CO2_vs_temp_2020.pdf 22 April 2020

**Atmospheric CO2 concentration**

Here is the monthly atmospheric CO2 concentration measured at the Mauna Loa Observatory, Hawaii, Latitude19.5̊ N, Longitude 155̊ W, elevation 3397m, for the 62 year period from March 1958 to January 2020.

Figure 1. Monthly atmospheric CO2 concentration, Mauna Loa Observatory, Source:[ Ref. 2]

The source file, Ref. 2, lists the data in 10 columns. The columns used here were column 4, the date in decimal format, column 9 being the measured CO2 concentration with missing values in-filled from a smoothed fit to the data and column 10 being the seasonally adjusted measurements again with missing values in-filled.

The monthly CO2 concentration had an average rate of increase over the 61 year period from January 1959 to January 2020 of 1.58 ppm pa. For the 5 year period March 1958 to March 1963 the rate was 0.69 ppm pa and for the 5 year period January 2015 to January 2020 the rate was 2.37 ppm pa, that is, there has been a steadily increasing rate of increase over time.

The amplitude of the seasonal variation was estimated to range from 5.2 ppm to 7.9 ppm, again increasing in amplitude over time, in an irregular fashion. The maxima occurred, on average, in early May, which is the beginning of Summer, and the minima in late September, at the end of Summer. This means that the CO2 concentration rose during the cool of Winter and fell during the heat of Summer, which is out of phase with the UN IPCC claim that increased CO2 concentration causes an increase in temperature.

Any proposition by the UN IPCC about the effect of CO2 on climate needs to be able to explain the source of the above variations.

**Temperature and CO2 concentration**

Here is 41 years of empirical data, showing a distinct lack of a relationship between the Tropics satellite lower troposphere temperature [ Ref.1] and the seasonally adjusted atmospheric CO2 concentration at the Mauna Loa Observatory.

Figure 2. Mauna Loa Observatory, Source: [ Ref. 1] and [ Ref. 2]

Figure 2 shows the monthly satellite lower troposphere temperature for the Tropics zone, 20̊ South to 20̊ North, in blue, and the relevant monthly CO2 concentration in red after removal of the seasonal variation so as to match the residual temperature series. The range for the monthly CO2 concentration is from 335.77 ppm to 413.33 ppm. The range for the Tropics temperature is from

-0.81̊ Celsius to +1.28̊ Celsius with respect to a 30 year average base value. The clear and obvious difference between the two raises the possibility that there may be no common causal factor whereby the CO2 concentration drives the temperature as claimed by the UN IPCC.

Calculation of the Ordinary Linear Regression between the two time series gave a correlation coefficient of 0.463 from the 494 monthly data pairs. This is a measure of the relationship between the background linear trend of each of the time series as shown by an almost identical correlation of 0.460 between the temperature and the time. The correlation between the CO2 concentration and the time was 0.995, that is, the CO2 concentration time series was practically a linear trend with respect to time. Any pair of linear trends, no matter what their source, will have a high correlation coefficient of about 1.0 which is necessarily of no causal significance as a background linear trend with respect to time can be calculated for any time series.

Detrending of the pair of time series in order to assign a statistical significance to the correlation coefficient gave a value of 0.062 showing that the above correlation of 0.463 was mainly the result of the positive linear trend for each series. Statistical tests of both time series indicated that neither series was a random, Normal statistical distribution. The Durbin-Watson test of the joint time series gave a value of 0.27 which indicates positive autocorrelation. The autocorrelation was estimated to be 0.86. This mandated the application of a First Order Autoregressive Model to the combined time series whereby the transformed series gave a correlation coefficient of 0.058 with a 20.5% probability that the correlation coefficient is equal to zero from the Spearman Rank test.

Applying the above procedure using the Tropics Land component of the satellite lower troposphere temperature gave a correlation of 0.563 between the temperature and the CO2 concentration. On detrending, the correlation was 0.068, the Durbin-Watson test was 0.44 and the autocorrelation was estimated to be 0.78. Applying the First Order Autoregressive Model gave a correlation of 0.048 with a 33% probability that the correlation was zero from the Spearman Rank test.

