Monday, February 22, 2016

Effect of increasing water vapor improves match after 2001 at

Cause of Global Climate Change

This monograph is a culmination of more than eight years of work which has now quantified the contribution of atmospheric carbon dioxide (CO2) change to average global temperature change and identified the factors which explain average global surface temperature (AGT) change since before 1900.

The word ‘trend’ is used here for temperatures in two different contexts. To differentiate, α-trend applies to averaging-out the fluctuations in reported average global temperature measurements to produce the average global temperature oscillation resulting from the net of ocean surface temperature oscillations. The term β-trend 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.

The Model
Most modeling of global climate has been with Global Climate Models (GCMs) where physical laws are applied to hundreds of thousands of discreet blocks and the interactions between the discreet 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, some of which are discussed at [1]. Growing separation between calculated and measured AGT as shown, e.g. at [2], discloses that nearly all of the more than 100 current GCMs are obviously faulty. The few which appear to follow measurements might even be statistical outliers of the ‘consensus’ method.

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 tme) 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.)

The model is expressed in this equation:

Tanom = (A,y)+thcap-1 * Σyi=1895 {B*[S(i)-Savg] + C*ln[CO2(i)/CO2(1895)] –                               F * [(T(i)/T(1895))4 – 1]} + D                                                                                 (1)

Tanom = Calculated average global temperature anomaly 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 being calculated
(A,y) = value of the net effect of ocean cycles on AGT in year y (α-trend), K
thcap = effective  thermal capacitance [3] of the planet = 17±7 W yr m-2 K-1
1895 = Selected beginning year of acceptably accurate world wide temperature measurements.
B = combined proxy factor and influence coefficient for energy change due to sunspot number anomaly change, W yr m-2
S(i) = average daily Brussels International sunspot number V1 [4] or V2 [5,6] in year i
Savg = average sunspot number = 34 (approximate average 1610-1940) for V1 and 62 for V2
C = influence coefficient for energy change due to CO2 change, W yr m-2
CO2(i) = carbon dioxide level in year i, e.g. ppmv
CO2(1895) = carbon dioxide level in 1895, same units as CO2(i)  (Law Dome 294.8 ppmv)
F = 1 or 0 to account for change to Stephan-Boltzmann radiation from earth due to AGT change or not, W yr m-2
T(i) = AGT calculated by adding 287.1 to the calculated anomaly, K
T(1895) = AGT in 1895 = 286.74 K
D = offset that shifts the calculated trajectory vertically on the graph, without changing its shape, to best match the measured data, K

Accuracy of the model is determined using the Coefficient of Determination, R 2, to compare calculated AGT with measured AGT.

Approximate effect on the planet of the net of ocean surface temperature (SST)
The average ocean surface temperature oscillation is only about ±1/6 K so it does 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 0.36 K total highest-to-lowest extent with a period of approximately 64 years (verified below).

The AGT trajectory (Figure 8) 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 repeats 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 contribution of the ocean oscillation in each year to AGT is given by the following:

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

where the contribution 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 1 for A=0.36.
Figure 1: Ocean surface temperature oscillations (α-trend) do not significantly affect the bulk energy of the planet.

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 [7] and ENSO3.4 [8]. This PDO data set has the PDO temperature measurements reduced by the average SST measurements for the planet.

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

            PDO(i) = PDO index [7] in year i
            ENSO34(i) = ENSO 3.4 index [8] in year i

How this calculation compares to the idealized approximation used in Equation (2) with A = 0.36 is shown in Figure 2.
Figure 2: Comparison of idealized approximation of ocean cycle effect and the calculated effect from PDO and ENSO.

The AMO index [9] is formed from area-weighted and de-trended SST data. It is shown with two different amounts of smoothing in Figure 3 along with the saw-tooth approximation for the entire planet per Equation (2) with A = 0.36.
Figure 3: Comparison of idealized approximation of ocean cycle effect and the AMO index.

The high coefficients of determination in Table 1 and the comparisons in Figures 2 and 3 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.

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 [10]. Spatial variations between sources have been found to be inconsequential [19]. The best current source for atmospheric carbon dioxide level [11] is Mauna Loa, Hawaii. Extrapolation to future CO2 levels, shown in Figure 4, is accomplished using a second-order curve fit to data measured at Mauna Loa from 1980 to 2012.
  Figure 4. Measured atmospheric carbon dioxide level since 1880 and extrapolation to 2037.

