
33. World electricity generation https://yearbook.enerdata.net/electricity/world-electricity-production-statistics.html
34. Fuel
sources for electricity generation https://www.eia.gov/outlooks/ieo/exec_summ.php
35. WV from
coal combustion http://energyeducation.ca/encyclopedia/Water_vapour
36. Energy
content of bituminous coal https://en.wikipedia.org/wiki/Energy_density
37. Global
water withdrawal http://www.fao.org/nr/water/aquastat/water_use/index.stm
38. Irrigated
agricultural area http://www.worldwatch.org/global-irrigated-area-record-levels-expansion-slowing-0
39. Annual
fresh water withdrawal http://www.fao.org/nr/water/aquastat/didyouknow/index2.stm
40. 70% of
withdrawal is for agriculture http://www.fao.org/nr/water/aquastat/infographics/Withdrawal_eng.pdf
41. Surface
irrigation https://water.usgs.gov/edu/irfurrow.html
42. Frequency
of furrow irrigation https://naldc.nal.usda.gov/download/54786/PDF
43. Pond
evaporation rate http://www.nws.noaa.gov/oh/hdsc/Technical_papers/TP13.pdf
44. Animation
of roiling SST https://www.youtube.com/watch?v=aKMY4JRN0kk
45. Q-M
applied to water vapor and carbon dioxide in the atmosphere (loads slowly): http://www.dtic.mil/dtic/tr/fulltext/u2/477312.pdf
46. NASA/GISS
TOA graph source https://www.giss.nasa.gov/research/briefs/2010_schmidt_05/
47. MODTRAN
calculator http://climatemodels.uchicago.edu/modtran/
48. MODTRAN6
calculator http://modtran.spectral.com/modtran_home#plot
49. Deleted.
50. Vapor
pressure of water https://en.wikipedia.org/wiki/Vapour_pressure_of_water
51. Theory of
redirected energy: http://energyredirect3.blogspot.com
52. HITRAN
data base calculator http://www.spectralcalc.com/spectral_browser/db_intensity.php
53. DIY
climate change analysis http://diyclimateanalysis.blogspot.com
54. Surface irrigation 86%: http://www.fao.org/3/I9253EN/i9253en.pdf
55. Bolton equation for water
saturation p T https://glossary.ametsoc.org/wiki/Clausius-clapeyron_equation
56. Ice and mixed phase clouds: http://www.cas.manchester.ac.uk/resactivities/cloudphysics/background/ice/
57. Wexler, vapor pressure of
water: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5312760/
58. Wexler, thermodynamic
calculations for the vapor pressure of ice: https://nvlpubs.nist.gov/nistpubs/jres/81A/jresv81An1p5_A1b.pdf
59. Ocean temperatures: https://rwu.pressbooks.pub/webboceanography/chapter/6-2-temperature/
60. Water vapor generated by
humanity is 90% from irrigation: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2001WR000355
61. Water vapor vs CO2 for planet
warming: https://watervaporandwarming.blogspot.com
62. Accurate formulae for calculating saturation
vapor pressure: https://journals.ametsoc.org/view/journals/apme/57/6/jamc-d-17-0334.1.xml
63. Ground
level WV 5 g/kg ≈ 8000 ppmv in 1992: https://www.eso.org/gen-fac/pubs/astclim/espas/pwv/mockler.html
Fig 1
64. Ground
level WV 8,000 ppm WV vs altitude Spectralcalc: https://www.spectralcalc.com/atmosphere_browser/modify_atmosphere.php
65. Wijngaarden and Happer paper: https://arxiv.org/pdf/2006.03098
66. Koutsoyiannis
May 2024 paper showing CO2 change follows temperature change: https://www.researchgate.net/publication/380457911_Stochastic_assessment_of_temperature_-_CO_causal_relationship_in_climate_from_the_Phanerozoic_through_modern_times