Applying the procedure using the Tropics Ocean component of the satellite lower troposphere temperature gave a correlation of 0.42 between the temperature and the CO2 concentration. On detrending, the correlation was 0.06, the Durbin-Watson test was 0.26 and the autocorrelation was estimated to be 0.87. Applying the First Order Autoregressive Model gave a correlation of 0.057 with an 18% probability that the correlation was zero from the Spearman Rank test.

In summary, the correlation between the satellite lower troposphere temperature and the CO2 concentration for the Mauna Loa Observatory was of the order of 0.05 with an indeterminate probability as to whether or not the relationship is significant.

The result was supported by data from Macquarie Island in the Southern Ocean at Latitude 54.48̊ South, Longitude 158.97̊ East, altitude 12 m. The Island is in the Southern Extension zone of the lower troposphere satellite temperature data, latitudes 90̊ South to 20̊ South. Analysis of the temperature data for the complete zone and its Land and Ocean components with respect to the CO2 concentration [Ref.3] showed that there was positive autoregression in each case requiring a First Order Autoregressive Model to be applied. The result for the whole zone was a correlation coefficient of -0.009, 308 deg. of free., t statistic -0.15, probability of zero correlation 88%. For the Land component, the correlation coefficient was -0.001, 308 deg. of free., t statistic -0.02, probability of zero correlation 98%. For the Ocean component, the correlation coefficient was -0.014, 308 deg. of free., t statistic -0.25, probability of zero correlation 81%.

Additional support is seen in a statistical analysis of the monthly CO2 concentration with respect to the satellite lower troposphere temperature for Mt Waliguan, Tibetan Plateau, China, Lat. 36.28̊ N, Long. 100.9̊ E, altitude 3810 m. Applying a First Order Autoregressive Model to the CO2 concentration [ Ref.4] for Mount Waliguan as the independent variable verses the Northern Extension zone satellite lower troposphere temperature, latitude 20̊ N to 90̊ N, gave results for the whole zone correlation coefficient of -0.13, 302 deg. of free., t statistic -2.30, probability of zero correlation 2.2%. For the Land component, the correlation coefficient was -0.12, 302 deg. of free., t statistic -2.18, probability of zero correlation 3%. For the Ocean component, the correlation coefficient was -0.13, 302 deg. of free, t statistic -2.32, probability of zero correlation 2.1%.

Further, applying a First Order Autoregressive Model to the CO2 concentration for Point Barrow, Alaska, as the independent variable verses the North Pole zone satellite temperature, latitude 60̊ N to 90̊ N, gave results for the whole of zone correlation coefficient of 0.06, 462 deg. of free., t statistic 1.23, probability of zero correlation 22.1%. For the Land component, the correlation coefficient was 0.08, 462 deg. of free., t statistic 1.66, probability of zero correlation 10%. For the Ocean component, the correlation coefficient was 0.02, 462 deg. of free., t statistic 0.50, probability of zero correlation 62%.

Further, applying a First Order Autoregressive Model to the CO2 concentration for the South Pole Station, as the independent variable verses the satellite lower troposphere temperature for the South Pole zone, latitude 60̊ S to 90̊ S, gave results for the whole of zone correlation coefficient of 0.007, 454 deg. of free., t statistic 0.15, probability of zero correlation 88%. For the Land component, the correlation coefficient was 0.027, 454 deg. of free., t statistic 0.58, probability of zero correlation 56%. For the Ocean component, the correlation coefficient was -0.019, 454 deg. of free., t statistic -0.41, probability of zero correlation 68%.

The same analysis applied to the CO2 concentration for Cape Grim, Tasmania, as the independent variable verses the satellite lower troposphere temperature for the Southern Extension zone, latitude 20̊ S to 90̊ S, gave a correlation coefficient of 0.018, 462 deg. of free., t statistic 0.39, probability of zero correlation 70% for the whole of the zone. For the Land component, the correlation coefficient was 0.013, 462 deg. of free., t statistic 0.27, probability of zero correlation 78%. For the Ocean component, the correlation coefficient was 0.015, 462 deg. of free., t statistic 0.33, probability of zero correlation 74%.

