Saturday, August 6, 2016

8/17/18
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
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, up to about 8-12 km, of the population density of water vapor (WV) molecules, explain why water has a dominate effect on climate. Atmospheric carbon dioxide (CO2) and other trace greenhouse gases have little if any effect on climate. Much of upward photon emission from water vapor molecules goes directly to space progressively more with increasing altitude especially up to about 10 km on average, 12 km at low latitudes. Above this, nearly all of emission from water vapor with wavenumber less than about 550/cm escapes directly to space.

Reported average global temperature (AGT) since before 1900 is accurately explained (96+% match with measured trend 1895-2018). Although the influence of WV increase is closely proportional to the increase due to the sun (which is quantified by a proxy; the time-integral of sunspot number anomalies), the temperature change 1909-2018 is probably best explained by derived attribution of ocean cycles to the average global temperature rise (21.7%), sunspot number anomaly proxy (17.8%) and increased atmospheric water vapor (60.5%). Since about 2005 the increasing water vapor has been countering the AGT decline which would 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’. In all that follows, insignificant factors are excluded whether explicitly stated or not.

1. Introduction
The only way that energy can significantly leave earth is by thermal radiation. Only solid or liquid bodies and greenhouse gases (ghg) can 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 64 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 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 energy 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 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:
1. In the late Ordovician Period, the planet plunged into and warmed up from the Andean/Saharan ice age, all at about 10 times the current CO2 level [3].
2. Over the Phanerozoic eon (last 542 million years) there is no correlation between CO2 level and AGT [3].
3. Antarctic ice core data show that during the last and previous glaciations AGT trend changed directions before CO2 trend [2].
4. Since 2001, average temperature uptrend calculated by Global Climate Models (GCMs, aka General Circulation Models) which assume CO2 causes AGW is about twice 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.

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]
6. Average global water vapor had been increasing faster than it should, calculated on the basis of increased vapor pressure of water resulting from temperature increase of the liquid surface water. (Section 8 here) This demonstrates that average global temperature increase has been driven by water vapor increase, not the reverse.
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.

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. Comparison by the ratio of the summation of intensities (line lengths) for each wavenumber for each molecule species is 8.7/0.07 = 124. On average at ground level, according to the low populations used by Hitran, WV molecules outnumber CO2 molecules by about 8,000/330 ≈ 24 to one. After accounting for molecule count, each WV molecule is still 124/24 ≈ 5 times more effective at warming (absorb/emit of thermal radiation) than a CO2 molecule.

The relative effectiveness of the increases of WV and CO2 over the last 30 years is calculated as follows:
CO2 increase in 3 decades, 1988 to 2018: 407 - 348 = 59 ppmv

Average global water vapor increase trend from Figure 3, which is a graph of NASA/RSS TPW data, is 0.04272/28.9 * 100 * 10 = 1.47 % per decade.

From Figure 2, at 30 degrees latitude (area to pole = area to equator) average global WV = 10,000 ppmv. WV increase in 3 decades = .0147 * 10,000 * 3 = 441 ppmv

Therefore, WV increase has been 441/59 * 5 = 37+ times more effective at increasing ground level temperature than CO2 increase 1988-2018. (Most of the world has been falsely indoctrinated)


Well above the tropopause, about 10 km (32,808 feet) radiation emitted from molecules there to space is primarily from CO2 molecules. If you ignore the increase in water vapor (big mistake), near the surface, WV averages about 10,000 ppmv. The increase in absorbers at ground level since 1900 is then about 10,410/10,295 ≈ 1%. WV above the tropopause is limited to about 32 ppmv because of the low temperature (~ -50 °C) while the CO2 fraction remains essentially constant with altitude at 410 ppmv; up from about 295 ppmv in 1900. The increase in emitters to space at high altitude (~> 30 km, 0.012 atm), and accounting for the lower atmospheric pressure, is (410 + 32)/(295 + 32) * 0.012 ≈ 1.6%. This easily explains why CO2 increase does not cause significant warming (except at the poles) and might even cause cooling. 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 is already low.


Figure 0.25: At zero altitude, CO2 absorb/emit is barely discernable compared to WV.