EPA mistake
At  the EPA asserts 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. When a ghg molecule absorbs a photon it immediately (within about 0.0002 microsecond at sea level conditions) bumps in to other molecules. If this happens before the molecule emits a photon, part of the molecule’s energy is transferred to the other molecule(s) greatly reducing the probability a photon will be emitted. The process of photon absorption and transfer of energy is called thermalization. The transfer of energy is gas-phase thermal conduction and explains most of how the atmosphere, which is about 98% non-ghg gases, is warmed. A common observation of thermalization by way of water vapor is cloudless nights cool faster when absolute water vapor content is lower.

The only way that energy can significantly leave earth is by thermal radiation. Only solid or liquid bodies and ghg can radiate/emit in the wavelength range of terrestrial radiation. Non-ghg gases must transfer energy to ghg gases (or liquid or solid bodies) for the energy to be radiated. The non-ghg to ghg energy transfer with subsequent radiation is called reverse thermalization. The spike observed in top-of-atmosphere scans at the nominal absorption/emission wavelength of non-condensing ghg molecules results from reverse-thermalization.

There are about 35 times as many water vapor molecules as CO2 molecules in the troposphere and each water vapor molecule can absorb/emit energy at hundreds of wavelengths compared to only one (broadened to a range of about 14-16 microns at sea level) for CO2. Thus, in the troposphere, reverse-thermalization is thousands of times more likely to be to a water vapor molecule than to a CO2 molecule. The same holds for all non-condensing ghg.

Therefore, because absorbed terrestrial radiation by noncondensing ghg becomes thermalized, GWP, as calculated by the EPA, is not a measure of their relative influence on average global temperature. As a consequence non-condensing ghgs are insignificant compared to water vapor in influencing average global temperature.

Figure 5 provides insight as to the fraction of atmospheric CO2 for various times and conditions. The planet came perilously close to extinction of all plants and animals due to the low level of CO2 at the end of the last glaciation. For plant growth, at the current level the atmosphere is impoverished for CO2.
Figure 5: Typical values for CO2 levels.

Sunspot numbers
Sunspots have been regularly recorded since 1610, The most widely accepted data set is the average daily Brussels International sunspot numbers. They compensate for increased instrument sensitivity over the years to put all values on a common basis. This set is shown in Figure 6.
Figure 6: Brussels International sunspot numbers. (V1) [4]

Sunspot numbers (SSN) are seen to be in cycles each lasting approximately 11 years. The current cycle, called 24, has been comparatively low, has peaked, and is now in decline.

The Maunder Minimum (1645-1715), 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 changes to average global temperature. 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 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 magnitude and time are accounted for by taking the time-integral of the SSN anomalies, which is simply the sum of annual mean SSN (each minus Savg) over the period of study.

SSN change correlates with change to Total Solar Irradiance (TSI). However, TSI change can only account for less than 10% of the AGT change on earth. Because AGT change has been found to correlate with SSN change, the SSN change must act as a catalyst on some other factor (perhaps clouds) which have a profound effect on AGT.

In 2015 historical (V1) SSN were reevaluated in light of current perceptions and more sensitive instruments. Although there are substantial yearly differences, version 2 (V2) SSN, on average, tend to be about 20% higher than V1.

Application of Equation 1 using the same method as before results in slightly different influence coefficients and a substantially different value for Savg. However, the end result of influence of CO2 on AGT is not markedly different. V2 SSN are shown in Figure 7.
Figure 7: V2 SSN [5]

The highest Coefficient of Determination (R2 ) over the period 1895-2015 for V1 was found with Savg = 34. For V2 SSN Savg = 62.

The values for Savg are subject to two constraints. Initially they are determined as that which results in derived coefficients and maximum R2. However, calculated values must also result in rational values for calculated AGT at the depths of the Little Ice Age. The necessity to calculate a rational LIA AGT is a somewhat more sensitive constraint. The selected values for Savg result in calculated LIA AGT of approximately 1 K less than the recent trend which appears rational and is consistent with most LIA AGT assessments.