A negative correlation implies that an increase in CO2 concentration caused a decrease in temperature, the complete opposite of the UN IPCC thesis. However as the probabilities of a positive correlation coefficient were not statistically significant, the UN IPCC proposition that increased CO2 caused increased temperature could not be supported and the conclusion must be that the null hypothesis applies, namely that the correlation coefficients were zero.

The above conclusion is totally at odds with the statements from the United Nations climate body, the Intergovernmental Panel on Climate Change. The Policymakers Summary from Climate Change, The IPCC Scientific Assessment, 1990, being the, then, final Report of Working Group 1 of the IPCC, opened with the statement, page XI:

“EXECUTIVE SUMMARY

We are certain of the following:

• there is a natural greenhouse effect which already keeps the Earth warmer than it would otherwise be

• emissions resulting from human activities are substantially increasing the atmospheric concentrations of the greenhouse gases carbon dioxide, methane, chlorofluorocarbons (CFCs) and nitrous oxide. These increases will enhance the greenhouse effect, resulting on average in an additional warming of the Earth’s surface. The main greenhouse gas, water vapour, will increase in response to global warming and further enhance it.” – end quote.

After decades of research into the relationship between the atmospheric CO2 concentration and temperature, the latest, Fifth Assessment Report, 2015, of the IPCC, the Synthesis Report, Summary for Policymakers, page 8, made the claim:

“SPM 2.1 Key drivers of future climate

Cumulative emissions of CO2 largely determine global mean surface warming by the late 21st century and beyond. …….” – end quote.

**Temperature and Rate of Change of CO2 concentration**

Here is 41 years of empirical data clearly showing a positive relationship between the satellite temperature and the rate of change of atmospheric CO2 concentration at the Mauna Loa Observatory.

Figure 3. Mauna Loa Observatory CO2 annual increment & satellite Tropics Land temperature.

Figure 3 shows the monthly satellite lower troposphere temperature for the Land component of the Tropics zone, in blue, and the annual change in CO2 concentration in red. The obvious correlation between the two raises the possibility that there may be some common causal factor whereby the temperature drives the rate of change of CO2 concentration. It is not possible for the rate of change of CO2 to cause the temperature level as a time rate of change does not define a base. For example a rate of 2 ppm per annum could be from 0 to 2 ppm in 12 months, 456 to 458 ppm in 12 months or any other pair of numbers that differ by 2.

Note that the satellite temperature data is supplied as a residual after adjustment for the estimated seasonal variation. This makes it directly comparable to the annual rate of change of CO2 concentration as taking the annual rate eliminates the seasonal variation.

Calculation of the Ordinary Linear Regression between the two time series gave a correlation coefficient of 0.65 from the 488 monthly data pairs. Detrending of the time series in order to determine the statistical significance gave a correlation coefficient of 0.53. However the Durbin-Watson test of the time series gave a value of 0.89 indicating positive autocorrelation which means that Ordinary Linear Regression is inapplicable. The autocorrelation was estimated to be 0.55. When applied to transform both time series, that is, applying a First Order Autoregressive Model, it resulted in a correlation coefficient of 0.22 with a probability of the order of 10^-6 that the coefficient is equal to zero from the Spearman Rank test.

Applying a First Order Autoregressive Model to the Tropics-Ocean component of the satellite temperature compared to the annual change in CO2 concentration gave a correlation coefficient of 0.26 with a probability of the order of 10^-9 that the coefficient is equal to zero from the Spearman Rank test.

It follows that this synthesis of empirical data conclusively reveals that CO2 has not caused temperature change over the past 41 years but that the rate of change in CO2 concentration has been influenced to a statistically significant degree by the temperature level. Note that it is not likely for a rise in CO2 concentration to cause the temperature to increase and for the temperature level to control the rate of change of CO2 concentration as this would mean that there was a positive feedback loop causing both CO2 concentration and temperature to rise continuously and the oceans could have evaporated long ago.

Support for this thesis is seen in a statistical analysis of the annual rate of change of the monthly CO2 concentration with respect to the 13 month average lower troposphere temperature for Macquarie Island in the Southern Ocean at Latitude 54.48 deg South, Longitude 158.97 deg East, altitude 12 m. Applying a First Order Autoregressive Model to the various components of the satellite temperature, Southern Hemisphere, Tropics, and Southern Extension and their Land and Ocean components gave a maximum correlation coefficient of 0.30, 294 deg. of free., t statistic 5.34, infinitesimal probability of zero correlation for a two month lag of the CO2 annual rate of change relative to the 13 month average temperature for the Tropics zone, latitude 20S to 20N.

