Tuesday, December 20, 2016

Solar activity, ocean cycles, & water vapor explain 98% of climate change since 1900, NOT CO2!

by Dan Pangburn, MSME


Thermalization and the complete dominance of water vapor in reverse-thermalization explain why atmospheric carbon dioxide (CO2) has no significant effect on climate. Reported average global temperature (AGT) since before 1900 is accurately (98% match with measured trend) explained by a combination of ocean cycles, sunspot number anomaly time-integral and increased atmospheric water vapor.


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 terrestrial radiation. Non-ghg gases must transfer energy to ghg gases (or liquid or solid bodies) for this energy to be radiated.

The word ‘trend’ is used here for temperatures in two different contexts. To differentiate, α-trend is an approximation of the net of ocean surface temperature oscillations after averaging-out the year-to-year fluctuations in reported average global temperatures. 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.

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 near the surface. The average temperature of the bulk water that is participating in these oscillations cannot significantly change so quickly because of high thermal capacitance [1].

This high thermal capacitance absolutely prohibits the rapid (year-to-year) AGT fluctuations which have been reported, from being a result of any credible forcing. According to one assessment [1], the time constant is about 5 years. A likely explanation for the reported year-to-year fluctuations is that they are stochastic phenomena in the over-all process that has been used to determine AGT. A simple calculation shows the standard deviation of the reported annual average measurements to be about ±0.09 K with respect to the trend. The temperature fluctuations of the bulk volume near the surface of the planet are more closely represented by the fluctuations in the trend. The trend is a better indicator of the change in global energy; which is the difference between energy received and energy radiated.

The kinetic theory of gases, some thermodynamics and the rudiments of quantum mechanics provide a rational explanation of what happens when ghg absorb photons of terrestrial thermal radiation.

Refutation of significant influence from CO2
There is multiple evidence (most identified earlier [2] ) that CO2 has no significant 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, 4].
3. During the last and previous glaciations AGT trend changed directions before CO2 trend [2].
4. Since AGT has been directly and accurately measured world wide (about 1895), AGT has exhibited up and down trends while CO2 trend has been only up. [2]
5. Since about 2001, the measured atmospheric CO2 trend has continued to rise while the AGT trend has been essentially flat. [21, 13]

Thermalization refutes CO2 influence on climate. (rev 10/21/16)
The relaxation time (amount of time that passes between absorption and emission of a photon by a molecule) for CO2 in the atmosphere is about 6 µsec [5, 6]. The elapsed time between collisions between gaseous molecules at sea level average temperature and pressure is about 0.0002 µsec[7]. Thus, at sea level conditions, it is approximately 6/0.0002 = 30,000 times more likely that a CO2 molecule, after it has absorbed a photon, will bump into another molecule, losing at least part of the momentum and energy it acquired from the photon. After multiple collisions, essentially all of the added photonic energy becomes distributed among other molecules and the probability of the CO2 molecule emitting a photon at sea level conditions becomes negligible. The process of distribution of the energy to other molecules is thermal conduction in the gas. The process of absorbing photons and conducting the absorbed energy to other molecules is thermalization. Thermalized energy carries no identity of the molecule that absorbed it.

Water vapor molecules can absorb (and emit) photons at hundreds of wavelengths in the wavelength range of significant terrestrial thermal radiation (nearly all in the wavelength range 6-100 microns) compared to only one (15 micron) for CO2 (wave length range of the single absorption band for CO2 is broadened to about 14-16 microns at sea level due to pressure, etc. but the multiple absorb/emit wave length bands for water vapor are equally broadened). 

Reverse thermalization, where the warmed jostling molecules excite some molecules to emit a photon is almost entirely to water vapor molecules at sea level conditions. The reason is relaxation time of some water vapor molecule rotational emission lines is 0.5 µsec compared to 6 µsec for CO2 molecules and/or the thousands more ‘opportunities’ for emission by water vapor.

Water vapor has more ‘opportunities’ for emission because there are about 35 times as many water vapor molecules in the atmosphere below about 5 km as there are CO2 molecules (See Figure 2) and each water vapor molecule has hundreds of emission bands compared to only one band for each CO2 molecule. Most, if not all, of the photons emitted by the water vapor molecules are at wavelengths different from the narrow band CO2 molecules can absorb. Effectively, energy absorbed by CO2 is rerouted to space via water vapor.

At very high altitudes, molecule spacing and time between collision increases to where reverse-thermalization to CO2 molecules becomes significant as does radiation from them to space.

Figure 1 is a typical graph showing top-of-atmosphere (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.

Figure 1: Terrestrial thermal radiation and absorption.