AGT measurement data sets
In earlier work, in an attempt to avoid bias, reported data were ‘normalized’ to HadCRUT4 data through 2012 as described at [12]. Reported data were essentially unchanged by the reporting agencies prior to 2012. Since then temperature data, especially land temperature data, have been changed which detracts from their applicability in any correlation.

All data sources appear to be fairly similar. 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, which coincides with an especially extreme El Nino, is especially distorting. It, at least in part, will be compensated for by an equally extreme La Nina which is sure to follow. In each data set the El Nino spike is compensated for by replacing reported AGT for 2013-2015 with the average 2002-2012.

 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.

At this point, it appears reasonable to consider two temperature anomaly data sets extending through 2015:

1) The set used previously [12] through 2012 with extension 2013-2015 set at the average 2002-2012 (when the trend was flat) at 0.4864 K above the reference temperature.
2) Current (5/27/16) HadCRUT4 data set [13] through 2012 with 2013-2015 set at the average 2002-2012 at 0.4863 K above the reference temperature.

These are co-plotted on Figure 8.
Figure 8: Examples of AGT anomaly data

The sunspot number anomaly time-integral is a proxy for a primary driver of the temperature anomaly β-trend
By definition, energy change divided by effective thermal capacitance is temperature change.

In all cases in this document, coefficients (A, B, C, D & F) which achieved maximum R2 for unsmoothed data sets were not changed when calculating R2 for smoothed data.

Incremental convergence to maximum R2 is accomplished by sequentially and repeatedly adjusting the coefficients. The process is analogous to tediously feeling the way along a very long and narrow mathematical tunnel in 4-dimensional mathematical space. The ‘mathematical tunnel’ is long and narrow because the influence on AGT determined by the SSN anomaly time-integral, at least until the last decade or so, is quite similar to the influence on AGT as determined by the rise in atmospheric CO2 level.

Measured temperature anomalies in Figure 9 use Data Set 1 shown in Figure 8. The excellent match of the up and down trends since before 1900 of calculated and measured temperature anomalies, shown here in Figure 9, and, for 5-year moving average smoothed temperature anomaly measurements, 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.

Projections until 2020 use the expected sunspot number trend for the remainder of solar cycle 24 as provided [6] by NASA. After 2020 the ‘limiting cases’ are either assuming sunspots like from 1924 to 1940 or for the case of no sunspots which is similar to the Maunder Minimum.

Some noteworthy volcanoes and the year they occurred are also shown on Figure 9. No consistent AGT response is observed to be associated with these. Any global temperature perturbation that might have been caused by volcanoes of this size is lost in the natural fluctuation of measured temperatures.

Much larger volcanoes can cause significant temporary global cooling from the added reflectivity of aerosols and airborne particulates. The Tambora eruption, 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 9: Measured average global temperature anomalies with calculated prior and future trends (Data Set 1) using 34 as the average daily sunspot number and with V1 SSN. R 2 = 0.913463
 Figure 10: Same as Figure 9 but with 5-year running average of measured temperatures. R2 = 0.978887. Data Set 1, V1 SSN.

Coefficients in Equation (1) which were determined by maximizing R2 identify maximums 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 occupied by each of the factors explicitly considered. The derived coefficients and other results are summarized in Table 1. Note that a coefficient of determination, R2 = 0.978887 means a near-perfect correlation coefficient of 0.9894.

The influence of the net effect of factors other than the net effect of ocean cycles on AGT can be calculated by excluding the α-trend from the AGT which was calculated using Equation (1). For the values used in Figure 9, this results in the β-trend as shown in Figure 11. Note that in 2005 the anomaly from other than α-trend, as shown in Figure 11, is A/2 lower than the calculated trend in Figures 9 and & 10 as it should be.
Figure 11: Anomaly trend (β-trend). Equation (1) except summation starts at i = 1610 and excluding α-trend. Data Set 1, V1 SSN.

How the β-trend could take place
Although the connection between AGT and the sunspot number anomaly time-integral 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 [14]. Marsden and Lingenfelter also report this in the summary of their 2003 paper [15] 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 [16] at CERN.

These papers [14,15] 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 change the AGT of the planet.

Simple analyses [17] 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, 0.2114 higher in 2000), substantially less cloud change would suffice.