Additional support is seen in a statistical analysis of the annual rate of change of the monthly CO2 concentration with respect to the annual average satellite lower troposphere temperature for Mt Waliguan, Tibetan Plateau, China, Lat. 36.28̊ N, Long. 100.9̊ E, altitude 3810 m. Applying a First Order Autoregressive Model gave a maximum correlation among the various satellite temperature zones of 0.14 for 290 deg. of free., t statistic 2.5, probability of zero correlation of 1.3% for a two month lag of the CO2 annual rate of change relative to the annual average Tropics Land temperature.

The above conclusions are supported by the sequence of events recorded at Mauna Loa Observatory for the major 1997 -‘98 El Nino event displayed in Figure 4.

**Chronological Sequence**

Figure 4: CO2 annual increment relative to temperature average and annual increment.

The above graph displays the time relationship between atmospheric CO2 concentration at the Mauna Loa Observatory, Hawaii, from the Scripps Institution, compared to the satellite lower troposphere Tropics-Land temperature provide by the University of Alabama, Huntsville, for the major 1997-‘98 El Nino event.

The maximum in the annual increment of the temperature, at October 1997, preceded the maximum in the annual increment in the CO2 concentration, at March 1998, by 5 months revealing that the CO2 change could not possibly have caused the temperature change. Statistical analysis of the complete data set extending from December 1978, when satellite measurements began, until January 2020, determined that a 4 month delay was the average throughout the 38 year period.

Further, it can be seen that the Average Temperature graph, being a plot of the 12 month running average temperature, corresponds with the overall variation in the CO2 annual increment. Again this is confirmed by analysis of the complete record which gave a statistically significant correlation between the two. It is not possible for a CO2 time rate of change to set the level of the average temperature but it is possible for the average temperature to cause the rate of change in the CO2 concentration in the same way that the temperature setting of a stove element determines the rate of evaporation of a pot of water. This supports the contention that the CO2 change has not caused the temperature change.

The conclusion that the temperature controls the rate of change of CO2 concentration explains the well known fact that CO2 change lags temperature change over a large time range. Ice core data has revealed that the cycle of ice ages and inter-glacial warm periods show CO2 change lagging temperature change by several centuries to more than a millennium while modern CO2 and global data shows lags of 9.5 to 10 months for atmospheric temperature and 11 to 12 months for sea surface temperature , Humlum et el., 2013 [Ref.5]. Cross correlation of the CO2 concentration at Mauna Loa and satellite lower tropospheric Tropics Land and Ocean temperatures showed that CO2 change lagged the temperature change by 4 months. If temperature controls the rate of change of CO2 concentration, local maxima in the CO2 rate must correspond to temperature maxima which, mathematically, must occur after the maxima in the rate of change of temperature. Likewise the CO2 concentration maxima must post-date the maxima in the CO2 rate and thus post-date the corresponding temperature maxima. Put simply, CO2 has not caused global warming.

**Periodic cycles**

Additional analysis of the Mauna Loa data gave the following autocorrelation function, Figure 5, for both the annual rate of change of the CO2 concentration (red line) and the satellite lower troposphere Tropics Land monthly temperature (blue line). The CO2 data covered the period March 1958 to January 2020 while the satellite Tropics temperature data was from December 1978 to January 2020. Considering the different lengths of the time series, the variables show a striking match in their periodic response. The fact that neither autocorrelation function decreases with increasing lag shows that neither time series is stationary in the statistical sense and dictates that the First Order Autocorrelation Model be applied as was done in calculating the above results.

Figure 5: Autocorrelation functions for Mauna Loa rate of change of CO2 concentration and Tropics Land satellite temperature.