Approximately 98% of atmospheric molecules are non-ghg nitrogen and oxygen. They are substantially warmed by thermalization of the photonic energy absorbed by the ghg molecules.

Figure 2: Water vapor declines rapidly with altitude. [9] (original from NASA)

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 when absolute water vapor content of the atmosphere is lower.

Jostling between gas molecules (observed as temperature and pressure) sometimes causes reverse-thermalization. At low to medium altitudes, EMR emission stimulated by reverse-thermalization is essentially all by way of water vapor.

At altitudes below about 10 km a comparatively steep population gradient (decline with increasing altitude) in water vapor molecules favors outward radiation with increasing amounts escaping directly to space. At higher altitudes, increased molecule spacing and greatly diminished water vapor molecules favors reverse thermalization to CO2. This is observed in the sharp peaks at nominal absorb/emit wavelengths of non-condensing ghg (See Figure 1).

Thermalization results in the influence of CO2 on climate to be not significantly different from zero.

Environmental Protection Agency mistake
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 no significant effect on climate because absorbed energy is immediately thermalized. 

Water vapor (Rev 8/26/16)
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 (even if thermalization did not eliminate CO2 as a significant warmer). Atmospheric water vapor has increased primarily (≈ 98%) as a result of increased irrigation, with comparatively tiny contributions from cooling towers at electricity generating facilities, and increased burning of hydrogen rich fossil fuels especially natural gas which is nearly all methane. Of course increased water vapor causes the planet to warm which further increases water vapor so there is a cumulative effect (in control system analysis as done by engineers, this is called feedback. The term ‘feedback’ has a somewhat different meaning to Climate Scientists). This cumulative effect also amplifies cooldowns. More water vapor in the atmosphere means more warming, probably acceleration of the hydrologic cycle and increased probability of floods. How much of recent flooding is simply bad luck in the randomness of weather and how much is because of the ‘thumb on the scale’ of added water vapor? Water vapor exhibits a logarithmic decline in effect of equal added increments (Fig. 3 of Ref. [12]).

Essentially all of the ghg effect on earth comes from water vapor. Clear air water vapor measurements over the non-ice-covered oceans in the form of total precipitable water (TPW) have been made since about 1987 by Remote Sensing Systems (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. The trend of this data is extrapolated both earlier and later 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. (The 1940-1950 flat exists in the Law Dome CO2 data base.)

Figure 3: Average clear air total precipitable water over all non-ice-covered oceans.

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).

The perception water vapor content of the atmosphere depends even minutely on CO2 content is profoundly misleading and precisely wrong because it ignores the partial pressure of water.

The AGT Model
Most modeling of global climate has been with Global Climate Models (GCMs) where physical laws are applied to hundreds of thousands of discrete blocks and the 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 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 growing separation between calculated and measured AGT as shown at Figure 17 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.)

The AGT model, a summation of contributing factors, is expressed in this equation:

Tanom = (A,y)+thcap-1 * Σyi=1895 {B*[S(i)-Savg] + C*ln[TPW(i)/TPW(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 [1] 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 V2 sunspot numbers [15,16] in year i
Savg = baseline for determining SSN anomalies 
C = influence coefficient for energy change due to TPW change, W yr m-2
TPW(i) = total precipitable water in year i, kg m-2
TPW(1895) = TPW in 1895, same units as TPW(i)  
F = 1 to account for change to S-B radiation from earth due to AGT change, W yr m-2
T(i) = AGT calculated by adding T(1895) to the reported anomaly, K
T(1895) = AGT in 1895 = 286.707 K
D = offset that shifts the calculated trajectory vertically on the graph, without changing its shape, to best match the measured data, K (equivalent to changing the anomaly reference temperature).

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 global ocean surface temperature oscillation is only about ±1/6 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 0.36 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 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 4 for A=0.36.

Figure 4: 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 [17] and ENSO3.4 [18]. 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 [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.

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.

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. Extrapolation to future CO2 levels, shown in Figure 7, is accomplished using a second-order curve fit to data measured at Mauna Loa from 1980 to 2012. 

Figure 7: Measured atmospheric carbon dioxide level since 1880 and extrapolation to 2037.

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, has peaked, and is now in decline.

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 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 most 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 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 [22]) which have a substantial effect on AGT.

Figure 8: V2 SSN [15]

Possible 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 value for Savg results in calculated LIA AGT of approximately 1 K less than the recent trend which appears rational and is consistent with most LIA AGT assessments.

PLEASE CONTINUE FOR REMAINDER OF ARTICLE AT DAN PANGBURN'S SITE for the Identity of the 3 factors in the equation which matches average global temperature (98% correlation from 1895-2015) at

HINT: CO2 is an insignificant factor. From the conclusions:


Three factors explain essentially all of Average Global Temperature change since before 1900. They are ocean cycles, accounted for with an approximation, influence quantified by a proxy; the  SSN [sunspot numbers] anomaly time-integral and, the gain in atmospheric water vapor measured since 1987 and extrapolated before and after using measured CO2 as a proxy.