9. Global average water vapor is about 10,000 ppmv (Figure 2). Based on TPW percent increase (Figure 3), WV increase since 1988 has been about 0.0425/29 * 10,000 = 14.66 ppmv per year. CO2 (348 ppmv in 1988) increase has been about (410 – 348)/30 = 2.067 ppmv per year. Therefore, about 14.66/2.067 ≈ 7 WV molecules were added for each CO2 molecule.
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%

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 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 the energy 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 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 water vapor which, by far, is the most important ghg and appears to be the only significant ghg.


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 that 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 relaxation time (average amount of time that passes between absorption and emission of a photon by a molecule) for CO2 in the atmosphere is temperature dependent [5, 6, 49]. (Common sense mandates that if relaxation time was zero there would be no way to determine absorption) The temperature dependency is shown in Figure 0.3. The elapsed time between collisions between gaseous molecules at sea level average temperature and pressure is about 0.0002 µsec [7]. Collisions result 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.

Figure 0.3: EMR energy absorbed by CO2 is thermalized. [5, 6, 49]


Radiation energy transfer at the gas molecule level is the mechanism of the misleadingly named greenhouse effect (GHE). Radiation energy travels from molecule to molecule at the speed of light but dwells in the ghg molecules for the relaxation time. More ghg molecules means longer cumulative dwell. 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 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. About 95% of thermal radiation that gets absorbed from the surface is absorbed by ghg within the first meter; 99% within two meters.

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.

A common observation of thermalization by way of water vapor 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 GHE and that water vapor is a ghg.


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.

Energy absorbed by ozone begins to be significantly redirected to WV above 10 km, reaches a maximum below 50 km and stays at the maximum level above 50 km.
Figure 0.5: 1976 Standard Atmosphere at MODTRAN6 default values.


Figure 0.6: 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 but is only about 73% of 382 – 269 = 113 W/m2 as calculated by MODTRAN.

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 at 20 km and higher 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 about 10 km means fewer molecules capable of absorbing radiation from water vapor molecules at lower elevation so most of the photons at these lower wavenumbers 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 CO2 (and O3) molecules becomes significant as does radiation from them to space.

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 such as shown in Figures 1 and 1.5 show the ‘notch’ associated with the CO2 absorb/emit band. Notch development with increasing altitude was shown in Figures 0.5 and 0.6. Existence of this notch demonstrates that terrestrial radiation in this wavelength range is absorbed by IR active gases which include water vapor and the ghg which do not condense in the atmosphere such as CO2

Perhaps not as obvious, the presence of the 600-740 wavenumber notch (~ beige area) along with smaller notch at ozone (O3) also demonstrates thermalization and that the radiation energy which was absorbed by trace IR active molecules was thermalized and substantially redirected to the absorb/emit lines of water vapor molecules. The WV molecules, progressively with altitude, emit the radiation energy to space.

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 is about 0.2 W /m^2 / cm^-1 * 140 cm^-1 = 28 W/m^2. The 46 – 28 = 18 W/m^2 that is not emitted at the wavenumber range 600-740 has to be emitted at other wavenumbers. The 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.


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 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.


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.


Liquid water has a vapor pressure which depends ONLY on the temperature of the liquid water. The relation is available from multiple sources. Numerical values from Wikipedia [50] are graphed at Figure 1.7 along with the fractional rate of change vs. temperature (dp/dT/p vs. T) over the temperature range of interest for earth climate.
Figure 1.7: Vapor pressure of water and fractional rate of change vs liquid water temperature.

The rate-of-change of vapor pressure is a measure of the ‘extra’ vapor pressure increase from temperature increase resulting from the added water vapor. It is fairly constant, reaching maximum, percent wise, at about 16 °C. This is most effectively calculated by fitting a quadratic (second order polynomial) to the vapor pressure vs. temperature data and then taking the derivative (as in calculus) of the quadratic. The per unit change (%/100 = 1/1) is obtained by dividing by the vapor pressure at that temperature.

The percent change of atmospheric water vapor is assumed to vary directly with the percent change in liquid water 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 and descended) leaving only about 32 ppmv WV above this altitude compared to a global average of about 10,000 ppmv at ground level. Accounting also for reduced pressure of about 0.26 atm results in a WV population per unit volume above the tropopause of 32/10000 * 0.26 ≈ 1/1200 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 32 ppmv above the tropopause, CO2 remains at its ground level value. Therefore, above the tropopause most of the remaining thermalized energy is reverse-thermalized to CO2 molecules which emit it to space.



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).