The autocorrelation series are basically identical upon taking into account that the temperature series was 494 months long while the CO2 rate of change was 731 months long, resulting in better definition of its periodicity. The maxima at about 38 months could be the response of both series to the conjunction of Mercury, Venus and the Earth and the maximum at 51 months could be due to the conjunction of Mercury, the Earth and Mars or the two may relate to the El Nino Southern Oscillation. The maxima at about 127 months may be due to the conjunction of the Earth, Moon and Mars. The maximum at 144 months may arise from the 11 year solar cycle due to the orbital period of Jupiter of 11.86 years. Prominent maxima at about 88 and 178 months coincide with multiples of the El Nino Southern Oscillation period. This result suggests that perturbations in the Sun’s irradiance, under the influence of the gravity effect of the planetary orbits largely control the temperature variation of the Earth which, in turn, controls the rate of change of the CO2 concentration in the atmosphere.

A matching response can also be seen in the Fourier Transform amplitude spectrum for each time series, as shown below:

Figure 6: Fourier Transform Amplitude spectrum – Satellite Lower Troposphere Tropics – Land

Figure 7: Fourier Transform Amplitude spectrum – Satellite Lower Troposphere Tropics – Ocean

Figure 8: Fourier Transform Amplitude Spectrum – Mauna Loa CO2 annual rate of change

The most prominent maximum on all three spectra is at x-coordinate 24 on the CO2 rate spectrum, 12 on the Land and 11 on the Ocean spectrum, representing a period of 42.7 months resulting from the well known El Nino Southern Oscillation. It corresponds to the first broad maximum on the earlier correlogram, Figure 5 above. This is in agreement with the paper from Geli Wang et al [ Ref. 6] who used wavelet analysis to detect a 3.36 year cycle in the Central England Temperature dataset, which they attributed to the El Nino Southern Oscillation.

Remarkably, the 42 month period was known by the Babylonians and Israelites 2500 years ago, being mentioned in the Book of Daniel, Chapter 12.11 “…..1290 days …”, in the Old Testament and the Book of Revelation, Chapter 11.2 “….42 months …” and 11.3 “…. 1260 days …”, in the New Testament of the Bible.

Maxima to which a cause has been attributed are:-

for the Land temperature:

Index 12 42.7 months El Nino

Index 29 17.7 months conjunction of Mercury, Venus, Earth

Index 40 12.8 months conjunction of Earth, Jupiter

Index 134 3.8 months conjunction of Mercury, Earth

Index 180 86.6 days 3 x Moon synodic period

Index 188 82.9 days 3 x Moon draconic period

for the Ocean temperature:

Index 7 73.1 months conjunction of Mercury, Venus, Earth

Index 11 46.5 months El Nino

Index 29 17.7 months conjunction of Mercury, Venus, Earth

Index 40 12.8 months conjunction of Earth, Jupiter

Index 45 11.4 months Earth sidereal period

Index 87 179 days 6 x Moon synodic period

Index 95 164 days 6 x Moon draconic period

Index114 137 days 5 x Moon draconic period

Index 131 119 days 4 x Moon synodic period

Index 136 115 days conjunction of Mercury, Earth

for the CO2 rate of change

Index 24 42.7 months El Nino

Index 58 17.7 months conjunction of Mercury, Venus, Earth

Index 67 15.3 months 4 x Mercury synodic period

Index 91 11.3 months Earth sidereal period

Index 130 7.9 months 2 x Mercury synodic period

Index 210 148 days 5 x Moon synodic period

Index 226 138 days 5 x Moon draconic period

Index 273 114 days conjunction of Mercury, Earth

Index 290 107 days 4 x Moon draconic period

Index 352 89 days 3 x Moon synodic period

Index 379 82 days 3 x Moon draconic period

Accurate predictions as to the period and source of the local maxima in the amplitude spectra are not feasible due to the course sample interval of one month and the short time series of only 494 and 731 months.

This has been partly resolved by using the weekly Mauna Loa atmospheric CO2 concentration time series as proxy for the atmospheric temperature as shown on the accompanying page “Mauna Loa Weekly Data”. It is notable that both the synodic and draconic periods of the Moon are apparent in the weekly series. An explanation for the synodic period is that each New Moon reduces the incoming Sun’s radiation to the Earth and its atmosphere as it passes between the Sun and the Earth.

Evidence that the 42 month cycle causes the El Nino event is seen in the responses over the South Pole as shown below. Once again the time series are of different lengths with the annual rate of change of the CO2 concentration (red line) covering the period June 1957 to December 2016 and the satellite lower troposphere South Pole Land monthly temperature (blue line) covering the period December 1978 to October 2017.

Figure 9: Autocorrelation functions for South Pole rate of change of CO2 concentration and South Pole Land satellite temperature.There is an obvious difference between the time series. The periodic nature of the annual rate of change of the CO2 concentration repeats the wavelength of that from Mauna Loa while it is barely discernable for the South Pole satellite lower troposphere temperature series. The power spectra confirm the difference as seen here:

Figure 10: Fourier Transform Amplitude spectrum – Satellite Lower Troposphere South Pole

Land

Figure 11: Fourier Transform Amplitude Spectrum –South Pole CO2 annual rate of change

The peak in the amplitude spectrum for the annual rate of change of CO2 concentration remains at the wavelength of 42.7 months. However the power spectra for the satellite lower troposphere temperature has the 42.7 month peak in fourth spot with greater amplitude peaks occurring at wavelengths ( in decreasing amplitude ) of 64 months (which may be the synodic period for the Moon and Mercury and/or Jupiter ), 26.9 months (which may be the synodic period for Mars and/or Jupiter) and 10.7 months (which represents 11 synodic cycles of the Moon). The reduction in the 42.7 month peak is reasonable considering the fact that the Sun’s rays are practically tangential to the polar surface or do not impinge on part of that surface for months at a time and the Moon’s orbit is inclined at 5̊ to the elliptic.

The CO2 concentration over the South Polar region has been, on average, 2.2 ppm less than over the Tropics for the 58 years of recording during which time the concentration at the South Pole increased by 86.8 ppm and at Mauna Loa the increase was 88.3 ppm with the difference being statistically significant at the 99% level.

The clear similarity between the autocorrelation function and the power spectra for the two time series, temperature and rate of change of CO2 concentration, from the Equatorial zone support the original contention that the temperature drives the rate of change of CO2 concentration. As the Tropics has the highest average temperature it must produce CO2 at the greatest rate. That CO2 must diffuse North and South away from the Equator into the Polar regions. As the solubility of CO2 increases with decreasing temperature it must be precipitated at the Poles within the hail and snow. That is, there may be a continuous circulation of carbon from the Equatorial Zone, through the atmosphere as CO2, to the Poles where it is locked into the Polar ice sheets until those sheets move sufficiently far from the Pole to melt. The CO2 is then concentrated in sea water and may return to the Equatorial zone via the Earth’s oceans.

That is, the Tropics is a source for the atmospheric CO2 and the Polar regions are a sink. As the seasonal variation from photosynthesis can be as great as 20 ppm in amplitude, it is possible that the almost 2 ppm per annum increase in CO2 concentration over the past 38 years has arisen from biogenetic sources driven by the natural rise in temperature following the last ice age. The Tropics has the greatest profusion of life forms throughout the Globe, so this may be a feasible source for the increase in CO2 concentration for that period. That could include an increase in the population of soil microbes thereby increasing the fertility of the soil leading to the greening of the Earth as can now be seen in satellite imagery. This is supported by an extensive study of global soil carbon which, quote: “provides strong empirical support for the idea that rising temperatures will stimulate the net loss of soil carbon to the atmosphere” end quote, Crowther et el 2016 [ Ref.7].

**Conclusion**

The conclusion is that there is no statistical evidence for the claim by the UN IPCC that a rise in CO2 concentration causes a rise in the temperature of the lower troposphere but there is highly significant evidence that the temperature determines the rate of change of CO2 concentration. Added to that is the secondary conclusion that there is a prominent 42 month cycle for the temperature due to a repeated occurrence of a configuration of the Solar system which is expressed in the Earth’s climate as the El Nino event. It also causes the same cycle in the rate of change of CO2 concentration. Furthermore other cycles in the temperature and the CO2 rate spectra may relate to orbital cycles of the planets indicating that, at least in terms of months and years, the orientation of the planets with respect to the Sun determine the changes in the Earth’s temperature which result in coincident changes in the rate of change of CO2. That is, climate change is the result of the continually changing position of the Moon and the planets relative to the Earth and the Sun and has nothing whatsoever to do with the concentration of CO2 in the atmosphere as this is a consequence of the climate change.