This paper tests various propositions underlying claims that observed global temperature change is mostly attributable to anthropogenic noncondensing greenhouse gases, and that although water vapour is recognized to be a dominant contributor to the overall greenhouse gas (GHG) effect, that effect is merely a “feedback” from rising temperatures initially resulting _{2}O]). However, this paper shows that “_{2}O]. The paper distinguishes between forcing and feedback impacts of water vapour and contends that it is the

The main technique used in this paper is econometric least squares regression analysis, which enables computation of the relative strength of proposed alternative and independent causal factors in determination of the dependent variable, temperature change. This procedure is not used in Solomon et al. [

Dessler and Davis [_{2}] from the c.280 ppm in 1900 of 3°C (central value) to 560 ppm implies an increase of 2.3°C from the extra 60 percent in [CO_{2}] from 2010, despite the observed only 0.83°C associated with the nearly 40 percent increase in [CO_{2}] between 1900 and 2010 (Gistemp). This paper’s regression analysis tests for the relative importance of changes in [CO_{2}] and [H_{2}O] and also as to which comes first, the former according to Dessler and Davis [

Not many researchers have used time domain econometrics methods to analyze climate change. Stern and Kaufmann [^{1}

None of these papers addresses the respective proportions of condensing and noncondensing GHGs to the overall greenhouse effect, and none mention [H_{2}O] as an independent variable with potential explanatory value for changes in temperature. Kaufmann et al. [_{2} on surface temperature.” These papers’ database regressions (Section _{2},” which could be more than a hundred years if their analysis is correct.^{2}

Hegerl et al. [^{3} Had these authors done some regression analysis, they could have been more precise, but they never did, nor do they report any by others.

Instead, for both Hegerl and Allen [_{2}] and other greenhouse gases.^{4} In practice, none of these papers perform any regression analysis of both natural and nonnatural forcings and ignore primarily “natural external forcings” like that from [H_{2}O]. Hegerl and Allen [_{2}]) are of the same anthropogenic origin in time and place as emissions of CO_{2} although from time to major volcanic eruptions increase both [CO_{2}] and [SO_{2}], with only local effects in the case of the latter. The other papers cited by Hegerl et al. [_{2}] and [SO_{2}] with just this mention of solar irradiation at the top of the atmosphere (TOA): “We used only a greenhouse gas and a greenhouse gas-plus-aerosol signal pattern, since the solar response pattern could not be sufficiently separated from noise and the greenhouse gas pattern,” a curious conclusion in the light of the title of that paper.

Stott et al. [^{5} use what they call “optimal detection technology” to conclude that “increases in temperature observed in the latter half of the century have been caused by increases in anthropogenic greenhouse gases offset by cooling from tropospheric sulphate aerosols rather than natural variability…” They claim that their “technology” is simply “just least squares regression in which we estimate the amplitude in observed data of prespecified [i.e., modelled] patterns of climate change in space and time” [^{6}

This paper uses overlooked NOAA-ESRL site-specific databases of statistics on a wider range of both human and natural climatic variables than is analyzed in any of the “detection and attribution” papers noted above. We show that a comprehensive analysis results in relegating [CO_{2}] to insignificance as a determinant of climate change, and that atmospheric water vapour arising almost exclusively from nonhuman sources is by far the largest source of radiative forcing and temperature change. We thereby hope to achieve a better response to the Kaufmann et al. [

Unlike mainstream climate science, which relies wholly on “general circulation models” (GCM) [_{2}] (following [^{2}), and _{2}O], in cm.)

It is important to establish that the RHS variables in (_{2}O] and _{2}], then we need to know if _{2}] variables is questionable, as on colder/hotter days offices and households are likely to use more heating/cooling, and if that involves burning of more hydrocarbon fuels, then large changes in _{2}]. I have done tests (not reported here) which show that changes in [CO_{2}] appear to have no impact on changes in [H_{2}O]. The outcomes of the regression analysis of (_{2}O] variables are independent, as “most of (the water vapour in the atmosphere) originates through evaporation from the ocean surface and is not influenced directly by human activity” ([_{2}] (see below for assessment of that claim).