7. Effect of water vapor increase

Energy goes from ghg molecule to ghg molecule by electromagnetic radiation (EMR) at the speed of light. But the photon energy absorbed by a molecule spends time in the molecule called the relaxation time. Relaxation time is shorter at higher temperature (Fig 0.3). It is about 5 microseconds at room temperature. More ghg molecules means more time spent in 'relaxation' and less time at the speed of light. That is why more water vapor (and at the poles more CO2slows the rate of energy flow from the surface to space so the surface temperature must be increased to produce the same energy flux.

The average global water vapor increase since 1895-2018 is about 10% (Fig 3). The average global temperature increase 1895 to 2018 attributable to WV increase according to Equation (1) and temperature data thru 2018 is about 0.76 K (Table 1).

The procedure to determine the effect of water vapor increase using MODTRAN 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 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 0.62 K to 0.76 K for 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 far more effective at absorbing terrestrial thermal radiation than CO2 molecules. Humanity’s contribution to atmospheric water vapor increase is primarily (≈ 96%) 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.

Because water vapor is a ghg, increased water vapor causes the planet to warm, which further increases 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 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 vapor pressure of water (Figure 1.7) contributing to the water vapor increase. At present water vapor is increasing faster than expected based on AGT increase alone. Global temperature increase since 2002 from the UAH trend is about 0.127 K per decade (this automatically includes any feedback effect). At 15 °C, (59 °F) increase in vapor pressure of liquid water is 6.5% per degree (Figure 1.7). With ‘continuous compounding’ this increases to 0.065 + 0.065^2 + 0.065^3 + … = 0.0695 = 6.95%. The percent increase in water vapor is assumed to be about the same as the percent increase in vapor pressure. Percent increase in water vapor due to temperature increase = 0.127 * 6.95% = 0.882% per decade.


Measured % increase of Total Precipitable Water (TPW) in 28 yr = (29.5-28.25)/28.875 = 0.043 = 4.3%. In 10 yr = 10/28*4.3 = 1.54%. Thus measured increase in WV is about 1.54/.882 ≈ 1.7 times the amount for liquid water temperature increase alone.

The comparison of the measured WV change with the WV change calculated from temperature change can also be shown graphically. The file for calculated change is generated in EXCEL where each row contains:

WVn = WV(n-1) + (Tn – T(n-1) * R * A

Where:
WVn = WV in month n, kg/m^2
Tn = temperature anomaly in month n, K
R = effective rate of WV increase resulting from temperature increase, 0.0695/K = 6.95 %/K
A = Average WV over the period of study = 28.9 kg/m^2

The starting calculated WV is adjusted to make the starting trends the same.


The highest calculated WV is obtained using HadCRUT4 reported temperatures and the lowest is obtained using UAH reported temperatures. The resulting graphs are shown in Figures 2.8 and 2.9.

Figure 2.8: Measured WV vs calculated WV based on HadCRUT4 reported average global temperatures.
Figure 2.9: Measured WV vs calculated WV based on UAH reported average global temperatures

The average ratio of measured WV/calculated WV is obtained by the ratio of the slopes of the regression lines. The ratio for HadCRUT4 is 0.04272/0.033571 = 1.27 and for UAH is 0.04272/0.02612 = 1.64. The observation that WV increased faster than the determination using temperature demonstrates that WV leads the temperature change instead of being caused by it as assumed in the GCMs.

The increased water vapor also causes increased cloud cover and/or lower average cloud altitude which counters temperature increase and will 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]).

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 = 4.5118 * ppmvCO2^0.31286. The result is the right-hand graph of Figure 3 which shows approximately 7% increase 1960-2005.

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 minimum is the average since mid-2016. Estimated future maximum is the slope of the monthly trend since 2003.

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).


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 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 * 0.61/0.28/510.1E6 = 0.00047 km = 0.47 m                       (j)

Water weighs 1000 kg/m3 so evapotranspiration amounts to 470 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. The total amount of WV resulting from irrigation is then
(0.1 * (1 + 0.47)/2 + 0.9 * 0.47) * 266E10 = 132.1E10 m3 = 132.1E13 kg/y                        (k)

These calculations are summarized in Table 0
Water vapor source
E13 kg/y
Irrigation
132.1
Transportation fuel
0.4
Fossil fuel for electricity generation
0.4
Cooling towers, etc. for electricity generation
4.0
Total
136.9
Table 0: Summary of contributions to atmospheric water vapor.

Approximately 132.1/136.9 = 0.96+ or 96+% 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 lower.


Given the earth area of 510E12 m^2 and average precipitation of about a meter or 1000 kg/m^2 the increased water use, mostly for irrigation, results in 136.9E13/5.1E17 = 0.0027 or only about 0.27 % equivalent increase in global precipitation.

10. Effect of TPW increase on clouds (added 9/17/18)
As TPW is increased, condensation (cloud formation) occurs at higher temperature and thus lower average cloud altitude. Lower altitude, higher temperature clouds radiate more energy to the cosmic background. This partially counters the warming 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 K. 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 approximately 0.29 K total highest-to-lowest extent with a period of approximately 64 years (verified by high R2 in Table 1).

The measured AGT trajectory (Figure 9) suggests that the least-biased simple wave form of the effective ocean surface temperature oscillation is approximately saw-toothed. Approximation of the sea surface temperature anomaly oscillation can be described as varying linearly from –A/2 K in 1909 to approximately +A/2 K in 1941 and linearly back to the 1909 value in 1973. This cycle is assumed to repeat before and after with a period of 64 years.

Because the actual magnitude of the effect of ocean oscillation in any year is needed, the expression to account for the attribution of the ocean oscillation in each year to AGT is given by the following:

ΔTosc = (A,y)             K (degrees)                 (2)

where the attribution of the net of ocean oscillations to AGT change is the magnitude of the effect on AGT of the surface temperature anomaly trend of the oscillation in year y, and A is the maximum highest-to-lowest extent of the effect on AGT of the net ocean surface temperature oscillation.


Equation (2) is graphed in Figure 4 for A=0.293
Figure 4: Ocean surface temperature oscillations (α-trend) do not significantly affect the bulk energy of the planet.


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 increases atmospheric water vapor which acts as a forcing and therefore has a time-integral effect on temperature. The approximation, (A,y), accounts for both ways.

SST data is available for three named cycles: PDO index, ENSO 3.4 index and AMO index. Successful accounting for oscillations is achieved for PDO and ENSO when considering these as forcings (with appropriate proxy factors) instead of direct measurements. As forcings, their influence accumulates with time. The proxy factors must be determined separately for each forcing. The measurements are available since 1900 for PDO [17] and ENSO3.4 [18]. This PDO data set has the PDO temperature measurements reduced by the average SST measurements for the planet.

The attribution of PDO and ENSO3.4 to AGT is calculated by:
PDO_NINO = Σyi=1900 (0.017*PDO(i) + 0.009 * ENSO34(i))        (3)

Where:
            PDO(i) = PDO index [17] in year i
            ENSO34(i) = ENSO 3.4 index [18] in year i


How this calculation compares to the idealized approximation used in Equation (2) with A = 0.36 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 saw-tooth approximation for the entire planet per Equation (2) with A = 0.36.

Figure 6: Comparison of idealized approximation of ocean cycle effect and the AMO index through 2017.

The high Coefficients of Determination in Table 1 and the comparisons in Figures 5 and 6 corroborate the assumption that the saw-tooth profile with a period of 64 years provides adequate approximation of the net effect of all named and unnamed ocean cycles in the calculated AGT anomalies.


13. Atmospheric carbon dioxide
The level of atmospheric carbon dioxide (CO2) 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 CO2 for various times and conditions. The planet came perilously close to extinction of all land plants and animals due to the low level of CO2 at the end of the last glaciation. For plant growth, even at the current level the atmosphere is impoverished for CO2.
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:

T/CO2 = T/Flux *Flux/CO2 * 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
T/F = 0.2/0.272 = 0.735
407
288.15
269.320
ꝺF/CO2 = -0.019/7 = -0.00271
T/CO2 = 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 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. The current cycle, called 24, has been comparatively low, peaked in 2014, and is now (Aug 2018) near zero.

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 2018


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.

The data set used for this assessment is the current (5/27/16) HadCRUT4 data set [23] extended through 2018. This set is shown in Figure 9.


Figure 9: HadCRUT4 data set as used here.


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 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,y) – (A,y)(n-1) + 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 saw-tooth 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
(A,y) = value of the net effect of ocean cycles on AGT in year y (α-trend), K
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 1895-2018.


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 (except # Aspl where B is specified), 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]

Projection until 2020 uses the expected sunspot number trend for the remainder of solar cycle 24 as provided [16] by NASA. After 2020 the ‘limiting cases’ are continuation of ocean cycles, continuation of WV trend or constant TPW of 29.5 kg m^-2, and, either assuming sunspots like from 1912 to 1923 or essentially no sunspots which is similar to the Maunder Minimum.

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 caused by mount Pinatubo, VEI 6.


Much larger volcanoes, volcano explosivity index (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 = 0.919070.

Notice also in Figure 10 the small difference in prediction with and without sunspots. This indicates that 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. 

The influence of WV is still quite proportional to solar as demonstrated by arbitrarily doubling the coefficient for SSN and maximizing R2 by adjusting only the coefficients for ocean (A), TPW (C), and starting anomaly (D). The resulting graph, Figure 10.5, looks much like Figure 10 (slightly lower projection) and the Coefficient of Determination is very slightly less but the contribution attributed to the sun is approximately doubled and attribution to WV is noticeably less.
Figure 10.5: Measured average global temperature anomalies with calculated past and future trends using Sref = 66, V2 SSN and sun coefficient B set to 0.000864. R2 = 0.918324.


Values of the derived coefficients and other results are summarized in Table 1. Note that a coefficient of determination, R2 = 0.919070 means a correlation coefficient of 0.96. Values for the coefficients and results are summarized in Table 1. Each % cause includes the added amount from its effect on AGT.

By simply changing the end dates in the R2 calculation, and adjusting the coefficients to re-maximize R2, the contribution of each factor can be determined for any prior year. This was done for 2005 and 2013 with results included in Table 1.

Another demonstration that the influences of WV and solar are similar (nearly proportional) is shown by smoothing the measured temperatures prior to maximizing R2. This converges to a substantially increased solar influence and higher R2. The resulting graph is shown in Figure 10.6 and the associated data as file # Aintsm 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 = 0.967033.


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.
As shown in Figure 11, the AGT increase trend referred to as Global Warming or Climate Change is 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 2018 for case identified as # Aint.


Figure 11.1 is similar to Figure 11 but is for the case identified as Aintsm. The main difference is increased attribution of solar and decreased attribution of WV.
Figure 11.1: Attribution of each factor to temperature change as of 2018 for case identified as # Aintsm.

The high attribution of WV to AGT is explained by the population gradient from global average of about 10,000 ppmv (1%) WV at surface (4% in the tropics) to 32 ppmv at top of tropopause. Most of the outward directed photons from WV molecules at high altitude but below the tropopause 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, Figure 1


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 and part of the temperature change is due to ocean oscillation (low in 1901, 0.1741 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 and V2 SSN. Measured temperature anomalies from Figure 9 and anomaly range estimates determined by Loehle are superimposed. (Rev 8/26/16)


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. If a consistent precision (~±0.1%) global cloud measurement can be established, cloud cover might be added to the equation as an independent parameter.


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.

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 noticeably more than expected from liquid surface water temperature increase alone. 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 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  http://www.middlebury.net/op-ed/pangburn.html
5. 6 microsecond relaxation time at 210 K in atmosphere  http://onlinelibrary.wiley.com/doi/10.1002/qj.49709540302/abstract                          
6. 7.1 microsecond CO2 relaxation in pure gas http://pubs.rsc.org/en/Content/ArticleLanding/1967/TF/TF9676302093#!divAbstract ).      
11. NASA/RSS TPW (they only report the latest month available, 06 means June) http://data.remss.com/vapor/monthly_1deg/tpw_v07r01_198801_201806.time_series.txt
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. Graphic of V2 Solar cycle 24: http://solarscience.msfc.nasa.gov/predict.shtml
20. CO2 level at Law Dome, Antarctica: http://cdiac.ornl.gov/ftp/trends/co2/lawdome.combined.dat
22. Sensitivity of AGT to clouds http://lowaltitudeclouds.blogspot.com
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
34. Fuel sources for electricity generation https://www.eia.gov/outlooks/ieo/exec_summ.php
36. Energy content of bituminous coal https://en.wikipedia.org/wiki/Energy_density
42. Frequency of furrow irrigation https://naldc.nal.usda.gov/download/54786/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
49. Relaxation time of CO2 vs temperature https://pure.tue.nl/ws/files/3478579/109243.pdf
51. Theory of redirected energy: http://energyredirect3.blogspot.com

53. DIY climate change analysis http://diyclimateanalysis.blogspot.com
54. Surface irrigation 86%: http://www.fao.org/3/I9253EN/i9253en.pdf