  1. But wait there's more! The article rightly states 15 um as the only frequency CO2 can absorb Infra Red radiation. However I believe it correct that 15um infra red radiation only occurs at around -80C which is approximately 90Km up? And photons from CO2 at -80C don't have the energy to raise any electron on a warmer gas, water or solid molecule to a higher orbit and so raise its temperature.
    The top of Mt Everest has a lot of radiative energy flying through the air, but the sir temperature is still very cold. Temperature is only a measure of kinetic energy and ignores all radiative energy. So I struggle to see how CO2 can cause any warming (or cooling) at all?

    A second point is that the daytime temps on the moon are way higher than on Earth and the night time temps way lower than Earths. So we can say that Green house gasses both cool and warm the atmosphere (though a much shorter day helps as well). Maybe more greenhouse gases will moderate daily temperatures even more?

    1. Yes you are indeed correct that by Wein's Displacement Law 15 microns corresponds to an emitting temperature of -80C, which cannot warm any other object to a temp >-80C!

    2. This isn't right either the "temperature" of a gas is the statistical average of the kinetic energy of the gas, so there is a poisson distribution of energies from absolute zero *stationary* up to thousands of degrees. Any collision above the critical energy can result in a bond vibration that can result in a photon emission. So 15u Emission can come from just about anywhere in the atmosphere. This is why the 15u glow (emission) ( around 15% of surface emission ) doesn't necessarily represent the portion of energy remaining after transit through the atmosphere, it may represents the statistics of the conversion of translational velocity (Temperature) into bond vibrations upon collision. IE that emission is sourced from convective heat, not from surface IR emission.

  2. cannot add comment see:

  3. "The only way that energy can significantly leave earth is by thermal radiation"

    Arrrgh, you are infected by the warmist disease - in your very first sentence. In general most energy degrades to heat, the rotational momentum of the earth is several million times Annual Insolation, the orbital kinetic energy of the earth is 800 Billion times annual insolation as is the gravitational potential energy of the earth's position above the sun. Convert just a little of the rotational/kinetic energy of the earth to heat and you have a massive thermal input. Conversely pressure differences due to differential heating cause wind and waves, thermal energy raises GT of water to great heights (10 km) to belt down upon the earth at great speed, the air motion creates static electricity which belts down upon the earth in great lightning bolts. Photons are absorbed by plants and used in chemical reactions to make carbohydrates, in Humans photons are absorbed by the skin surface and used to chemically convert cholesterol to Vitamin D, there must be hundreds of other endothermic reactions driven by solar energy. Bio energy (the heat created by cellular respiration) is by my calculation at least 3 Watts per square meter. EM energy is both input from and sunk to many places and it is wrong to assume that radiation to/from space is the only source/sink. The idea that the earth is some ideal perpetual motion machine (Shortwave In - Longwave out = 0) is from an engineers point of view fanciful Climatologist dream state.

    The proper formulation is

    EM Exitance=Insolation+NRG-NRL where NRG is Non Radiative Gains, and NRL is Non Radiative Loss. Until all NRG and NRL sources and sinks are known for all sources and sinks 2 orders of magnitude below the supposed energy imbalance the imbalance can be considered WRONG. This means all sources and sinks above 6 mW per square meter need to be known to high precision.

    That IR Exitance is approximately the same as Insolation is a mere coincidence, not some fundamental feature of the climate.

    1. The photo-chemical processes you describe are limited term energy sinks. Long term they come to zero on the total balance. So thermal radiation is, long run, the only way for heat to leave Earth. But what carbon climatists fail to consider is where that radiation is emitted, assuming that the surface must be directly cooled by radiation, when convection and phase change can carry heat to altitude far more efficiently. Then in the stratosphere "greenhouse gases" can radiate heat in thermal equilibrium with the rest of the universe.

  4. "A common observation of thermalization by way of water vapor is cloudless nights cool faster when absolute water vapor content of the atmosphere is lower."
    A cloud forms when the atmosphere is saturated with water vapor. Water vapor carries a great deal of latent heat, released when the atmosphere cools across the dew point. Thus when a cloudy sky cools, condensing water vapor counters the cooling. But a cloudless sky has insufficient water vapor to condense and release latent heat.

  5. This is a most interesting article. I have read through it several times and understand much from it (my PhD from decades ago is biochemistry so that is a handicap!) This seems like an important distillation -- has this (or will this) work be submitted for peer reviewed publication? If not I think it should be?