There has been considerable debate since Granger and Newbold [^{7}. For example, many time series in economics have a steady upward trend similar to that of the concentration of carbon dioxide in the atmosphere [CO_{2}]—numbers of television sets, mobile phones, computers, and their broadband connections all show steady upward trends worldwide, but none of these trends can plausibly imply either direct or inverse causal relationships with [CO_{2}] despite no doubt striking correlation coefficients between them and rising [CO_{2}].

One widely applied solution to the problem of nonstationarity in time series is first to difference the series in question, by subtracting the present value of a variable from the previous value, and so on for all values in the series.^{8} A simple regression model is merely a

In this paper’s _{2}] and [H_{2}O] and any other causative variables should be linearly independent. A key requirement—spelt out in rule (5) in the list below—is that this noise must have a constant variance over the distribution of samples; it must be

In general, the various rules or conditions that must be satisfied for a valid regression are the following:

the predictor samples

the unknown

the predictors must be linearly independent;

the unknown

the unknown

Evidently, there is no particular requirement that the vectors

The aim is to establish if the level of [CO_{2}] is or is not—the main explanatory variable of average global or local temperature—in some quasimonotonic relation. For simplicity we stick to basic linear regression.

The Mauna Loa Slope Observatory in Hawaii has provided a test range of CO_{2} from 315.71 ppm in April 1958 to 393.39 ppm in April 2011 and such current levels are confirmed by other measurements that started some years later, like those at Pt. Barrow in Alaska and elsewhere, including Cape Grim in Tasmania^{9}. We may call this the independent “^{10} Perhaps so, but it makes no difference whatsoever in the testing whether

One obvious candidate for determining mean maximum (i.e., day) temperature in addition to [CO_{2}] has to be localized solar surface radiation SSR in Watt hours/sq. meter which I call here _{2}O] at any given time and place, closely related to the relative humidity (RH) that is well known to make any given temperature level seem “hotter” than otherwise, has a no more evident relationship with [CO_{2}] than the level of solar surface radiation. That is because [CO_{2}] is invariant across the globe, at all given times and places, while [H_{2}O] varies enormously at any given latitudes and times.

Again for simplicity let us introduce this one further possible explanation as _{2}] at that location in that year. Whether time series

What a first differencing exercise may usefully show is a better exhibition of a rising trend in temperature since the “noise” in the measurements hopefully has been reduced by introducing the additional independent variables using _{2}O], in the hope of revealing a better measurement of a linear trend in temperature (which would be otherwise nondiscernible for the data assembly in our selected sites).

Again, what really matters is the statistical property of the error sequence _{2}] plays at best a marginal role—and one that is usually statistically insignificant—in explaining the temperature changes at various locations in USA over the 47 years inclusive between 1960 and 2006 (when the NOAA discontinued reporting the data sets used here, although a similar but less comprehensive series with data from 1948 to 2011 for locations defined by their latitude and longitude is available from ESRL-NASA).^{11}

The “BEST” data sets [_{2}] observatory in 1958. In Supplementary Material I also report regressions of data from various other locations.

Table 7 presents a specimen of the NOAA-ESRL raw data from Point Barrow, in the arctic circle at the northernmost tip of Alaska, where if [CO_{2}] is to be significant anywhere, it has to be there, given mean temperatures that have always been negative since 1960, despite [CO_{2}] levels there that are almost identical to those at Mauna Loa in Hawaii and elsewhere on the globe.^{12} Not only that, Barrow being in the Arctic Circle is a pristine site, far removed from confusing elements such as the urban heat island (UHI) effect, which is why it was selected as one of the gold standard locations for measurement of [CO_{2}]. That is also why Keeling selected Mauna Loa for his first [CO_{2}] measurement station, as it too is far away from other anthropogenic influences, at an altitude of 3,500 meters above sea level.

I first regress the global mean temperature (GMT) anomalies against the global annual values of the main climate variable evaluated by the IPCC Hegerl et al. [^{13}

Regression of Gistemp anomalies on total noncondensing GHG-radiative forcings.