Hind Cast Estimate
Average global temperatures were not directly measured in 1610 (thermometers had not been invented yet). Recent estimates, using proxies, are few. The temperature anomaly trend that Equation (1) calculates for that time is roughly consistent with other estimates. The decline in the trace 1615-1700 on Figure 11 results from the low sunspot numbers for that period as shown on Figure 6.

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 1610. Equation (1) is modified to begin integration in 1610. The coefficient D is changed to make the calculated temperature in 2005 equal to what it is in Figure 9.

Temperature anomalies thus calculated, estimate possible trends since 1610 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 9 and V1 SSN. Measured temperature anomalies from Figure 8, Data Set 1 and anomaly range estimates determined by Loehle are superimposed.

A survey [18] of non-tree-ring global temperature estimates was conducted by Loehle including some for a period after 1610. 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 the equations. The fit appears reasonable considering the uncertainty of all values.

Calculated temperature anomalies look reasonable back to 1700 but indicate higher temperatures prior to that than most proxy estimates. They are, however, consistent with the low sunspot numbers in that period. 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 19). Worldwide assessments of average global temperature, that far back, are sparse and speculative. Ocean oscillations might also have been different from assumed.

Data Set 2 with V2 SSN
Similarly, graphs 13,14 and 15 were determined for Data Set 2 and V2 SSN using Equation (1).
 Figure 13: HadCRUT4 (as of 5/28/16) 2012 and earlier, 2013-2015 flat at 0.4863 K. V2 SSN.
Figure 14: β-trend, HadCRUT4 (as of 5/28/16) 2012 and earlier, 2013-2015 flat at 0.4863 K. V2 SSN.
 Figure 15: Calculated temperature anomalies using Equation (1) with the same coefficients as for Figure 13 and V2 SSN. Measured temperature anomalies from Figure 8, Data Set 2 and anomaly range estimates determined by Loehle are superimposed.

Projection from 1990

Figure 16 shows the calculation using Equation (1) with coefficients determined using HadCRUT4 measured temperatures to 1990. The calculated temperature trend in 2020 with the 1990 projection is 0.08 K cooler than the projection using Data set 2 which is through 2015.
Figure 16: Same as Figure 13 except coefficients determined using data through 1990.

Imposed constraint of limiting influence of CO2.

Figure 17 shows the AGT trajectory that occurs for the condition that the CO2 level is arbitrarily constrained to the noted limit. Same Equation (1), Data Set 2, V2 SSN as for Figure 13.
Figure 17: Calculated trajectory if influence of CO2 is constrained. Data Set 2.

Step changes in AGT
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 [3] for thermal response of the planet to a step change in forcing.

Influence of atmospheric CO2 on AGT
The temperature increase through 2015 attributable to CO2 is the net of the increase from CO2 and the decrease from added S-B radiation due to the part of the temperature rise above the 1895 value of 286.74 K attributable to CO2. The net effect is designated ΔTCO2.

At least until the last decade or so, the influence on AGT due to CO2 has been quite similar to the influence on AGT determined by the SSN anomaly time-integral. This similarity has resulted in calculation of CO2 influence erroneously much greater than indicated by other evidence. For example, in the late Ordovician Period the planet plunged into and warmed up from the Andean/Saharan ice age all while the CO2 level was approximately ten times the present [20].

Values for the coefficients and results are summarized in Table 1.

Table 1: A, B, C, D, F refer to coefficients in Equation 1. The column headed # is a code identifying the particular EXCEL file used.




Note that the R2 decreases only about a half per cent when the influence of CO2 on AGT is artificially constrained to 4.4% compared to the case (#S) for maximum R2.