Regression statistics | |
---|---|

Multiple | 0.814 |

0.662 | |

Adjusted | 0.651 |

Standard error | 12.384 |

Observations | 31 |

Durbin Watson | 1.749 |

ANOVA

Df | SS | MS | ||
---|---|---|---|---|

Regression | 1 | 8718.49 | 8718.49 | 56.85 |

Residual | 29 | 4447.51 | 153.36 | |

Total | 30 | 13166 |

Coefficients | Standard error | |||
---|---|---|---|---|

Intercept | −80.581 | 16.278 | −4.950 | 0.000 |

Total radiative Forcings | 53.584 | 7.107 | 7.540 | 0.000 |

Modifying (

First-differenced regression of Gistemp temperature anomalies on total noncondensing GHG-radiative forcing.

Regression statistics | |
---|---|

Multiple | 0.183 |

0.033 | |

Adjusted | −0.001 |

Standard error | 16.467 |

Observations | 30 |

Durbin Watson | 2.760 |

ANOVA

df | SS | MS | ||
---|---|---|---|---|

Regression | 1 | 262.454 | 262.454 | 0.968 |

Residual | 28 | 7592.513 | 271.161 | |

Total | 29 | 7854.967 |

Coefficients | Standard error | |||
---|---|---|---|---|

Intercept | −10.073 | 12.601 | −0.799 | 0.431 |

dTotalRF | 339.775 | 345.366 | 0.984 | 0.334 |

Plot of first differences in temperature anomalies and total radiative forcing (by all noncondensing GHGs). Source: Muller et al. [

The minimal level of _{2}O], with results shown in Table _{2}] and [H_{2}O] has such minimal statistical significance and can in no sense be described as “control knobs.”

Regression of temperature change against radiative forcing of [CO_{2}] and year-on-year changes in [H_{2}O].

Regression statistics | |
---|---|

Multiple | 0.088 |

0.008 | |

Adjusted | −0.034 |

Standard error | 0.169 |

Observations | 51 |

ANOVA

df | SS | MS | ||
---|---|---|---|---|

Regression | 2 | 0.011 | 0.005 | 0.188 |

Residual | 48 | 1.372 | 0.029 | |

Total | 50 | 1.383 |

Coefficients | Standard error | |||
---|---|---|---|---|

Intercept | −0.030 | 0.084 | −0.360 | 0.721 |

RF CO_{2} | 0.038 | 0.071 | 0.544 | 0.589 |

Δ[H_{2}O] | 0.017 | 0.072 | 0.230 | 0.819 |

Sources: ESRL-NOAA and CDIAC.

Next, I use first differences regressions to include NOAA data on nonanthropogenic variables at various locations of atmospheric water vapor [H_{2}O], and solar surface radiation in addition to [CO_{2}] as the main atmospheric GHG^{14}

I first run this model for mean _{2}O] variable is highly statistically significant in regard to what are night temperatures, at the better than 99 percent level, while the coefficient on the differenced [CO_{2}] variable is barely positive and remains statistically insignificant.

Determinants of temperature change at Pt. Barrow. Mean minimum temperature 1960–2006.

Regression statistics | |
---|---|

Multiple | 0.660 |

0.435 | |

Adjusted | 0.409 |

Standard error | 1.227 |

Observations | 46 |

ANOVA

df | SS | MS | ||
---|---|---|---|---|

Regression | 2 | 49.913 | 24.956 | 16.566 |

Residual | 43 | 64.779 | 1.506 | |

Total | 45 | 114.692 |

Coefficients | Standard error | |||
---|---|---|---|---|

Intercept | 0.001 | 0.473 | 0.002 | 0.998 |

Δ [H_{2}O] | 17.225 | 3.076 | 5.600 | 0.000 |

Δ [CO_{2}] | 0.007 | 0.311 | 0.021 | 0.983 |

Sources: _{2}:

The adjusted _{2}O] variable is statistically significant, accounting for more than 90 per cent of the changes in mean maximum temperature over the period 1960–2006, thereby going beyond the assertion by Schmidt et al. 2010 cited above that atmospheric water vapor accounts for only 50 per cent of the total greenhouse effect [

The conclusion from the limited model used in Tables _{2}] at Pt Barrow attributable to anthropogenic emissions plays no role in explaining the climate there since 1960. We are also able to show that which proves to be the case for all the other locations where the same regression analysis is possible (see examples in the Supplementary Material).

Determinants of temperature change at Pt. Barrow. Determinants of

Summary output. Dependent variable: year-on-year changes in mean maximum temperatures

Regression statistics | |
---|---|

Multiple | 0.593 |

0.351 | |

Adjusted | 0.321 |

Standard error | 1.314 |

Observations | 46 |

ANOVA

Regression | 2 | 40.162 | 20.081 | 11.633 |

Residual | 43 | 74.228 | 1.726 | |

Total | 45 | 114.390 |

Coefficients | Standard error | |||
---|---|---|---|---|

Intercept | −0.075 | 0.743 | −0.101 | 0.920 |

ΔH_{2}O | 15.456 | 3.207 | 4.820 | 0.000 |

RF abs | 0.065 | 0.648 | 0.100 | 0.921 |

Sources: _{2}:

I now provide here one further site-specific regression analysis, for the Slope Laboratory at Mauna Loa itself (Table _{2}] do not imply that changes in [CO_{2}] at the foot of Mauna Loa have had “most” (Hegerl et al. [_{2}O] accounts for more than 90 per cent of temperature change near where C. D. Keeling began his measurements of the atmospheric concentration of CO_{2} back in 1958.^{15}

Regression analysis of _{2}] and [H_{2}O] 1977–2009.

Summary output. Dependent variable: year on year changes in mean maximum temperatures

Regression Statistics | |
---|---|

Multiple | 0.631 |

0.399 | |

Adjusted | 0.356 |

Standard error | 0.565 |

Observations | 46 |

ANOVA

df | SS | MS | ||
---|---|---|---|---|

Regression | 3 | 8.876 | 2.959 | 9.281 |

Residual | 42 | 13.389 | 0.319 | |

Total | 45 | 22.265 |

Coefficients | Standard error | |||
---|---|---|---|---|

Intercept | −0.248 | 0.219 | −1.133 | 0.264 |

Δ[CO_{2}] | 0.195 | 0.145 | 1.346 | 0.186 |

Δ[H_{2}O] | 2.564 | 0.548 | 4.676 | 0.000 |

ΔAVGLO | 0.001 | 0.000 | 3.721 | 0.001 |

Durbin-Watson: 2.834 |

I noted above that water vapor is the most potent greenhouse gas because it absorbs strongly in the infra-red region of the light spectrum, first demonstrated by Tyndall [_{2}O] variable in the NOAA’s database proves to be a remarkably powerful determinant of climate variability over the period from 1960 to 2006 not only at Barrow but across all USA, as it is always highly statistically significant at better than the 95% level of confidence for both annual mean minimum and maximum annual temperatures. This is hardly surprising, if only because in reality, as Tans has noted^{16}, “global annual evaporation equals ~500,000 billion metric tons. Compare that to fossil CO_{2} emissions of ~8.5 billion ton C/year,” and even the total level of [CO_{2}] is only 827 billion tonnes of carbon equivalent. It would seem to be a case of the tail wagging the dog if the additions to [CO_{2}] from human burning of hydrocarbon fuels have raised global temperatures enough (just 0.0125°C p.a. since 1950) to generate annual evaporation of 500,000 billion tonnes of [H_{2}O], especially when as I have shown here, its role in explaining temperature changes is much less than claimed by the IPCC’s Hegerl et al. [

Trends in annual _{2}] Mauna Loa Slope Observatory 1977–2009. Notes: neither of the trends has good linear fits, with

This paper has used basic econometric (multivariate least squares regression) analysis of observational evidence to falsify or confirm two null hypotheses, first that “most” of observed global warming since around 1950 has

The second null derives from this statement by Lacis et al. [

This assessment comes about as the result of climate modeling experiments which show that it is the noncondensing greenhouse gases such as carbon dioxide, methane, ozone, nitrous oxide, and chlorofluorocarbons that provide the necessary atmospheric temperature structure that ultimately determines the sustainable range for atmospheric water vapor and cloud amounts and thus controls their radiative contribution to the terrestrial greenhouse effect. From this it follows that these noncondensing greenhouse gases provide the temperature environment that is necessary for water vapor and cloud feedback effects to operate, without which the water vapor dominated greenhouse effect would inevitably collapse and plunge the global climate into an icebound Earth state.

Schmidt et al. [_{2} gives a global mean temperature changes of about −35°C and produces an ice-covered planet (A. Lacis, pers. communication).” These paper’s regressions do not invalidate the null that_{2}] have major social benefits in terms of supporting the rising food production needed to feed a global population now at 7 billion and projected to reach 9 billion by 2050 [_{2} by Hegerl et al. [

The basic physical science underlying the results above is very straight forward, despite the misleading claims in Solomon et al. [^{17} These and others distinguish between so-called “long-lived” noncondensing GHGs and the certainly short-lived nature of [H_{2}O] arising from evaporation created by solar energy, since it is true that condensation and precipitation generally follow evaporation within at most around ten days. But that does not eliminate nonanthropogenic evaporation, for as Lim and Roderick show [_{2}O] is around 3-4 litres per square meter throughout the year^{18}. That is a result of the solar radiative forcing of 342 W/sq. meter [_{2}O]. The maximum is known as the saturation vapour pressure, ^{19}_{2}O] attributable to rising GMT of 0.0125°C p.a. that could be accommodated in the atmosphere is only 0.047 per cent p.a., not enough to have any measurable effect on GMT, far less than the 2°C to even 3°C and more claimed by Solomon et al. 2007 or Schmidt et al. 2010 for a doubling of [CO_{2}] from the preindustrial level of 280 ppm.

The data underlying my regressions showing that in general variations in [H_{2}O] account for as much as 90 per cent of observed changes in temperature both globally and

A joule is the unit of energy. The Watt is the unit of power and equal to a joule per second, or, equivalently, a joule of energy equals a wattsecond, and a watthour, Wh, equals 3.6 kilojoules of energy. The daily average solar radiation at Barrow in June 1991 (per square meter), 3918 Wh, was 14.1 MJ (mega or million joules)—which lies in the range noted here. The IPCC’s [_{2} accumulated since preindustrial times exerts 1.6% of the power of the sun on a summer’s day in Barrow. More precisely, AVGLO is the average daily total radiation for the “Global” horizontal component of solar radiation (Wh/m^{2}). “Global” solar exposure is the total amount of solar energy falling on a horizontal surface. The daily global solar exposure is the total solar energy for a day. Typical values for daily global solar exposure range from 1 to 35 MJ/m^{2} (megajoules per square meter). The values are usually highest in clear sun conditions during the summer, and lowest during winter or very cloudy days… Irradiance is a measure of the rate of energy received per unit area and has units of Watts per square meter (W/m^{2}), where 1 Watt (W) is equal to 1 Joule (J) per second. Radiant exposure is a time integral (or sum) of irradiance. Thus a 1 minute radiant exposure is a measure of the energy received per square meter over a period of 1 minute. Therefore, a 1-minute radiant exposure equals mean irradiance (W/m^{2}) × 60(s) and has units of joule(s) per square meter (J/m^{2})” (see ^{2}, so “AVGLO” of 3918 Wh/m^{2} at Point Barrow in June 1991 is equivalent to 94,032 W/m^{2} per day or 65 W/m^{2} per minute. Thus at Barrow the SSR for the year 1960 amounted to a daily average of 2006 Wh/m^{2}, or 17,572,560 Watts/m^{2} over the year. The AVGLO data in Table ^{2} (not Wh/m^{2}) for its measures of the (net) ^{2} (per minute), that is, 156 Wh/m^{2}, in 2005 [^{2} at Barrow in June 1991. However, the former is the IPCC’s radiative forcing, a change in the balance of the energy fluxes at top of the atmosphere measured in watts per square meter. The latter is the total energy incident on an average day in say June 1991 on a square meter of Barrow measured in watt hours per square meter, but modified by [H_{2}O] and other factors like aerosols and albedo. The IPCC’s radiative forcing is gross, that is, without taking into account any of the other factors affecting the level of solar radiation actually reaching the surface at Pt Barrow or anywhere else.

Specimen of NOAA Data Base. Point Barrow 1960–2006 (selected solar and atmospheric variables, data on average windspeed and relative humidity, and so forth are also available). 700260 BARROW W POST-W ROGERS AK -9 N71 19 W156 37 10 1012.

1960 | AVGLO | AVDIR | AVDIF | AVETR | AETRN | TOT | OPQ | H_{2}O | TAU | MAX_ | MIN_ | AVG_ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

January | 1 | 28 | 1 | 9 | 399 | 4.7 | 3.4 | 0.31 | 0.07 | −21.89 | −28.5 | −25.2 |

February | 259 | 879 | 174 | 692 | 8541 | 5.1 | 3.9 | 0.29 | 0.08 | −24.36 | −30.95 | −27.66 |

March | 1568 | 3422 | 767 | 2980 | 15482 | 4.5 | 3.1 | 0.27 | 0.09 | −22.79 | −29.52 | −26.17 |

April | 3672 | 5181 | 1819 | 6387 | 21863 | 5.1 | 3.8 | 0.32 | 0.11 | −15.19 | −22.82 | −19.01 |

May | 4661 | 2925 | 3367 | 9870 | 29980 | 8.1 | 7.4 | 0.58 | 0.12 | −4.33 | −9.8 | −7.05 |

June | 4898 | 3687 | 3131 | 11824 | 31777 | 7.9 | 7.1 | 1.02 | 0.14 | 3.49 | −1.26 | 1.13 |

July | 4456 | 3878 | 2627 | 10926 | 31671 | 7.7 | 6.8 | 1.38 | 0.14 | 7.24 | 0.89 | 4.08 |

August | 2624 | 1576 | 1962 | 7760 | 24588 | 8.9 | 8.3 | 1.26 | 0.13 | 5.75 | 0.75 | 3.26 |

September | 1338 | 715 | 1125 | 4262 | 17865 | 9.2 | 8.7 | 0.81 | 0.11 | 1.01 | −2.76 | −0.86 |

October | 478 | 451 | 413 | 1450 | 11513 | 8.5 | 7.7 | 0.46 | 0.09 | −7.74 | −12.89 | −10.3 |

November | 25 | 92 | 21 | 110 | 2665 | 7 | 6.1 | 0.32 | 0.08 | −15.85 | −21.59 | −18.72 |

December | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.29 | 0 | −20.68 | −27.31 | −24.01 |

Source: ^{2}). SDGLO/DIR/DIF: Standard deviation of daily total global, direct, and diffuse solar radiation (see note (2) below) (Wh/m^{2}). AVETR & AETRN: Average dally total global horizontal (AVETR) and direct normal (AETRN) extraterrestrial solar radiation (Wh/m^{2}). TOT, OPQ, H2O, TAU: Average TOTal and OPaQue sky cover (tenths), precipitable water (cm), and aerosol optical depth (unitless). MAX_

It is Precipitable water vapour (cm.) The total atmospheric water vapour contained in a vertical column of unit cross-sectional area is extending between any two specified levels, commonly expressed in terms of the height (cm. in Table

Opaque sky cover is the amount of sky completely hidden by clouds or obscuring phenomena, while total sky cover includes this plus the amount of sky covered but not concealed (transparent). Sky cover, for any level aloft, is described as thin if the ratio of transparent to total sky cover at and below that level is one-half or more. Sky cover is reported in tenths, so that 0.0 indicates a clear sky and 1.0 (or 10/10) indicates a completely covered sky (excerpt from _{2} in the atmosphere could be expected to _{2}] in the local data sets examined here tends to have a

Aerosol optical depth is a quantitative measure of the extinction of solar radiation by aerosol scattering and absorption between the point of observation and the top of the atmosphere. It is a measure of the integrated columnar aerosol load and the single most important parameter for evaluating direct radiative forcing. The optical depth expresses the quantity of light removed from a beam by scattering or absorption during its path through a medium. If

The author is grateful to M. S. Hodgart for his methodological insights and to many others for invaluable comments on early versions of this paper but is responsible for all views expressed and for any remaining errors.

Tol and Vellinga [

The textbook by von Storch and Zwiers

If only two independent variables are specified, “most” must mean more than 50%; if there are three or more, then “most” means that the preferred variable, in this case [CO_{2}], must have greater potency than the sum of the others; for example, 40% is not sufficient if the others sum to 60%. If the criterion for “most” is only that [CO_{2}] be the single most potent (and significant) of all the variables, that could be only 1% if all the others _{2}] account for “most” observed global warming are consistent with all states of the world.

The basic formula for the radiative forcing attributed to rising [CO_{2}] is RF = 5.35(LN(_{2}] in ppm., and

Stott has 11 citations as a lead author in Hegerl et al

Muller et al. [_{2} emissions of the US electric power sector between 1990 and 2008. While coal-fired power’s CO_{2} emissions increased by nearly 200 billion tons over that period, SO_{2} emissions by the coal-fired power industry fell from 14.28 million tonnes to 5.5 million tonnes, and similarly for _{2}, but there is no evidence to support that. Kaufmann et al. [_{2} emissions in China, but their estimate of such global emissions at 65 million tonnes p.a. seems trivial relative to annual emissions of over 30 GtCO_{2}.

“In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space. As a result, parameters such as the mean and variance, if they exist, also do not change over time or position.” (Wikipedia, October 2010).

A stationary series

The US data are available from

In the Supplementary Material, I report basic regressions of Gistemp’s “global temperatures” as a function of the radiative forcing of the level of [CO_{2}].

Graphing highly autocorrelated time series data showing rising CO_{2} concentrations and rising temperatures is not enough to “prove” that the data support the theory that the former is responsible for the latter.

Point Barrow is also an ideal test of Arrhenius’ model [_{2}] would be significantly higher (6.05°C) at Barrow’s latitude (71°N) than at the equator (4.95°C) [_{2}], and 3.52°C for just a 50 percent increase in [CO_{2}], compared with 3.15°C at the equator [_{2}] implies that its mean annual temperature would have warmed by more than 3.52°C from the actual minus 12.54°C in 1960 to around minus 9.02°C in 2006, whereas the actual so far is minus 10.2°C, a warming of only 2.52°C. At Hilo near the equator, the predicted “warming” from 1960 to 2006 actually turned out to be a cooling of 0.12°C for the same near 40 percent increase in [CO_{2}], but consistent with Arrhenius’ prediction that warming would be greater at higher latitudes than lower.

If the Durbin-Watson statistic is substantially less than 2, there is an evidence of positive serial correlation, “Durbin-Watson statistic,”

Kaufmann et al. [

See also Curry at al. [

Pers. Comm. See also Tans [

Trenberth [_{2}) has a long lifetime, over a century...,” is at variance with Houghton et al. [_{2} is continuously recycled between the earth’s surface and the atmosphere. Moreover, if atmospheric water vapor arising from solar-based evaporation is “rained out” within 9 days, as claimed by Trenberth and Fasullo [_{2}O] attributable to rising temperature via the Clausius-Clapeyron relation (see below).

One millimetre of measured precipitation is the equivalent of one litre of rainfall per metre squared. The estimates in Lim and Roderick [_{2}O] of c. 4 litres per day per metre squared. See also Kelly [

Wikipedia, “Clausius-Clapeyron”, accessed 30 October 2011, and Pierrehumbert et al. [

_{2}: principal control knob governing earth's temperature

_{2}dependence of photosynthesis, plant growth responses to elevated atmospheric CO

_{2}concentrations and their interaction with soil nutrient status. I. General principles and forest ecosystems

_{2}and global warming in a multi-factor world

_{2}and an outlook for the future