Possible explanation of why CO2 change has no significant effect on climate.
1) Firmly acknowledge the established fact that gas molecules can absorb/emit photons only at specific discreet wavelengths (which might be broadened from pressure, etc.). This fact makes spectroscopy possible. Full spectrum (Plank’s law) Stephan-Boltzmann (S-B) radiation applies to liquids and solids, not to gases.
2) From gas kinetics, the time between atmospheric molecule collisions is extremely short (The Hyperphysics calculator calculates approximately 0.0002 microsecond at sea level pressure and temperature).
3) The elapsed time between absorption and emission of a photon by a CO2 gas molecule is perhaps shorter at higher temperature but must be greater than zero or there would be no evidence that absorption-emission had occurred.
4) At sea level conditions, some or all of the photon energy that is absorbed by a (so called) greenhouse gas (ghg) molecule might be immediately transferred to other molecules by collision. The process of absorbing a photon and transferring (thermal conduction in the gas) the added energy to other molecules is called thermalization. A common observation of thermalization by way of water vapor is that cloudless nights cool faster when absolute water vapor content is lower.
5) The reduced radiation flux on both sides of the 15 micron CO2 absorption line, as observed in most Top of Atmosphere (TOA) measurements results because some of the EMR energy absorbed by CO2 has been thermalized.
6) Terrestrial radiation is nearly all in the wavelength range 6-100 microns. Thermalized energy carries no identity of the molecule that absorbed it.
7) Jostling between the molecules sometimes causes reverse-thermalization. At low to medium altitudes, EMR emission stimulated by reverse-thermalization is mostly by way of water vapor. The TOA spike at 15 microns results from reverse-thermalization to CO2 molecules at very high altitude.
8) 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.
9) The population gradient of ghg molecules, (especially water vapor above about 3 km, declining with increasing altitude) favors radiation to space. Ghg molecules that emit a photon are ‘recharged’ by reverse-thermalization (or by absorbing a photon of appropriate wave length).
10) Clouds (average emissivity about 0.5) consist of solid and/or liquid water particles (each particle containing millions of molecules) that radiate according to S-B law. Low and declining amount of water vapor above clouds and widening molecule spacing allows increased radiation directly to space with increased altitude.
11) The tiny increase in ghg from increased CO2 causes absorption/thermalization to occur at slightly lower altitude which very slightly increases the convection rate.
12) The increase in absorbing molecules near the surface is at least partially compensated for by an equal percent increase in emitting molecules high in the atmosphere radiating energy from the planet.

Because CO2 is only a trace gas in the atmosphere (approx. 0.04%), if CO2 change does not cause significant temperature change, it cannot cause significant climate change. Thus the CO2 change from burning fossil fuels has no significant effect on climate and climate sensitivity (the effect on AGT of doubling CO2) is not significant. Estimated magnitude is

Climate Sensitivity = 0.291 * ln(2)/ln(400.31/294.8) = 0.66 K

The finding that CO2 has no significant effect on climate might appear to conflict with the known absorption of 15 micron radiation by CO2. Suspected explanations for this include that there are so many more 'opportunities' for absorption by water vapor molecules (hundreds of absorption lines per molecule times number of molecules) that the added CO2 'opportunities' have an insignificant effect (single absorption line in the range of significant terrestrial radiation) and/or added TOA CO2 molecules emitting to space compensate, at least in part, for the added molecules absorbing at low altitude.

The EPA erroneously asserts 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").” [21].

The EPA calculation erroneously overlooks the fact that any effect the ghg might have on temperature is also integrated over the “lifetime” of the gas in the atmosphere so the duration in the atmosphere cancels out. Therefore GWP is not a measure of the relative influence on average global temperature of ghgs on a molecule basis.

Two factors can explain most of AGT change since before 1900. They are ocean cycles, accounted for with an approximation, and, influence quantified by a proxy; the SSN anomaly time-integral.

Others have looked at only amplitude or only duration factors for solar cycles and got poor correlations with average global temperature. The excellent correlation comes by combining the two, which is what the time-integral of sunspot number anomalies does. Prediction of future sunspot numbers more than a decade or so into the future has not yet been confidently done.

As displayed in Figures 11 and 14, the β-trend shows 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.

Figures 10 and 13 show the near perfect match with calculated temperatures which occurs when random fluctuation in reported measured temperatures is smoothed out with 5-year moving average.

Long term prediction of average global temperatures depends primarily on long term prediction of sunspot numbers.

3. 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 
5. V2 sunspot numbers
6. Graphic of V2 Solar cycle 24:
10. CO2 level at Law Dome, Antarctica:
12. Previous measured AGT data set
14. Svensmark paper: Phys. Rev. Lett. 85, 5004–5007 (2000)
15. Marsden & Lingenfelter 2003, Journal of the Atmospheric Sciences 60: 626-636
17. Sensitivity of AGT to clouds
19. 2008 assessment of non-condensing ghg
21. EPA determination of global warming potential of ghg: